27 20 5655 https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/c75f8c59a393743e7c3ffe6c62a134e1.pdf 7cb9d0cdb02b95ce18841a7c0e9025ab PDF Text Text BULLETl/N o/ The Friends of St. John's College ANNAPOLIS, MARYLAND ' march, 1950 �THE FRIENDS OF ST. JOHN'S COLLEGE THE LANGUAGE TUTORIAL Sponsors The seminar, although the heart of the St. John's program, cannot alone suffice as a means to the end of general education unless aided by more specialized and stricter disciplines.. By its very nature the seminar does not give to the students an opportunity to cultivate the habits of methodical and rigorous study. It has to be supported, therefore, by other instructional devices, 'principally the language and mathematics tutorials. Throughout the four years of a student's course at St. John's two tutorials or classes are scheduled each morning, one in language and one in mathematics. Here a.round a table eight to fifteen students study and learn together under thi;:. direct guidance and instruction of one of the tutors. Other tutors often attend, but in the guise of students seeking to learn about a particular subject. Each tutorial is one hour in length and meets five days a week, except that one hour of each fortnight is relinquished to choral exercises, as will be explained later. WALTER S. BAIRD REV. DR. C. EDWARD BERGER RICHARD F. CLEVELAND MRS. CHARLES S. DEWEY ARCHIBALD EDWARDS .JOHN ERSKINE CLIFTON FADIMAN Gov. WILLIAM P. LANE MEYER KESTNBAUM FRANCtS PICKENS MILLER WILLIAM LENTZ MORRIS DR. THOMAS PARRAN MRS. H. L. RADOFF . MRS. H. R. SLACK, JR. M. ROBERT, JR. REV. DR. H.P. VANDEUSEN EDWARP.. f'. LATHROP MARK VAN DOREN Excc.ft~~e Secretary · ''~.:.:~;·'~;~, : ·~..'~'; v}; ·. ,~- ·!: ·,.;.,_,.,w The entire St. John's community ha~ ~e;;~'· ~~tjidened by the death of Hervey Allen whose devotion to the College w~s~great. Mr. Allen was a membe;~ of the Board of Visitors and Governdrs and also served as Chairman ~l the Sponsors of the Eriepds of St. John's. .. tt This is the second issue of the Bulletin devoted to presenting the curricular activitie$ of the College. In the December issue the seminar was described. The current' number is devoted to the Language Tutorial. Succeeding articles will deal with the Mathematics Tutorial. the laboratories, the formal lectures, and the chor.alexercises. These activities, taken togefher, represent sirjgle. unified cour.se of study in the liber.~1 arts, organized ti.found the literary and scientific traditiof1'.of Western Civil' tion as contained ' in a reptesentative list·'.~f gre~t or impq books. These Bulletins will seek to''present not 0 .. t e'titi'.Joward which ~he College aspires in this program, t also certain probieriis and diffi.culties which arise in the actual opeartion of the program. a Volume II 1950 ... MARCH, ·.,,.1.: ' Pub'lished ·Quarter! y ·. Number 2 Reserving discussion of the Mathematics Tutorial to a subs2quent issue of the Bulletin, we shall consider first the Language Tutorial. ,, PRIMARY .AIM The primary purpose of the language tutorials is not the mastery · of any foreign languages. By studying them, however, and by translating from them into English, by comparing them with each other and with English, the student learns something of the nature of language in general and of his own in particular. During the four years, then, he is studying language as such, the discourse of reason, and, through the medium of foreign tongues, his own native English. He is discovering the resources of articulate speech and learning the rules that govern it if it is to be clear, consist~nt, and effective; if it is to be adequate and persuasive. The media for accomplishing this are Greek in the first and second years, German in the third year and French in the fourth. GRAMMAR. RHETORIC. AND LOGIC The advent of specialization in higher education has led to a profound neglect of language skills. As country is separated from country by the barrier of language, so profession is separated from profession· by the use of technical jargon. The language tutorial attempts to remedy this condition by a training in the means of precise communication and persuasion. In a broad sense, it may be conceived as a resurrection of the age-old disciplines of grammar, rhetoric, and logic. The tutorials concern themselves with seeking to understand the relation between language and thought. To do this they must study the basic articulations of speech, the modes of siga.ifying things, the VJried connotation; �and ambiguities of terms, the role of metaphors and analogies, and the logical relation between propositions. During the early sessions of each language tutorial, the emphasis is of necessity on the primary grammatical forms and constructions and the basic vocabulary of the language in question. But after a relatively short period of time, which is longer in the first year, the tutorial has <>hifted to something more concrete: the slow and careful reading and discussion of great works of poetic imagination or philosophical thought. Thus, the rapid reading for the seminar with its attention focused on the large outlines, the general trend, the development of the central ideas, is supplemented and corrected by a more precise and refined study, concerned with every detail and partciular shade of meaning, and also with the abstract logical structure and rhetorical pattern of a given work. These are matters that do not often come directly into seminar discussion. The student's concern with them in the language tutorials improves all his reading, for whatever immediate end, deepens and enriches his understanding, and increases his ability to think clearly and to talk well. similate the subtlety of Greek grammar and syntax in a single year. During the second year of Greek, the student reviews the grammatical work of the first year and then resumes the reading and translating of important texts, with greater understanding and enjoyment. The texts are in the main taken from Platonic Dialogues, the works of Aristotle, a Greek tragedy, and the Gospels. While in the first year the grammatical analysis is supplemented at certain points by the study of formal logic, the emphasis in the second year is on the rhetorical power as well as on the philosophical meaning of the texts. The close reading of Plato and Aristotle in the Language Tutorial throws decisive light on the pnblems discussed in the seminar. SECONDARY AIM The French tutorial in the fourth year, although reproducing in grneral the pattern of the preceding tutorials, is devoted mainly to the studying of the great works of French literature. The fourth year seminar is strongly supported by the continuous analysis of the nature of the novel in the language tutorial. It is also supported by the study of language from the point of view of symbolic logic, which is taken up by the tutorial for a certain period of time. At this point the Language Tutorial and the Mathematics Tutorial converge. Thus, while the primary purpose of the Language Tutorial is the understanding of language as the vehicle of thought and more particularly a better understanding of the student's mother tongue, the second purpose of the language tutorial is support of the seminar discussion. The student reads and carefully analyzes a few great examples and models of prose and poetry in Greek, German, and French. Some of these relevant texts are not parts of the seminar readings. The further the student advances, the more the Language Tutorial tends to influence the seminar discussion by bringing issues to the fore which otherwise might have been neglected and by introducing more precision into the terms in which a problem is being discussed. GREEK OVER LATIN The choice of Greek, German and French is in part dictated by the exigencies of the seminar reading schedule and is in part arbitrary. A different set of languages might well be used without changing the basic patterns and aims of the language tutorial. At one time Latin was included in addition to the three languages now studied. This resulted in a scattering of energies with no real and lasting profit to the student. Greek was retained in the curriculum in preference to Latin because its flexibility and expressiveness seem to make it the best instrument for inculcating in the student a better understanding of the nature of language in general. Moreover, the amazing deterioration in our linguistic habits and the almost total lack of grammatical training shown by many secondary school graduates make it particularly difficult for them to as- GERMAN AND FRENCH The German tutorial in the third year is structually a condensation of the pattern of the two-year Greek tutorial. Poetry and prose alternate in the reading schedule. Here again, the close reading of Kant provides an indispensable aid to the seminar discussions. The close reading in the language tutorials of the third and fourth years is done partly in German or French and partly in English. The original version is brought into play as often as possible whenever a work is read in English translation. The problem of translating, that is, the problem of articulating the same thoughts and delineating the same images in the various language media, never leaves the language tutorials throughout the four years. THIRD AIM We have seen that the two main purposes of the Language Tutorial are to make the student understand the nature of language as the human way to articulate and convey thoughts, especially with respect to their own mother tongue; and to support the seminar by a much closer scrutiny of texts. A third aim-and one of minor importance-is the learning of the three foreign languages themselves. In the time allotted to the study of each language, mastery of any one of them is,· of course, impossible. What the student can reasonably be expected to attain is a knowledge of the basic grammatical forms and a feeling for the pc- �culiarities of the language. To experience the individuality of another language is to extend the limits of one's sensibility. READING KNOWLEDGE EXAMS AND ESSAYS To implement this aim, the reading knowledge examinations were instituted. The St. John's requirements for the final degree of Bachelor of Arts include the passing of reading knowledge examinations in two of the three foreign languages. By the end of the second year each student has to take a reading knowledge examination in Greek. The examination in French or German may be taken at the student's convenience. In each case the s~udent can use his dictionary freely duri:c_g the examination. Failure the first time in any of these examinations does not preclude later attempts. In each of the four years the students test their linguistic skills by writing two essays on themes emerging from the discussion in the tutorials-or in seminars·--and approved by their language tutors. These essays are subject to a thorough criticism on the part of the tutors who, if occasion requires it, arrange special meetings with the individual students for the diagnosis of particular difficulties. St. John's is concerned that each student acquire ability to express himself dearly and skilfully, not less in writing than in speaking. The Language Tutorial is one of the means that contribute to this end. COLLEGE NEWS A central office to coordinate placement activities for St. John's graduates has been established under the direction of Ivir. Edward F. Lathrop. Friends of St. John's are invited to send in suggestions. A series of eight radio seminars on "The Background of Democracy" has been arranged as a public service with Station WASH-FM in Washington, D. C., starting March 26th. Every Sunday evening at 6: 3 0 P.M. (E.S. T.) two tutors, two students and a distinguished guest will discuss a book bearing on this central theme. Among the guests will be William Preston Lane, Governor of Maryland; Admiral James L. Holloway, Superintendent of the United States Naval Academy; Mr. Frank L. Pace, Director of the Bureau of the Budget; and The. Rev. A. T. Mollegan, of the Alexandria Theological Seminary. C. Ranlet Lincoln, 19 5 0, is serving as director and program manager. WASH-FM is making these broadcasts available to all FM stations on the Continental Network. The schedule follows: March 26 April 2 April 9 April 16 April 23 April 30 May 7 May 14 Declaration of Independence, Constitution The Federalist Machieve!E: The Prince Calvin: On Civil Government focke: SecoNd Essa Representative ' . Government Rousseau: Social Contract Rousseau: Social Contract John Stup.rt Mill: On Liberty ion The following Sunday evening meetings have been held since last fall: LECTURE AND CONCERT SCHEDULE April 7 April April May May May 21 28 5 12 19 May 26 June 2 Robert Fitzgerald: "The Ethics and the Tragic Epiphany" A. T. Mollegan: "Faith and Reason" Concert: Ralph Kirkpatrick, harpsichordist John S. Kieffer: "The Paradox of Rationality" Luther A. Weigle: "Bible Translations" E. J. McShane: "The Fundamentals of Statistics as the Basis of Modern Physics" Play Reading: Shakespeare's "King John" Blair Kinsman: "Alice in Wonderland" Nov. 20-William S. B. Lacy, Acting Director of the Office of Philippine and Southeast Asian Affairs, Department of State; The Indonesian Problem. Dec. 4--James Frederick Green, Associate Chief of the Division of United Nations Economic and Social Affairs, Department of State; The United Nations in Action. Dec. 11-Rear Admiral James L. Holloway, Jr., Superintendent of the United States Naval Academy; The Naval Academy and its Curriculum. Jan. 17-.Tswenling Tsui, Counselor of the Embassy of the Republic of China; The Chinese Situation. Jan. 29-Dr. Imdad Husain, Cultural and Educational Attache, The Embassy of Pakistan; Pakistan: Birth of a New Nation. Feb. 12-Niles W. Bond, Officer in Charge of Korean Affairs, Department of State; Korea. March 5-Dr. Henry Sloane Coffin, President Emeritus Union Theological Seminary, New York City; The Christian Conception of God. �� Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource <em>Bulletin of the Friends of St. John's College</em> Description An account of the resource The <em>Bulletin of the Friends of St. John's College</em>. Published from 1949 to 1950. Creator An entity primarily responsible for making the resource St. John's College Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, Md. Rights Information about rights held in and over the resource St. John's College holds the rights to this publication. Identifier An unambiguous reference to the resource within a given context BulletinFriends Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Page numeration Number of pages in the original item. 8 pages Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context Bulletin March 1950 Curricular Activities The Language Tutorial Vol. II No. 2 Title A name given to the resource Bulletin of The Friends of St. John's College, March 1950 Description An account of the resource Volume II, Number 2 of the Bulletin of the Friends of St. John's College, the Language Tutorial. Published in March 1950. Date A point or period of time associated with an event in the lifecycle of the resource 1950-03 Creator An entity primarily responsible for making the resource St. John's College Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Rights Information about rights held in and over the resource St. John's College owns the rights to this publication. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/4d9bcbf7b1fa30f33d8aaef883cc643b.pdf f975eba75aba0ebffdbabb9fb863c842 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource College Catalogs and Statements of the Program Creator An entity primarily responsible for making the resource St. John's College Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Description An account of the resource Statements of the Program are published each Academic Year. They provide an overview of the program and historical information about the college.  <br /><br />The titles of these publications have changed over the course of the College's history. From the 19th century through 1971 they were titled Catalogue. During this period, some Catalogues were distributed as issues of <em>The Bulletin of St. John's College</em>. The title changed from Catalogues to Statement of the Program with the 1972-1973 publication. <br /><br />Also included in this collection are Graduate Institute catalogs and promotional publications about the St. John's program.  <br /><br />Click on <strong><a title="College Catalogues" href="https://digitalarchives.sjc.edu/items/browse?tags=College+catalog&amp;sort_field=Dublin+Core%2CDate">Items in the College Catalogs and Statements of the Program Collection</a></strong> to view and sort all items in the collection. Identifier An unambiguous reference to the resource within a given context collegecatalogs Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Page numeration Number of pages in the original item. ii, 18 pages Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context GI Catalog 1988-1989 Creator An entity primarily responsible for making the resource St. John's College Title A name given to the resource Bulletin of the Graduate Institute in Liberal Education, St. John's College 1988-89 Date A point or period of time associated with an event in the lifecycle of the resource 1988-1989 Description An account of the resource GI college catalog for the years 1988 to 1989. Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Santa Fe, NM Publisher An entity responsible for making the resource available St. John's College Language A language of the resource English Type The nature or genre of the resource text Rights Information about rights held in and over the resource St. John's College owns the rights to this publication. Format The file format, physical medium, or dimensions of the resource pdf Catalog Catalogue College catalog GI catalog Graduate Institute https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/f750cab2f01a746491d43d73dd8daa0b.pdf c488ca067e025c05291ad1fa56bb28fd Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource College Catalogs and Statements of the Program Creator An entity primarily responsible for making the resource St. John's College Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Description An account of the resource Statements of the Program are published each Academic Year. They provide an overview of the program and historical information about the college.  <br /><br />The titles of these publications have changed over the course of the College's history. From the 19th century through 1971 they were titled Catalogue. During this period, some Catalogues were distributed as issues of <em>The Bulletin of St. John's College</em>. The title changed from Catalogues to Statement of the Program with the 1972-1973 publication. <br /><br />Also included in this collection are Graduate Institute catalogs and promotional publications about the St. John's program.  <br /><br />Click on <strong><a title="College Catalogues" href="https://digitalarchives.sjc.edu/items/browse?tags=College+catalog&amp;sort_field=Dublin+Core%2CDate">Items in the College Catalogs and Statements of the Program Collection</a></strong> to view and sort all items in the collection. Identifier An unambiguous reference to the resource within a given context collegecatalogs Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Page numeration Number of pages in the original item. ii, 18 pages Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context GI Catalog 1991-1992 Creator An entity primarily responsible for making the resource St. John's College Title A name given to the resource Bulletin of the Graduate Institute in Liberal Education, St. John's College 1991-1992 Date A point or period of time associated with an event in the lifecycle of the resource 1992-1992 Description An account of the resource GI college catalog for the years 1991 to 1992. Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Santa Fe, NM Publisher An entity responsible for making the resource available St. John's College Language A language of the resource English Type The nature or genre of the resource text Rights Information about rights held in and over the resource St. John's College owns the rights to this publication. Format The file format, physical medium, or dimensions of the resource pdf Catalog Catalogue College catalog GI catalog Graduate Institute https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/f5f9948f49807af6de020c12e59dbe63.pdf 2f2d82d86ed7dc7f1a667192c70c5275 PDF Text Text BULLETIN ST. JOHN'S COLLEGE WOLUME XIV, NO. 1, MARC.H 1962 �CURTIS A. WILSON ALLEN R. CLARK GERALD E. SACKS FORMALISM IN LOGIC AND MATHEMATICS .A FORMALIST APPROACH TO MATHEMATICS WHAT IS GODEL'S THEOREM? PAGE 2 PAGE 18 PAGE 24 "" BULLETIN ST. JOHN'S COLLE 5 p E c I A L I s s u W. G. SPOHN •• PAGE 28 MARCH 1962 VOLUME XIV NUl'ABER 1 O N MATHEMATICS STAFF Co-Editors Theodore B. Stinchecum Managing Editor Michael H. E lias M ichael H. E li as Curtis A. Wilson Dean, St. John's College. ANNAPOLIS, MARYL.A' Num!J March, 1962 I Published Quarterly Entered as Second-class matter, February 18, 1949 at the Post Office, at Annapolis, Maryland, under the Act, of Augus 1912. Copyright 1962 ST. JOHN'S COLLEGE Volume XIV Gerald E. Sacks Ph .D. in mathematics Cornell University 1961 · present1 ' ' ' In st~ a member of the School . of Mathematics, The itute f Ad or vanced Study, Princeton, New J ersey. Art Director T heodore B. Stinchecum Advisor Eva Brann Secretary Donna A . Parmalee Business Man.ager E dwa rd L. Matti son Allen R. Clark Mathematical L ogician ; Tutor, St. John 's College, 19541956. W. G. Spohn Alumnus, St. John's College, 1944 ; presently at th e Applied Physics Laboratory, The John s Hopkin s Universi ty. �3 l ~ 1 FORMALISM IN LOGIC AND MATHEMATICS CURTIS WILSON From the beginning of modern times there has been, in the air, so to speak, the notion of a universal symbolic science. This notion was advocated, in particular, by Leibniz. "In Philosophy," he says, "I have found a means of accomplishing in all sciences what Descartes and others have done in Arithmetic and Geometry, by Algebra and Analysis. ·This method is the combinatorial art"-Ars Combinatoria, or as he also called it, Characteristica Universalis. "By this, all composite notions in the whole world are reduced to a few simple ones as their Alphabet; and by the combination of such an alphabet a way is made of finding, in time, by an ordered method, all things with their theorems and whatever is possible to investigate concerning them." Thus Leibniz claimed to have discovered a symbolic method of the following sort: There would be a fundamental alphabet of all the simple ideas, which would be represented by ideograms, that is, symbols standing directly for the ideas rather than for sounds, as do ordinary written words. Secondly, there would be prescribed rules for combining the symbols, in such wise as to yield every possible true combination, and so obviate the necessity of thinking. "If we had (this method)," he says, "we should be able to reason in metaphysics and morals in much the same way as in geometry and analysis ... If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, to sit down to their slates, and to say to each other (with a friend as witness, if they liked): Let us calculate." Even among more empirically-minded philosophers, there has persisted the notion of a symbolic method, adequate for the discovery of all non-empirical truths. Thus C. S. Peirce, the 19th-century philosopher, states: "In regard to the ideal world we are virtually omniscient; that is to say, there is nothing but lack of time, of perseverance, and of activity of mind to prevent our making the requisite experiments to ascertain positively whether a given combination occurs or not. Thus every proposition about the ideal world can be ascertained to be either true or false." According to Wittgenstein in his Tractatus LogicoPhilosophicus, published in 1922, "in logic and mathematics there are no surprises." Now these claims of Leibniz, Peirce, Wittgenstein, and others have been proved during the last thirty years or so to be mistaken. In logic and mathematics, there are surprises. The discovery of all mathematical, logical, or philosophical truths cannot be reduced to a technique of calculation, or experiment as Peirce calls it. This result is the main point I have to make. That such a result can be proved may seem unimportant if one has always assumed that the Leibnizian program could never be carried out. One might say, for instance, that the simple notions of which Leibniz speaks are not the beginning of philosophy, but rather that at which philosophizing aims, as a goal, and that Leibniz fails to recognize how intricately involved we are in medias res, in the middle of things. I think this is right. Butjt is important to note that the incompletabili~ of the Leibnizian program was proved only after, and on the basis of, a very remarkable systematization of mathematical and logical disciplines, so that Leibniz's claim seemed well on the way to realization, at least in the case of these particular disciplines. Actually this systematization was approached from two different sides; on the one side the aim was the carrying out of the Leibnizian program, on the other it was rather the elimination of certain difficulties inherent in modern mathematics since Descartes. Later on I shall say something about this second side of the coin; but first let me try to indicate roughly what logic is, and in what way symbolic logic differs from the logic of everyday discourse, or from the logic employed, say, in Euclid's Elements. The fundamental notion of logic is that of a logical consequence. One statement is said to be a logical consequent of others, called the premisses, if the truth of the premisses entails that of the consequent, if the consequent follows from the premisses. Under what circumstances does such entailment occur? I cannot be expected to answer this question in any final way, since it is a corollary to the main point I am making that no exhaustive account of the meaning of logical consequence is possible. However, as Aristotle was the first to show, logical consequences are characterized by the fact that they depend on formal features of statements rather than upon their full meaning or content. What I mean by this is that, whenever we have a logical consequence, it should be possible to perform certain substitutions on the statements or parts of statements of the sequence without destroying the consequence. The words other than those for which we can substitute in �5 4 this fashion are the words upon which the consequence depends essentially; they may be called logical words. Examples of words which may occur as logical words are: "and", "or", "not", ''if-then", "all", "some", "any". For instance, given the premiss, "If p then q", where p and q are any statements, and given in addition the premiss "p", then the statement "q" follows as a logical consequence from the premisses. The logical character here depends essentially on the meaning we attach to the words "if-then"; in other logical consequences it would depend on the meaning of other logical words. I am unable, as of now, to analyze the general notion of logical consequence beyond the point where we arrive at the meanings of certain logical words. So for the space of this essay, I shall regard logical entailment as a basic ingredient of discourse, an ingredient which perhaps has some ground in the structure of the world; but I shall not attempt to state what that ground might be. Now the art of logic-if I may introduce that term -has the task of trying to specify the valid forms of logical consequence. That is, it will try to specify schemata of logical consequences, schemata in which the logical words appear and in which blanks or dummy letters are put for the statements or parts of statements which admit of substitution and which are therefore inessential to the drawing of the conclusion. Insofar as an art of logic can exist at all, it would seem to have to depend on this possibility ~of cataloguing logical consequences in terms of their forms; without this possibility there could hardly be general rules independent of the specific content of statements, and hence we could hardly speak of an art. And as an initial gesture toward characterizing symbolic logic, we may say that it merely exploits this possibility to the full. It adopts all possible means of presenting the schemata of logical consequences in as succinct a form as possible. In the first place, the cataloguing of valid forms of consequence will be considerably facilitated if we adopt ideograms for the logical words. For instance, instead of the words "if-then", one placed before the protasis of a conditional statement and the other placed between the protasis and the apodosis, we may use the single symbol, ":::i", placed between the two component statements of the conditional. This constitutes a certain economy. Moreover, the use of such ideograms enables us to ignore certain non- logical connotations of words in everyday discourse and to pay attention solely to their logical function. For instance, in the statements: Castor is here although Pollux is away, and Castor is here but Pollux is away, the words "although" and "but", in addition to their logical function of effecting a conjunction or joint assertion of the two component statements, have meanings which are ordinarily irrelevant to the business of drawing logical consequences; for purposes of logic they can just as well be replaced by the word "and". But even the apparently innocent word "and", used as a connective between statements, frequently serves weighty non-logical functions on account of the context. For instance, m the conjunction: She took arsenic and she fell ill, the "and" serves not only the logical function of effecting a joint assertion, but also implies temporal sequence and even causal connection. It does not make the same sense at all to say: She fell ill and she took arsenic. So for logical purposes we will do well to use a single symbol, say the ampersand, "&", which will carry only the logical sense of "and". Again, some words of ordinary discourse bear more than one logical function, and it is convenient to distinguish these by means of separate ideograms. The word "or" is a case in point; sometimes it is used in an inclusive sense and sometimes in an exclusive sense. "p or q", where p and q are statements, may mean that p is true or q is true but that both aren't true, or it may mean that p is true or q is true or both are true. Latin had two words for the two meanings, "aut" and "vel", but English is not so favored. So it will be convenient to adopt different symbols for different senses; say, "V" for the inclusive sense and "/\" for the exclusive sense. Again, in ordinary idiomatic discourse we sometimes find words playing a logical role although one might suppose them, out of context, to bear a quite different meaning. Thus in the statement: The sum of the angles of a triangle is always equal to two right angles, -the word "always" has nothing to do with temporality, and we really mean: The sum of the angles of any triangle is equal to two right angles. Becaus: of s_uch irregularities in the use of logical words 111 ordmary discourse, it should be clear that the cat~loguing and schematizing of forms of argument will proceed more easily if we replace the logical words by a special set of symbols with constant meanings. Such replacement is an important step in the development of a symbolic logic. . Still, it is important to note that the use of such ideograms does not supply us with any magical powers. We achieve a certain economy, a greater degree of recognizability of logical forms, but we are no~ thereby enabled to carry out any deductions whic_h we could not have carried out before adopting the ideograms. In order to establish the validity of ~n argument, we may be helped by schematizing it m terrr_is of the ideograms and dummy letters, but to recogmze the schema as valid, we have to take thought, we have to recognize somehow that the conclusion cannot be false if the premisses are true. Now this state of affairs can be somewhat improved upon, if we develop a science of logic. But before describing what a science of logic would be I want to stress one particular aspect of what is me~nt by speaking of an art of logic. By using the term "art", I_ imply that the discipline I am talking about ?as an instrumental character; it is used in the carrying out of arguments, or in the construction of a deductive science. The rules of the logical art-we call them rules of inference-are not themselves mentioned in the argument or the deductive science· they belong to a different level, so to speak. ' . Consider as an instance the rule of inference tradit10nally called modus ponens. Suppose that p and q are dummy letters for any statements. Then, suppose that I have obtained as a line of a proof a statement of the form p :::i q; and suppose that I have also obtained as a separate line the statement p. I want to write a new line, namely q. That is, I need the rule which states that, whenever I have proved a conditional statement, and have also proved its antecedent, then I may assert its consequent to be true. This rule may be said to be justified by the logical truth that statements of the form [(p :::i q) & p] :::i q are true, where I understand that the statements in question will be obtained from the schema or statement-form [(p :::i q) & p] :::i q by uniform substitution of statements for the dummy letters p and q. (The parentheses, of course, are used to show grouping.) :o every rule of inference, there corresponds a logical truth. The one must not be confused with the other, and above all, I must not suppose that I can get along in the business of deduction without the r~les of inference. Without permissive rules, directives, we cannot proceed with the artful action of carrying out a deduction. On. the other hand, there may be some point in studymg ~he schemata used in stating the logical truths which correspond to the various rules of inference. It may turn out that they are related to one another, so that some of them can be deduced from others. This fact appears to have been noticed for the first time by Aristotle, who deduced the moods of the second and third figures of the syllogism from the moods of the first figure, using as rules of inference the rules of conversion, contraposition, and so on. Note that such a deductive science of schemata ?f logical tr~ths _has itself to make use of rules of mference which 111 a sense lie outside the science and which tell how the deductions are to be made'. N?"'. such a science may have the advantage of permitting us to deduce new and more complex logical truths from those which we have previously accepted. And each of these new truths will justify a new rule of inference. The symbolic logicians attempted to do just thisdevelop a deductive science of logic, starting from a small number of axioms and using a small number of rules of inference, for instance, modus ponens and the rule of uniform substitution (for any given dummy letter, the same statement is always to be substituted). Before I describe how this was done, however, I should poiht out that symbolic logicians from the start, had other concerns than that of constructing a deductive science of logic. In particular, I should like to note that, even should we succeed in developing a deductive science of logic, we _should not have all that Leibniz required of his Umversal Characteristic or symbolic science. In general, one would expect that a Leibnizian philosopher, or even an ordinary practicing mathematician will start wi~h a question about a sentence-say, ~ sentence which can be stated in the ideograms of �7 6 logic together with symbols for certain other notions, in case he is concerned with a science other than symbolic logic itself. He wants to know whether the sentence or formula can be proved or not on the basis of the first principles of his science. Now the procedures used by symbolic logicians in constructing deductive sciences-namely the explicit formulation of all rules of inference in terms of the forms of sentences or schemata-may provide a certain facility in generating deductions; the generation of theorems is reduced to a comparatively mechanical procedure, involving only the rather elementary process of recognizing the logical forms of certain sentences or schemata initially assumed or previously proved, and then writing down new sentences or schemata as permitted by the rules of inference. The happy moron may, by merely following instructions, churn out one theorem after another. But faced with a given sentence or schema expressed in the symbols of the theory, and asked whether it is a theorem or not, he will not be able to say unless he has actually produced a proof of it already. If the sentence or schema is in fact deducible, we may expect him to churn it out at some time or other, barring his untimely death. But we can form no estimate as to when he will do so, and the sun may grow cold before he does. Meantime, the theorems he churns out are perhaps totally irrelevant to the problem m I, I hand. What Leibniz actually required was a method of calculating the answer, or as it is called today, a decision procedure. That is, faced with a sentence or schema expressed in the symbols of the theory, he wanted to have a method whereby he could definitely decide, in a finite number of predetermined steps, whether the sentence or schema was deducible or not. For instance, if asked whether one integer is exactly divisible by another, I do not have to try to deduce this divisibility from a set of axioms for arithmetic. I have only to carry out a long division. The process of long division constitutes a decision procedure for the problem, since it is guaranteed to establish in a finite number of precisely predetermined steps, whether the remainder is zero or not. Moreover, the number of steps in this case can be predicted in advance. From the start symbolic logicians were interested in finding a decision procedure for logical truths. Of course, given a deductive science of logic, they would already be in possession of a decision procedure for proofs; that is, they could always decide in a finite number of steps whether a given sequence of schemata constituted a proof of a given schema, by examining the sequence in the light of the rules of inference, which are assumed to be finite in number and to have been expressly stated. What the logicians wanted may be stated more precisely as follows. Given a deductive science of logic, such that all and only the logically true statement-forms or schemata are deducible from the axioms, the logicians wanted to discover a characteristic belonging to all the provable schemata and to none of the unprovable schemata, and which moreover could be shown to characterize or not to characterize a given schema framed in the symbols of the science in a foreseeably finite number of steps. I shall return to this problem later. What we have to see first is the way in which a deductive science of logic was constructed. Broadly speaking, we can divide logic, the art or the science, into two parts. First, there are logically true schemata or rules of inference which depend solely on statement connectives and on the particle "not" as applied to a statement in order to obtain its denial. This branch of logic may be called the logic of unanalyzed statements. The logical truths with which it deals depend on an analysis of compound or molecular statements into component statements, but not on an analysis which goes within what we may call atomic statements-statements which cannot be broken up into further statements. The logically true schema which corresponds to the rule of modus ponens is an example: [(p :i q) & p] :i q. For any statement obtained from this schema by uniform substitution of statements for the letters p and q will be true, no matter what the component statements p and q are about, no matter what are the terms which go to make them up. Another instance would be the logically true schema corresponding to a reductio ad absurdum argument: [( '""P :i '"'-'q) & q] :i p. (The twiddle ",.__," means "not".) Incidentally, this kind of logic is by no means a modern invention; numerous rules of inference belonging to it were catalogued in antiquity and the middle ages. For philosophical reasons, it was not much studied by Aristotle, who was rather interested in what he called demonstration, the proof through the definition of a subject that a property belongs to it. ~his brin~s us to the second kind of logic, for the of Anstotle's Prior Analytics, primarily the logic of t~e syllogism, requires that we analyze statements mto parts which are no longer statements but terms. Consider, for instance, mood Ferio of Figur~ I of the syllogism: No Mis P Some Sis M log~c Some S is not P This is stated as a rule of inference, but I could also state in a single line the corresponding logically true sc?ema. Bes~des the moods of the syllogism, the Prior Analytics also gives rules for inferences ~rom a single premiss, these rules once more dependmg on an analysis of statements into terms. One of the rules of conversion, for instance, is: No Sis P No Pis S And one of the rules of subalternation is: No Sis P Some S is not P In _all cases the inferences depend essentially on the logical words "all" ' "some" ' "no" ' "not" , ""lS "·, the letters S, M, P may be considered dummy letters for_ nouns or adjectives. In all cases the logic of the !'rior Analytics requires an analysis of statements mto terms-on the one hand terms which are essentially general or singular names or adjectives, and on the other logical particles which do not name but serv: to i~dicate affirmation or denial, universality or particularity. Now there is nothing fallacious about Aristotle's logic, i~ we are simply interested in possible ?e?uctions, 1t has two limitations. In the first place, it is based on the assumption that all the terms which m~y be subs~ituted for S, M, and P designate existing thmgs. If this assumption is not made, certain untoward consequences follow. Thus from "No men are gods" it follows by conversion that no gods are men· an~ from this latter statement it follows by subalter~ nation that some gods are not men. This final staten:ient clearly implies the existence of gods, a conclusi on w h"ic h may come as a surprise to some moderns who would yet be willing to admit the initial premiss that no men are gods. ?ut k" A secon? limitation consists in the fact that certain mds of inference which we might like to make ' and whi~h depend on the analysis of statements into term~, simply do not come within the scope of Arist?tle s rules. For instance, from the statement "All circles are figures" we should like to be abl t _ "All h d e o con 1 cu d e: w o raw circles draw figures" " d f "All h · nn rom orses are animals", we should like to c 1d · "All h one u e. . . eads of horses are heads of animals". Aristotle, mcidental_ly,_ would ?ot deny these consequences; he draws a simi_lar one m his book the Topics; but from the standpom~ of his ontology, he simply did not reg~rd the logic of relations which is involved here as important. r Modern symbolic logic has gotten round these . . i~mtat10ns by making an analysis of statements different from the subject-predicate analysis of Aristotle. Thus a universal affirmative statement, "All M is P", becomes: (Vx)(Mx :i Px). Read this: Whatever x is, if x is M then x is p. or whatever you consider, if it is M then it is p The' upsi"d e-d ~wn "A" f ollowed by "x" is called a ·universal quantifier. M has lost its full function as a subject term or name, and has become merely a predicate. and the "x" serves as a kind of pronoun, indicatin~ the cross-references between quantifiers and redicat:s: The word "is" is symbolized merely by fuxtaposit10n of the M and the x, and of the p and th B t . h ex . . Y urnmg t e universal affirmative into a condit10nal, we av~id the implication of existence: we merely b saymg that, if anything is an M , th en 1 "t . p are is a , ~t we are not asserting that anything is M. The particular affirmative "Some S i"s P" b ecomes: (3:x)(Sx & Px). Read this: The.re exists an x such that xis Sand xis P, or: there exists something which is both S and P. !he ~ackwards "E" followed by "x" is called an existential quantifier. The universal negative stat _ . e men t "N o S is P" b ecomes: (Vx) (Sx :i ,.__, Px). (Whatever x .is, if x is S then it is not p) Th e par· 1 · ticu ar negative statement "Some S is not P" becomes: '"'-'(3:x)(Sx & Px). (There does not exist an x such that x is both S and P.) The question whether these ways of symbolizing statements. play fast and loose with our ordinary u~derstan~mgs I am not going to argue, but I do wish_ to pomt out that this new analysis and notation admits of an easy extension to kinds of argument �9 8 for which Aristotle failed to provide a rule, for example, the arguments about those who draw circles and about heads of horses. What is involved in these cases is a relational predicate; we need to have a notation, for instance, to express the relation of y to x such that y draws x; this can be supplied by "Dyx". The argument about the circles, then, goes into symbols as follows. The premiss is: (Vx)(Cx :i Fx). (Whatever x is, if x is a circle then x is a figure.) The conclusion looks more complicated: (Vy)[('.3.x)(Cx & Dyx) :i ('.3.x)(Fx & Dyx)]. (Whatever y is, if there exists an x such that x is a circle and y draws x, then there exists an x such that x is a figure and y draws x.) There can also be triadic predicates, in which three terms are related, as in "John gives the book to Mary", and there can be predicates which relate even greater numbers of terms. What symbolic logic here provides is a notation for expressing such relations in a uniform way. The next step would be that of collecting logical truths involving such predicates, and attempting to develop a deductive science such that all and only the logical truths of this type would be theorems. This branch of logic, which goes beyond the logic of unanalyzed statements by analyzing statements into predicates and quantifiers, is called quantificational logic. Thus the two branches of logic I have talked about will be concerned with schemata expressing logical truths of two types; schemata expressing the first type of logical truth will contain dummy letters for sentences or statements, and schemata expressing the second type of logical truth will contain dummy letters for predicates. None of these schemata are statements; they are rather statement-forms. Only if we specify particular predicates for substitution in the quantificational formulas do we obtain sentences, properly speaking. And when we do this, we pass beyond the boundaries Df logic proper into other subject matters. Any particular predicate will have special properties, and if we choose to develop a deductive science concerning this predicate, we shall have to set down axioms appropriate to it, expressing its special properties. For instance, suppose we wish to develop a deductive science involving the binary or dyadic predicate of equality (as in "x = y"). This predicate has special characteristics not common to predicates in general; for in- stance, it is transitive, as expressed in the statement (and note that this is a genuine statement): (Vx)(Vy)(Vz)[(Exy & Eyz) :i Exz)]. This is the symbolic notation for C.N.I. of Euclid. Once we pass the bounds of logic proper, we shall be dealing with particular subject matters as expressed in particular predicates. Now I am not going to develop quantificational logic deductively, but rather I shall take the logic of unanalyzed statements as an illustration and show one way in which it can be presented as a deductive science. In line with the Leibnizian program, we will require the science to be formal, in the sense that the inferences can be carried out simply in terms of notational patterns, and quite independently of what the symbols mean. Thus it will be necessary that all the formulas of the science be composed solely from a specified alphabet of ideograms, with dummy letters for statements; it will be necessary further that any sequence of symbols which is a formula be recognizable as such simply by means of its form. And it will be necessary finally that all the axioms and rules of inference be listed. The axioms, of course, will be formulas stated in the symbols of the science, and the rules of inference will have to be sentences stated in English, so that we can understand what we are permitted to do in carrying out deductions. The alphabet of signs will be ,...,,, &, V, /\, :i, together with as many dummy letters p, q, r, and so on, as may be necessary, and parentheses to indicate grouping. The formation rules for formulas can be specified by three English sentences: (1) p, q, r, and so on, are formulas; (2) if p and q are formulas, then so also are p & q, p V q, p /\ q, p :i q, and ,...,,p; (3) there are no other formulas besides those specified by (1) and (2). Before going on to state the axioms and the rules of inference, let me introduce a simplification. As it turns out, we can define some of the statement connectives in terms of others. For instance, we can define the inclusive "or" in terms of "and" and "not", as follows: ,...,,(,...,,p & ,...,,q) for p V q. The definition seems adequate, since all that the inclusive "or" does is to exclude the possibility that both p and q are false. The exclusive "or" can also be defined in terms of "and" and "not": ,...,,(,...,,p & ,...,,q) & ,...._,(p & q) for p /\ q. This ~gain appears to be adequate, since what the e~~lusive "or" does is to exclude both the possibility that both p and q are false, and the possibility that both are true. Finally, "if-then" may be defin d M: e ""'(p & "-'q) for p :i q. This might be quarreled with; what it says is that "If p th en q " means that it is not the case both that . p ·is 1true and that p is false. This defi m't' . 10n is cert am? not adequate for all meanings of "if-then". for mstance, the subjunctive meaning involved i~ Newton's First Law of Motion: If a body were ~o be acted upon by no forces, then it would continue m a state of rest or uniform rectilinear motion. Newton never meant to assert that th ere is ever . b . . any ody which is not subject to forces any body for which either the antecedent or the 'consequent would ~e true. Even the statement of such common ~ropertles as solubility or conductivity appears to mvolve this su b' · . . JUnctive or contrary-to-fact condit10nal: ~o .say that a body is soluble in water is to say that if it were placed in water then it would dissolve. s~1:1bolic logicians have not succeeded in systematizm~ .or ex~licating the use of this contraryto-fa:t con~it10nal m a fruitful way, and much of physical science as ordinarily stated appears to d d . epen upon it. Still, the "if-then" relation previous!~ defined appears to be adequate for most mathematical uses, as mathematics now stands. So no': our ,~cience will deal fundamentally with the particles and" and "not"., th'is economy is . h' ~c iev:? at a price, of course; but there is also a gain m facility of deduction. And we can still use the other symbols as abbreviations. For the axioms let me choose: 1. p :i (p & p) 2. (p & q) :i p 3. (p :i q) :i [,...,,(qr) :i "-'(rp)] (No~e that I continue to use the conditional sign in st~tmg the axioms, for the sake of brevity.) These axioms may appear silly. An exemplification of the first would be: "If Plato is right then it is both th :ase that Plato is right and that Plato is right." mstance of the second would be.· "If Pl a t o is ng h t . . d a.n seven plus five equals twelve then Plato nght" A n mstance of the third would be· "If 't is . ' · th · . · i is e case that, if psychoanalysis is valid then head~che powders are helpful, then, if it is not the case . ot~ that headache powders are helpful and Plato is nght, then it is not the case both that Plato is A~ ri~h.t _and psyc~oanalysis is valid." Despite their tnviahty,. the axioms permit us to deduce indefinitely many .logical truths, including all the familiar ones belongmg to this branch of logic. The rules o~ inference will be as follows: First, the rule of umform substitution: I may substitute ne~ formulas for any of the letters of any of the ax10ms, so long as, in any particular case, I substitute o~e and the same formula for every occurrence of a given. letter in the axiom from which I start. Secondly, we will have the rule of modus ponens: A, A :i B B This means that, given A and B as well-formed form~las or schemata, then if A and A :i B occur as axioms or proved formulas, I may write down B as a proved formula or theorem. To illustrate these rules -they are the only ones permitted-let me prove ""' ( "'P. & P) · Please recall that my ability to carry out this proof depends on a lucky discovery; as yet I have no method to show me how to construct a p~oof of any given formula which may be provable. First I write: (1) p :i (p & p) , which is simp1 · . y A 1 XlOm • Seco~~ I write: (2) "-'[(p & p) & ,...,,p], which by defimtion of the conditional sign can also be written as (p & P) :i p, which in turn comes from Axiom 2 by substitution of p for q. Third I write: (3) [p ~ (p & p)] :i ["-'((p & p) & "-'P) ~ ~(,...,,p & p)]. This comes from Axiom 3 by substitution of (p & p) for q, and ,...,,p for r. Fourth. I ':'rite: (4) "-'[(p & p) & "'Pl :i "-'("-'p & p), which. is gotten from lines (1) and (3) by modus ~onens, smce the antecedent of line (3) is sim J (1), and line (4) is simply the consequent of Fm~lly, by a second application of modus ponens to Imes (2) and (4) I obtain: h~e ~r. (5) "-'( ""'P & p) ~or !ine (2) is the antecedent of line (4), and line (5) is simply the consequent of line (4). Q.E.D. So I have succeeded in proving a rather obvious sch . other derivable schemata may be more complema, ex. Now of course I shall never be able to derive all th: theorems of this science, since human life is fi~1te. But there are still some questions about the sc:ence as a whole, consisting of the axioms together with the totality of the theorems, which I should very much like to have answered. I should like to �11 10 know whether it is inconsistent; that is, whether it is possible to prove both a formula p and its negation not-p. If this were the case it would be disastrous. For it is a provable theorem of the science that p ::i (,.._,p ::i q). Now suppose that p is provable; then by modus ponens we obtain (,.._,p ::i q) as a theorem. But since we are assuming that not-p is also provable, a second application of modus ponens gives q as a theorem, where q can be any formula. Hence all formulas would be provable. Also, I should like to know whether the science is complete. Roughly speaking, what is meant by the completeness of a science is that it contains among its axioms and theorems all the truths which are capable of being stated in the symbols of the science. Whereas consistency requires that only truths be provable, completeness requires that all truths which we can express in the symbols of the science be provable. Unfortunately this problem is a bit tricky, for one might ask: What do you mean by speaking of a formula as true if you do not mean that it is deducible from the axioms by the rules of inference? Let me first take the case of a deductive science for which an answer can be devised fairly easily, say arithmetic. We can construct countless arithmetical formulas, stating equality, divisibility, and so on, between numbers. Each of these formulas is a statement, a proposition; it must be true or false. If it is false, then its negation will be true, and vice versa. So a possible criterion of completeness might then be that precisely half the formulas of the science be derivable from the axioms by the rules of inference. I could assert the science to be complete if, given any statement p formulable in the symbols of the science, then either p is provable or not-p is provable. The unprovable formulas would consist precisely of the negations of the provable ones. I shall have occasion to use this criterion of completeness later, but unfortunately it is not available in the deductive science of logic itself. For the science of logic deals, not with statements, which we may assume to be true or false, but with statement-forms, schemata, which are neither true nor false. Whenever I have spoken previously of a logically true schema, what I have meant is a statement-form such that the result of making any appropriate substitutions for its dummy letters is a true sentence simply in virtue of the logical words or particles. Elliptically, let me speak of such a schema as a logical truth. It is not the case that any s'.:hema or formula framed in the symbols of logic is either a logical truth or a logical falsehood. Take, for instance, the logical formula (p & q); neither it nor its negation is a logical truth. Thus it is not the case that precisely half the logical formulas are logical truths, and that the other half, namely the denials of the logical truths, are logical falsehoods. vVe have an intermediate category of consistent formulas, formulas which come out true under some interpretations of, or substitutions for, the dummy letters and false under other interpretations. So in the case of a deductive science of logic, if we are to talk of completeness at all, we will have to have a different criterion from that used in arithmetic. For the moment, and rather inadequately, I shall supply only an informal criterion of incompleteness: we do employ rules of inference in ordinary discourse, and we believe them to be based on logical truths. We should like all such truths to be deducible in our science. Thus we would probably judge our deductive science to be incomplete if it were found to be impossible to deduce from the axioms, by the rules of inference, the logical truth corresponding to the reductio ad absurdum inference. Finally, besides consistency and completeness, we would very much like to find a decision procedure for logical truths of the type belonging to our science; that is, faced with a formula framed in the symbols of the science, we should like to be able to decide in a predictably finite number of predetermined steps whether it is provable or not, without engaging in the rather tedious process of trying to find a proof for it or its negation-a search in which there is no guarantee that we shall be successful. Now these three questions of consistency,. completeness, and decision procedure are important in relation to any deductive science. They are questions which Leibniz would certainly have wanted answered in the case of his Universal Characteristic. And one of them, the question of consistency, assumed a critical importance in mathematics at the turn of the last century. I stated earlier that the modern systematization of mathematics and logic was actually approached from two sides: on the one side there was the aim of carrying out the Leibnizian program of a Characteristica Univer salis; on the other, that of trying to eliminate certain difficulties inherent in modern mathematics from its inception. Before discussing how the questions of consistency, com- pleteness, and decision procedure might be answered, I want to look briefly at this second side of the coin. of Whitehead and Russell, published between 1910 and 1913. Modern mathematics began with the invention of algebra, which effected a peculiar wedding between the science of discrete quantity and the science of continuous magnitude. Algebra provided a powerful method, but the theoretical justification of its rules, and more particularly the nature of the objects with which it dealt-functions of what are oddly called real numbers-remained obscure. The mathematics of the 17th and 18th centuries, including the differential and integral calculus which were constructed on the foundation of algebra, was primarily a. successful technology rather than a science. Now although the entire reduction of mathematics to logic and the predicate of class membership had been undertaken in order to supply higher mathematics with a sound foundation, it was not known whether the system was consistent. A usual method of assuring oneself of the consistency of a deductive science is to find a definite group of objects which can be presented to the imagination, and to which the postulates are clearly seen to apply. Presumably what can be presented to the imagination in complete definiteness and clarity must be logically consistent. This may be called the method of models. For instance, we believe that plane Riemannian geometry is consistent because it can be mapped onto, or translated into, the Euclidean geometry of the sphere; so if spherical Euclidean geometry is consistent, so is Riemannian plane geometry. But the geometry of the sphere can be presented to the imagination in complete definiteness and clarity, so it would appear ridiculous to doubt its consistency. But this method of models was not open in the case of Principia Mathematica, in particular because Principia Mathematica had to postulate the existence of classes containing an actually infinite number of members, as in the definition of the real numbers; and to form a clear image of such a class or aggregate of objects is impossible. In the 19th century an attempt was made to remedy this situation by a return to the deductive methods of Greek geometry. The first stage was the arithmetization of analysis; that is, the attempt to derive the notions of algebra and the calculus from the notions of elementary ari th me tic; in particular the attempt by Dedekind and Cantor to define the real number in terms of infinite aggregates of rational numbers or fractions, and thus ultimately in terms of integers. The second stage was the development of arithmetic itself as a formal deductive science. Finally, in the third stage, the structure so far achieved was brought into relation with the work of symbolic logicians, notably Boole and Frege. Thus the attempt was made to define the "primitive" notions of arithmetic in terms of what were claimed to be yet more "primitive" logical notions. Use was made not only of the logic of unanalyzed statements and quantificational logic, but also of the special properties of a particular binary predicate, that of class membership, as in "x is a member of y". More strictly, with all the formulas of the logic of unanalyzed statements and quantificational logic available-and recall that these branches of logic provide only statement-forms with dummy letters for statements or predicates, rather than statements properly speaking-a single predicate was introduced, namely that of class membership, along with the axioms appropriate to this predicate. The attempt was then made to show that the deductive science of this predicate included in its further reaches all the theorems of mathematics. The integers, for instance, turned out to be classes of classes. The accomplishment of the entire program, the development of all mathematics deductively on the basis of the predicate of class membership, appeared to be complete in the Principia Mathematica The question of consistency was all the more urgent because certain modes of reasoning with classes, which appeared fairly straightforward, were found to lead to contradictions. For instance, it might be supposed that, given any clearly defined property, it should be possible to posit the existence of a class of all those entities which possess the property. Thus the class of all cats is not a cat, while the class of all thinkable objects is itself a thinkable object. The class of all cats is not a member of itself, while the class of all thinkable objects is a member of itself. So we have the clearly definable property of classes of being either self-members or non-self-members. It should then be possible to form the class of all those classes which are not members of themselves. But as Russell discovered, this class of all classes which are non-self-members is altogether self-contradictory. Presumably it is either a member of itself or it is not. Suppose it is a member of itself; then by its own definition it cannot be a member of itself. Then suppose it is not a mem her of itself; by defini- �13 12 tion it must be a class which is a member of itself. Either alternative leads to a contradiction. This contradiction could be avoided only by making rather artificial restrictions on the formation of classes. But it was still not clear that other paradoxes might not arise. In these circumstances, David Hilbert proposed another method of proving consistency. First the deductive science was to be completely formalized, in the sense that the meaning of all the symbols employed in the science could be entirely neglected in the carrying out of proofs; all that one would have to understand would be the rules of sentence formation and the rules of inference. Assuming this doneit is a very difficult and tricky business-one might begin to study the strings of symbols which express the science, but which we may treat, for the purposes of our investigation, as devoid of significance, as constituting simply a mosaic or abstract design of marks. Clearly we can make certain statements about the strings of symbols. Already we know that there is a certain class of sequences of symbols, recognizable by form alone, which may be called sentences; and we also know that there are certain kinds of sequences of sentences, recognizable by form alone, which constitute proofs or deductions. And by reasoning about the sequences we may also be able to establish that there will never occur among the proved sentences both a sentence and its negation; that is, we may be able to establish the consistency of the science. This kind of study of a deductive science Hilbert called metamathematics. Note please, that our reasoning on the strings of symbols will be carried out in ordinary language. Just as the rules of sentence formation and rules of inference have to be stated in words which we understand, so all reasoning on the formalized system must be carried out in a meaningful language. Following Carnap, we call the formalized language the object language, because it is the object of study; and we call the language used to talk about the formalized system the metalanguage. Thus we have three distinct levels: first, a deductive science which has a meaningful interpretation but is not formalized; second, the same science completely formalized, and regarded as emptied of meaningful content; third, the informal metalanguage used to describe the formalized science. It is conceivable that one might formalize the metalanguage; this would be an entirely distinct process, and it is not clear at this stage whether any advantage would be gained by it; we would still have to have an informal, meaningful meta-metalanguage in which to describe the metalanguage. Thus the final appeal must be to reasoning processes carried out in ordinary English. However, there is one important restriction on the modes of reasoning to be used in the metalanguage: we would not want them to be more dubious than the modes of reasoning used in the formalized language which is under investigation and whose consistency is in doubt. Let me now undertake a metamathematical investigation of the logic of unanalyzed statements, as I have previously outlined it. In this case we can prove consistency, completeness, and the existence of a decision procedure without too much difficulty. In the case of consistency, I will depend on a result mentioned previously, namely, that if both a formula p and its denial non-p are provable, that is, if the science is inconsistent, then any formula will be provable. The procedure will be to hit on a characteristic which is common to the patterns of signs constituting the axioms, and which is "hereditary", that is, it belongs to all the formulas which can be deduced from the axioms. Then if we can find one formula of the science which does not possess the characteristic, the consistency of the science will be proved, since this formula will not be deducible, and hence not every formula will be deducible. Let me repeat: we know that if the science is inconsistent, then all formulas are provable. Our strategy will be to hit on a characteristic which is common to all axioms and theorems, and then show that it is not shared by all formulas. The characteristic we shall use is actually suggested by the interpretation of the science. When I assert (p & q), I mean that both p and q are true; that is, the truth of the conjunction depends on that of its components; if they are true, it is true, and in all other cases it is false. We can represent this fact by what is called a truth table: p q p&q T F T F T T F F T F F F Here I list all the possible combinations of truth and falsity of the components, and in the last column I list the corresponding values, truth or falsity, taken by the conjunction. For negation, we have another table: p T F F T This merely states that if p is true, then not-p is false, and vice versa. Since all the other statement connectives, "if-then", inclusive "or", and so on, are defined in terms of "not" and "and~1 , we can construct similar tables for them on the basis of the tables already constructed. For instance: p ::i q is defined as ,..._,(p & ,..._,q). p q ,..._,q p& ,..._,q ,..._,(p & ,..._,q) T F T F T T F F F F T T F F T F T T F T First I list the possible combinations of truth and falsity for p and q; then, following the table for negation, I make a column for "'q. Next, working from the table for "and", I construct a column for p & "'q; this will be true only when both components ar~ true. Finally, I make a column for "'(P & "'q), usmg the table of negation. It turns out, thus, that "If p then q" is false only in case the antecedent p is true and the consequent q is false. The truth tables are like multiplication or addition tables, except that here we have only two objects, T and F, rather than the whole series of integers. What we have now is a method whereby, given an assignment of T's and F's to the component statements of a compound statement, we will always be able to compute, in a finite number of predetermined steps, a value T or F for the statement as a :"hole. This procedure, although suggested by the ~nterpretation of the science, can be carried out quite mdependently of any interpretation of the symbols of the science, simply by working in accordance with the truth tables. Now a characteristic of the axioms and theorems of the logic of unanalyzed statements is that they come out with the value T under any assignment of T'~ and F's to their component statements. To prove this, one first shows that it is true of the axioms. Consider, for instance Axiom 2: (p & q) ::i p. We construct a truth table as follows: p&q T F T F p ,..._,p q T T F F (p & q) T F F F ::J p T T T T First we construct a table for p & q as before, then we follow the table for "if-then", which tells us that a conditional statement is false just in case its antecedent is true and its consequent false. Now since the antecedent of Axiom 2 is true only in the first row, and in this row the consequent p is also true Axiom 2 always takes the value T. The same resul~ goes for Axioms 1 and 3. In order to show that all the theorems deduced from the axioms always take the value T, we have to examine the rules of inference. Modus ponens is: A, A::i B B Assume the formulas A and A ::i B always take the value T; then from the truth table for "if-then" we know that B also must always take the value T'. For if the antecedent of a conditional always takes the value T, and the conditional itself always takes the value T, then the consequent of the conditional must always take the value T. The other rule of inference, namely that of uniform substitution likewise preserves this property. For suppose w~ substitute compound statement-forms or formulas for dummy letters in a given formula which always takes the value T. What has been substituted in all ca10es will take either the value Tor F, and so no new combinations of T's and F's will turn up, and the new schema will therefore continue to take the value T in all cases. The. fi?al step in the proof of consistency is merely to exhibit a formula which does not always take the value (p_ & q) is an instance, as we have already seen, smce it takes the value F except when both p and q take the value T. Thus, having proved that all axioms and theorems of the science have a certain characteristic, I have proved that not all formulas are provable. Since the inconsistency of the science would imply that all formulas are provable, I have therefore proved that the deductive science of unanalyzed statements is consistent. It is also complete. That is, all the logical truths of t~e science are deducible from the axioms; the addition of further axioms or rules of inference would not '!'· �14 enable us to deduce any logical truths which we cannot derive already. To prove this, we turn once more to the truth tables. For on reflection, we see that the truth tables constitute a criterion of logical truth independent of deducibility. If a formula belonging to this science is a logical truth, then it must take the value T under any assignment of T's and F's to its component statements. The proof of completeness, then, consists in showing that, if we have a formula that always takes the value T, a proof of it can always be constructed starting from the axioms we have laid down. I shall not turn aside to give this demonstration; it is fairly easy but very long. Finally, it should be clear that in answering the questions of consistency and completeness, we have in this case answered our third question as well; we have already turned up a decision procedure for logical truths of the kind we are dealing with. For the truth tables provide a method of computing, in a finite number of predetermined steps, whether a formula is a logical truth or not. For all practical purposes, the deductive science we have constructed is quite unnecessary. Logical truths belonging to the logic of unanalyzed statements are always detectible by means of truth tables. So in this branch of logic we have all that Leibniz could possibly ask. Of course, we should remind ourselves that we have subjected the statement connectives of ordinary discourse, particularly the conditional, to some torture, some straight-jacketing, to achieve this result. But statement connectives in ordinary discourse are frequently truth-functional, and our science does provide a streamlined method for testing many of the inferences used in everyday argument. Next, what about consistency, completeness, and the existence of a decision procedure in the case of quantificational logic, and also in the entire system of mathematics and logic as built up in Principia Mathematica? As it turns out, that part of quantificational logic which deals with monadic predicatespredicate letters which are followed only by a single pronoun letter, as in the case of the predicate letters used in representing the Aristotelian syllogism-this part of quantificational logic is consistent and complete, and possesses a decision procedure. But with quantificational logic involving relational predicates like "y draws x" the case is otherwise. And with a deductive science of sufficient scope to include the predicate of class membership and hence the whole of mathematics as presented in Principia Mathema- 15 tica, the case is otherwise still. I have at last come to the point of this essay. In 1931 a mathematician named Godel, then in Vienna but now at Princeton, introduced a new and curious technique into metamathematical studies. What he did in effect was to map the statements of metamathematics onto arithmetic; that is, he translated the statements of metamathematics into a language which employed the same symbols as arithmetic, and the same rules of syntax or sentence formation-this arithmetical language being part of the very system of Principia Mathematica which metamathematics is designed to investigate. This is indeed an astonishing procedure. Let me indicate how it was done. The symbols used in Principia Mathematica or in any formalization of logic and mathematics are in general finite in number, and can in any case be listed. In talking about these symbols we have to use names of them; and for this purpose we can certainly use, if we wish, the symbols which are normally used to name the integers. For instance, a system of logic and mathematics like Principia ~Mathematica can be developed using only the following nine symbols: ,....., & :::i \{ ( ) E X 1 2 3 4 5 6 7 8 9 These symbols may then be given, as names, the symbols normally used to name the integers one through nine. The numerical names are called Godel numbers. Now suppose we consider any well-formed formula, framed in the symbols of our science, say: rv(Vx) (x ex). (It is not the case that, whatever x is, xis a member of x). I suppose this is true, but no matter. What we want to show is that we can associate with any well-formed formula, true or not, a unique numerical name or Godel number. We have ten marks in the formula, each having a Godel number; in order, the Godel numbers are: 1, 5, 4, 8, 6, 5, 8, 7, 8, 6. Now in order to obtain a unique Godel number for the formula, Godel proposed that we use the numbers just listed as exponents of the first prime numbers taken in order, then take the prime numbers raised to these powers and multiply them together. Thus we get, as the numerical name or Godel number of our formula: 2i X 35 X 5 4 X 78 X 11 6 X 135 X 17 8 X 19 7 X 23 8 X 29 6 • This is a rather large number, but since, by a well- known theorem of arithmetic, a number can be factored into prime factors in only one way, it constitutes a unique name for the formula, and given the number we can reconstruct the formula through factorization and looking up the meaning of the exponents of the prime factors in our dictionary. To each distinguishable well-formed formula of our scienc:, then, there corresponds a unique number; and given any number, we can always find whether it is the name of a formula by fa.ttorization. · By a similar process, we can obtain a unique Godel number for any sequences of formulas, sequences such as we have in proofs or deductions, for instance. For instance, if we have a two-formula sequence such that the successive formulas have the Godel numbers m and n, then the Godel number of the sequence will be 2m X Jn. Thus to any sequence of formulas there corresponds a unique numerical name; and given the number we can reconstruct the sequence of which it is a name by factorization. Some of the sequences, of course, constitute proofs. Now let me remind you that metamathematics is committed to dealing with the formulas of logic and mathematics simply as meaningless marks. It is committed, in particular, to describing theoremhood simply in terms of characteristics of sequences of formulas. Suppose, for instance, that the only rule of inference in our science is modus ponens. Then the metamathematical definition of theoremhood might run as follows: "the formula ip is a theorem" means that there exists a sequence a of formulas such that 'P is a member of a (presumably the last one), and such that any formula t/; which is a member of a is either an axiom, or else it is preceded in the sequence by some formula x and also by a formula "if x then t/;". Every provable formula is thus associated with a sequence of formulas of a certain kind, which constitutes a proof of the formula, and which can be recognized as such simply in terms of notational patterns. Now Godel showed that, for systems of logic and ~athematics like Principia Mathematica, it is possible to find an arithmetical property of numbers, such that if a formula is provable, then its Godel number has the property, and otherwise not. I shall not a~tempt to state what this property is precisely, but simply try to indicate the possibility that such an arithmetical property exists. To every Godel number of a provable formula, we mav correlate the Godel number of a sequence of formulas which con- stitutes a proof of the given formula. The Godel number of the given formula will be an exponent of a prime factor of the Godel number of the sequence. It is conceivable that Godel numbers of sequences which are proofs constitute a class of numbers distinguished by certain arithmetical properties. It is therefore conceivable that the Godel number of a provable formula itself has a distinguishing arithmetical property, namely that of being an exponent of a prime factor of some number belonging to a special class of numbers. Let me go over the same ground again in a different way. Suppose we have a formula ip, belonging to the language of Principia Mathematica; I shall call this language L. With ip is uniquely associated its Godel number x. Now Godel discovered a property of numbers (let us call the property "Bew") such that the formula stating that x has this property M ip is provable G is not provable t L ip G.N. x Bew(x) G ! = ""-'Bew(n) n (viz. the formula "Bew(x) ") is expressible in L, and moreover, when this formula is interpreted metalinguistically instead of arithmetically, it means that 'P is provable. In other words, the property Bew has been so selected that if xis Bew, then the formula ip of which x is the Godel number is provable, and vice versa. Note, please, that Bew (x) is a genuine arithmetical formula, quite independently of its metamathematical interpretation. From the arithmetical standpoint, it merely says that x is an exponent of a prime factor of a number belonging to a certain class of numbers. Next step. Godel was able to prove that L cons. :::i (Bew(x) is provable Bew(x) is true). (I use the equivalence mark to indicate mutual logical entailment.) To say that Bew(x) is provable is to say that a certain formula in L is provable, and to say that Bew(x) is true means, metamathematically, that another formula in L, namely ip, is provable. Thus what Godel shows here is that, on the assumption that Lis consistent, if the formula ip is provable, then the formula Bew(x) is provable, and vice versa. In other words: if L is consistent, then one formula of L is provable if and only if another formula, uniquely associated with it, is also provable. Last step. Godel was able to show that, for systems like Principia Mathematica, it is possible to construct �17 16 a formula G with Godel number n, such that G is the formula rvBew(n). Interpreted metalinguistically, G says that G is not provable, which may seem to involve an objectionable kind of circularity or selfreference. But recall for a moment that G is a genuine well-formed formula of arithmetic; it must be true or false; and therefore, if our system of logic and mathematics is to be complete, it must be possible to prove either G or not-G on the basis of the axioms. Recall, too, that we have the theorem: L cons. :::i (Bew(x) is provable_ Bew(x) is true). This is true for all numbers x which are Godel numgers of formulas; in particular, it must be true for n which is the Godel number of G; hence we may write: L cons. :::i (Bew(n) is provable Bew(n) is true). Now Bew(n) is simply the denial of G, therefore to say Bew(n) is provable is to say that rvG is provable. On the other hand, Bew(n) is true if and only if the formula with Godel number n is provable, and the formula with Godel number n is G. So what we have is: L cons. :::i (rvG is provable_ G is provable). So on the assumption that L is consistent, the provability of G logically entails the provability of not-G and vice versa. If we assume one of them is provable, then the other will be provable too, and hence L will not be consistent. The only alternative is to assume that neither G nor not-G is provable. But of course one or the other of them must be true. Hence if we assume that L is consistent, it turns out that L is incomplete; that is, there is an arithmetical formula in L such that neither it nor its denial is provable, although one or the other is true. Even if we add new axioms to L so as to be able to prove G, Godel shows that it will still be possible to construct a statement G' such that neither G' nor its denial not-G' is provable. Godel's theorem has a very general character. Given any formally characterizable deductive system of logic and arithmetic, there are indefinitely many arithmetical truths which cannot be proved on the basis of the axioms. This completes the account of the proof, but please note that we have also discovered that, if L is consistent, then the formula G is true, though unprovable. For not-G cannot be true, since its truth would imply the provability of G, which we have seen that we have to deny. But G or not-G, one or the other, must be true, so we have to choose Gas the true one. Now I would like to mention two more results obtained by Godel's method. Godel also proved that if L is consistent, then its consistency can be proved only by using more powerful-and hence more dubious-modes of inference than those used in L itself. Such a proof, then, would beg the question. Secondly, in 1936 Alonzo Church of Princeton, using once more the arithmetical techniques of Godel, proved that there exists no decision procedure for formulas of quantificational logic involving relational predicates, predicates which take more than one argument, as "x draws y", or "x is the head ~f y", or "x is a member of y". Quantificationa~ logic can be proven to be consistent and complete, m the sense that all and only the formulas which are true can be derived from a set of axioms; but given a formula of quantificational logic involving relational predicates, there can exist no method of deciding, in a finite number of predetermined steps, whether the formula is provable or not. The conclusion, then, is this: The logic of unanalyzed statements and that part of quantificational logic dealing with monadic predicates are consistent, complete, and possess decision procedures. There is no problem of these branches of logic which cannot be solved by mechanical calculation. The logic of relational predicates is consistent and complete, but does not possess a decision procedure. We can set up a deductive science such that all quantificational truths are deducible from the axioms; but the determination whether a given formula is deducible or not is contigent on time, cash, ingenuity, and intelligence directed toward a goal, and there is no guarantee that we shall ever succeed in answering the question. That is. we are unable to envisage the total outcome of a series of acts whose generating principle we can envisage with complete clarity. Finally, any deductive science of sufficient scope to include elementary arithmetic lacks a general decision procedure, and, worse yet, is such that, if it is consistent, then it is not complete. Granting its consistency, which can only be proved by the use of methods more dubious than those employed within the science itself, then there are sentences which can be formulated within the language of the science and which are formally undecidable; that is, no investigations carried out within the deductive science itself can disclose whether these sentences are true or false. This does not mean, of course, that these sentences will not be deducible in another formalization of arithmetic. It does not mean that there is any par- ticular truth or particular set of truths which man is prevented, in the nature of things, from discovering. Suppose we imagine an omniscient number-theorist. His agility to see infinitely many arithmetical truths at once would presumably enable him to recognize as correct some principles of deduction which we humans could not discover ourselves. But Godel's proof shows that any correct formal system which this omniscient arithmetician could reveal to us, telling us how it works without telling us why, would be incomplete. Mathematical truth is essentially informal; it cannot be defined in formal terms, in terms of notational patterns. Godel's result for arithmetic reflects back curlously on the deductive sciences of logic, the logic of unanalyzed statements and quantificational logic. These sciences, although they are complete formal 'theories of a particular conception of logical consequence extorted by violence from the vague and intuitive concepts of everyday usage, do not exhaust the notion of logical consequence. Godel's proof shows that in any deductive science with a subject matter as rich as elementary arithmetic, however much we supplement the ordinary rules of inference with new structural rules, it is possible to construct sentences which follow in an everyday sense of logical consequence from reflections on the science as a whole but which nevertheless cannot be proved within th~ theory, on the basis of the previously accepted rules of inference. The formula G is an instance. Hence the art of logic, understood as modes of inference arrived at through luck and insight, must always retain a certain priority over any science of logic which seeks to reduce that art to a system of calculation, or even to a formal deductive theory. And therefore the Leibnizian program is, in the nature of things, incapable of being carried out. [1] This essay grew out of a Faculty Study Group which met regularly during the academic year 1956-57 to study symbolic or mathematical logic. The essay was originally presented as a lecture, and was intended as a piece of haute vulgarisation-an introduction to the fundamental notions of symbolic logic and to Godel's theorems of 1931. �19 Bertrand Russell has said "Mathematics is the subject in which we never know what we are talking about nor whether what we say is true." Underneath the typically Russellian wisecrack lies a profound truth; for mathematics is not really "about" anything, nor are its theorems "true"-they are merely valid. To say that they are valid means that they would hold true of any universe in which the axioms of the mathematical system hold true; but we do not know whether the universe we live in is such a universe. This is merely another way of saying that pure mathematics is concerned merely with the logical relations that hold among its axioms and theorems and not at all with the question of whether these apply to any physical reality. In short, mathematics is concerned with form, not content. The task of abstracting form from content in mathematics is, however, a difficult one. Historically it began as early as Euclid, who attempted to deduce all geometrical propositions from a few sentences, called "postulates" and "common notions", by methods which were apparently intended to be, so far as possible, purely formal, and hence not to depend upon "intuition" or visual examination of diagrams. If Euclid was attempting to formalize geometry, his attempt was not entirely successful, for his common notions and postulates do not quite suffice to permit the deduction from them, by purely logical means, of all the Euclidean propositions. A FORMALIST APPROACH TO MATHEMATICS ALLEN CLARK THE FORMALIZATION OF GEOMETRY The formalization of geometry was, however, carried out by David Hilbert in his book Foundations of Geometry, published in 1899. Hilbert shows that all the propositions of Euclidean geometry can be deduced, by purely logical means, and without any appeal to geometrical "intuition", from a certain set of twenty axioms, the first group of which may be expressed as follows: 1. Two points determine a line. 2. Three points not in the same line determine a plane. 3. If two points of a line lie in a plane, then every point of that line lies in that plane. 4. If two planes have a point in common, they have at least two points in common. S. In each line there are at least two points, in every plane there are at least three points not in the same line, and in space there are at least four points not in the same plane. The formalistic character of Hilbert's axioms is somewhat obscured by the fact that he still employed the terminology of geometry, using such words as "point", "plane", and so on. In fact, however, nothing in the way that these axioms are used in proofs depends in the least upon the meanings of any of these geometrical terms. The geometrical terms could as well be replaced by meaningless or undefined terms, or arbitrary symbols. I shall, therefore, translate Hilbert's axioms into a language that employs no geometrical terms whatever. Let the system consist of undefined elements represented by capital letters A, B, C, etc., of sets ofele~ ments, and of classes of elements. ''i 1. To any two distinct elements A and B there corresponds just one set, called L(AB), which contains both A and B. 2. For any three distinct elements A, B, C, if there is no set that contains all of them, then there is just one class that contains all of them. 3. If a class contains two elements of a set, it contains all elements of that set. 4. If two classes have a common element, they have at least two common elements. S. Every set contains at least two distinct elements; every class contains at least three distinct elements that are not all in the same set; there are at least four elements that are not all contained in the same class. From these axioms alone various theorems can be deduced. For example, the theorem which in geometrical language would read "Two distinct lines have either one point or no point in common" can be translated into purely logical language as "Two distinct sets have either just one element in common or no element in common." The proof in the logical language goes as follows: If the two sets had two elements, say A and B, in common, there would (by Axiom 1) be just one set L(AB) containing both A and B, and hence each of the two given sets would be identical with L(AB), and hence with each other, contrary to the hypothesis that they are distinct; therefore they have at most one element in common. Hilbert shows how all the propositions of Euclidean geometry can be derived from the twenty axioms by methods which do not depend at all upon the meaning of any of the terms used, but purely upon the �20 abstract logical relations among the undefined terms as stated in the axioms. The axioms can thus be regarded as given strings of meaningless marks on paper, and the rules of logic as the rules of a game permitting the marks to be rearranged in certain ways, and a theorem as any arrangement of marks that can be reached from the given strings of marks. by means of permissible "moves". THE FORMALIZATION OF ARITHMETIC The success of Hilbert's formalization of geometry encouraged attempts to formalize arithmetic by divorcing it from any intuitive conception of "number" and treating it merely as a game of manipulating meaningless marks on paper. Only in this way can we be sure that what we regard as "proofs" in arithmetic depend purely upon logic, and not upon some unconscious inferences from our intuitive acquaintance with numbers. I shall present a construction of arithmetic so purely formal that the symbols employed in it represent purely typographical operations, such as erasure or transposition of letters. [1] There are only three marks: /, K, A. The stroke / is used to combine letters into "words" by the following two rules: 1. Any single letter is a word. 2. If x and y are words, then /xy is a word. Thus the effect of the stroke mark is simply to combine the following two words into a single word. K is an erasure operator whose effect is exhibited by the following example: Dl Kxy = x That is, we are permitted to erase the second word after K, followed of course by the erasure of K itself. The operator A is explained by the definition D2 Axyz = xz/yz where x, y, z are any three words. Thus an occurrence of A gives us permission to rearrange the next three words in the manner indicated in D2, followed of course by the erasure of A. (It will be understood that the letters 'x', 'y', 'z' never occur in this system; in Dl and D2 they merely take the place of unspecified strings of A's and K's.) Now let us consider the string AK. Its effect upon words following it in a string is shown by: AKxy = Ky/xy = y (in consequence of Dl and D2 above). Thus AK is an erasure operator that erases the next word following AK. We abbreviate AK by 21 D3 0 for AK Thus Oxy = y, and hence Ox represents zero occurrences of x. Therefore 0 can be taken to represent zero. To construct higher numbers, we need the string A/KAK, which we abbreviate by D4 B for A/KAK Then Bxyz = A/KAKxyz = KAx/Kxyz = A/Kxyz = Kxz/yz = x/yz. B will later be shown to be the multiplication operator. Now we construct the string AB, whose effect is exhibited by ABxyz = By/xyz = y//xyz. We abbreviate AB by DS S for AB Now if we construct the string SO we see that SOxy ABOxy = Bx/Oxy =x//Oxy = xy. Thus SOx represents one occurrence of x, and hence we introduce the abbreviation D6 1 for SO The string Sl, when followed by other words, has the following effect: Slxy = x/ /lxy = x/xy, wherein we see that there are two iterations of x, and hence we abbreviate Sl by D7 2 for Sl Similarly, S2xy = x//2xy = x/x/xy, wherein there are three iterations of x, so S2 is 3, S3 is 4, and so on. Thus S is the successor operator. The various operators 0, SO, Sf SO, S/S/SO, and so on, may be called iterators, ·since the effect of any of them is to cause an iteration of the following word a certain number of times. We can therefore identify the iterators with the natural numbers. Having constructed the sequence of the natural numbers, we now proceed to develop the arithmetic of the natural numbers, using only the materials so far developed. B, as promised, turns out to be the multiplication operator, for if m and n are two iterators, i.e., natural numbers, then by D4, Bmnxy = m/nxy. Now nx, as explained above, is the ·n-fold iteration of x, and m/nx is the m-fold iteratiOn of nx, and hence the m-fold iteration of the n-fold iteration of x, or in short the (m·n)-fold iteration of x, where · (m · n) is the arithmetical product of m and n. Thus Bmn is (m ·n). To construct an addition operator, we first introduce the abbreviation D8 D for BB so that Dwxyz = BBwxyz = B/wxyz = wx/yz. Then the addition operator is BAD, for BADmnxy = A/Dmnxy = Dmx/nxy = mx//nxy; if m and n are iterators, i.e., numbers, then nx is the n-fold iteration of x, and mx is the m-fold iteration of .x, and thus mx//nxy contains an m-fold iteration of x followed by an n-fold iteration of x, or in short an (m + n)-fold iteration of x, where (m + n) is the arithmetical sum of m and n. Hence BADmn is (m + n). To construct powers of numbers we do not need any new operators. For by the preceding we know that n/nx consists of n 2 iterations of x, and n/n/nx of n 3 iterations of x. Hence to produce nm iterations of x we need only iterate nm times. But the m-fold iteration of n is mn; hence in our notation mn represents what is written as nm in the usual arithmetical notation. Thus to prove that 2 + 2 = 4, where 4 is defined a~ S3, we proceed as follows. In our notation 2 + 2 is BAD22, and BAD22xy = A/D22xy = D2x/2xy = 2x//2xy = 2x/x/xy = x/x/x/xy. But S3xy = x//3xy = x/x/x/xy. Thus we see that BAD22 and S3 produce the same effect upon any following words xy, and hence are equivalent operators. The construction of subtraction and division operators is considerably more complicated, but enough has been shown to illustrate the general method of constructing arithmetical entities and operators out of the two purely typographical operators K and A. All the abbreviations, such as 0, B, S, D, etc. can be eliminated, and each expression written out in full as a string consisting solely of K's, A's and strokesbut only at the cost of intolerable prolixity. Thus the number 2 in unabbreviated form would be A//A/ KAK//A//A/KAK!AK. But in principle the whole of arithmetic could be written out in such strings of A's and K's, and the proof of any arithmetical theorem would consist in mechanically performing the indicated typographical operations in accordance with rules Dl and D2, without supposing that the marks on paper represent anything at all. GODEL'S THEOREM Now if such a formalization of arithmetic could be carried out, the task of proving any truth of arithmetic would be reduced to a mere mechanical routine that any dunce could carry out, given enough time and patience. A result obtained by Kurt Godel in 1931, however, shows that there are certain limitations upon the possibility of carrying out such a formalization of arithmetic. In his paper entitled "Uber formal unentscheidbare Sii.tze der Principia Mathematica und verwandeter Systeme" (On formally undecidable propositions in Principia Mathematica and related systems), he showed that for any formal language adequate to express all the truths of arithmetic, there must exist some arithmetical proposition whose proof cannot be expressed within that language, although it can be shown to be true by methods lying outside that language. Hence, no formal language can express the proof of all arithmetical truths. In short, arithmetic can never be completely formalized. Godel's method of proof was very ingenious and skirted close to paradox without, however, falling into it. It consisted essentially of showing that if every proposition and proof in arithmetic can be stated in formal language, then it can be assigned a unique number, called its Godel number, and hence statements about the logical relations among the propositions and proof can be translated into statements about the arithmetical relations among the corresponding Godel numbers. Therefore all statements about arithmetic can be translated into statements within arithmetic, i.e., arithmetical formulas expressing equalities and inequalities among integers, and the like. Thus arithmetic can be used as a language in which to "talk about" itself, and hence arises the possibility that some formula in arithmetic may happen to be the "translation" of a statement about that very formula-for example, the statement that that formula is unprovable. Godel in fact shows how to construct just such a formula, and then he derives the proof of his theorem. The essence of his method can be presented in the following very simplified version. ( Suppose that every proposition in arithmetic or about arithmetic can be expressed in the symbolism of symbolic logic, and that an expression in symbolic logic consists of a finite string of marks on paper. Only a few different symbols are needed. For example, a system of symbolic logic has been constructed that uses only the four symbols: I KA F 1 2 3 4 Below each symbol has been written a number, called its Godel number. Obviously, the symbols can be unambiguously represented by their Godel numbers. Thus the string /AK could as well be writ- �22 ten 132. Each formula, each proposition, each proof can be uniquely designated by its Godel number. Now let P1, P2, Pa, etc. be various properties of numbers, such as primeness, evenness, oddness, and so on. The subscripts are the Godel numbers of these various properties, determined as follows: Let the sentence "x is prime" be translated into symbolic logic; there it is represented by some string of marks, having a Godel number, say 37. Then Pa1 is the property of primeness, and P31(n) is the proposition that n is prime. Suppose that the assignment of Godel numbers has been made for each arithmetical property. Now note that some number may be proved to possess the very property of which it is the Godel number. For example, if P 37 (n) is the proposition that n is prime, then P31(37) is the proposition that 37 is prime, and this is provable. Thus 37 can be proved to possess the very property of which it is the Godel number. Let us, adopting the language of Bertrand Russell, call numbers that do this autological numbers, and write 'A(n )' for 'n is autological'. All other numbers we call heterological, and we write 'H(n)' for 'n is heterological', i.e., for 'n cannot be proved to possess the property of which n is the Godel number.' Thus we have the equivalence: (1) H(n) 'Pn(n)' is unprovable. But the proposition H(n) can itself be written out in the symbolism of symbolic logic, and hence must have some unique Godel number, say the number h. Hence H is the property Ph, and thus we have the equivalence: (2) Ph(n) 23 ,. j 'Pn(n)' is unprovable. This equivalence holds for all numbers n = 1, 2, 3, etc., and hence in particular holds for the number h. Therefore (3) Ph(h) _ 'Ph(h)' is unprovable. Thus we have constructed a proposition, 'Ph(h)', which in effect declares its own unprovability. It is true if and only if it is unprovable. If it is false, it is provable. But if logic is consistent, no false statement is provable. Therefore if logic is consistent, we must conclude that the proposition we have constructed (call it G) is true, but unprovable. Note however, that we have not proved it to be true; for if we proved it to be true it would be false. We can only conclude by our informal reasoning about it that G must be true, although no formal proof of G can be given within the symbolism of the logic that we are employing. Thus Godel concludes that if S be any consistent system of logic adequate to express all of arithmetic, then (1) it can express some proposition for which it cannot express a formal proof, although the proposition can be shown to be true by methods lying outside the system S; (2) the consistency of S cannot be proved by methods that can be formalized within the system S itself. In short, if S is consistent, .it is incomplete. It also follows, of course, that if S is incomplete it is consistent, for if S were inconsistent it would suffice for the proof of all propositions, even the proposition that S is consistent. Thus if S were inconsistent, it could prove its own consistency! Thus the very inability of a system of logic to prove its own consistency is, in an informal sense, a "proof" of its consistency~ such an informal "proof", however, cannot be formalized within the system itself. Godel's theorem does, therefore, show that the formalist approach has limits. The hope of finding a finite set of axioms from which all mathematical truths can be deduced is shown to be impossible to fulfill. On the other hand, Godel's theorem does not by any means invalidate the formalistic approach to mathematics. Quite the contrary, Godel's proof itself is one of the triumphs of mathematical formalism, since it employs the most extremely formalistic method, namely that of treating mathematical formulas as typographical displays on paper and assigning their Godel numbers simply according to their typographical properties. He does not show that any unformalizable or intuitive methods are needed or valid in mathematics, but merely that outside of any given formal system there lie methods which are not expressible within that system. But, of course, a wider system can be constructed which will include those methods. Even the wider system, however, is subject to Godel's limitation: there will be some true proposition which lies beyond the reach of its methods. We have, therefore, a kind of infinite regress: no mathematical truth is inherently unprovable, yet for every formal system there are problems which it cannot solve. The present task of the mathematical formalist, like that of mathematics itself, is the casting of ever wider nets of formalism with which to catch more and more mathematical truths, yet remaining always aware that beyond each net there are truths whose capture awaits the construction of still wider and stronger nets. [1] This development originated with Moses Schonfinkel in 192 4 . �25 It is our purpose here to give a brief, non-technical account of the content of a celebrated theorem of Kurt Godel. [1] We hope that we can be non-technical without sacrificing too much precision. We begin with an intuitive formulation (statement S) of Godel's theorem and follow it with remarks on the significant notions which occur in the formulation. Statement S: There exists a sentence F of arithmetic which is true but unprovable. The first notion occurring in S which we consider is that of existence. It is conceivahle that a proof of S could be given by means of a reductio ad absurdum. Such a proof would begin with the supposition that every true arithmetical sentence is provable and would conclude with some easily recognized contradiction. Although reductio ad absurdum arguments are perfectly acceptable to the great majority of mathematicians, they do leave something to be desired when they are used to prove the existence of extraordinary objects. And a true but unprovable sentence of arithmetic is a most extraordinary object! The most convincing way to prove S would be to write down an arithmetical sentence F and then to demonstrate in some direct fashion that F is true but unprovable. Fortunately, Godel's proof of S is of this nature. He does not actually exhibit F; instead he gives concrete instructions for writing F down. These instructions have the property that they could be employed to build a machine M capable of printing F. M would have the ability to print Fin a finite length of time and to turn itself off when its job was done. The reason that Godel does not exhibit F (except, of course, in abbreviated form) is that it is too long. In the account of Godel's theorem given by Kleene [2], the sentence F, if written out in full, would be thousand of pages long. WHAT IS GODEL'S THEOREM? GERALD SACKS The next notion occurring in S which we discuss is that of arithmetical sentence. It would not be appropriate to present a formal definition here of the notion of arithmetical sentence; we, therefore, merely consider some of its properties. An arithmetical sentence can be thought of as an elementary, mathematical statement concerning the natural numbers. (By natural number we mean any member of the sequence 0, 1, 2, · · · .) The only mathematical concepts permitted to occur in an arithmetical sentence are the concepts of addition ( +), multiplication ( ·) and equality ( = ). When an arithmetical sentence is written down in full formal detail, all the symbols employed, other than the three given above, are purely logical in nature. We give three examples of arithmetical sentences rendered informally: (1) the result of adding one to an odd natural number is an even natural number; (2) if a natural number n is positive and is one less than a perfect square, then there exists a natural number m such that the product of m and m plus 2 equals n; (3) if n is an odd natural number greater than one, then n plus one is a perfect square. Both (1) and (2) are true arithmetical sentences, but (3) is false. In order to clarify the notion of truth employed in S, we consider what is meant by the assertion that (1) and (2) are true but (3) is false. Suppose a very patient and skeptical person P wondered if (1) were true. He might investigate the matter by performing the following five hundred calculations: 1 + 1 = 2, 1 + 3 = 4, 1 + 5 = 6, · · · , 1 + 999 = 1000. At the end of his calculating, he would feel safe in concluding that the result of adding one to any odd natural number less than 1000 is even, but he might still entertain some doubts concerning the truth of (1). P might be so skeptical that the only way he could eliminate all doubt from his mind would be to check every member of the following infinite list of calculations: 1 + 1 = 2, 1 + 3 = 4, 1 + 5 = 6, .... When we say that (1) is true, we mean that P has somehow checked everyone of the above calculations and has satisfied himself that everyone of them is true. (P could convince himself that (1) was true in one second by checking the first calculation in half a second, the second calculation in a quarter of a second, the third in one-eighth of a second, and so on.) When we say the (2) is true, we mean that P has again satisfied himself by making infinitely many calculations. He has listed all the non-zero natural numbers which are one less than a perfect square, and for each such natural number n, he has been able to find two natural numbers differing by two whose product is n. Finally, when we say that (3) is false, we mean that P made the following calculations: 5 + 1 = 6, 12 = 1 ~ 6, 22 = 4 ~ 6, 32 = 9 ~ 6, and so on. We observe that every arithmetical sentence 1s either true or false. This is merely another way of saying that given any arithmetical sentence A, P can always satisfy himself as to whether or not A is �'' '' 26 true. (The false arithmetical sentences are, by definition, those sentences which are not true.) The only significant notion occurring in S not yet discussed is that of provability. Whether or not an arithmetical sentence is provable depends, of course, on what the rules of proof are. It is entirely possible that a given arithmetical sentence may be provable in one system of formal arithmetic and unprovable in another. Thus statement S does not make sense unless some particular system of formal arithmetic is specified and unless provability is taken to mean provability within that system. By a standard system of formal arithmetic, we mean a system which embodies all the elementary principles employed by number-theorists and in which no false sentences are provable. Observe that although the notion of provability is relative, the notion of truth, which we sketched above with the help of the skeptic P, is absolute. There is a concretely definable class C of arithmetical sentences consisting of just those arithmetical sentences which are true. If K is a standard system of formal arithmetic, then the class CK of all sentences provable in K is a subclass of C. Statement S tells us that CK is actually smaller than C. Statement S must not be taken to mean that there exists a true sentence F which is unprovable in every standard formal system of arithmetic. Given any true sentence of arithmetic, it is always possible to find a standard formal system of arithmetic in which that sentence is provable. Statement S says there is no standard formal system of arithmetic in which all true arithmetical sentences are provable. Furthermore, the method of Godel's proof is such that it includes a constructive procedure which, when applied to any standard system K, yields a true arithmetical sentence unprovable in K. Since we have been deliberately vague on the subject of what constitutes a standard formal system of arithmetic, it is reasonable to ask: Could we embody in some formal system the procedure followed by the skeptic P when he determines whether or not a given arithmetical sentence is true? If the answer to this question were yes, then there would exist a formal system K such that every true arithmetica sentence would be provable in K; consequently, the answer is no. The reason for this negative answer is that the arguments that the skeptic P makes use of are sometimes infinitely long. It is, of course, a necessary property of a formal system of arithmetic that all proofs associated with it be of finite length. Now it is true that some of the arguments employed by P, although of infinite length, can in a certain sense be rewritten in such a manner as to have finite length. This last is possible in the case of (1) above, since the infinitely many calculations that P performs in order to verify that (1) is true possess a repetitious pattern whose nature can be communicated in finitely many words. But, unfortunately, not every argument of P can be thus rewritten. Thus it is a certain lack of uniformity which occurs in P's arithmetical calculations that is responsible for the existence of a true but unprovable arithmetical sentence. The true but unprovable sentence F which Godel shows how to construct has the following form: every natural number n has property Q. If P wished to convince himself that F was true, he would have to examine every one of the following sentences: 0 has property Q, 1 has property Q, 2 has property Q, and so on. Each of these sentences is an instance of F. Since F is true, every one of the above instances of F is true. In addition, F is so constructed that every one of these sentences is provable. The fact that F is not provable is a consequence of the fact that there is no uniform method of proving the instances of F; that is, the nature of the proof that a given natural number n has property Q depends heavily on the value of n. If the proofs of the infinitely many instances of F fell into a repetitious pattern, then it would be possible to describe one general argument which could be used to prove any instance of F, and then F would be provable. [1] Kurt Godel, "Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme I," Monatshejte fur Mathematik und Physic, vol. 38 (1931), pp. 173-198. [2] S. C. Kleene, Introduction to Metamathematics, New York, Toronto, Amsterdam and Grotingen, 1952. �29 There is a tremendous tendency to specialize in all areas of human endeavor in the twentieth century. Mathematics is no exception. The isolation in the branches of mathematics is further accented by the tendency for each one to prove its major theorems in its own context. Thus an algebraist does not want to accept an analytic proof, nor the analyst a geometric proof. This specialization has its advantages. It enables one to move rapidly down a given stream to get to the frontiers of knowledge where one can develop new results. However, without a link to other fields the stream may become sterile and will quite likely fade to oblivion. Mathematicians are continually rediscovering theorems and methods that have long been forgotten. Thus, it is the link between the streams of mathematics and other disciplines that gives mathematics its unity, vitality, and significance. Going across current is difficult; it is slow and painful. The chances of success are slim. Perhaps, the most notable links are found by chance. One stays in his stream, but is always on guard looking for the big opportunity to cut across. Often the quest for the solution of a difficult problem will cause one to find a link more important than the problem itself. We chose the number in the title of this paper, because it gives a notable example at an elementary level of the connection of many areas of knowledge. It also provides a good starting point for our discussion, since all of us are acquainted with some of its magic from Euclid's Elements. We remember its role in the Golden Section, mean and extreme ratio, and the regular polygons and polyhedra. Recall that a line is divided into mean and extreme ratio when smaller part is to larger part as larger part is to the whole. If the two parts are taken as adjacent sides of a rectangle, it is the Golden Section. The Golden Section is said to form such a beautiful rectangle that postcards are modeled from it. The ratio of the sides of the Golden Section is the irrational number of our title. This number keeps recurring when one considers the metrical properties of the regular figures, the pentagon, decagon, dodecahedron, and icosahedron. We set (1) ,;:s. + 1 T 2 1.618. Then (2) r2 = 1 (3) <+ T- 1 3 = T ;, 2.618, 2 1 = -l +vs 2 T (4) + vS +! T ~ 0.618, vs~ 2.236. x - 1 0, = 1 We note that rand - - are roots of T x2 (S) - whence (6) 1+f5 2 W. G. SPOHN x2 - x - 1 = 1 (x - r)(x +-). T We put some of these statements in verbal form. r is a number whose square exceeds it by one and whose reciprocal is one less than itself. rand its negative reciprocal are conjugates. (We define a - bvcas the conjugate of a + bvcif a, b, care rational numbers and c is not a perfect square). Is r the only number with these properties? We do not pursue further this contact with algebra, the theory of algebraic numbers and quadratic fields. [1] In trigonometry one can consider the problem of finding the exact radical values of the trigonometric functions. Identities exist so that if the value of one function is known, then the values of the other five can be determined. Furthermore, e 1 - cos e tan - = (7) 2 sine �30 31 and formulas exist for all multiple angles; for example, (8) sin 20 = 2 sin 0 cos 0 (9) cos 30 = cos 0 - 4 cos 0 sin 2 0. Hence, if the values are known for a given 0, then they are known for all multiples of 0 . Such 211 multiples would be ±0 ±20 ±30 ±40 . . . ±~ ± 30 ± 50 ± 70 ±~ ± 30 ' ' ' ' ' 2' 2 ' 2 ' 2 ' 4' 4 ' We need a starting point. Do we know a functional value for any angle? 0 30 8' 8' tan 22! 0 = v2 - :. 11%0, 1. Another base point is (12) cos 60° = ! from which we can handle all multiples of 60°, 30°, 15°, base points? Let us find sin 18°. Recall J! 0, .... Are not these the only possible (13) cos (90° - 0) = sin 0. 'N"ith x = 18°, 0 = 2x, this becomes (14) cos 3x = sin 2x. Solving (14) with the aid of (8) and (9) and rejecting extraneous solutions one gets (15) sin 18° = - l + ~with an interval of length ±- ± - (10) tan 45° = 1 gives us a base point. We can now find the functions for all integral multiples of 45°, 22! 0, .... For example, (11) interval? They form a denumerably infinite set which is dense in the interval. The rationals have Lebesgue measure zero. [3] This is shown as follows. Consider an enumeration of the rationals as 0 1 1 1 2 1 3 1 2 3 4 1 . . . . l' l' 2' 3' J' 4' 4' S' S' S'S' 6' .... Take an arb1tranly small positive number €. Cover v 5- =_!__· 4 2r Thus all multiples of 18°, 9°, 4! 0, etc., become accessible. You may have guessed that this problem is related to the question of the constructibility of the regular polygons by means of ruler and compass. (10) yields the construction of the regular polygons of 4, 8, 16, ... sides; (12) yields those of 3, 6, 12, ... sides; (15) yields those of 5, 10, 20, ... sides. Gauss showed that the possibility of construction is tied in with the primality of the Fermat numbers 22n + 1. [1] [2] The only such numbers known are 3, 5, 17, 257, 65537. Thus the only known constructible regular polygons have the number of their sides the product of 2° and one of the numbers 3, 4, 5, 15, 17, 51, 85, 255, 257, ... , obtained by taking all possible products of the above numbers along with 4. Note that there are 32 numbers in all. Returning to our trigonometry problem, there are 32 . I t 1s d ou b t f u 1 t h at t h e rad"1ca1 va 1ues h ave . b as1c ang 1 es, name1 3600' 3600' 3600' 3600 y, 3 - 54 rr-' . . . . been worked out in all these cases. The game Nim is played with toothpicks and has a mathematical strategy related to base 2. Wythoff's Game is played with two piles of toothpicks, each of unspecified number. The person drawing the last toothpick wins. A player may draw any number from a single pile or may draw from both piles, provided he takes an equal number from each. One strives for the combinations (1, 2), (3, 5), (4, 7), (6, 10), (8, 13), (9, 15), (11, 18), (12, 20), · · · , where the nth pair is ]). ([nr], [nr2 [x] means the greatest integer not exceeding x. Two curious properties occur here. First, the difference of the numbers in the nth pair is n. Second, a multiple of r or r 2 , but never both, falls between every pair of consecutive positive integers, that is, every positive integer appears once and only once in the enumeration. [2] Can any additional pairs be added to the above set without resorting to computation? A question of great importance in analysis is the measure of sets of points. If the set contains every number in an interval, then there is no problem; the measure of the set will be the length of the interval. However, what measure would we associate with the rational numbers in a unit Cover~ I centered on the point ~- Cover f by a centered interval of length ~· by a centered interval of length interval of length 2:. Notice that}+ and so on, that is, cover the nth rational by an l+i+ ···· = €. Hence all the rationals are covered by a denumerably infinite set of intervals of arbitrarily small total length and for this reason they are said to have Lebesgue measure zero. (A non-denumerable set may have measure zero; for example, the Cantor ternary set is of measure zero). When we consider that some of the intervals overlap and that some extend outside of the interval [O, 1], the total effective length is even less than E. Thus as soon as E is less than 1 some points of the unit interval must not be covered. (Would this do for a proof of the existence of irrational numbers?) There seems to be a paradox here. Since the rationals get arbitrarily close to every point and are covered by intervals, how could any number fail to be covered? We think it will be significant to exhibit irrationals which are not covered. We consider the interval [1, 2] for convenience. This is equivalent to considering [O, 1] because a rational plus one is a rational and an irrational plus one is an irrational. Let us change the problem a bit so as to make it more dramatic. This will require that we return to our investigation of the number r. In equation (6) we replace x by the fraction £ of the q interval [1, 2], that is, 1 _:::;_ ~ _'.'.S. 2. We take the fraction to be a reduced fraction. / x I means absolute value of x. Then Ip_ q (16) T I·/£ + q lT I = I (£) 2 q (£) - 1 I q I P2 - pq - q 2 I > = q2 - l. q2 This is true because/ p 2 - pq - q 2 I is 0 or a positive integer and cannot be 0, else E would be a root of (5), which is impossible. But q 1£ + !1 < Q (17) T 2 - +1 T T2 ' whence i I (18) e - I ~-~22" i q rq T This says that in a certain sense, determined by its denominator, no fraction can get too close to r. For P > r it says q p q (19) F or p < q r 1 -2 rq 2 -> 7• . 1t says p q ( 20) Thus the intervals - [e_ - 2rq ! q 2, 1 + rq 2 -< -2 T. E + 2 2 ] of length ~ centered on£ never touch r. But if q q rq r 2q q ! is a prime number, p can take on q - 1 values in the interval, so that the total length of the in- �32 33 tervals with prime denominator q is q ; /,which for large q is approximately -}. Since the sum Tq Tq of the reciprocals of the primes is infinite [1], we have covered the rationals of [1, 2] by intervals of infinite total length and yet have failed to cover T. However, the effective total length is exactlv one. We see then how irrationals fail to be covered. If we take a sequence of rationals conver~ing on an irrational, we simply cut down on the lengths of the covering intervals so that none of them reach the irrational. The reader might try showing that y2 is not covered by the . . 1? above covering. How small must Ebe for the first ment10ne d covenng not to cover-. T We shall go more deeply into this matter of Diophantine approximation so as to exhibit the very special role played by T. How well can we approximate rational numbers by rational numbers? We shall see that we cannot do very well if we take the size of the denominator of the approximating fraction as a measure. Let~ be the reduced fraction we wish to approximate by · P · · · reduced fract10ns -. For convenience ta k e q an d Q pos1t1ve. q IE - ~I s·mce P q -" Q-, r- P - qP I > ___!._ > .!___, (q > Q). (21) qQ -qQ q2 q Q Thus there are at most a finite number of fractions that can approximate any fraction as well as one over their denominator squared. In fact (21) yields the stronger statement, that for any I pQ = q . p . . . . . fract10n Q' t h ere exist on 1 ya fi mte num b er o f fract1ons p satis fymg p Iq - (22) 3 22 333 355 . ) Suppose I pull the numbers - ' -• - ' - out of a hat. How well do they approximate 7r' 1 7 106 113 3 I1 333 I 106 - 7r 7r I I= = 1 (7.1)(1)' 1 (113)(106)' 22 I7 - 7r I= 355 I 113 Proof: Lett be an arbitrary positive integer. Let q take the t + 1 values 0, 1, · · · , t. Define p = [aq], the greatest integer not exceeding aq. Then 0 < aq - p < 1. We divide the interval [O, 1] into t pigeonholes of length }. Since there are t + 1 values of aq - p, at least two of them must be in the same pigeonhole. Call them aq' - p', aq" - p". Without loss of generality we may suppose q" > q'. Set q" - q' = s, p" - p' = r. Then 0 < s < t and (27) I (aq' - p') - (aq" - p") I I (p" - p') - a(q" - q') = 3 Ii 333 I 106 - 7r 7r I I= = 1 (7.1)(1)2' 1 -c1-.1-)(_1_06-)2' I 22 7 - 7r 1 (113)(7)' I= 1 (32776)(113) 1 1 - 7r I 355 I 113 - 7r (16) (7/ I= 1 (293)(113)?. The coefficient now seems more controlled. We begin to suspect that decimal approximations are in general poor for they approximate only to the order of the denominator, unless a string of zeros or nines appears. This is confirmed by the theorem: For any irrational a there are an infinite number of rationals E such that q = J r - as J < { < ~· Divide through by s to get (26). We can find an r and s for every t. If only a finite number of pairs rands were distinct, I r - as I would have a minimum value A < 0. This contradicts (27) since } can become arbitrarily small. The theorem is proved. Can the proof be refined to yield strict inequality in (26)? Statements (22) and (26) show the difference in the approximability qualities of rational and irrational numbers. One wonders if irrationals can be classified further by such qualities. The answer is yes, though in some cases further refinements of the tests are necessary. Recall that an algebraic number is a root of a polynomial equation with rational coefficients. If a real number is not algebraic, it is transcendental. The algebraic numbers are denumerable and hence of measure zero. Almost all numbers are transcendental, though we know only a few. For example, e, 7r, 7r 2, e7r, and log 2 are transcendental. Some algebraic numbers are v2, T, v2 + v3, and ~/ v2 - ~/S. All irrationals satisfy (26) for an infinity of rationals; however, only a set of measure zero satisfies 1P (28) I q a - I< _1_ 2+E' q infinitely often. [1] Roth in 1955 [4] substantiated a long standing conjecture that all numbers which satisfy (28) for an infinity of P are transcendental. Thus if a number can be approximated q too well it is transcendental. The first numbers known to be transcendental were of this type. They were exhibited by Liouville in 1851. a = 10-11 + 10-21 + 10- 3 1 + 10-41 + ... is such a transcendental number. We shall gain some further insights through continued fractions. [1] Every real number a can be represented as a simple continued fraction (29) a = ao 1 + ----- - - - 1 ar + - - - - - 1 The coefficient of q in the denominators of the right members seems to be getting out of hand. Let us use q 2 in the denominator. (25) J -'is, p 1 Q- I < q 1+E• for arbitrarily small E. From our acquaintance with decimal fractions we might expect that the same holds true of rational approximations to irrationals. For example, the first 5 decimal approximants to 7r yield 314 1 1 31 3 1 I- - 7rl (2.4)(10)' I 100 - 7r I= (6.3)(100)' I 1 - 7rl = (7.1)(1)' 10 (23) 31416 1 3142 1 I 10000 - 7r I = (13.6) c10000) I 1000 - 7r I = (2.5)(1000)' (24) (26) aa + where the a's are all integers and only ao may be other than a positive integer. It is known that ~he expansion of a rational number has a finite number of terms and that the expansion repeats, if and only if, the number is a quadratic surd, that is, an irrational root of a quadratic equation with integer coefficients. We use dots to indicate the repeating terms. Thus, [1, 2, 2, 2, 2, .. ·] = • • • • • [1, 2] or [1, 2, 3, 1, 2, 3, · · ·] = [1, 2, 3] or [1, 2, 3, 4, 3, 4, · · ·] = [1, 2, 3, 4]. If we divide (2) by T and successively replace the right hand T by the original expression we get (30) T= 1 +:;: 1 1 +I+l 1 T 1+l+l 1 1 + [1,1,1,···] • [1]. �35 34 We shall see shortly the special significance of this simplest of continued fraction expansio~s. We achieved this expansion by a special device which will not work for all numbers. We now give the algorithm that always works. Suppose the real number is xo , we form [xo] Xo - [xo] (38) [x1] X1 - [x1] Since for the convergents of r, Pn approaches r as n goes to infinity (written Pn __.,. r), hence qn qn [x2] x0 X2 - [x2] I qn + ! I __.,. r + ! Pn 1 Xo - [xo] 1 X2 = X1 - [x1) X1 = (31) From (16), (17), and (18) we are led to suspect that the estimates in (37) can be improved. They can be improved to T and the true asymptotic result is obtained: T (39) The middle column gives the a's in the order indicated in (29). Let's take xo 7r 3 .1415926535 7.06251331 7 .06251331 15 .9965933 (32) 15.9965933 1.00341834 1 .00341834 292 .539653 292 .539653 = 7r, for illustration. Other interesting results from the theory of continued fractions are that for any real number a, every convergent satisfies p Iq - (40) at least one of every two consecutive convergents satisfies 1 J p - aJ < 2q2 -, q (41) Thus (33) 7r = and at least one of every three consecutive convergents satisfies [3, 7, 15, 1, 292, .. · ]. Now take x 0 = y3, the algorithm gives v3 v3 + 1 1 2 v3 + 1 v3 + 1 (34) 2 Recursive formulas exist for the convergents Po (3 6 ) (an+i + 2)qn2 qn < _1_ . an+iqn2 = ao, Pi = a1ao + 1, Pn = anPn-1 + Pn-2, (n > 2) (43) qo Since for r all an = = 1, (n > 2). 1, the difference equation for Pn and qn takes the simple form (44) Xn = Xn-1 + Xn-2. Thus, if the pump is primed with the first two terms, (44) readily generates more terms. For we g·et for u a \ 2 can be approximated infinitely often as well as is indicated in (42). This improves (26). .. < \ Pn - vs q q Thus (35) y3 = [1, 1, 2]. If we terminate the continued fraction expansion for a in (29) after an we get the nth convergent Po 3 p1 22 p2 _ 333 Pn = [ao, ai, a 2 , ... , an]. From (33) we get the convergents for 7r: qo = l' qi = 7' q 2 - 106' qn pa = 355. We now see the hat from which these numbers were drawn earlier in this article. We q3 113 get the following measure of the degree of approximation of the convergents to any real number a 1 a\<~--· e is a convergent. Thus in view of (39) we get the best possible result: Every irrational number a .,/3 1 - We see that no improvement can result from considering four consecutive convergents because the irrational r spoils matters in view of (39). Since (42) holds for every three consecutive convergents, it must hold for an infinite number. Another theorem states that if (41) is satisfied, y3- 1 1 2 2 J - q y3 - 1 v3- 1 2 1 p (42) 1 1 I<-, I q2 a o. r 's, 1, 2, 3, 5, 8, 13, 21, · · · ·for q's 1 1 2 3 5 8 · · · ' q 1 1 ~' ~' ~' ~.8 , · · · · ·for P, !, 2 3 5 13 ' , , , , , , _ , We use these convergents to illustrate a general property of the odd and even convergents of any number, namely, For 7r we had for the coefficients of qn2(n = 0, 1, 2, 3) the numbers 7.1, 16, 1.1, 293. This is consistent with (36) for 7 < 7.1 < 9, 15 < 16 < 17, 1 < 1.1 < 3, and 292 < 293 < 294. We note that if we stop just short of a big number, we get an especially good convergent. Thus, for 7r, (45) pa = 355 1s accurate to six d ec1ma1 paces. . · .1 q3 113 The numbers 1, 1, 2, 3, 5, 8, · · · · are called Fibonacci numbers. Since the difference equation (44) can be solved, we get an explicit formula for the Fibonacci numbers and for the convergents ~ For (37) r all the an are 1, so that (36) yields for the convergents of _1_ < 3qn2 J Pn qn T J < _!_, qn 2 T of T. 1 1 3 8 < 2 < S < .... < Set Xn = tn. Then t 2 - t - 1 = O; t = r, X1 = 1, X2 = 1; A = 1 -VS' B = - 1 vs' whence 13 T 5 2 < • ... < S < J < 1· -~;general T solution: Xn = Arn + B(-!)n; but T �t= 37 36 (54) (46) Notice the curious form for an integer. Since ! -~ J< 1 and T > 1, we have the asymptotic relation Xn "-' also, (48) xn = [ :sl [;SJ + 5. (55) 1, n odd. 3 8 21 = Fibonacci numbers are seen by vs [L(l) 72 L(x) = 1 - x +1 - x2 L(l)], 74 where x3 - + - - -x + .... · 1 - a - x2 When one takes consecutive Fibonacci numbers for a and b, a 2 - b 2, 2ab, a 2 + b 2 become the sides of pythagorean right triangles which become more and more nearly similar to the right triangle with legs of lengths 1 and 2 and hypotenuse When we consider (16) and (38) carefully, we realize that for all the convergents of T, Pn 2 - Pnqn - qn 2 = 1; thus we have an infinite number of solutions of the Diophantine equations vs. J J x 2 - xy - y 2 = ± 1. (50) Continued fractions supply solutions to other quadratic Diophantine equations, notably Pell's equation x 2 - ny 2 = 1. If (42) is multiplied through by q we can interpret our result as a theorem about linear forms; thus 1 (51) lx-ayl<_ 1 v5 x has an infinite number of solutions in integers x and y for every irrational a. Multiplying by q 2, we can say there exist an infinite number of solutions in integers x and y to (52) f x I· I x - ay I < ~s· Note the close connection to the theorem: Integers (x, y) (53) or I ax2 + bxy ~ b ~ 0, would l::e the hardest to approximate. All such numbers are of the form aT CT (49) x n > 3, has only a finite number of solutions in integers x and y. The inequality (36) leads us to believe that a number with all an = 1 for all sufficiently large n some in the mathematical dissection of masterpieces of painting and sculpture, by others in the protean numbers of religion, in phyllotaxis and in the convolution of sea shells. If we take a different starting point in (44), namely, x 1 = 1, x2 = 3, the Lucas numbers are generated. These play a striking role in the tests of primacy of Mersenne numbers, which in turn render the only known perfect numbers. Computers are quite active in this area at the present time. The sum of the reciprocals of the even numbered Fibonacci numbers gives us an interesting link with the Lambert series. [5] + ~ + ~ + __!_ + .... I xy I < 1 Related to (28) is the theorem of Diophantine equations which says Thus the nth Fibonacci number is the nearest integer to ; 1 + by [ · I ex + dy [ ~ ~ I a~~ be I . vs. VS Xn = n even ax The related theorem in the Geometry of Numbers is that the non-convex star body has E>.(K) = [1] [4] Tn (47) J (0, 0) exist such that + cy2 I < ~ I b2 ~ 4ac I_ c, d with ad - be = ±1 and are said to be equivalent to . _;- . are of this form, but not v 5 = [2, 4] nor nor any irrational not of the form - • • T. + db + We see that.!= [O, vs 8, 2] T T = [l, .. nor vs = T for integers a, b, iJ and . iJ . [O, 1, 2, 1, 1, 2, 1, 2, 2, 2] avs + b for a and b rational. v2 = [1, 2J, 3 + 2vT3 V3 = [1, 1, 2]. In fact if the irrational is not one of the special numbers equivalent to are an infinite numl::er of rational approximations satisfying (56) [2, T2 T, = [JJ, there JE-aJ<-1-· q v8 q 2 If we cannot approximate a number very well, then it is a rational number. T is the irrational that can be approximated least well. Herein, then, lies the power of T for it is on the boundary of the irrationals, being the most rational of them all. [1] [2] [3] [4] [5] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press. London, 1954. W. W. R. Ball, Mathematical Recreations and Essays, The MacMillan Company, New York, 1944. L. M. Graves, The Theory of Functions of Real Variables, McGraw-Hill Book Company, Inc., New York, 1946. J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press, England, 1957. K. Knopp, Theory and Application of Infinite Series, Blackie and Son Limited, London, 1948. � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The Bulletin of St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Description An account of the resource <em>The Bulletin of St. John's College</em> was published quarterly by St. John's College from 1932 to 1968. It was distributed to alumni, faculty, and staff. Some issues include the Report of the President, the official statement of the St. John's program, the Catalogue, the Polity of the college, or the Dean's Statement.<br /><br />The publication was continued by <a href="https://digitalarchives.sjc.edu/collections/show/12" title="The College (1969-1981)"><em>The College</em> (1969-1981)</a>.<br /><br />Click on <strong><a title="The Bulletin" href="http://digitalarchives.sjc.edu/items/browse?collection=37&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in The Bulletin of St. John's College Collection</a></strong> to view and sort all items in the collection. Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Page numeration Number of pages in the original item. 37 pages Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context Bulletin-March 1962 Vol. XIV No. 1-Special Issue on Mathematics Title A name given to the resource Bulletin, March 1962 Description An account of the resource Volume XIV, Number 1 of the Bulletin, Special Issue on Mathematics. Published in March 1962. Date A point or period of time associated with an event in the lifecycle of the resource 1962-03 Creator An entity primarily responsible for making the resource St. John's College Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Rights Information about rights held in and over the resource St. John's College owns the rights to this publication. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/d0ded2b8a2415634c8a9e6469a51e4b5.pdf bd9dcc25f4b72bb9bd835cc345a27ce0 PDF Text Text ·St. John's College Politics · and the Liberal Arts �Bulletin St. 1ohn's College Vol. XII No. I A Letter from the Editor to the Reader There can be no discussion without contradiction. MONTAIGNE This issue of the Bulletin is a trial issue of a ST. JOHN'S REVIEW, a periodical intended primarily for the friends of the College and those members of the community no longer in residence. Conversation, as the core of education, is the primary activity of the College. The written word, however, has at least one advantage over the spoken word: it overcomes time and distance. By means of a periodical the absent members of the St. John's Community and those who wish to learn more about the College would be able to eng~ge regularly in its primary activity. They could participate both as speakers and as listeners: as interlocutors in a dialogue or seminar, reply. ing to the views expressed in each issue. The review would afford members of the faculty, as well as the students, an I opportunity for fuller and more carefully considered expressions of opinion than the exchanges of classroom discussion allow. It would also make possible the presentation by a student of a finished example of the kind of exercise with which he is concerned: translation, demonstration, interpretation of a text. The reasons for choosing Politics. and the Liberal Arts as the subject for this ' issue will perhaps become clear to the reader as he reads the review it~elf. In part, I this issue is an inquiry into the relationship between a community such as St. John's and the larger body politic from which it comes and in which it is bred. We J are now planning a second issue which will be titled Words and Music. Eventually we hope to produce a regular publication, in' which case a subscription fee to cover the cost of the periodical will be necessary. The content of this issue may be considered the opening remarks of the first speakers of a dialogue. Our interlocutors must reply if the dialogue is to continue. "There can be no discussion without contradiction"; for contradiction is the stimulus to self-examination and learning. H.J. S. EDITORIAL STAFF HARRISON J. SHEPPARD Managing Editor and Editor-in-Chief THEODORE BARNES STINCi-IECUM Associate_ Editor ROBERTA IRWIN Secretary to the Editor ]AMES W. FORRESTER Copy Editor EDWARD L. MATTISON Research Editor OSCAR MOLINARI-HERRERA Assistant to the Editor CHARLEN FOSBERG Recording Secretary PALI BIJL DAVID BRUTZ N ICOLAS H. EKSTROM JOHN KOHL, JR. AMANDA MAYER PETER N ABO KOFF \iVILLIAM RANDALL SALISBURY DAVID R. SCHILLER RICHARDS. FREIS o~ August 24, 1912. Table of Contents The Reverend J. Winfree Smith FACULTY ADVISORY BOARD EVA BRANN COVER DESIGN AND LAYOUT THEODORE BARNES STINCHECUM Our American Republic 2 On The Merits 7 Imago Tyranni 10 12 Oratio Tyranni 15 Marcellus and Archimedes 19 The Problem of Freedom PALI BIJL J. J . BODINE SUSAN CLIVER Suzy MILLER MARY STORM SPECIAL ADVISOR Annapolis, Maryland ST. JOHN'S COLLEGE Number 1 Volume XII January, 1960 . Published Quarterly · Entered as Second-class matter, February 18, 1949 at the Post Office, at Annapolis, Maryland, under the Act Politics and the Liberal Arts The Appearance of Athens TYPISTS RICHARD SCOFIELD, Chairman CLARENCE J. KRAMER L. HARVEY POE J . WINFREE SMITH COPYRIGHT 1960, ST. JOHN'S COLLEGE January 1960 21 Book Review: Power Without Property 26 Richard F. Cleveland Theodore Barnes Stinchecum Eva Brann Elton Ray Davis Harrison J . Sheppard Jacob Klein William H. Brubeck �The l{everend J. Winfree Smith Our American Republic Any investigation of political matters, like any investigation of any matters, has to start with facts, opinions, and questions that are before us and are apparent to an attentive man. The present political fact, which, more than all others, occupies the attention of men is the division of human kind into two parts. We describe this division as that between the communist world and the free world. We think of the communist world as living under tyranny and of ourselves as free and democratic. The communists recognize the same fact but describe it differently. Nikita Khrushchev, in his television address just before leaving the United States, said, "Everyone in Soviet society really enjoys freedom," and went on to imply that not everyone in the United States does. He also said, "The constitution of our state is in reality the most democratic," implying that the constitution of the United States is less democratic. Mr. Khrushchev may have been engaging in a certain amount of deliberate deceit or propaganda designed for the American public, but in speaking also to Russians he speaks of Soviet society as free and democratic. Propaganda too, perhaps. Nonetheless, it is significant that, although we seem to mean different things by freedom and democracy, we use these same words. The situation here described is typical of the human situation. There are facts about which there is some general agreement. There are words that are common. But there are different and, to a large extent, conflicting opinions. The conflict of opinions necessitates the questioning and criticizing of opinions. We must ask: who has the right opinions? We may find that our disagreement arises because we are talking about different things. We in the United States, seeking to define freedom, might refer to the Bill of Rights and say that what we mean by freedom is freedom of religion, of speech, of the press, of assembly, of the person under habeas corpus, of business enterprise, etc. We might say that what we mean by democracy is the right of the people to rule themselves through their freely elected representatives. The communists, on the other hand, might say that free- dom is freedom from the restraints imposed by bourgeois law, morality, and religion, which are only the instrument of the oppression of the people. They might say that what they mean by democracy is the rule of the Communist party, which alone represents the true interests of the people. Such defining and such clarification have only exposed the need for further defining and clarification. What common concept of human freedom lies back of the freedoms enumerated in the Bill of Rights? What conception of freedom lies back of the notion that bourgeois law, morality, and religion must be swept aside if freedom is to be achieved? Answers to these questions might disclose deeper disagreements. Moreover, the distinctions that have been made do not show what good either kind of freedom or either kind of democracy is. One might say that it is an obvious good that men not be forced to believe, or to act as if they believed, certain things; or that they not be forced to say, or refrain from saying, certain things; or that they not be forcibly deprived of what their own labor has produced. Or, if one is more radical and does not go that far, one might say that it is obviously better that a man of his own will believe what he ought to believe, say what he ought to say, and not say what he ought not to say, than that he be forced to any of these things; or that it is better that he sacrifice willingly the product of his own labor for the good of others, than that he be forcibly deprived of it. In any case, the opinion that it is good that man be free from certain restraints or oppressions is not separable from the question of what man is good for, of what it is good for him to be and do. In other words, thought about political matters must inevitably raise the comprehensive question of what the human good is, of what is good for men as men. And if it be said that it has to do only with the common good rather than the private good, one would still have the problem of distinguishing what is common from what is private and of evaluating this distinction. Political thought must 3 then concern itself with the whole of human life. But it must do more. It matters to the understanding of the human good, public or private, whether human life is derivative from or dependent on that which is higher than man or that which is lower than man. Therefore, political thought cannot divorce itself from a consideration of that which is other than man, that which is called nature. Or, to put it another way, the humanities and the natural sciences cannot be separated. Or, to put it a still better way, political philosophy cannot be separated from philosophy in general, from the inquiry into the whole of things. This is where the liberal arts enter. The liberal artstraditionally understood as grammar, rhetoric, dialectic, arithmetic, geometry, astronomy, and harmonics-are the tools of philosophy. They are arts because, like all arts, they presuppose knowledge and proceed according to rules. They are liberal because, unlike other arts, their purpose is not utilitarian. Rather, their purpose is to raise the mind above the level of mere fact and to free it from the tyranny of mere opinion and prejudice, that it may seek its proper excellence in the intellectual virtues, in knowledge for its own sake, or in that kind of knowledge which is necessary for the common or private human good at all levels. Of the liberal arts, the tools of philosophy, the first three are more immediately relevant to political philosophy. But the mathematical arts are also relevant, and not only in the obvious sense that they are essential for the science of nature. Political philosophy has always to have its eyes open to political life as we know it, as it exists on this earth at this time. But also and inevitably, perhaps unfortunately, it must turn its eyes to certain books. This does not mean that it becomes a literary study except insofar as it is necessary, if one is to grasp the thought of men about the perennial political problems, to understand the several modes in which, for various reasons, they express, or express: while concealing, their thought. There are books that not only illuminate but form and produce, political fact. It may be difficult to measure the exact effect of Locke's treatises on civil government upon the formation of the American republic. That they had such effect cannot be doubted. \i\Thatever qualifications or modifications of Marx's theory may be represented by the Soviet Union now existing, it is clear that Marx's Capital has had a formative effect on the Soviet Union. In the following pages an attempt will be made to show the role of political thought in forming the American republic and to suggest the role that it has in under- standing and in judging the American republic. The men who founded our republic, who wrote the Declaration of Independence and the Constitution, were men of political experience who had read widely and thought hard about political matters. In their view there are "laws of nature and of nature's God" which transcend positive law and to which they could therefore appeal against positive law. Only thus could they justify the separation of the colonies from British rule. Since, however, natural law may mean different things, we must ask what they took natural law to be. If we should follow the Declaration of Independence, we would conclude that natural law means natural rights. The colonies were entitled to a "separate and equal station among the powers of the earth" because the rights the colonists had by nature had been infringed by the British monarch. Natural law is obligatory in the sense that it obliges men to respect the rights of one another. Alexander Hamilton, maintaining that there is an eternal and immutable natural law originating in God, sees this law as that on which natural rights depend, the rights to life, liberty, and property. He says, "In a state of nature, no man had any moral power to deprive another of his life, limb, property or liberty: nor the least authority to command or exact obedience from him, except that which arose from the ties of consanguinity." Thomas Jefferson, arguing that men may change their laws and institutions as it suits them, says, "Nothing then is unchangeable but the inherent and unalienable rights of man." His principal abjection to the Constitution as originally adopted was that it contained no bill of rights. One might understand the inclusion of the Bill of Rights as a spelling out of what was meant in the preamble by establishing justice. Political justice consists in the guarantee of rights. Since the establishment of civil government necessarily means the surrender of certain rights, and since no man can surrender the rights of another man, civil government derives its authority from a voluntary compact on the part of the people. They allow their rights to be limited in order that their rights be secured. The sovereignty resides ultimately in the people. It is they who "ordain and establish" the Constitution. They no longer retain the natural rights to life, liberty, and property as unqualified rights. In accordance with the Fifth Amendment, they may be deprived of any of these by "due process of law." "Due process of law," the form of legality, sanctioned by the will of the people, became the standard of justice. The very existence of the Constitution is indicative of the importance that was attached to formal �~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - - . _ , , , , - ~ , ~ , _ _ _ ~ ~ ................................................_____________________________..______ 5 4 institutions with strict definition of their several powers of making, administering, and interpreting law. As is well known, a certain disagreement arose among the founders of the republic as to what institutions would best protect life by ensuring domestic tranquillity and providing for the common defense, best secure the blessings of liberty, and best promote the general welfare in the expanding acquisition of property. Hamilton in the Constitutional Convention advocated that an executive and a Senate be elected for life, because he thought these necessary to check the imprudence, "the turbulent and uncontrolling disposition" of the popular assembly. "The people are turbulent and changing; they seldom judge or determine aright." Once the Convention had adopted the Constitution, Hamilton supported it vigorously and labored for its ratification. Jefferson feared monarchy, as Hamilton did not; and he had more confidence in the people. But one should not overemphasize his disagreement with Hamilton. Like Hamilton, he saw as the principal evil of even representative democracy "the turbulence to which it is subject." "The executive in our government," he says, "is not the sole, it is scarcely the principal object of my jealousy. The tyranny of the legislature is the most formidable dread at present, and may be for many years." Like Washington and Adams, these men were not doctrinaire democrats, whom they called "speculative thinkers" and "theorists." They were not J acobins ; they hated that name. If the founders of the American republic thought the people to be turbulent, they also thought that rule by enlightened statesmen with disinterested motives was not a practical possibility, or if a possibility, could not be of any long duration. "Enlightened statesmen," said Madison in the Federalist, "will not always be at the helm." It was their aim, therefore, to secure both good and stable government by means of "rational" institutions designed for the protection of natural rights. "Men," says Hamilton, "are rather reasoning than reasonable animals, for the most part governed by the impulse of passions." Madison, starting with this premise, argued that both religious and moral motives lack efficacy to control the passions and hence to remove the causes of faction. The institutions established by the Constitution would, however, be the best means of controlling the effects of faction, provided the country be sufficiently large, factions sufficiently numerous, and no one faction dominant. The various interests or passions of sections of the population would be represented in the national legislature, in the Senate and in the House of Representatives. Debates in the legislative bodies would never be carried on in pure philosophic detachment; the Senator or Representative would, in all probability, share the interests and passions of his constituents. The debates would, however, lead to some sort of reasonable compromise in which the various particular interests would be adjusted within the general overriding interest of all in security and liberty. The system of "checks and balances" would operate in a similar way among the legislative, executive, and judicial branches of the government. No one was so sanguine as to suppose that this system of government would work like a perfect machine or that any institutions can prevent the evil effects of passion in the complete absence of virtue. Those should rule who are best qualified to rule. The qualifications are virtue and talent. According to Jefferson, who was perhaps the most "democratic" of the founding fathers, there exists among men a natural aristocracy based on virtue and talent as distinguished from the pseudoaristocracy based on wealth and birth; and "that form of government is best, which provides most effectively for a pure selection of the natural aristoi into the offices of government." What Jefferson understood by virtue is not virtue in the highest sense, since "the test of virtue is utility." But even virtue as he understood it cannot be produced without training, i.e., without education. Jefferson therefore proposed for the State of Virginia a scheme of free public education which would educate the body of the people to a certain degree and select for higher education the gifted few. He imagined that the body of the people, educated to a certain degree, would then elect "the really good and wise" to the offices of government. For the country as a whole he recommended an amendment to the Constitution in aid of public education. We must now ask: what is the meaning of the presuppositions which guided the founders of our republic? What is the meaning of the statement that governments are instituted among men to secure natural rights? Whence the idea of natural rights? There are those who maintain that this idea originates in Christianity, in the Christian conception of the dignity and liberty of the individual. But then it does not take much reading of the New Testament (and presumably the New Testament is a reliable guide to Christianity), to see that this cannot be true. It would seem that there is very little dignity or liberty in him who is a slave of sin. But even if there be a dignity or liberty in a man as created by God, even if this dignity and this liberty be not obliterated by sin, it does not follow that this man possesses rights. Even if he has a duty to love every other man as Christ loves men, he may not claim the love of another as his right any more than he may claim the love of Christ as his right. Indeed one may say that the attitude of the man who claims his rights, the attitude of self-assertion, is antithetical to the Christian attitude of self-denial, of submission, or of grateful acceptance. A statement of Hamilton's may be useful as a guide: "The science of politics, like most other sciences, has received great improvement. The efficacy of various principles is now well understood, which were either not known at all, or imperfectly known to the ancients." Hamilton believed in the superiority of modern to ancient political science. That Jefferson shared this belief is sufficiently attested by his very low opinion of Plato's Republic and his very high opinion of Locke's writings on civil government. This suggests that we must look not to the Biblical tradition or to the tradition of ancient political science, but to the tradition of modern political science. Hamilton and Jefferson apparently were not fully aware of all the points of conflict among these traditions. They seem to have taken on face value those statements of Locke in which he appears to be in agreement with the pre-modern or pre-Hobbesian teaching about natural law : that there is a natural law ordained by God, knowable to man through reason and prescriptive of duties. Hamilton says that God endowed man "with faculties by the help of which to discern and pursue such things as were consistent with his duty and interest; and invested him with an inviolable right to personal liberty and personal safety." Jefferson says, "The practice of morality being necessary for the wellbeing of society, he [the creator] has taken care to impress its precepts indelibly on our hearts." They do not seem to have recognized Locke's dependence upon Hobbes. They mention Hobbes but rarely, and when they do, it is to express disagreement. Nevertheless, at certain decisive points they share with Locke and with Hobbes views which make the essential difference between modern and ancient political science. According to Hamilton, the former is superior to the latter in that the efficacy of various principles is now understood. One may say that modern political science seeks to determine what is politically best and desirable on the basis of what is politically efficacious, whereas ancient political science seeks first to determine what is politically best and desirable and then to consider what compromises must be made for the sake of efficacy. The appeal to natural rights is more efficacious than the appeal to natural duties, because natural rights are rooted in the desires and passions, which in most men are stronger than reason or virtue. The right to life is rooted in the desire for self-preservation or the fear of death. This desire and this passion lead men to form and to maintain civil society. The right to liberty is rooted in the desire to be free to pursue one's desires. The right to property is rooted in the desire for "commodious living." Instead of a criticism of the desires and passions, certain desires and passions are endowed with the sanction of right, because they are politically efficacious. The truth of the proposition that natural rights are rooted in the passions was brought home to this author while attending a political rally during a recent presidential campaign. One of the presidential candidates was the principal speaker. He spoke about the rights of this group and that, groups represented in the audience. He was warmly applauded. He would probably have been less warmly applauded, or applauded not at all, had he sternly reminded the audience of their duties, had he spoken in the manner of Amos, or had he said with Jes us of Nazareth, "Blessed are you when men revile you and persecute you ... for your reward is great in heaven." Furthermore, it is the doubt of the political efficacy of disinterested right reason that makes the problem of sovereignty as important for the founders of our republic as it was for Hobbes and Locke. The answer to this problem could not be that those men should rule who have the political wisdom to rule. Hence the founders of the American republic sought to substitute for rule by political wisdom "rational institutions," which derive their authority from the consent of the people, the people being motivated by a concern for their rights. As we remember our past and our fathers, we may be proud of their political perception; we may be proud that the American republic has for so long been able to combine stability of government with liberty, a thing unknown to the democracies of ancient times. Security and liberty are still dominant considerations. Our concern for security governs our foreign policy. For reasons of security we have military bases around the world, we give military and economic aid to foreign nations, and we are anxious about our rate of economic growth as compared with that of the Soviet Union. Security is a necessary object of government. But an exaggerated concern for security may endanger liberty. The Supreme Court, in its recent decisions in favor of liberty, has been essentially conservative, since liberty is written into the basic positive law of our land. One might suggest, however, that an exaggerated con- �R._icliard F. Cleveland 6 cern for security and liberty may endanger human goodness. The appeal to natural rights, to life and liberty, may always be necessary in order to enlist the desires and passions for the popular support that government needs. But an appeal to duties may possibly find a listening ear in a telling number of politically responsible, decent men. These decent men may see the following truths : that we should not think of liberty as the freeclorn to do what we please regardless, or even as the freedom to do \vhat we please as long as it does not interfere with the same freedom in others ; that freedom of speech or of the press is meaningless apart frorn the obligation to the truth; that freedom to acquire wealth is meaningless apart from the obligation to use that wealth for the common good; that freedom to elect one's representatives is meaningless apart from the obligation to elect good representatives rather than those who are merely the slaves of the desires of their constituents. Of course, homes and schools play a major part in producing or in failing to produce decent men. \A/ e need rnuch better homes and much better schools than we now have if our citizens are to use well the leisure that modern technology has made available, i.e., if they are going to be educated for the hurnan goodness of which they are capable according to their several capacities. The proper hierarchy of political objects is not security, liberty, and virtue in that order; but virtue, liberty, and security. Any American patriot must hope that if Mr. Khrushchev, or his grandson, bury us, it will not be because we deserve to be buried. 7 On the Merits 1\ lawyer relates his profession to the liberal arts with better reason than the Irish student whose familiar essay on the elephant was entitled "The Elephant and the Irish Question." \:Vithout comparisons with other callings, many of which can claim that their provinces share in some sense the broad territory of the liberal arts, it is a fact that the major occupation of lawyers is to man the machinery of justice. Justice rests on truth, and parenthetically it may be noted that justice rests on both abstract truth and specific truths-a statement calculated to embroil a St. John's seminar. \Vith a witness on the stand, sworn to tell the truth, we cannot adjourn court to pursue the meaning of truth; we want only (and how hard it is to get that) to know what A told Band when, whether a shipment of seeds was spoiled, whether a driver gave a proper turn signal. Such truths, which lawyers boldly call facts, are bricks and mortar of justice. Before getting into the role of the profession of lavv in abstract truth and justice, it is good to clear the air by pointing out that it is rarely the function of a lawyer, serving his clients in or out of court, toquestion the applicable rules and standards. His sworn duty is to get the best (another seminar word) for his client under the rules. The best may or may not correlate with moral and ethical goodness. The late Justice Holmes said that legal rules had been washed in a cynical acid. There are, of course, rare legal contests where the applicable rule of law is vulnerable or uncertain, which invite argument as to what the rule should be, but even then any court below the highest would be rash and imprudent indeed to announce a new rule in any specific case. A possibly superfluous footnote should, in the interest of perspective, recognize that in at least nine-tenths of all litigated cases the result turns on application of the admitted law to the facts. For this reason, while all contests in court arc exciting to the participants, few of them are significant in the evolution of the law. Uniform adherence to precedent in the administra- tion of the machinery of justice means that legal rules often lag behind current economic and social thinking, even unofficial legal thinking. This is not only inevitable, it is good more often than bad. Basically, the balance of governmental powers, rooted in the Federal Constitution, and made explicit in early policy decisions of the Supreme Court, contributes to the deliberate and measured pace of the evolution of the administration of justice. This part of the Constitution was the wise product of streams of divergent beliefs on the relative roles of the legislature and the courts. Nor did the advocates of greater legislative freedom die with their defeat in the Constitutional debates. Within the last two years (1958-9) unwelcome decisions of the Supreme Court have roused renewed efforts to limit the judicial power. In 1935, some of Franklin Roosevelt's bold schemes, supported by substantial public desperation, \Vere frustrated by a Supreme Court variously described as Nine Old Men still groping in the horse and buggy age, or as steadfast saviors of the American \Vay of Life. Less dramatic conflicts have arisen throughout the Court's history. Perhaps the best proof of the wisdom of the Constitutional arrangement is that the Supreme Court has been charged at different times with reaction and revolution. Laymen may better understand the function of courts in the vwrds of young and new J ustice Potter Stewart: when asked if he was a conservative or a liberal, he said he wanted only to be considered a good lawyer. Judges apply the law to specific sets of facts between two contestants. If "new" law is made by judges, it is by extension and analogy to fit the case. Any lawyer who reads this will sense the oversimplification, but must agree that in all but the rarest cases, and those in the highest courts of last resort, judges are but the current bearers of lights reflected from hundreds of thousands of judicial sparks over hundreds of years. It is not their function to legislate bright new ideas.Judges, too, are conditioned by their training to think within the living fabric. �w , I l 8 They are also bound to follow what higher courts have done. No lawyer can advise a client, or draw papers for him, without at least subconsciously relating the transaction to what a hypothetical court would decide if the matter unhappily came into dispute. Virtually all legal advice is prospective; and whatever the question involves, which could be any facet of human needs and desires, what the client wants is certainty. Without assurance that the act or venture would in the future meet the test of binding legality, every man's life would be chaos. Law is the answer to the basic need for predicted order. There could be no fabric of society if every prospective commitment were at the mercy of the subjective views of a judge. Law could not, in the nature of things, be anything but conservative. These are platitudes but are not always understood. What has this heavy prelude to do with the liberal arts? Simply that the law is the distillation of human experience, human needs, aspirations and desires, boiling away in constant turmoil over the centuries. Law evolves out of the orderly settlement of actual struggles and clashes of living people. To the extent that lawyers and judges are liberal artists-that is, informed in universal terms and skilled in judgmentthe distillation will truly reflect present ingredients and will insure wise extensions into the changing future. This parallels the proper role of education in the liberal arts: to prepare young people to cope with the existing fabric, to be sure, but also to contribute to its adaptation to unmet needs. The purpose here is certainly not to assign greater importance to lawyers than to philosophers, or any other calling, but simply to point out, first, that lawyers are by definition the actors at the very heart of the distillation, and second, because of that responsibility, they must or should be ideally universal in the breadth of their understanding. Indeed one of the attractions of the legal calling is the opportunity, as well as the necessity, of learning much about many things. The "much" is usually less than expertise but must be enough to know the intellectual and practical coin of brewing, shipbuilding, psychiatry, and a hundred other pursuits. Perhaps the degree of necessary knowledge in these varied fields is roughly comparable to the understanding acquired by St. John's students in language tutorials. So much, however disfigured by abbreviation, for tlie,work of lawyers and judges as journeymen crafts- men. Without more, the tempo in meeting new and changing needs could well lag dangerously. But many lawyers are not only workers who contest for favorable action before judges. They are persistent criticsin cases unrelated to theirs, to be sure-of the art of the judges. Informally in conversation, more formally in speeches, law review articles, and text-books, they hammer away at the premises, reasoning, and conclusions of courts. This is more productive than protests over a baseball umpire's blindness. It focuses attention on significant decisions, it informs and enlightens the bar and bench, even professors of law and editorial writers. Important as lawyers are in the process of deciding specific conflicts on their merits, the backlash of detached, almost philosophical criticism probably contributes more to the progress of the law. "On the merits" is a great concept, equivalent to justice. Where does the law find justice? Precisely in the processes already described. Finite minds are helped by picturing a law of nature as the ideal, hovering in the sky, waiting to be pulled down and mortalized piece by piece into human law; but no such excursion into metaphysics can be launched here, and it is wholly immaterial whether judges discover or invent, for they must be equally wise for either task. It will be clear by now that the merits, or' justice, in the practical administration of justice, are a combination of pragmatic experience and abstraction. The law must provide certainty simply because daily living demands it, and it must keep pace with new and changing needs for the same reason. From time to time, however, the course of the evolution of law in specific areas is reoriented by statutes. Legislatures have the power, within constitutional limits, simply to say that the evolution of centuries of decisions by courts is no longer applicable. This happens rarely in important areas, but good examples are the workmen's compensation statutes and statutes regulating labor conditions. In the former area, the evolved law, following the basic principle that there is no liability without fault, denied compensatory damages to a workman injured in an occupational accident unless his employer was negligent or otherwise at fault. Against this intellectually respectable doctrine loomed the social consequences of unavoidable accidents. Statutes, in the early years of the twentieth century, attempted to put the burden of such injuries on industry by creating insurance funds from which 9 workmen could be compensated regardless of fault. In the earlier court conflicts between the familiar doctrine and social needs, the old doctrine won, but it crumbled in later decisions. Statutes regulating hours and conditions of labor, designed to protect the health of men and women in industry, ran up against the basic doctrine of freedom of contract; i.e., if a woman agreed to work longer hours than were good for her, that was her sacred privilege. Again the social interest prevailed. These are important examples of a relatively modern trend against treating any legal contest as a purely private fight. In the trade, the trend reflects what is aptly called the sociological school of law, as contrasted with the analytical and historical schools. It is fashionable now to say that in every lawsuit there are three parties: plaintiff, defendant, and the social interest. It would be imprudent, however, to underrate the tenacity of the evolved common law. Many a statute, laid on the Procrustean bed of the common law, has been stretched or cut to size by court interpretation. The built-in evolutionary conservatism of lawyers is tough and resourceful-and this is as it should and must be. If it could be effectively decreed that all existing law be wiped off the books today, the law would be continued without serious interruption in the minds and instincts of lawyers. A large segment of the mechanics of justice is now committed to administrative bodies, semi-judicial agencies of government regulating specialized activities. Space does not permit adequate discussion except to point out the underlying impasse of providing prompt and efficient administration while safeguarding the fundamental rights of persons whose interests are at stake. The dual capacity of administrator and judge calls for angels, and there are not enough to go around. In this field, the pressure to mold a government of laws into a government of men is ever present. The effrontery of a mere journeyman lawyer in undertaking a primer to an introduction of the legal processes is magnified by an epochal event of June, 1959: the publication of the very great Roscoe Pound's Jurisprudence 1 a few months before his ninetieth birthday. In his five tough volumes is the history of man's struggle for justice, for the ordering of human life on the merits. It is a rare and wonderful thing that the ablest living scholar is able to pass on his life work in one available prodigious record. If what I have so inadequately said here leads a few readers to Dean Pound's store of treasure, the reward will be great indeed. 1 Jurisprudence, (c) 1959 by Roscoe Pound. West Publishing Co. -Ed. note ��--------------------------------------------....,·--------------------13 Eva Brann 12 The Appearance of Athens ... this land, shaped to be intimate with excellence and appropriate to thought . . . Plato, Critias 109c With respect to the Greeks it is of a certain consequence that they actually existed. This is neither immediately obvious nor always true. The Greeks are most articulately before us in the Texts-these are the alpha and omega of our acquaintance with them. Examine then one of these texts for its closeness to "actual existence," defined as palpable daily living, productive of palpable semi-permanent paraphernalia such as cooking pots or city plans: '' AvBpa /Wt ~1'VE7rE, Moilcrn, 7roA.vrpo7rOV . . . Tell me the tale, 0 my Muse, of the versatile man ... And the Muse conveys this recitation to some anonymous person who tells it from our printed page. But this page was copied from a manuscript which was in turn copied from another, and so back through a paper-andparchment genealogy to a voice which came by it in whatever manner men come by poetry. Where in this transmission chain could "actual existence" insinuate itself? Would it be of the slightest consequence that the fairy-tale Phaeacians were actually visited by an Ithacan prince or that a goddess in whose veins flowed real ichor reported this to a person whose name was actually Homer? Probably not. But there are other texts of a different sort ; for instance, histories : 'Hpo86rov 'AA.tKapV'f}<J'<Jlo> iuropt'f)> 1h68E~t> ~BE . . . 1 So begins one of these texts ; someone, somewhere, in his own person, invokes the aid of the Muse in reciting a poem. The person himself gives a certain sober summary such as one might compose without divine inspiration: the versatile man sacked Troy, saw cities and knew the mind of men, suffered in soul while at sea, and so forth. But without the Muse he knows neither how to tell the man's telling name nor the pattern of his wanderings. The Muse has been invited to "begin where she will," and she begins "there where all the others who had fled sheer destruction, fled war and sea, were home,'' and Odysseus alone was still at sea. She unfolds the story, and Odysseus arrives in the land of the Phaeacians where he himself takes up the tale; for the versatile man is also, perhaps first of all, a poet. Here let us add up the removes from some "actual existence" through the poem to us. A man Odysseus tells a tale of himself; he introduces himself in this way: I am Odysseus, the son of Laertes, whose numerous wiles made his fame among men ... 2 and having thus established his credit he tells his fairytale travels at one of the stations of his fairy-tale route. Herodotus of Halicarnassus publishes this inquiry . . . so that the great and wonderful works accomplished both by the Greeks and by the Barbarians may not go without fame ...3 Here the author's identity and credentials are of greatest interest. The first person singular, that spurious personal presence which turns the page into a libretto, is therefore given up. Herodotus identifies himself in the third person and so turns himself into a fact like any other in his history. He adds that he comes from Halicarnassus, because that city straddles the boundary between Greeks and Barbarians. He says clearly what it is that follows, namely "the publication of an inquiry,'' and in appropriate places he makes clear the manner of his inquiry. For example, in Book II, 29 he says "I myself went as far as Elephantine and am an eyewitness ; of the parts beyond, my inquiry depends on hearsay." The reason that the author and his method are so much more explicit here is that the subject is so much 1 Homer, Odyssey, I, 1. 2 Odyssey, IX, 19. 3 Herodotus, History, I, 1. more palpable. Homeric epic tells the "fame of men," 4 Herodotean inquiry purposes that the "works accomplished by Greeks and Barbarians shall not go without fame." That is to say, Homer deals with what men are and Herodotus with what they did and made; so the former tells true lies, but the latter verifiable fact. Nor is it enough for Herodotus to treat one particular state or strand of events, but to ascribe fame fairly he must take the past into account : I shall describe in turn greater and lesser cities, since many of those that were formerly great are now small, while many which are great in my time were small before. 5 One last text must be cited: ®ovKvUB'f}> 'ABYJvafo> ~viypaif!E rov 7r6A£p,ov ... Thucydides the Athenian wrote up the war between the Peloponnesians and the Athenians ... 6 No more anonymous applications to the Muse, no inquiries published in the interests of fame, but simply a bald statement that one Athenian wrote up the warnota bene, not a history of the war, or a tale of the war, but simply "wrote up the war" between Sparta and Athens, because he thought that it was the greatest war that ever happened. He is here directly up against sheer fact and must work with strictest exactitude ( aKpt{3Eia) since any deviation from actual happening has the effect of a mere lie. To sum up: Homer's theme is a man, his means poetry, his geography the vast world of the soul; Herodotus tells of nations, his manner is full and fair account, his geography includes the known earth, its continents and rivers; Thucydides records a war between cities, intending to preserve the strictest correspondence to fact, and his scene is set by the significant details of local geography. One would expect him to deal with the city plans of his protagonist cities. In the introduction to his history, the so-called Archaeology, he observes as follows: If the city of the Lacedaemonians were to be deserted and only her temples and the foundations of her constructions were to be left, I think that after a long lapse of time there would be a good deal of scepticism among later generations about her claim to fame ... but if the same thing happened to Athens, they would, judging from her appearance, reckon her power at double its real strength. 7 Thucydides has predicted well ; to many investigators of their deserted cities the Spartans have seemed half and the Athenians twice as real as the true power status of each warranted. Greek cities are crystals of "actual existence,'' little growths in whose physical structures the life of their citizens is at once expressed and carried on. If Sparta possessed no such structures, if she had no appearance adequate to her power, perhaps this indicates some essential unreality in her polity of the sort also indicated by the unstable behavior of her citizens when abroad. However that may be, Sparta is hardly worth looking at, but in Athens, Thucydides implies, there is much to see. Archaeologists have investigated her, in part with the painstaking care of people who find little to cherish at home. Sometimes History has been indulgent and the finds have illustrated or corroborated the Texts. For instance, Diogenes Laertius in his Lives of Eminent Philosophers, Book II, 122 tells of one Simon, a cobbler, who used to take notes when Socrates came to converse with him. Lo and behold, a few years ago there came to light at the edge of the ancient market-place of Athens, which is being excavated by the Americans, the foundations of a little house in which were found a number of hobnails and a drinking cup marked -;i,[p,ovo>, "of Simon" who is thus proved to have actually existed. Or again, Thucydides reports in Book IV, 12 that Brasidas, the Spartan general, lost his shield in a battle at Pylos ; Aristophanes also mentions captured Spartan shields in the Knights. Such a shield was found in the Athenian market-place, in the position of its last use as the cover of a cistern. It bore the following legend : 'ABYJvafoi a7ro AaKEilaip,ov[wv eK ITvA.ov The Athenians [took it] from the Lacedaemonians from Pylos Vv ell, these are pretty coincidences which may make a text vivid or prove it correct. But we are looking, not for random items to make single textual points concrete, but for the grand artifact on which the sequence of historical accounts (for Homeric epic was also history to the Greeks) and thus, as it were, history converges, namely the plan of the city of Athens; and we might expect it to express both what a city should always and everywhere be and also what only Athens was. 4 Odyssey, VIII, 73. 5 History; I, 5. 6 Thucydides, Peloponnesian War, I, I. 7 Peloponnesian War, I, 10. �Elton J{ay Davis* The land of Attica, then, wherein the city is set is "shaped to be intimate with excellence and appropriate to thought." The beauty of this landscape is so elusively definite that whole anthologies of attempted descriptions have been published. It is acknowledged even by scholars. Let three platitudes suffice here: it has praeternaturally rational arrangement, utterly clear lines, and subtle coloring different for each time of day. The city lies in a plain ringed by mountains of long, low lines. The sea is in sight, but the city is not a harbor. The city's harbor, the Piraeus, is a few hours' walk away from the city; it was laid out by Hippodamus the cityplanner according to a very functional grid-system such as modern American cities display. The Piraeus was connected with the "upper city," the city proper, by the so-called Long Walls, which made one of the two. The city itself was circular-the Delphic Oracle as quoted by Herodotus, Book VII, 140 calls her the "wheel-shaped city" ( 7ToAi> Tpoxon8~>). Her shape exP.ressed nicely the essential self-sufficiency of which Pericles speaks in the Funeral Oration (Thucydides, Book II, 35 ff: "We have provided the city with everything for War and peace, SO that she is avmpK€aT<fr'f}V-aS self-sufficient as possible."). This self-completeness which her round plan expressed was, however, of a peculiar kind, and this peculiarity was again expressed in her physical connection with the functional Piraeus through which the goods gathered from her dominions were funnelled in. She was a double city, at once complete in herself and dependent on the outside, which, however, was largely hers. Within the wheel of her walls there were public places and private houses. The latter have gone the way of Sparta's whole city-they were built largely of mudbrick, a lowly and ephemeral building material expressive of the minimal importance the Athenians attached - to this side of life. The center of the circle (and most of the public life of the city took place about its physic;1J center) is, on the other hand, still or again (through excavation) open to view. It consists of two parts: a high place, the Acropolis or simply "the City," and a low area, the Agora or market-place. The Acropolis is a long flat rock with the appearance of an altar. On it stand the offerings of the Athenians to their city's goddess Athena, the Doric Parthenon and the Ionic Erechtheum. The Parthenon is a marvelously subtle monolith-alr10st in the literal sense; for the marble from the nearby Mount Pentelikon has been fitted together with such precise mortarless joints that it has in some places actually grown together-while the Erechtheum with its elaborate graces is irreconcilably tripartite. It has not escaped travellers that these two buildings somehow sum up between them the Athenian character. One descended from this natural altar into the valley of the market-place via the Sacred Way. The marketsquare itself was literally a rough square. Along the western side the public buildings from which the Athenians governed themselves were ranged. Toward the north of this side, not far from the place where the Sacred Way enters the market-place on its course toward the Acropolis, stood the Stoa of the King, where Socrates' conversation with Euthyphro concerning piety took place. Just at the point where the Sacred Way entered the market-place there was an altar of the Twelve Gods and this spot was considered the center of the city for purposes of distance measurement. The geometry of this topography is rather pretty : the square of civic life is crossed diagonally by the road of religion and the point of crossing is the true center of the city. (By way of explanation it should be mentioned that the Sacred Way connected the Hall of Mysteries at Eleusis to its smaller branch on the Acropolis.) The other sides of the square were bounded largely by stoas. Stoas are long buildings with these essential features : a back-wall, a colonnade out front, and a roof. In Athens they were the citizen's building par excellence, for their plan expressed perfectly that passing into one-another of Inside and Outside which is the modus vivendi of a member of a community. The center of the square, on the other hand, was empty-this was the free field of congregation, a space to be filled only by men. The Romans, who held Athens after 86 B.C., paid no attention to the natural expressiveness of the city plan. In the center of the market-square the Roman Agrippa, son-in-law of Augustus, placed a disproportionately large auditorium designed in a tritely modernistic style. Later on they even covered the area with a sprawling gymnasium. By then the Athenians themselves had lost the sense of their city, and if they had been asked why they accepted such inappropriate gifts, they would probably have answered "that they had been offered them." Why look at Athens? To learn that a real city has a site appropriate to itself, that a real community shapes for itself a plant "intimate with excellence and appropriate to thought." In other words, in order to learn how to anchor goods in appearances proper to them. Oratio T yranni In the sixteenth year of the Peloponnesian War (431404 B.C.), the Athenians dispatched an expedition of thirty-eight ships against the island of Melos, a colony from Sparta. Melos had refused to submit to the Athenians and wished to remain neutral in the struggle. But after Athens began to plunder the island, the Melians became openly hostile. Upon the arrival of the ships the Athenian generals sent envoys to the Melians. What fallows is a new translation of Thucydides' account of the diplomatic talks. As the dialogue begins, the Athenian envoys, having been refused permission to speak publicly, are addressing ·the Melian council. W.R.S. ATHENIAN AMBASSADORS: Your intention in bringing us before a select few is perfectly clear to us. It is so that we might not dupe the populace, who would hear continuous and designedly forceful speeches at one sitting. Since you have decided that the arguments are not to take place in public, why don't you· who are sitting here make your position even safer? Do not speak point by point in one speech, but take up and answer immediately any point which does not seem conclusively made by us. First tell us if what we have said is agreeable to you. MELIAN COUNCILLORS: To instruct one another at leisure is fair enough and not at all objectionable. But your preparations for war are a present and not a future matter, for we see that you have come with your minds made up. And it seems that if we win this argument on the count of justice and so do not give in, the outcome brings us war; and if we lose, it brings us slavery. kind, rather than planning about the safety of your city from present circumstances and from what is before your eyes, we may as well stop talking. If you decide on the second course, we may have something to talk about. MEL: It is natural and allowable.that men in such a position as ours turn to many possibilities in their speeches and considerations. But you are right; this assembly is concerned with our safety. If this is the order of the day, let the argument be in the manner you dictate. ATH: Then, we will not applaud ourselves with fine phrases, saying that because we destroyed the Mede 1 it is just that we rule, or that we now attack you because we are treated unfairly. We want to avoid suspiciously long arguments. Neither do we expect you to contend that you have not joined forces with the Lacedaemonians, whose colonists you are, nor to undertake the argument that you have not treated us unfairly. We each think, and rightly so, to gain our ends from the means available for use. For both of us know full well that justice has a voice in men's deliberation when contending forces are equal. Otherwise, strong men wield their power and the weak give way. MEL: Our belief in the matter is that it would be useful for you not to destroy what is a common good (notice that we speak as you advise, putting the profitable *Translator. ATH: If you are considering the matter on the basis of suppositions about the future, or something of the 1 "Fighting as champions of Greece at Marathon [490 B.C.] the Athenians/Brought down the Persian power, forced low the gold-burdened Mede." Quoted by Lycurgus in his speech against Leocrates, 109-Ed. note �alongside the just): namely, standards of right and justice, as well as weighty arguments on a technicality, for the help of one who finds himself in danger. And this is no less your concern than ours. For if you were defeated, you would take the heaviest punishment and become an example to others. ATH: Even if our rule were to end, we would not be completely in despair. In the first place this particular struggle of ours is not with the Lacedaemonians. But anyway, the leaders of the other enemies, such as the Lacedaemonians, are not so terrible to the defeated as the colonists would be if they ever were to attack and overpower their leaders. But let us take the risks involved in these affairs. Since we are here to speak about the advantage of our rule and are now investigating arguments about the safety of your city, we will clarify these two things: that we wish to rule you without trouble and to save you in a way profitable to us both. MEL: And how might enslavement be as profitable to us as supremacy is to you? ATH: As far as the justice of the matter goes, they will not be able to distinguish your case from ours. They believe that they are trying to survive as best they can and that if we do not attack, it is because of fear. So that, since we are striving to rule more empire and to safeguard against our being overthrown, it is crucial that you, who are islanders and even weaker than the others, should not overcome us, the masters of the sea. MEL: So you would not welcome us should we behave peaceably, be your friends instead of your enemies, and be allies of neither side? ATH: Your enmity does not distress us so much as your friendship. The latter shows plainly to our subjects an example of our weakness, while the former merely shows your hatred of our strength. MEL: Is this what your subjects think is fair: to place in the same group with your many colonists (some of whom are conquered rebels) those who in no way belong to you? MEL: But we know full well that on the battlefield it is more common for the weaker to have success than a difference in numbers would suggest. Yielding brings us despair immediately; activity leaves us hope that things may yet come out aright. MEL: ATH: Don't you believe your safety lies in our suggestion? We have abandoned our arguments of justice; you have persuaded us to attend to your arguments of expediency. Even so, if what we have learned to be useful to us should equally suit you, we must then attempt to persuade you of this common profit. How will you avoid making yourselves enemies to those who are not now allies of either side? Because they have seen these events, they will think that you may sometime come against them. And what else results from this but that you strengthen what enemies already exist and convince other men, who do not now intend it, to become your enemies against their will? ATH: It will be useful for you to submit rather than to suffer to the extreme. For our part, we might stand to profit if we do not destroy you. be if the sides were equal. Nor will you incur shame. Rather, your planning concerns survival and hence should not include opposing those who are so much stronger. ATH: We don't believe that these are such a great menace to us. How many mainland colonies, here and there, procrastinate in guarding against us, simply because they have freedom! But the islanders not under empire, such as you, and those driven to extremes by our rule are more of a menace. For those who are completely beyond reason may precipitate themselves and us into predictable danger. MEL: Well then, if you take such risk not to lose your empire and if those enslaved take such risk to be free of it, then if we did not try everything to hold out against enslavement, it would show the greatest weakness and cowardice. ATH: No! You will not have to risk everything if you plan sensibly. Your bravery is not in question, as it would Hope, the comfort of those in danger, is not the downfall of those who enjoy it because of their abundant resources, though it may hinder even them. The understanding of this comes simultaneously with their defeat to those who have risked everythinghope is, by nature, extravagant. Whereas, when there is yet time for safeguards, it seems more than adequate. Now, as you are weak and at a crucial point in your affairs, do not deliberately subject yourselves to such experiences. Do not imitate the many men who ignore those ways of being saved which lie within human power. When obvious hopes desert them in their extremity, they turn to less obvious ones: divinations and oracles and such things, which entail hopes and thereby cause destruction. MEL: You may be certain that we know that it is difficult to contend against your power and good fortune unless there are factors of equality. Nevertheless, with regard to fortune, we feel we will not be weakened by lack of divine assistance, for we take our stand as reverent against impious men. With regard to our lack of power, the alliance of the Lacedaemonians will be a factor in our favor. We believe they will be moved by a sense of shame and will be bound to aid us, if for no other reason than that of our kinship. So we do have some small cause for confidence. ATH: But neither do we feel that we will be deserted by the grace of divine assistance. For we are not unlike other men; their attitude toward divine power and their own intentions accord with what we plan to do. Both gods and men rule where they are able; we know it of the former by general opm10n, of the latter by a necessity of their nature evident in all they do. Neither did we institute the law nor were we the first to follow it when fixed. But we do follow it now as we inherited it and shall leave it thus to eternity. For we know that both you and others would do the same should you come to have the same power as we have. Apparently, then, we need not fear being weak for lack of divine assistance. As for your opinion of the Lacedaemonians, which leads you to believe that a sense of shame will move them to help you-bless your innocence! We do not envy your folly. The Lacedaemonians, by themselves and in their local laws, appear most virtuous. As for how they behave toward others, that is a long story, no matter who tells it. In short, one might show that they are the most notorious of all we know for believing pleasant things good and advantageous things just. Such a line of reasoning does not suit your senseless feeling of safety. MEL: We acknowledge this very thing that is said of them. But because it is to their advantage, they will not wish to betray the Melians, who are their colonists. For if they did so, they would establish themselves as faithless among those of the Greeks who are welldisposed towards them, and they would be helpful to their enemies. ATH: Don't you agree with the belief that the useful is found with what is secure and that justice and good are accompanied by those very dangerous deeds which the Lacedaemonians usually undertake most feebly? MEL: But our belief is that for us they are more likely to take risks on themselves and to consider it safer than in other cases. For we lie close by the Peloponnese, which fact is significant with regard to the actions possible to them; and in reference to their opinion, it is a factor that we will be more faithful than others by reason of our kinship. ATH: Friendliness does not offer much security. Potential allies in battle look for a decisive superiority in action �''"J' m those who summon them. The Lacedaemonians look to this even more than others do. Because of misgivings about their country's resources, they attack even their neighbors in the company of many allies, so that it is not likely that they will cross to an island while we command the sea. to give way to a very powerful city when it makes such moderate demands: namely, that you become allies and keep the fruits of your land. When you have been given the choice between war and survival, you need not choose the won;t part from obstinacy. ATH: You may yet live through some such action, and the only result will be that even you will learn that we Athenians have never yet abandoned a siege operation from fear of intervention. We are greatly concerned that, though you have said you would plan for your safety, you have as yet mentioned in all these arguments nothing in which men might trust, and trusting, hope to be saved. Your strength lies in future expectations. Your resources are too scanty for you to survive the force marshalled against you. And your thinking is unreasonable if you do not come up with something more sensible than these other things after you have given us leave to go. Don't get caught in notions of dishonor. They prove for the most part destructive to men who come into debasing and predictable dangers. For many men, though trying to look to the future, have found that once disgrace is mentioned, it lures them on by the potency of its seducing name. And by their bondage to this word they are willingly betrayed into real and irreparable damage. The dishonor that they then must bear because of their own extravagance is more shameful than that which true misfortune might have brought. If you plan well in your own behalf, you will guard against this. You should not think it unsuitable Marcellus and Archimedes Unyielding to their equals, well-mannered to the strong, fair-minded to the weaker - such men cannot go wrong. MEL: They might have others to send. The Cretan Sea is vast. Those who rule it find it more difficult to seize ships than those on ships who wish to escape notice do to gain their safety. If they should be overcome in that attempted crossing, they would turn upon not only your land but as many of your remaining allies as Brasidas 2 has not attacked. You will not then need to struggle for a territory which does not belong to you; the struggle will be closer to home-for your allies and for your own land. Harrison ]. Sheppard Therefore, when we have left you, observe carefully and consider often that you are deliberating about your country, the only one you have, and that on this one decision depends success or failure. The Athenians then withdrew from the debate. The Melians, left to themselves, saw things the same way as they had at first. They answered as follows: Things appear to us no differently from the way they did at first, Athenians. We will not rob ourselves overnight of our 700-year-old city's freedom. Until now we have trusted that we might save i.t by the assistance of divine power. By such power and by the aid of men, namely the Lacedaemonians, we will try to save ourselves. However, we call on you to consider us as friends, enemies to. neither side, and to withdraw from our land after you have made treaties suitable to both of us. As the Athenians withdrew from the debate they said: In making these decisions you certainly appear unique. You choose things in the future as more distinct than what you see; by the strength of your desires you view unseen things as though they were actualities. As completely as you have trusted in the Lacedaemonians, in good fortune, and in your hopes, just as completely will you be destroyed. • • • All the male youths the Athenians seized, they slew; the women and children they threw into slavery. 2 A succeesful Lacedaemonian general.-Ed. note. Give me a rod long enough, and a point at which to stand, and I shall move the earth. Archimedes The ancient geometer was concerned primarily with ideal figure. Proceeding from a set of definitions, postulates, and common notions, he derived the propositions which demonstrate the properties of diverse figures, as well as the relationships among the figures. Once we accept the premises on which geometry is based we cannot deny the validity of the propositions; for the proofs follow from these premises directly and irrefutably, and hold inviolably so long as we adhere to our acceptance of the axioms. Therefore this mathematical science is ultimately not dependent upon observations of the physical world. A mathematical system is the result of the intellect's drawing the proper inferences from certain premises. Hence the development of mathematics (and this seems to be the case with all pure sciences) does not depend in any direct way upon knowledge of the activities of other human beings. The mathematician needs only a place to work and time to apply his own intellect to the given premises or prior propositions ; then he can proceed to produce indefinitely those beautiful and elegant propositions that delight his spirit and compel his soul. Archimedes (287-212 B.C.) was one of the foremost mathematicians of antiquity. He was so engrossed in the pleasures of geometry that when he was occasionally carried by absolute violence to bathe or have his body anointed, he used to trace geometrical figures in the ashes of the fire, and diagrams in the oil on his body, being in a state of entire and unending preoccupation, and, in the truest sense, divine possession with his love and de. light in science. 1 This sort of preoccupation with study is a familiar one. Archimedes' behavior is much the same as that of the person who neglects to put his shoes on in the morning because he has been absorbed in some perplexing problem all night. In fact, Archimedes is the classic example of those venerated and comic figures we now term "absent-minded professors." And since Archimedes is a great man, his passionate preoccupation is doubly comic. Archimedes' friends compensate for his utter ignorance of the external world by tending him as they would a child. And we can forgive this eccentricity just as his friends did, for it only holds the trivial in contempt: that a body be oiled is not so important as that a great mind continue to develop mathematical truths. But the comedy of Archimedes' preoccupation continues: In accordance with a request by King Hiero of Syracuse [Archimedes' city], Archimedes transferred some of his geometrical constructions into actual machines ; not as matters of any real importance, but rather as geometrical amusements. Hiero, however, considered them to be very important indeed, for they were amazingly effective in their use, being capable of hurtling immense masses of stone and all sorts of missiles. Thus when the Romans, under the general Marcellus, attempted to seize Syracuse, they were repulsed time and time again by Archimedes' machines. After many attempts, the Romans finally gained access to the city and turned the battle into a rout. While the defeated city was being overrun by the Romans, Archimedes was, as fate would have it so intent upon some diagram, that he never noticed' the incursion of the Romans, or the sack of the city. In this transport of study and contemplation a soldier approached him and commanded Archimedes to follow him to Marcellus ; for Marcellus had the greatest admiration for Archimedes and wished to see and speak with this amazing man so that he might learn from him. Archimedes ignored the soldier at first, and then repeatedly declined to go along with him until he had fully worked out his demonstration. The soldier, enraged by Archimedes' contempt, drew his sword and ran him through. 1 Plutarch's Lives (Marcellus) �, '?' 20 The death of Archimedes greatly affected Marcellus. He wept when he learned of it, and always regarded the soldier who killed Archimedes as a murderer. 2 Obviously the character of the comedy has been transformed, and there are some serious questions which present themselves as a result of that transformation. It is clear that Archimedes' activity is, in some ways, more important than any of the details of mundane existence, and that it demands the kind of attention which he devotes to it. But it is not so clear that Archimedes' ignorance is simply of details. Vv e must ask: 1) At what point is Archimedes no longer comical; at what point is the disproportion of his preoccupation no longer desirable? 2) Is Archimedes' inability to deal with the situation, inevitably thrust upon him, as much an example of stupidity as the soldier's passionate act? Study, thought, and contemplation are private, apolitical activities. It is necesary that the liberal artist pursue his studies with the help of some political entity, such as Syracuse. From these two facts arise the difficulties that make Archimedes' situation so problematical and paradoxical. And perhaps the first question we must ask of Archimedes' position is : Can the earth be moved from a theoretical point? 2 Cf. Ibid. Jacob Klein The Problem of Freedom* I have been assigned as subject for this lecture Men, Machines, and Slaves. This is the first lecture in a series of lectures on the general theme "Human Freedom." I hope you will grant me the freedom not to speak of machines tonight. I shall speak of Freedom and Slavery, deeply conscious of the vastness of this theme and its immense complexity. The lecture will probably degenerate into a sermon. Grant me the freedom not to apologize for that. The theme of Freedom has immediate political connotations. And this is as it should be. For Freedom-let me state this at the very outset-is essentially and foremost a political and social problem. It is not surprising, therefore, that right now, for example, in international politics and in the wrangling on domestic issues a great deal of talking is devoted to "Freedom." We hear accusations, protestations, claims and counterclaims on this subject. But let us not forget that all these claims and counterclaims are merely echoes of more universal conflicts. Since I am in the fortunate-or unfortunateposition of delivering the first lecture on the Subject of Freedom, I propose to discuss this subject in its universality. I am not trying to brush aside the very concrete and burning questions that confront all of us today. I am trying to win the right perspective in which to see them. When am I free? When nothing compels me to act in a certain manner, when nothing compels me to do certain things, when nothing compels me to think in a certain way. That is to say, we cannot consider Freedom without considering its opposite : Compulsion. Nate please: all the symbolism about Freedom is about its opposite. In any account of Freedom the great symbols are chains and fetters. There is no universal and immediately transparent symbol of Freedom as such. The torch of the Statue of Liberty, the Phrygian cap, the gesture of open and uplifted arms-these all symbolize freedom at best indirectly, by way of some historic or sentimental connotations. But chains-that's different. They mean directly; always and under all circumstances, compulsion. Why is this so? I think, because, in the most concrete way, we are never free. We are inescapably bound to the necessities of life, we cannot escape death ; we depend intrinsically on everything around us, in the present as well as in the past. We are chained by Necessity with a capital N. We are at best Prometheuslike. In what sense then is it still possible to say that we can be free of compulsion? Let me answer tentatively : we can be free-or unfree-1) as thinking beings, 2) as beings having a will, 3) as beings living with other beings, i.e. as social and political beings. In what sense are we free or unfree as thinking beings? We are always immersed in our daily routine, our eyes are closed to many aspects of things, we cannot detach ourselves from our immediate tasks, worries and fears. We do not think about the world we live in, it has been thought through for us by others. We do not think, others think for us: customs, current opinions, lawgivers behind some screen, determine what we think and how we think. Moreover, passions obscure any clear vision. They are as much the masters as customs and current opinions are. The world rules tyrannically over our thinking. We are its slaves. This is, in fact, the great theme of ancient philosophy, which has never been abandoned completely in the vicissitudes of the succeeding ages. Here is the classical picture: we are prisoners in a cave; we are chained to our passions and prejudices; we listen to echoes; our speaking is babbling; if we think at all, it is in a shadowy way and about nothing but shadows. To free ourselves from the rule and the chains of the cave, we have to be led out of the cave into sunlight*Text of lecture presented at The Aspen Institute for Humanistic St1tdies. (1952). �23 22 an arduous task. We become free in our thinking by detaching ourselves from the familiar, the self-evident, by turning away from the easy pillows of our waking sleep. This can only be done by educating ourselves. The very idea of education is the consequence of our striving for freedom in our thinking. This idea conceived in antiquity has ever since dominated the western world. It has suffered modifications, has been made subservient to ends of a very different nature, has even been perverted completely, and yet it is still a decisive factor in our lives. At worst, we pay lip service to it. As long as lip service is felt to be necessary, the idea is still a force. But once this freedom of our thinking is secured, a grave difficulty seems to arise: Must we not think in the right way, that is, avoid error? Must not our thinking, in which the truth of things is supposed to be revealed to us, be guided by truth? Is not our thinking under the authority and rule of truth? To accept its authority, one might say, is to accept a new tyrant. That is what has bothered the "free thinkers," the "free minds" of all ages. It does not seem enough to shake off the chains of the cave. No other authority can be tolerated, if we want to be really free. Free means then-free to err; or free to withhold judgement. There is no freedom in thinking but at the fork of truth and error. At any other point we are not really free in our thinking, so the argument goes. And yet the authority of truth has to be accepted. It hardly matters how we understand "truth" ; compliance with some criteria of right thinking seems unavoidable. May we conclude then that freedom in thinking is the freedom to accept this authority of truth? But this again seems to depend on an act of will. Is then this freedom based on another one? Let us examine the next point. In what sense are we free, or unfree, as beings having a will ? We seldom follow our will. We yield to external impulses, we follow trends, we consider ourselves, even while acting, victims of circumstance. Necessity, the origin of which is not to be found in ourselves, _seems to dictate our actions. Not merely whims guide us, not merely spontaneous and irresistible desires, but also the trepidation of our hearts, the generosity of our feelings or the cowardice of our flesh-but not the will. The will is not the undisputed master. To make the will free, i.e. to make our own will the very origin of our action or inaction, of our thinking and not thinking, amounts to winning mastery over all necessities, amounts to finding in ourselves something that nothing and nobody can challenge or suppress. This is the great teaching of the Stoics. I am free when I follow nothing but my own will. It is within my power to do so. My bodily existence can be crushed but not my free will. I might appear a slave but I am not a slave. I enjoy sovereign independence. It is within my power not to be touched by feelings of misfortune, by anger, envy or jealousy. It is within my power, my sovereign power, to be like God. Needless to say, the freedom of the will is also one of the great themes of the Judaeo-Christian tradition. There is, of course, a profound and unbridgeable difference in the understanding of the very nature of the will in the Stoic and the Christian traditions. But what is common to both traditions (and I may add to the Epicurean also) is precisely the emphasis on the freedom of the will. According to the Christian tradition, the will is the only freedom that man has. Man has been created in the image of God, and the similitude is confined to the will. Man himself decides what he wills. But here again a new sense of unfreedom emerges. This freedom of the will-for Stoics and Christians alike, in spite of their profound and unbridgeable difference-is related to the divine will. Our will is free, paradoxically enough, when it wills what it ought to will-in conformity with what is right and good according to the divine decree. We are free to accept or to reject the Good, but this freedom itself is mad, or corrupt, or guided by Satan, if we reject it. The authority of the Good determines whether the will is really free or unfree. The will is thus bound by golden chains, but golden chains are still chains. May we conclude then that freedom of the will is the freedom to accept the authority of the Good? This would be the freedom that makes us 1110ral beings. And this would still be the case, if the Good loses its divine connection, and becomes the expression or summary of a "code of ethics," as we are fond of saying. And are we not then enslaved again? Let us turn to the third point. In what sense are we free or unfree as social and political beings? There is an everlasting experience of mankind-and this is oppression. It has many guises and disguises : the rule of a despot, the reign of an "ideology," the discrimination against groups of people, the "insolence of office," the bullying of a master sergeant. All these and many more are the forms of Tyranny. The paradigm of all tyrannical relationships is the relation of Master and Slave. It is perennial. Perennial also is the rebellion against it. The relation of Master and Slave is one of the three possible relationships between men, in which or by means of which things that are wanted by men can be accomplished. The other two are Friendship and Con- tract. I may do things or be prevented from doing them out of friendship. I may do things or be prevented from doing them by agreement, by contract. All three, MasterSlave, Friendship, and Contract, are society-building and state-building relationships. If what we do and what we do not do depend on the arbitrary decree of one man or a group of men who have the power of life and death over us, we are slaves under tyrannical rule. The political wisdom of all ages has tried to establish forms of political life which would eliminate, to some extent at least, such arbitrariness of political rule and would make perpetual rebellions unnecessary. It has tried, in other words, to secure a minimum of freedom. For to be free as beings living with other beings means to be free from arbitrary, i.e. tyrannical rule. How can this state of affairs be brought about? How can things be done or left undone if we are not ordered to do or not to do them? Either in virtue of a commonness of purpose based on friendship. Or by contract. The first possibility, that of friendship, although often enough actualized on a small scale, does not seem to be operative on a larger one. It still remains the dream of anarchists, for example. The second one, that of contract, is more powerful. Social freedom, that is, freedom from arbitrary rule, can be achieved, if the acceptance of social ties is based on agreements among the persons involved. But an agreement among people needs something that will make it valid, that will set a penalty if a breach occurs. It needs a higher sanction. And this is the sanction of the Law, the sanctity of the Law. To escape arbitrary rule means to accept the rule of the Law. This insight is as old as mankind, as old as Tyranny and Slavery. But here again the question arises: is not the Law a new kind of tyrant? Cannot laws rule as tyrannically over us as despots do? Was not even slavery a lawful institution? That is, construed as the result of a contract or as the application of the laws of war? Is there a way to make the law or the laws, be they written or unwritten, the safeguard of freedom without any tyrannical ambiguity? This is the real political problem of all ages. It has been actually solved in modern times, in the 17th and 18th centuries. And this solution is one of the great achievements of the modern age, rivalling the only other one: the conception of a mathematical science of Nature. In what does this solution consist? The danger of laws becoming tyrannical has its root in the fact that laws can be imposed upon people, be they bad or even good laws. In other words, the lawgiving is the problem. To avoid the danger, the law- giving itself has to proceed in terms of a contract. The very notion of a contract has to be generalized. Two men entering a contract do so out of their own free will, and the procedure of contracting is prescribed and protected by the Law. Roman Law had set the precedent. The political philosophy of the 17th and 18th centuries generalized the contractual procedure in applying it to the Law itself. The law itself has to be understood in terms of a contract in which the two partners happen to be one and the same. The people as a whole makes a contract with itself to observe certain rules. By this very act Law is generated. It cannot henceforth be understood as imposed upon men-it is self-imposed. I obey the law because I participated in the lawgiving, I gave it to myself. In recognizing the authority of the Law I remain free because it is my own authority that I recognize. This primordial political act of lawgiving, in constituting the social and political body, establishes once and for all political freedom. Nothing compels me in this act but myself. The political body, the state and all its manifestations, are a free creation of man. The state and its laws, far from endangering the social freedom of man, is the very embodiment of this freedom. Such is the grandiose conception of the thinkers of the 17th and 18th centuries. The primordial act of lawgiving is perpetuated in all succeeding lawgiving operations. It is important to understand that what this theory of lawgiving is primarily interested in, is not the giving of good laws but the securing of the lawfulness of the law itself. The emphasis is altogether on the procedure by means of which laws come into being, the procedure of self-imposition. The emphasis is on the way in which a law is being enacted, the way in which its constitutionality can be tested and secured in terms of the primordial lawgiving act, and on the machinery of representative government. The content of the law, its goodness or badness in terms of human welfare, in terms of the common good, is not the ultimate concern. Here in the United States, this fact is somewhat obscured by the maintenance of the spirit as well as of the letter of the Anglo-Saxon common law. But at the very root of the modern understanding of political life is the desire to be free from arbitrary, tyrannical rule. That is the idea of Freedom. Let me pause here for a moment. There is something admirable in this solution of our problem. Freedom appears as a free creation of men. Oppression and Tyranny appear crushed forever. The indignation of man facing the perennial phenomenon of enslavement seems to have had its way. The lawfulness of the law is not only �the safeguard of freedom but also of justice. There is something not only admirable in this solution, but also something deeply fascinating. And to this fascination let us now turn our attention. The fascination exerted on human minds by the problem of freedom and especially by this solution of the problem accounts, I think, for the fact that the problem of the content of the laws has been seriously neglected. The content of the laws was supposed to emerge as a result of the fights between the contending interests of men. The lawfulness of the lawgiving once secured, the laws themselves had to come out by way of trial and error, by way of compromise among those contending interests. The idea of a political art, of Politics, based on practical wisdom seemed to transform itself into the idea of tactical maneuvering for votes, for parliamentary advantage, for bargaining positions. Witness the strange modification in the meaning of the term "politics." But what is perhaps more important is the influence that the political solution of the problem of political freedom has had on our understanding of our freedom as thinking beings and as beings having a will. Let me retrace my steps. When I spoke of these two freedoms, I constantly used, and had to use, terms derived from the political domain. I spoke of the authority of the truth and the rule of truth, of tyranny and slavery in the relation of the Good to the will, of truth to thinking. Freedom in our thinking, I had to conclude, was freedom to accept the authority of truth. Freedom of the will-the freedom to accept the authority of the Good. I could not help using these terms because our terminology, our thinking itself, is deeply influenced by considerations derived from our experience as political beings. This is nothing new or exceptional, of course. The problem of Freedom is, as I said in the beginning, a predominantly political one. More generally, almost the entire body of traditional philosophical terminology is derived from the language of political life, and especially from the language of the courts. This shows the general preponderance of political interest in all our thinking. It was primarily the questioning of political patterns and habits which gave rise to an inquiry into the nature of things, gave impulse to philosophical questioning, led to the idea of a contemplative life. Classical philosophy arose out of the preoccupation with political problems and tried to give guidance to political thought. Its dependence on politics is of a genealogical, not a logical, nature. Kings always needed wise counsellors, and the wise counsellors could not live without the kingly purse, but the wisdom of those counsellors was quite independent of the kings and their purses. It was meant to guide them and not to be guided by them. The fascination with the problem of freedom and the solution I have spoken of seems to have changed this relation of wisdom to political action profoundly. Moreover it changed our understanding of our freedom as moral and as thinking beings. As far as our free will is concerned, the political solution showed the way to a re-interpretation of the relation of the will to the Good. The Law, to safeguard our political freedom, was understood as self-imposed. Why cannot that which the will ought to will be also determined by the will itself? If the Good is not given to the will from the outside, as it were, but set by the will itself, man as a willing being, as a moral being can dispense with those golden chains, can be completely free, completely autonomous. This is possible, if the willing itself is identified with the self-imposition of what ought to be willed, if the character of the categorical demand is identified with the very freedom of the will. This is Immanuel Kant's solution, the influence of which on all of us is greater than many seem to realize. And there can be no doubt here that Kant transposed deliberately and consciously the political solution of the problem of freedom, especially in the form given to it by Rousseau, into the moral sphere. There can be no doubt that here the fascination with the problem of freedom has done its work. The lack of content in Kant's understanding of the Good is apparent. But far beyond the Kantian teaching goes the understanding of the will as setting its own goals and determining as good whatever it wills. It does not make much difference whether the will is understood as the will of an individual or as the collective will of a people or a culture. This teaching is current in the schools the world over, in the form of historical sociology or sociological history or history of cultures. Here again the fascination of freedom is at work. This teaching makes us morally free indeed, but rather empty. As far as our freedom as thinking beings is concerned, it seemed to be endangered by the compelling nature of Truth. But what if truth itself is of our own making? Could not truth be the product of our thinking? a "construction of our mind" ? Could not the fullness of our thinking be identical with truthfulness? This possibility has not merely been envisaged. You will have no difficulty in recognizing the prevailing philosophical opinion of today. I said these consequences of the fascination exerted by the problem of freedom are more important than the impoverishment of our political life. In fact, it is these consequences that contribute the most to it. How can the art of politics flourish, if it is not guided by political wisdom? But the availability of this wisdom depends, in turn, on our ways of thinking and our ways of willing. The three freedoms I spoke of in the beginning cannot be neatly separated from each other. That is what makes the problem of Freedom so immensely complex. Let me raise a strong objection to what I am saying. The art of politics, as I understand it, namely guided by political wisdom, has never existed. There were some writers who propounded it and some pupils and apprentices in this art who failed miserably. It might be proper to recall the saying of that old Swedish chancellor to the effect that one can hardly imagine with how little wisdom this world is actually governed. Will that not always be the case? Should we not be satisfied with the practice of political freedom that we have inherited and defend it as best we can? But the point is that what we have inherited is indeed our own creation of freedom, a most precious thing which it is in our power to preserve or to lose. The state of affairs we live in is itself a product of art, a manifestation of freedom and perhaps one of the greatest manifestations of that freedom. We have gone far beyond the realm of natural life lived by our ancestors. Once again, it seems to me, we should examine our assumptions, try to discover at what point our thinking and willing enter the mechanism and automatism of our political practices or are subjugated by them. Once again, we have to face the immense task of education which such an exploration entails. Once again, we have to picture ourselves in a cave, perhaps a deeper and vaster one than our forefathers ever imagined. The freedom we enjoy has perhaps created more chains and chains of a novel nature that hold us down. Once again we have to try to disentangle ourselves. We might fail in this enterprise, of course. But in failing we would still be exerting our freedom. �Book Review William H. Brubeck_ concerned, a stock certificate is just a case of mistaken identity. Power Without Property' In a hearing of the Senate Antitrust Subcommittee a couple of years ago, the president of one of the country's largest steel companies gave two good reasons \'l:hy his firm would not cut prices, even if it could afford to do so. For one thing, he said, if one company cuts prices, the others follow suit, and the vvhole industry is competitively hack where it started from-but with lower profits. Besides, cutting prices would probably force the least efficient companies out of business, which would be very sad. This remarkable gloss on Adam Smith went unchallenged. So do many others. :Modern decentralization of industry in the Cnited States owes more to the Supreme Court decision outlawing the basing-point price system1 than to any economic force. Expansion of the steel industry in the 1950's came not as a response to demand but, primarily, as a reaction to President Truman's threat to put the government into the steel business. A successful Broadway comedy of recent years was built around the hilarious notion of stockholders' actually choosing a corporation's management. These random examples of free enterprise at work in the United States have one thing in common: they illustrate how varied and unsystematic and how remote frorn the traditional rhetoric of free enterprise our econornic practice really is. At the center of this varied and confusing reality is the modern corporation, the dominating fact of American society in the middle of the tvventieth century. \Vith its ancestry going hack at least to Rome and with its future apparently unlirnited, the corporation is a conceptual labyrinth in which philosophers and economists, social scientists and lawyers wander endlessly without ever getting to the heart of the matter. Only businessmen fail to get lost in it. Perhaps that is because, for the most part, they try only to operate it, not to understand it. Fully half of us live out our lives in the comfortable and intensely-managed employ of the corporation without ever knovving much about our employer. But our employer knows a lot about us. The five hundred largest Arnerican corporations (neatly catalogued each year by Fortune) own twothirds of American industry. They accumulate most of the new capital generated for industrial growth, produce most of our goods, and, by their advertising, play a major part in deciding what we will want and-if we can manage the down payment-what we will buy. They are immortal and soulless, yet, in our impoverished legal logic, they are treated (under the Fifth and Fourteenth Amendments to the Constitution) as persons. \Ve are at a loss to accommodate their power and status or to justify their effects in any theory of liberal democracy. Thanks to our inability to ignore the obvious indefinitely and to Berle and Means' 1vlodern Corporation and Private Property (written nearly thirty years ago) , we are beginning to realize that the power of corporate management is largely autonomous and that corporate ownership is a vestigial irrelevance. This truth is becoming well known at just about the time it is ceasing to be true-or, at least, when it is becoming seriously misleading. It is true that ownership, as we used to understand it, has been attenuated to the point of invisibility. The shareholder has only a beneficial interest. "Ownership" means quarterly dividends and, with luck, capital gains; a shareholder in AT&T has no further claim, not even to a telephone pole. He has nothing to do with management decisions, production, sales, employee relations, or with any other function of the body corporate. Among 3,000 corporations, in 1957, there were only twelve proxy fights. So far as Locke's concept of property 2 is *Power Without Pr.operty, (c) 1959 by A. A. Berle, Harcourt, Brace and Company, Inc. 1 Jr. Federal Trade Commission vs. Cement Institute 333 C S. 683; 1948-Ecl. note. 2 See Locke's Second Treatise on Ch1il Gouernment, v (Of Property) .-Ed. note. But the economy evolves faster than our comprehension of it. Abont the time we are realizing that management is independent of ownership, the corporation is acquiring a potential new master. Specialists in economic specialization, Americans have developed a new specialty-the management of ownership. And these nevv specialists-managers of mutual funds and pension trusts, and other institutional investors-may have much to say about the conduct of the corporation. Institutional investors-the funds, insurance companies, venturesome colleges, and the like-are becoming increasingly important in the investment picture. They control great blocks of stock and are by far the most important "outside" source of new capital for the corporation. ·while the suffrage of the individual investor has become weak and ineffective, the concentrated power of the institutional investor is growing. At the rate they are growing, these institutional investors have, or soon will have, a voting voice loud enough to take a serious part in choosing and firing managements and in setting corporate policy. So far, they have shown little disposition to do so. Instead, they vote by buying or selling and thus affecting the price of stock. This in itself is a potent persuader; managements are becoming increasingly solicitous of the good opinion of institutional investors. 'fhese managers of ownership are also a new power in the capital markets. Traditionally, the thrifty individual, investing his savings as risk capital, was supposed to exercise an important leverage in the economy. But in fact, four-fifths of all new equity capital now comes from "internal" corporate sources : depreciation allowances, retained earnings, and bank credit. Of the other one-fifth, the great bulk comes from the institutional investors. The venerable and revered Thrifty Individual is alrnost invisible. Among the institutional investors in com1non stocks, the largest arc mutual and pension funds-the managers of ownership-and they are growing at a great rate. Tims to corporate management is being added another notable partner in the control of corporate enterprise. Economic power is increasingly in the hands of this curious duumvirate. The new power holders have no personal stake in their holdings. Their function is to conserve and enlarge their trust against the demands of its claimants, the "ovvncrs . ., Yet these owners do not own the stock itself but only an ultimate claim on the collective fund. \Vho owns the stock? More important what is the effect of such change on our society? To the comparatively compact and homogellcous group that manages our large corporations is added another, even more close-knit group-the few hundred financiers, mostly in Kew York and Boston, who rnanage the mutual and pension funds. The two groups arc much alike, already partly interwoven by the ramifications of finance into industry. In Sears, Roebuck, an employee-"owned" stock fund is controlled by management trustees, and the circle is cornpletc. Corporate autonomy is perfected; the corporation owns itself. This is a rare case. For the most part, fund management and corporate management are formally distinct. Yet, though the duumvirate complicates the picture, power remains in the hands of self-perpetuating, nonowning, salaried managers, while the questions of social control and social responsibility remain unanswered. II All of this is the subject and the problem of A. A Berle's Power without Property, his latest foray into the labyrinthine mysteries of the corporation. ;vr r. Berle has been conducting and reporting on his explorations for more than thirty years, beginning with The .il/I odern Corporation and Private Property. He has been a pioneer and an illuminating guide in the study of the corporation, and his latest report is one of his best. Power, Berle observes, has been divorced from property. It is in the hands of the managers and the trustees. vVhat are the consequences of this climactic amendment of liberal economics? Unfortunately, we tend to approach such questions as exercises in "problern solving" and to define our problems in narrowly constitutional terms. \V c seek "gimmicks" to furnish the universal solvent of democratic sanction for power phenomena. So, to replace the disappearing O\vner, Berle invokes "public consensus" as the constitutional censor of corporate power. l\ ow this is a point of some importance. The fund managers and corporation managers have escaped some of the formal disciplines of the economic process itself, but public opinion and the threat of political intervention are chastening forces (witness the television quiz-show scandals). There is evidence that businessmen arc seriously and sensitively concerned with the attitudes of public and politicians, and convinced that the cor- �poration's well-beii1g depends on these attitudes. The growth in size and importance of the public relations staff in the corporate hierarchy is a measure of the corporation's concern with "the public consensus." As it has become less bound by traditional economic controls, the corporation has become more amenable to political controls. It is changing more and more into a public institution, socialized and "politicized." But Mr. Berle's observations tend to end just at the point where they are becoming most interesting. He begins by observing that the corporation is far more than an economic phenomenon and is a proper subject for all the social sciences. But most of his own analysis is economic, and his conclusions barely escape the dismal science. If the environment and motivating forces of our economy have so changed, what are the likely consequences? We get only hints. Mr. Berle r ecognizes, for example, that both public consensus and the predilection of the corporation powerfully push a socialized economy in the direction of social planning. He even sees our pluralized economy and the Russian totalitarian economy moving along convergent lines of development. Yet our likely course toward social planning appears to be an evolution of isolated sectors of incr eased rationalization, in a persisting pluralism. For example, the automobile industry may be forced toward a more rational planning of production, an ironed-out production cycle, in place of the present irrational boom-and-bust of the annual model. Then what transforms the essential irrationality of the sum of these plural centers of rationality into a unity of social planning? I have a suspicion that such a theory only replaces the old animism of " natural economic harmony" with a new one, in which groups r eplace individuals and "social planning" replaces profit as fuel for the machine. Isn't it more likely that the forces pushing us toward economic rationalism will seek and find channels for truly integrated planning that simply do the least violence to our liking for the appearance of pluralism, while they achieve the r eality of integration ? For example, a great variety of institutional means for integration ar e emerging : contraction of the power elite to a comparatively small group of managers who are, in fact, in close communication, as Berle observes; the increasing efficiency of trade associations in concentrated industries; the activities of congressional committees, Presidential factfinders, the r egulatory agencies, the Council of Economic Advisers. A ll these are subtle but nonethe- less real agencies through which integrated planning is furthered. With all the exploration of the corporation that is now going on, too much emphasis is still placed on the narrow project of problem solving and too little emphasis on just understanding. If, for instance, we are headed toward g reater and greater social rationalization in terms of economic goals, (then regardless of whether our "solutions" to the formal problems are correct), what are the meaning and the consequences of this evolution for the business of living-which is still, presumably, our most important preoccupation? Max Weber once observed, in this same context of the development of the corporation, that a completely rational life would be unendurable for human beings. Here is at least as important a matter as Berle's concern with fo rmal accountability. The fact is that the corporation is the most important subject of social philosophy-the biggest social fact since the emergence of the nation-state. Yet far too often we approach it as social-science technicians rather than as liberal artists. We seize on its sympto1ps, and we solve its mechanical problems, but we make little progress toward mastery through understanding. It is as t hough Aristotle had limited his study of the polis to a statistical report on election by lottery or to a history of ostracism. In our study of the past, we tend to be determinists. In our approach to the present, we ar e volitionists. We assume that our society is a machine whose effect on our lives is largely subj ect to our decision. So long as the corporation is subj ect to "public consensus," we are its masters, and our problem is solved. But in fact, we control our environment far more by understanding it and, consequently, by r eacting intelligently, than we do by manipulating it. So we need to know where the corporation is headed on its own, not just where we are steering it, and to understand what its own demands and effects are. We are making little progress toward such knowledge. We learn a little about the "organization man" and "countervailing power" and the "lonely crowd," but we lack imagination and perspective on a scale grand enough to capture the total dimensions of corporation society. The philosophers of the Fund for the Republic (A. A. Berle among them) , in the quiet precincts of Santa Barbara, are engaged in a notable attempt at speculation on such a scale. From their lyceum, or some other, the social theory of the corporation will perhaps be p:·o- duced. If so, the theory will be much more of an Aristotelian inquiry into nature than a Lockean rationalization of power. III Karl Polanyi, in that remarkable book The Great T ransformation,3 argued that liberalism was both utopian and revolutionary in its polarization of state and individual, its denial and attempted destruction of society. Perhaps our difficulty in political thinking now ·lies in the handicaps of a theory that has no place for society. T he corporation is neither private nor, in the usual sense, political-neither an individual nor an aspect of the state. In a political theory that gives .society no place, how do we understand a political institution that is neither individual nor statist but social? Perhaps, indeed, our immersion in such categories as "individual" and "state" is too parochial. When organization has become so pervasive and omnipotent a fact of life, maybe the old categories lose meaning. Corporation is only the archetypal form of the great fact of twentieth-century life-organization. How much individual meaning and freedom have we really rescued by subjecting corporate power to public consensus, if the consensus itself is .part and parcel of the same organized system as the corporation? What happens to the relations of individual and state when both are captured by organization itself? It is true that, in theory, Athens and medieval Christendom were as thoroughly organized, made as many demands, and claimed to comprehend the individual as totally as does modern society. The polis claimed to embrace all that was worth while in life (except the ~ltimate individuality of contemplation) , and public opinion was tyrannical. Medieval Christian theory allotted every man his station and duties, circumscribed all values within its eschatological goals, and tried vainly to subdue the disorganization of the lords temporal to the organization of a papal lordship. Perhaps all of history is simply a struggle of men against organization. W hy get so concerned about its incidence in our -lives? Partly, I think, because its demands are so total. It is doubtful whether we have any operable escape into freedom as valid even as the Greek ideal of the contemplative life or as the medieval realm of man's ultimate relation to God. I~ practice, if not in profession, we have few claims against the combined demands of state and commerce. But even more clearly, we are up against somethiqg never faced by men before. Only in the twentieth century have the technical resources of organization become adequate to its aspirations. If Pope Gregory V II had been able to c.;ommand the IB M machine, the telephone ( and . the "bug"), the management engineer, and the tranquilizer, what might the medieval church have accomplished ? The Apology might have been very different if the techniques of brainwashing had been available to the Athenian democracy. Organization doesn't even have to be so sinister. Television is warm and glowing and banal. Teamwork is steeped in. piety. But the fact remains that organization generates imperatives, and modern technology provides it with the instruments to enforce them. Maybe public consensus conditions corporate behavior. But both of them exist within a degree of institutional organization more marvelous, complete, and dynamic than we have ever dreamed in our philosophy. W e badly need to dream a philosophy adequate to this gigantic reaHty. 3 ( c) 1944 Beacon Press. �Contributors The Reverend J. Winfree Smith Tutor, St. John's College Richard ·F. Cleveland Chairman, Board of Visitors and 1 Governors, St. John's College; A.B., 1920, M.A., 1921 Princeton, L.L.B ., I Harvard 1929; Member of the law 1 firm of Semmes, Bowen, & Semmes, Baltimore. Theodore Barnes Stinchecum Student, St. John's College Eva·Brann Tutor, St. John's College Elton Ray Davis Student, St. John's College Harrison J. Sheppard Student, St. John's College Jacob Klein Tutor, St. John's College William H. Brubeck Alumnus, St. John's College A.B., 1948; Ph.D., Harvard; Assistant Professor of Political Science, Williams College, Lecturer, Columbia 1 University; Congressional Staff member. Private Consultant on Politics and Public Affairs, Newmyer Associates, Inc. I � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The Bulletin of St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Description An account of the resource <em>The Bulletin of St. John's College</em> was published quarterly by St. John's College from 1932 to 1968. It was distributed to alumni, faculty, and staff. Some issues include the Report of the President, the official statement of the St. John's program, the Catalogue, the Polity of the college, or the Dean's Statement.<br /><br />The publication was continued by <a href="https://digitalarchives.sjc.edu/collections/show/12" title="The College (1969-1981)"><em>The College</em> (1969-1981)</a>.<br /><br />Click on <strong><a title="The Bulletin" href="http://digitalarchives.sjc.edu/items/browse?collection=37&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in The Bulletin of St. John's College Collection</a></strong> to view and sort all items in the collection. Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Page numeration Number of pages in the original item. 30 pages Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context Bulletin January 1960 Vol XII No. 1 Politics and the Liberal Arts Title A name given to the resource Bulletin, St. John's College, January 1960 Description An account of the resource Volume XII, No. 1 of the Bulletin, St. John's College, Politics and the Liberal Arts. Published in January 1960. Date A point or period of time associated with an event in the lifecycle of the resource 1960-01 Creator An entity primarily responsible for making the resource Sheppard, Harrison J. (Editor-in-Chief) Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Rights Information about rights held in and over the resource St. John's College owns the rights to this publication. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/0dd84fd469f79a84234fe6ed107c89b4.pdf 6583724dca685c83134b6025d399ce65 PDF Text Text Bulletin St. John's College Rhetoric JAN UAR Y 19 6 1 I VOLUME THIRTEEN NUMBER ONE �Bulletin h . St. 1ohn's College Vol. XIII No. I A Letter from the Editors to the Reader EDITORIAL STAFF H ARRISON J. SHE PPARD M anaging Editor and Co-Editor ... rhetoric we look upon as the PJJwer of observing the means of persuasion on almost any subject presented to us; and that is why we say that, in its technical character, it is not concerned with any special or definite class of subjects. ARISTOTLE, Rhetgric, I,2 T H EODORE BARNES S TINCH E CUM January 1961 Rhetoric Co-Editor and A rt Director D ONNA A. PARMELEE Secretary to the Editors ] OH N KOHL, JR. What are the most effective means a periodical such as this can use to do what it sets out to do? This problem arose at the outset of our work on the first issue, and remained an important question after its publication. While we were still discussing this question Mr. Klein gave his lecture on The Problem and the Art of Writing. Through that event, fortune seemed to reveal to us the appropriate title for the subject about which to form the second issue of the Bulletin. However, we soon discovered that the subject could be approached from so. many different points of view, that it became difficult to find its precise limits. Were we going to deal only with the art of writing ? Did we not also have to consider composition in general? Should we discuss only prose? Or poetry as well? And music? Persuasion in all its forms then? Politics· again? What kind of article would be appropriate? Only prose writings? Or would it be proper to include some poetry too? Should we be concerned solely with writings directed to the reason? Or with compositions designed to excite the passions? Our subject seemed to expand and contract; either it encompassed every aspect of human activity, or it reduced itself to the problem of understanding particular compositions. Despite the protean character of our subject, we finally risked giving this issue the title Rhetoric. But we were aware of a necessary restriction: just as the rhetorician employs only the best means of persuasion available on a given occasion, so we must work within the limitations of time and space associated with the publication of a particular issue. The content of this issue might be very different if it had been published a year ago, or if it were published a year from now. Nevertheless, it is our hope that from the many subjects discussed heremusic, poetry, prose, musical analysis, performance, oratory- will emerge some understanding of the elusive art of rhetoric. Some remarks about the word "rhetoric" are appropriate. In ordinary usage "rhetoric" is often associated with persuasion through deception. A "rhetorical" argument is often misunderstood to mean an argument that deceives by means of a devious or "tricky" use of language, or one which attempts to direct the passions · of the audience regardless of the reasonableness of the opinions expressed. This I opinion is based on the fact that rhetoric can be used to change m~n's opinions to the worse by appealing only to their passions ; but this does not imply ~hat it necessarily so used. ·Rhetoric may be the art truth uses to express itself most vividly. The subject of the next issue of the Bulletin will be the mathematical liberal arts : arithmetic, geometry, astronomy and music. H . J. S. T. B. S. Annapolis, Maryland Number 1 January, 1961 Published Quarterly Entered as Second-class matter, February 18, 1949 at the Post Office, at Annapolis, Maryland, under the Act of August 24, 1912. ST. JOHN'S COLLEGE Volume XIII B usiness Secretary H on GRAY Man uscript Editor } AMES F ORRE STE R AMANDA MAYER Table of Contents Co py Editors M ICHAE L H. E LIAS GEORGE KELL DAVID R. SCHILLE R A NDREW GOULD R ichard D . Weigle A Letter to t he Reader T he Problem and the Art of Writing 3 P hrases, Cadences a nd Punctuation 11 P la to 's Gorgias-T he P roblem of Masks 14 Poet ry a nd M adness 17 P rologue to A ntigone, Bertolt Brecht First T ranslat ion into E nglish T heodore Barnes Stinchecum 22 T hree Short Speeches 26 T he Rela tionship Bet ween A nalysis and Performance T he R everend Charles E dward B erger Assistants to the Editors 2 28 On Preachi ng 31 Deligh t in t he Given 33 J acob K lein D ANIEL D EVEREAUX W ILLIAM RANDALL SAL I SBUR Y R esearch Editors MARGERY T URKIN D ouglas Allanbrook R ecording S ecretary ]ACK KAP NER EDWARD L. MATT I SON R ANDOLPH ] ORDAN E YVIND R ONQUIST A RLENE ANDREW J. J. B ODINE MARGARET C ORASICK C H ARLEN FOSBERG R ICHAR D S . FRE IS GEORGE K LADNI K D AVID K RIMINS W ALTER VOI GT J ames Forrester Charles G. Bell Eyvind R onquist TYPISTS MARGARE T CORASICK B ARBARA K ULACKI NATALIE C HAMBLISS MARY SCHENCK ] VD! LAWS MARGARE T CAPRON LYNN KOPKE C AROLE BENJ AMI N R obert K o.fl FACULTY ADVISORY BOARD RICHARD Sc EvA B RANN OFIELD , CLARENCE KRAME R J · WINFRE E S MITH . Chai rman P aul P riest James Taylor SPECIAL ADVISORS Artifice and Accide nts Book R eview : P oetics of J\fusic 36 DOUGLAS ALLANBROOK E VA B RANN LEGAL ADVISOR R. C RESAP DAVI S, Counsel COP YR I GHT 1961, .ST . JOHN ' S COLLEGE -------1____ ___ _ �Jacob Klein 2 A Letter to the Reader "In a way this tradition of ours is not in the books, it is rather the heritage by which we live, the spirit which permea~es ou: thinking and speaking, our attitudes and concerns. This heritage, however, can wither away. It is necessary, then, and on more than one occasion to go back to its sources and to reflect on what they have to say." ST. JOHN'S CATALOGUE For the second successive year the first issue of the Bulletin of St. John's College is in the form of a St. John's review, a publication designed to bring together into one community those presently on the campus ~n~ those w.h~ once were here but are now widely scattered over the country. This issue too .1s m the nature of an experiment, and the editors and I will welcome the reactions and suggestions of former students and friends of the College. The first issue devoted itself to politics and the liberal arts. In the words of the editor, it was "an inquiry into the relationship between a co~muni~y s.uc.h as St. John's and the larger body politic from which i~ come~ and m w?1~h it is bred." The second issue is entitled "Rhetoric." In Aristotle s phrase,. it is concerned with "the available means of persuasion"; it aims to explore vanous forms of communication between man and man, in lyric or epic poetry, in sermon or political address, in musical phrase and cadence. It is proposed that this issue of the Bulletin become a~ annual or se~i-annual periodical. It can succeed only as tutors, students, alurr:m, ~n~ o~her fnend~ contribute articles commentaries, and letters. The Bulletin fails if it cannot, m the fashion of the ~eminar, become a forum to stimulate discuss~on on. the pa~t of its readers. It must create in each reader some sense of belongmg still to this community of learning. The College continues to have a certain obligation to students who have spent one to four years in its halls. This is the obligation to conti~ue.to provide a measure of stimulus so that the tradition of learning as embodied m the books may not wither and die. Occasional visits to the campus, lectures,. a~d co~v~rsa­ tions with faculty members may serve this purpose for those l~vmg w1~hm a reasonable radius of Annapolis. Perhaps to some small extent this Bulletin can reach others at a greater distance so that in them the "spirit which permeates our thinking and speaking, our attitudes and concerns" will remain alive and vigorous. RICHARD D. WEIGLE President ST. JOHN'S COLLEGE The Problem and the Art of Writing· The subject of this lecture is The Problem and the Art of Writing. And that is what I am going to talk about. My real theme, however, the theme that prompts me to deliver this lecture, is-Reading. For what we do here, are supposed to do here, most of the time, isreading. I submit-and I hope you will not mind my saying this-that, on the whole, we do not read too well. There are obviously many reasons for this failure, varying from individual to individual, from circumstance to circumstance. It would be quite a task to try to account for all of them. But there is one reason-one among so many-which is conspicuously noticeable. Reading means, first of all, to face a written text. And it seems to me that we do not sufficiently reflect on what this fact entails, on what writing itself implies or presupposes, and on what it, of necessity, precludes. To talk about Reading leads thus unavoidably to the subject of Writing. Hence this lecture. • In reflecting about writing it is impossible to disregard the spoken word. How could we, indeed? For human speech, this marvel, this greatest marvel perhaps under the sun, is right there, behind or beneath or above the written word. It is difficult (although not impossible) to conceive that there could have been writing without human speech existing in this world. I mean, writing seems to follow speaking. Writing and speaking exhibit, at any rate, common aspects as well as aspects in which they differ. Let me discuss those similarities and differences at some length. The differences are not as clear as one might suppose at first. Speaking, we might say, appears, of necessity, as an audible sequence of sounds, a sequence in time; actual human speech is never available as a whole, while nything written is visibly there at once, in a book or n a piece of paper or a chunk of stone. While reading, en silent reading, takes time, as does the act of writing, a written text, which takes up some space, is present all at once in all its parts. But what about a tape-recorded speech or conversation? Is not the whole right there, on the marked tape? Are not written records of the proceedings, say, in a law court complete in such a way as to project the temporal sequence of all the speaking that goes on into a more or less limited space in which the entire sequence is duplicated, and thus preserved, at once? Such projections, duplications, and preservations, of live speech by means of manual skills or mechanicoelectrical or electronic devices amount to canning processes. The result is indeed canned speech that can be released again into its proper medium by vocal or mechanical or electrical means. The written word, however, is not at all canned speech. The primary cause for the existence of the written word is not the desire to duplicate and to preserve the sound of the spoken word, but the desire to preserve its meaning so that it could be conveyed to others over and over again. \7\Triting tends, therefore, to a shortening of the spoken word, a shortening that manifests itself in a variety of ways. Let us consider this phenomenon in some detail. First of all, any writing is shorthand writing. Any writing will do violence to the sound of the spoken word for, although it cannot help reproducing words, its primary purpose is to convey the meaning of those words. The various methods of writing show that clearly. Chinese characters, as you all know, although they can be read, are drawn not to be read but to be understood without recourse to the medium of sounds. They are appropriately called ideograms. Egyptian hieroglyphics, at least the oldest ones, convey their meaning directly, even though out of them evolved a syllabic and alphabetic script, something that happened to Chinese characters, too. But even alphabetic writing, i.e., writing reproducing the sounds of words with the help of some thirty letters and combinations of letters, can often be *Adapted for the Bulletin from text of lecture presented at St. John's College (1959). �5 4 read only if the meaning is grasped first. This is particularly true in the case of English writing. We would not know how to pronounce, for instance, the assemblage of the three letters B 0 W or R 0 W without the context that gives this assemblage one of its several meanings. The reason for this ambiguity is that the number of letters is not sufficient to indicate the various sounds we are producing while speaking. Although in many cases, as in the examples given, it might be easy to remedy the situation by changing the spelling, it does not seem possible to reproduce in writing the sound of all spoken words with complete faithfulness. And that would probably still be true if we adopted a phonetic system of signs, as the linguists do, unless we multiplied the number of those signs immeasurably. It is rather remarkable that the inadequacy of our sign systems does not really bother us. It is true that something very similar can be said of spoken words (in any language) inasmuch as the same sound may convey different meanings depending on the context, as for example the sounds "spell," "lie" (lye), "die" (dye), or the sound of inflections in nouns and verbs. In cases like those, writing might help to distinguish the meanings, but it does not always do that. The relation of written signs to the sounds of words seems, on the whole, more ambiguous than the relation of those sounds to their meanings. Now, what seems to me significant is that the shortcomings of our character or letter systems appear to reflect the tendency inherent in all writing to shorten the flow of spoken words for the purpose of clarifying and, above all, of preserving their meaning. This shortening is done by reducing the number of the spoken words, by condensing them, as it were, and this in turn is done by selecting and arranging them in a proper way. That is where the problem of writing begins to emerge. Such shortening and condensing cannot be attempted, let alone achieved, unless the whole of what is to be written is in some way present to the writer-I mean the whole as a whole, not necessarily in all its details. In shortening and condensing the spoken word, writing extends the devices by which words and sentences are conjoined in live speech.· The device of shading the meaning of words by inflections or prepositional and adverbial linkages, and above all, the device of combining not only words but whole sentences by means of conjunctions and variations of verbal forms-the sum total of all such devices constitutes what we call the arts and disciplines of Grammar and Syntax. These terms refer to disciplines which are the result of some reflection on the manner of our speaking. It is not without interest to observe that such reflection bore fruit, in other words, that those disciplines took shape, in confrontation with the written word, as the very word "grammar" indicates. But writing itself transforms those grammatical and syntactical devices by applying them on a much larger scale to the whole of a written work. The term "syntax" ( cn!vrn~t<>), in particular, acquires a much more comprehensive meaning. The word means "co-ordering," "putting things together in a certain order," "com-posing." Anticipating the whole of what is to be written down, the writer has to fit the parts of that whole into a proper order. We have a direct pointing to this procedure in the title of Ptolemy's book that we study here: it is called Mathematical C oniposition ( cn!vrn~i" µ,a0.17µ.aTtK~)-"mathematical" in contrast to a possible non-mathematical composition relating to celestial phenomena. But the same term <TVvrn~i" could be applied to all written works. The anticipated whole imposes upon the writer the task of com-posing its parts with the graduated emphasis due to each of them. And just as the devices of such a composition are extensions of syntactical devices (in the restricted sense of the term "syntax"), the devices involved in varying emphases, the devices of articulation, appear to be extensions of grammatical shadings observable even in simple sentences of live speech. The shortening and condensing of spoken words in writing demand, then, modifications and extensions of grammatical and syntactical devices. In writing, the devices of Articulation and Composition add a new dimension above and beyond the one governed by grammatical and syntactical rules. It is in these new devices that the problem of writing resides. That problem can be formulated as follows: how can the anticipated whole be made to unfold itself so as to become an actual whole, that is, in Aristotle's immortal phrase, to become something that has a beginning, a middle, and an end? Right at this point, we see that the term "writing" may be somewhat misleading if it is understood to suggest that the act of writing must be done with some kind of instrument on some visible material. A speech in a political assembly, in an election campaign, or on some other public occasion (a lecture, for example) may well be delivered without any written text, even any written notes ; the speaker could, of course, have prepared his speech beforehand in writing, but he need not have done so; he must, however, have prepared it somehow by thinking about what he is going to say and about how he is going to say it; he must thus have anticipated the whole of his speech and have committed this whole to his memory, again not necessarily in all its details, but in such a way that its composition and it$ Jnain articulations are present to his mind. A speaker of this kind is a writer, too. His rhetorical problem is not different from the problem the writer faces. The speaker's memory is covered, as it were, with the "imprints" of the whole. On the other hand, a letter, a hastily scribbled note, can, on occasion, be something like canned speech, if that letter or note reproduf:es faithfully what would have been said without writing. The distinction, then, between the spoken word and the written word reduces itself to the distinction between saying something spontaneously and saying something in the light of an anticipated whole. Yet, this does not seem sufficient. It could become more meaningful if we looked at the effect speaking or writing may have or may not have on the listener or reader. We all remember a phrase that Horner uses so often when describing human speech, the phrase "winged words" ( i!11w 71"TEp6Evrn ) . Whence this image? In most cases, the phrase occurs when a personage, a god or a man, addresses another single personage, a god or a man. Occasionally it is also used when someone speaks to a group or a crowd of people. Minstrels in Homer are never said to utter or to sing "winged words." Now, words are not called "winged" to indicate their soaring or lofty quality. The image seems rather to imply that words, after escaping the "fence (or barrier) of the teeth" (lpKO<; oS6vTWV)' as Horner puts it, are guided swiftly, and therefore surely, to their destination, the ears and the soul and the understanding of the addressee. \Vords, especially spontaneous words, can indeed be spoken in such a way as to "sink in," as we say. But this possibility grows more uncertain with the growing indefiniteness of the addressee. It is more difficult to reach a crowd of men than a single man. Exertions of a special kind are then required. In writing, the indefiniteness of the addressee becomes almost complete. Live speech is spontaneous, not confined within the boundaries of an anticipated whole, and more often than not endowed with wings. Written speech, visibly put down or invisibly committed to memory, is prepared, composed and articulated as a whole, and may yet lack wings. The problem of writing, then, is: how to ~ive wings to written words so that they may reach their destination, the soul and the understanding of men. To solve this problem, that is, to know how to comose and to articulate words so as to give them wings, to possess the art of writing. However artful the PJposition, some of us, of course, will not be touched the wings. There are no safeguards against that. • In the main, there are two ways in which this problem can be solved. One is : to say explicitly all that is necessarv for the meaning of the written text to be grasped, th~t is, not to omit any link in the chain which binds our understanding, and not to say anything which could disrupt that chain. This kind of composition is conspicuously present in mathematical works, in Euclid, Apollonius, good calculus textbooks, and so forth; it is prevalent in any writing meant to convey to us an understanding of the ways of nature, of nature's structure, of the interlocking of natural phenomena; its traces may be found elsewhere, too, especially in legal writing. The articulation of such works tends to follow the sequence of logical inferences. In fact, it is the reflection on what is implied in this kind of composition that leads to the conception and establishment of a very special art and discipline. This discipline has as its subject that element in human speech, that element of the A6yo'>, which gives it the character of reasoned discourse. It concerns itself with the pure structures of the t\6yo., and bears therefore the name of Logic. Subsequent reflection may make us doubt whether words derived from actual speaking can serve as vehicles of logical inferences. This doubt, in turn, leads to more refined versions of the discipline of logic, leads to what is called today Symbolic Logic. Any writing termed mathematical or scientific is under the spell of the idea of a strictly logical demonstrative discipline that proceeds from accepted premises through a chain of inescapable inferences to irrefutable conclusions. Seldom, if ever, does a composition embody this idea in its purity. The degrees to which this idea is being approximated form a wide range. What interests us here is the character of the wings proper to compositions of this kind. This character is the necessity inherent in our thinking. The other way in which the problem of writing can be solved is quite different. Here what is most important and decisive is not said explicitly at all. Compositions of this kind tend to articulate the whole in such a way as to raise questions about the link that holds them together. It is our answer that will either illuminate the whole or plunge us into further darkness out of which we shall be groping anew for light. Writings of this kind taunt us. The character of the wings proper to them is the taunting presence of a hidden answer, yet of an answer within our reach. In what follows I �7 6 shall try to give examples of this second way of writing. I shall take them from Homer and Plato. But before embarking upon this dangerous enterprise I have to add a not unimportant remark to what I have just said. I said that in the main there are two ways of solving the problem of writing and I have tried to indicate what they were. I said "in the main" because there are-as always-border cases and fringe phenomena in writing that may loom large before our eyes and glow in a peculiar light. Among the oldest cases of writing are, for example, written laws. There are also monuments, themselves something like imprints on the collective memory of mankind, but imprints made visible, and there are inscriptions on them glorifying the deeds of some great man or of some great ruler or of an infamous one. There are epitaphs. There are short poems expressing a mood or a whim, aphorisms, sayings, and proverbs. I omit mentioning other_ examples. (There are too many of them.) We tend to cherish such border cases and fringe phenomena and to devote special attention to them. But I should venture to say that they find their place on the map of writing in terms of coordinates derived from the two main stems of writing I was talking about. • And now, let me turn to the first example of the second of these main stems. Consider the Iliad. Among the great many events that follow each other in the story and the description of which constitutes the whole of the poem, there are certain ones of decisive importance, which are quite familiar to us: (I) the quarrel between Agamemnon and Achilles which leads to Achilles' withdrawing from the fight; (II) the victorious advance of the Trojans; (III) the intervention and death of Patroclus; (IV) the reappearance of Achilles on the field of battle; (V) the death of Hector; (VI) the funeral of Patroclus; (VII) the surrender of Hector's body to Priam. All these decisive events could be put in a diagram as follows: I TIN NY~W ·---------------- -X--:--------.z .z5 J6 ZO ZJ Z:L Z :!! L'f Disregarding the more or less superficial division into books or songs and even allowing for all kinds of tampering with, and dislocations of, the original text, there is no denying that the decisive events are crowded into the last third of the whole. Between (I) and (II) events of great significance certainly do occur, as for example, the death and the wounding of many and important warriors, the Diomedean terror, the wounding of two gods, the encounter of Diomedes and Glaucus, the peaceful scenes in Troy, the unsuccessful embassy to Achilles, inconclusive duels among men and delightfully treacherous actions on the part of the gods-all of which contribute in varying degrees to the unfolding plot. In the main, however, the battle is swaying back and forth all the time until finally the Trojans reach the ships of the Achaeans. During all that time Achilles sits in his tent, sulking, and only occasionally watching the fight. The pivotal event, the death of Patroclus, which changes, which reverses everything, occurs very late in the poem, in the sixteenth book. It is as if the poem took an exceedingly long breath to reach that point and afterwards rushed with breathtaking speed to its end. This is the more remarkable since the entire period of time the poem encompasses is one of 49 days and Patroclus' death occurs on the 26th day, that is, very nearly in the middle of that period. Why is the composition articulated in such an unbalanced way, we wonder. Let us see. There are two events-among many others-which I have not mentioned at all. Yet it is these two events that seem to be the two foci from which all light dispersed throughout the poem stems. The first takes place when Thetis, Achilles' mother, is visiting Zeus to ask for his help on behalf of her son, reminding Zeus of the help he once received from her. She wants Zeus to turn the scales of the war, to let the Trojans have the upper hand until finally, in the hour of the Achaeans' greatest peril, Achilles, and only Achilles, might be able to save them from certain defeat, lead them to victory, and thus regain his honor, which he allegedly lost through Agamemnon's action. It is then said (I, 511-12) : "But Zeus, the cloud-gatherer, said nothing at all to her and sat in silence for a long while ( 8~v) ." An awful silence! Thetis repeats her plea. At last, Zeus consents and nods, a sign of an irrevocable decision. Olympus shakes. Thetis departs, apparently satisfied that she has accomplished her mission. Has she? The second event occurs after Patroclus' death (XVIII, 165-229), while the battle for Patroclus' body rages before the ships between Hector and the Aiantes and while Thetis is on her way to get new arms for her son from Hephaestus. Hera sends Iris to Achilles, without Zeus and the other gods knowing anything about this mission, to urge Achilles to intervene in the struggle for Patroclus' body. Since Achilles has no arms at this juncture, he is asked by Iris to do nothing but to show himself to the Trojans, to frighten them by his mere appearance. Achilles, "dear to Zeus" (203), obeys and does more than what Hera through Iris asked him to do. Pallas Athene, who is nearby, does her share: she casts the tasseled aegis around his shoulders and she sets a crown in the guise of a golden cloud about his head and from it issues a blazing flame. Thus he appears-alone, separated from the other Achaeans-in the sight of the foe, a flaming torch. But not only does he appear, he shouts, three times, a terrible shout, clearly heard-and "from afar Pallas Athene uttered her voice" (217-18). Unspeakable confusion and terror seizes the Trojans. Patroclus' body is saved. What kind of shout is this? Is it one of triumph? Of threat? Is it an ordinary war cry, raised to a very high pitch? It is certainly not like the bellowing of the wounded Ares ( V, 859, 863) . Two verbs are used to describe that shout, one of a rather neutral taint, and, at the decisive moment, another, 1&.xw (228), which has a range of meanings. One of these meanings is "crying out in grief." Shortly before (29) the same verb was used in precisely this meaning to describe the lament of the maidens at the news of Patroclus' death. It will be repeated shortly afterwards (XIX, 41) to describe Achilles' shouting when he rouses the Achaeans to battle. Why does Achilles shout now, though not urged to do so by Iris? Certainly, to frighten the Trojans, to make them desist from Patroclus' body. But can this shouting fail to express the unspeakable pain that fills his heart, the pain which had just brought his mother to him from the depth of the sea? Here indeed is a terrible sight to behold : a man raised to his highest glory by Pallas Athene, wearing the aegis, crowned by flames, radiant, truly god-like-and this same man crushed by grief, miserable in his awareness of having himself brought the immensity of this grief upon himself. The apotheosis of Achilles is the seal of his doom. And it is his voice, his brazen voice (XVIII, 222), his terrible shouting, which brings terror to the foe, that expresses his misery and his doom. Pallas Athene's voice seems but a weak echo of that of Achilles or is even completely drowned out by the latter's intensity. But are not these two events related? I 1 II JII . TIZ "SL ~W -----------------'----j[----18-- ' .z~ Does not Achilles' shout sonorously echo Zeus' silence? Can we not guess now why Zeus remained silent for a long while? Surely, he had to take account of the susceptibilities of his wife, as any husband would-and in his marital relations Zeus is no exception-but is it only Hera whom he was silently thinking about? Must he not have been concerned about the whimsical nature of Achilles' plight and Thetis' plea? And, on the other hand, how could he have refused to satisfy Thetis in whose debt he was? Is it not right then and there that Zeus decided, in wisdom and sadness, irrevocably too, to accede to Thetis' demand, to give honor and glory to Achilles, but to do that in a manner which neither Thetis nor Achilles suspected? The long stretch of the poem which corresponds to Achilles' inactivity fills Zeus' silence. While the tide of the battle is being reversed, Patroclus' approaching death is announced twice (VIII, 476; XV, 64-7), the steps which lead to it are carefully pointed out (XI, 604, 790-804, especially 792-3). Achilles will get what he wants, but at the price of the greatest loss he could suffer-the loss of his beloved friend, his other self (XVIII, 7982). In the hour of his triumph he will be the most miserable of men. The ways of Zeus are as wise as they are crooked. Zeus does not know about Iris' mission. But do the strong-headed and light-minded goddesses, Hera and Pallas Athene, know what is going on? They do not, nor does Achilles' mother (XVIII, 74-5) . While Pallas Athene transfigures Achilles into a god, Achilles is mortified. He has grasped Zeus' intent. He says himself (XVIII, 328) : "Not all the thoughts of men does Zeus fulfill" ; as Homer has said before (XVI, 250-2), commenting on Achilles' prayer before the slaying of Patroclus: "One thing the father granted him, the other he denied." Zeus denied him the safe return of Patroclus. He denied it for Achilles' true glory's sake. For, as Zeus confides to Poseidon, mortal men are his concern even in their perishing (XX, 21). That is what neither Hera nor Pallas Athene understand. Hera does not understand the biting irony of Zeus' remark to her (XVIII, 357-9): "Well, then, you have accomplished this, you have aroused Achilles �8 9 fleet of foot. Verily, the flowing-haired Achaeans must be your children." Achilles' suffering at the moment of his triumph is Achilles' own. It cannot be matched by anything on Olympus. It is as much the prerogative of a mortal as it is the attribute of a hero. Homer is the teacher no less of Aeschylus than he is oLPlato. This, then, is one example of the way in which a piece of writing taunts us to understand what is being said not in so many words, but through the articulation and composition of the whole. The answer I have given may not be the right one or may not suffice. It is up to you to find a better one. • Let us turn to the second example, Plato's Phaedrus. This example has the virtue of being not _only an example of writing, but also a piece of writing the main theme of which is writing itself. The two people who do the talking in this dialogue are Socrates and Phaedrus. Phaedrus is a young man who loves passionately everything connected with words. He is a cf>i/..O)wyo> and so is Socrates. The conversation is between two lovers of words and takes place, on a summer day, outside the walls of Athens, near a cool brook, under the shade of a tree in which cicadas make a continuous and, I suppose, sometimes deafening noise. The dialogue is divided as follows : there is an introductory part which I shall omit, although it is highly significant. Then there are two clearly distinguishable parts as follows : ~ !J's. / JI The whole dialogue is framed, as it were, by two figures. One is Lysias, a famous speech-writer, who, at the very beginning of the dialogue, appears on the scene in the most suitable mask, to wit, as the scroll in Phaedrus' left hand. (The scroll contains a speech written by Lylsias.) Lysias remains present in that guise (although presumably not always in Phaedrus' left hand) throughout the entire dialogue. The other figure is Isocrates, another famous speech-writer, who is conjured up by Phaedrus and given stature and dignity by Socrates at the very end of the dialogue. One emerges as a past master of bad writing and the other as full of promise of becoming a writer of superior standing. Between these two extremes Phaedrus is confronted with the problem of Speaking and Writingand so are we. In the first part, three speeches are heard, the one written by Lysias and read by Phaedrus, the other two spoken by Socrates who keeps attributing their authorship variously to somebody he cannot remember, or to the local deities, the Nymphs and Pan, or to the poet Stesichorus, or to the cicadas, or to Phaedrus. The two speeches spoken by Socrates are, at any rate, painstakingly elaborate, and, if they are not to be taken strictly as written speeches, can hardly be conceived as improvised unless, indeed, they are "inspired," that is, dictated by divine or superior powers. Lysias' speech is the plea of a man to a young boy, in which it is contended that it is better to favor a nonlover than a lover. Phaedrus considers it a wonderful speech, "charming," as he would say today. Socrates finds plenty of faults in it and proceeds to deliver a better speech on the same theme, except that this speech blames the lover and stops short at the point where it is supposed to begin praising the non-lover. Phaedrus does not succeed in making Socrates finish that speech. It remains truncated. Instead, Socrates, by way of recantation-because he has offended Love-delivers another speech in praise of Love. This speech, the most eloquent, occupies the middle part of the dialogue and is spoken by Socrates while the sun goes through its highest course. There is a definite change in the tenor of the dialogue after the speeches are done with, and this changed tenor persists throughout the second part. The conspicuous difference in the tenor of the two parts poses the problem of the dialogue's composition. Socrates and Phaedrus begin to speak, quietly and soberly, about the spoken and written word and continue doing so until the very end of the dialogue. Phaedrus agrees with Socrates that the real problem concerning writing is to distinguish good writing from bad writing and is ready to embark on a discussion of this subject. It is here (258E-259D) that Socrates calls Phaedrus' attention to the cicadas over their heads. He tells a story about their origin : they were once human beings, even before there were Muses; now, in their present form, so says Socrates, they are supposed to report to the Muses and to tell them who among men honors whom among the Muses; they are watching, says Socrates, him and Phaedrus now, at noontime, and if they see both talking to each other and not asleep<like sheep and most men-they might be pleased and ,report accordingly. The question arises: why does Socrates tell this marvelous and fantastic story of the cicadas' origin and nature at this moment? It seems to be done to underscore that, from now on, Phaedrus and Socrates, instead of exchanging elaborate speeches, that is, written or dictated words, will, in leisurely and sober fashion, converse about speech-making and :speech-writing and thus restore to the spoken word its proper and unchallengeable function. The trouble is that Socrates' tale interrupts this sober conversation. And let us not forget that this sober conversation is embodied in a written text. In what follows, we witness the previous speeches being criticized and analyzed. The beginning of Lysias' speech is subjected to a special scrutiny. And in the course of it this beginning of Lysias' speech is made to repeat itself, twice (262E; 263E-264A), word for word. VI/ e hear Socrates interpreting freely the speeches he himself made, assuming the role of the.ir "father," so freely indeed that they appear somewhat changed : the doubtful is omitted, the wording is modified, additions are made (264E ff.). It is Socrates' way of supporting and defending the truth they might contain. \Ve observe Socrates and Phaedrus bearing down on various books which claim to teach the art of speaking. Phaedrus, the "lover of the Muses," is not altogether satisfied with this kind of conversation which he describes as "somewhat bare" (262C). At the crucial point, when the discussion seems to revert to the problem of good and bad writing ( 274 B) , it "is again interrupted by Socrates. He suddenly asks : "Do you know in what way you would best please divinity in the matter of words, either in making speeches or talking about them?" Phaedrus replies : "I certainly do not. Do you?" Socrates: "A tale, no more, I can tell from hearsay, a tale that has come down from our fore-fathers ; as to the knowledge of the truth, it is theirs alone." And Socrates casually adds : "But should we ourselves find this truth, would any human fancy or opinion ( 86~aap.a) about it still be of any concern to us?" To which Phaedrus replies: "A ridiculous question!" Urged by Phaedrus to report what he heard, Socrates proceeds to tell the tale of Theuth and Th~mous, legendary Egyptian personages, a tale in which Theuth is reported to have invented letters, and thereby writing, and to have presented this invention to the god-king Thamous. I shall read now what Thamous, according to Socrates, says (274E-275B): "Most artful Theuth, one man has the ability to beget artful things, another the ability to judge of their usefulness or harmfulness to their users ; and now you, who are the father of letters, have been led by your affection to ascribe to them a power the opposite of that which they possess. For this invention will produce forgetfulness in the minds of those who learn to use it, because they will neglect their memory, inasmuch as their trust ·in writing will make them recollect by means of external marks which are no part of themselves and will not make them recollect from within through their own effort. You have thus discovered an aid not to memory but to reminding. And you give to those who learn not truth but merely the appearance of wisdom : they will become acquainted with many things without proper teaching and will seem to know, while remaining for the most part ignorant and hard to get along with siuce, instead of getting wise, they will merely have acquired the reputation of being wise." We should not forget that this is a tale and that we have been warned by Socrates: hearsay is no substitu,fion . for our own discovery of .the truth. Again, we should not forget that this tale presents itself to us as a written text which, according to the very content of the tale, cannot be relied upon without proper teaching. Neither should we forget that the discussion of the problem of good and bad writing has, once more, been successfully interrupted. What follows in the written text is a description of writing that makes it appear a playful thing, undertaken for "amusement's sake" (276B-D). One cannot expect written words to be serious. For, as Socrates says (275D), "you would think that they (the written words) speak as if they had understanding, but should you, from a desire to learn, ask -them anything about what they say, they do nothing but repeat always one and the same thing." They cannot, therefore, defend themselves against misunderstanding and abuse. Furthermore, they cannot and do not discriminate between those to whom they speak. Any author who holds that there could be much solidity and clarity in his written work, whatever its subject, deserves to be blamed for that, regardless of whether there is anyone to voice the blame or not (277D-E; 275C). ·what, then, about the distinction between good and bad writing that Socrates and Phaedrus set out to discuss? Nothing is said about it. The answer to that question has been-of necessity, it seems-playfully �Douglas Allanbrook_ 10 withheld. Still, whatever has been said about the problem of writing has been enacted in the dialogue. The repetitiousness of the written word, its inability to defend itself, the superiority of the spoken word in spontaneous conversation which interprets with understanding what was written down-all that has been enacted by Socrates and Phaedrus in the dialogue. Must we not continue the conversation to solve the problem of good writing, to find the answer which was not stated in the dialogue? And does not precisely the Phaedrus, as it is written, offer an example of how good writing can be done? • I have a few concluding remarks. Is Plato right in attributing superiority to the spoken word, to any conversation in which winged words can be exchanged spontaneously? There is a point at which this superiority seems to disappear altogether. A most remarkable similarity obtains between words, spoken words of live speech, and money, money, that is, available in coins and bills. Both are precious, both circulate freely, coins and bills from hand to hand, words from mouth to mouth. The imprints on coins and bills are gradually erased, effaced, rubbed off, just as the meanings of words seem to become fuzzy, blurred and empty with the passage of time. There is even counterfeiting in language as there is in money. Human speech, that greatest marvel perhaps under the sun, can and does indeed deteriorate to an extent which renders it obnoxious and totally wingless. It is at this point that the written word may come to its rescue. As we so aptly say, words can be "coined." This happens both ways : words can be coined in support of cliches, fostering and increasing the ever-present tendency to diminish the vigor and meaning of speech ; but words can also be coined afresh. In a letter to a friend, Virgil, a writer, says that he gives birth to verses in the manner of bears and according to their custom ( parere se versus modo atque ritu ursino), that is to say, that he handles his verses the way the mother bear handles her newly born cub: assiduously and persistently she licks it into its proper shape. Such assiduous work, performed on the written word and undertaken to assure the right articulation of a composed whole, can and does restore and preserve the integrity of human speech. It is thus that the written word repays its eternal debt to the spoken word. 11 Phrases, Cadences, and Punctuation It is always a bit distressing to find that a discussion on Poetics degenerates into talk about the meaning of meaning. It is quite literally meaningless to talk of the "meaning" of a sonnet when one leaves out what its words are saying, or in any context to talk about the "meaning" of a fugue. The truly pathetic fallacy consists in ascribing meaning and knowledge to that which moves us by its beauty of articulation, certainly a more serious and deep-reaching mistake than the lovely simplicity which finds its mood reflected or mirrored in a sunset. That we are moved means no more than that we are moved; the illusion enters when we say we are moved and that therefore something has become clearer or even known. To be sure, we are often profoundly moved when we do grasp something; however, the proposition is by no means reversible. Our terror or joy before nothing or before the cosmos, in front of beauty or ugliness, are admissions of our human state of ignorance, and if there be any jump from such moments it must be that of faith and not that of knowledge. It is perhaps more pertinent to point out with La Rochefoucauld that we are generally prouder of our tastes than of our insights in such matters. One of the reasons for this deep confusion probably lies, as far as the talk about Poetics is concerned, in the fact that speech (the expression and communication of thought), poetry as such, music, and dance are all articulated upon the same underlying ground. It is hardly a coincidence that we use such words as "poetic feet," "up" and "down" beats, or the eloquent Latin terms Elevatio, and Depositio to describe the pulsing life of any of the temporal arts. Certainly one part of the study of Poetics is entirely involved with the arrangen;ient and orders and articulations of this most basic and musical element of those made wonders that pass before us in splendor. All of these temporal arts are arts of movement, whether these movements be of the body or of the soul. The word "soul" is a peculiarly poetic word in certain languages, referring as it does to the midriff, the seat of the breath, the wind that animates. If one says, at least in English or any other language of stress, that the accent is the soul of the word, one is at the heart of this poetic discussion . The accent, after all, delineates and defines the breathed and spoken reality of the word, it orders its parts into an identifiable unit and is essential to its use in any formal and musical structure. It is the order of the musical flow in its smallest nodule. Rhythm, the ordering of movement, is the common link among all of the temporal arts. 1 A syllable by itself is no more "musical" than a single note ; their combination in time by the ratios of rhythm is the beginning of the music. These arts then are all "cinematic." They all unwind in time in combinations of "feet." Often there is present a regular clicking by of events as in the case of the discrete, discontinuous, and regular motion of the frames of a moving picture. This as such is no more a musical phenomenon than the division into the meters of triple or duple measures in written musical notation is per se a rhythmic one. Ordered motion goes from here to there, from up to down ; in any context, large or small, it has (so simple to say and yet not at all banal) a beginning, a middle, and an end. Its order is that of something becoming in time; when it is over it has become, and only then is it anything. It is opposed to the anarchy of chance events, but is just as opposed to anything eternal. There is nothing in it to convince the intellect, and there is everything present to captivate the heart. To forget this distinction is to deny proper glory and to reduce Poetics to the namby-pamby world which makes no distinctions, a world which begins with the over-stuffed comfort of ascribing transcendence to everything which moves it, and ends in the hot-house of despair. The deception partly lies in the articulating character 1 "But the diction which is without rhythm is indefinite. It is necessary, however, that it should be bounded, though not by metre. For the infinite is unpleasant and unknown, and all things are bounded by number. The number of the figure of diction is rhythm." Aristotle, Rhetoric, III, 7. �~2 I I il I~ ~I ~· 11 .I I of the rhythmic order. The word app.ovla (the modern "harmony") means a fitting together, a joint, a union, also a decree, an intonation, an agreement, a certain temper. The modern use of the word "harmony" in the art of tonal music certainly reflects this old definition. Triads, themselves harmonious consonances based on the very nature of vibrating bodies, are used rhythmically in combinations which articulate phrases, phrase members, periods, period groups, and whole compositions. It is an art particularly rich in cadence formulas. A cadence may be "perfect" if the dominant chord goes where expected and the motion begun is fulfilled as expected. A cadence is "deceptive" if the dominant chord moves not to the polarizing center, the tonic, but to the chord on the sixth degree, and the motion begun is delayed or swerved from its goal. This might seem exactly like the difference between saying "star-spangled banner" and "star-spangled banana," but it is only a crude analogy. The likeness lies in the organization of a certain segment of time and the surprise that hits us at the end of that segment. The real difference lies in the fact that entirely different faculties are behind the surprise. The articulations of thought can be, perhaps, only expressed in the rhythmic articulations of language. A rhetorical syllogism, pounding through the majesty of its three-part rhythmic form, is no more than sounding brass and is indeed much less specious and more glorious when detached entirely from the balky words, and moves in freedom in the amoral realm of notes, barlines, flutes, and fiddles. Words have a double life; notes do not. Notes convince the heart, which delights in harmony, but they can hardly lie; they can only fail to move. The words "colon," "comma," and "period" are terms of ,punctuation. There are perhaps grammatical rules for their use, rules often governed by thought and its divisions into parts as expressed in language. There is immediate difficulty with this understanding of "punctuation" in examining, say, the punctuation used in the folios of Shakespeare. "Comma" comes from Kop.p.a, a chip, or a cut, that which is struck, the stamp of a coin, hence a short clause-the first organized group above a basic foot. It refers to the grouping of words itself and not to the sign which will set off the group. A Kw>..011 (colon) is a limb, a member or a part of anything, hence a member or a clause of a sentence. IlEpfollo> (period) is a going round, a circuit, a map, a period of time, the orbit of a heavenly body, and hence a wellrounded sentence. Aristotle says in the Rhetoric that a 7rEp£ollo> (period) is the kind of speech that has in the 13 beginning the end in view. Periods are composed of articulated members of Kw>..a (colons) . The Kw>..a, or members, resemble the stones which support and hold together a vaulted dome, to quote from another classic study of poetics. 2 The proper length for these members is generally felt by Aristotle to be governed by the amount of breath. Measure is without measure if we run out of breath, and it would be merely frantic if all of our members were gasped out breathlessly. Certainly hexameters are for heroes, and nicely modulated triplets are fit for sirens, but the numbers must be nicely modulated to fit, and the modulation depends precisely on the most human limitation of breath. These terms seem to refer essentially to the musical art which is composed of breath-lengths. Kop.p.ara (commas) are the first articulations of long and short syllables into rhythmic parts. In English these parts are made from stressed and non-stressed syllables; in modern music they are the distinguishable cuts or fragments or motives ; in plain chant they are the pneumes. The Kw>..a are the lengths of breath which will number the first cuts or Kop.p.ara and the 7rEplollol (periods) are the rounding of groups of these complete breaths into an harmonious whole. The whole of the period in discourse is grasped by the mind if the discourse is not nonsense. The whole of the period in "poetics" or music or whatever we may call it is delineated and brought before us by cadences or falling points. Our emotion, our delight, or our boredom is dictated by the elegance of the proportions and is made possible by the most human limits of our bodies themselves-hearts, lungs, and the straight-standing spinal cord. It is a particular and most human delight to be moved by lengths and proportions which have as their material the imitation of our very breathing and which pulse like the warm red heart. The making of these marvels in time is under number ; they consist of parts and balances and the most delicate punctuations and are memorable because of this. They can be retained or said, recited or played many times over without the diminishing of delight. They are never departed from in their cherished reality. To state it a bit more formally, they are not, insofar as they are musical, symbolic. They point to nothing beyond themselves. They are lesser miracles, these musical things, than words and the crux of the poetic fallacy would be to consider them as playing any part in the highest faculties of substitution and transposition which are involved in thought with words and symbols. 2 Demetrius (345-283 B.C.), On Style. The century of those two musical divinities, Bach and Mozart, whatever its failings may have been, kept this distinction clear. The view of music as expressing the will of the world, the aesthetic and Hegelian notion of its symbolizing the reality of what has become, not only reduces the art to nonsense but, more gravely, it eliminates the simplest and the most common understanding of every-day talk. The profundity of emotion in the Beethoven Ninth Symphony lies in the first three parts of the piece-not in its finale, where the "notes" take over to express the ineffable, which is unspeakable. Philosophic talk of any subtlety whatsoever is always involved in the irony of this double nature of words. Mathematicians and musicians have no such ironies. Poets are often embarrassed by words and should prefer them to be cages for the capture of the uncatchable, and they envy the musician his so-called "pure" notes. Any philosophic attack on poetry is never an attack on its power or its beauty; it is, on the contrary, always made with a poignant awareness of this power and beauty. The philosophic ire in its presence is always to be understood as impatience with its assumption of pointing at anything except itself. The irony is intensified by the necessity of pointing out this fallacy as well as possible-in other words, of moving and convincing the thoughtful by using the very means of poetry. Music is a part of us and our thoughts are breathed through it. The attempt to talk seriously in mathematical language about important things is only depressing, and if the talk is about us, it also does a real violence to our natures. The double work of words corresponds to our paradoxical condition, suspended as we are between two ·unknowns and yet still able to talk. ·wholes have parts in time because of articulation. The parts are of various lengths but are under the limits of breath. The ends of parts are delineated by special kinds of down beats : in modern music, cadences; in verse, structures by special artifices of perhaps rhymed down beats at the ends of lines; in prose and speech by definite articulations of stress and pitch at the end of the thought being expressed. These cuts and commas, phrases and Kw>..a, sentences and periods are present in all speech and prose, in all verse and dancing, in all singing and instrumental music. The temporal arts in this sense are one art of articulated breath lengths, taking as their unit the warm pulse of the heart, and ordering and ennobling these lengths and breaths as the spinal cord rules straight the flux of our flesh and our nerves. This is an art which can make memorable, which can move deeply. The memory here is not a memory of anything pointed at, or of any relation of parts in the world. The memory here is of the music and of the movement inseparable from it. This is its glory, a particularly human glory-alive, pulsing, non-abstract, non-transcendent. This power and eloquence is not thought, nor is it under a real faculty of the mind. It has more to do with the middle of us. Words can and indeed must partake of this "music" ; otherwise speech would hardly be human. It would indeed become a "formula" rather than a mobile "form." The words as such, however, the stones of the rhythmic structure, are not like notes, but are far greater things. Their prior dignity and true meaning must harness the music, punctuate its length, sit as a pilot with a wary but passionate eye at the top of the spinal cord. �James Forrester Plato's Gorgias The Problem of Masks Last year a small group of people began a joint attempt to explicate Plato's dialogue, the Gorgias. It soon became apparent that the group as a whole could not issue a meaningful report, that everybody had his own ideas about the dialogue. The fault (if one can call it that) lay in the Gorgias itself; what seemed simple became on close analysis fantastically complicated. The dialogue by its nature admits only of minority reports stemming, probably, half from Socratic discourse and half from one's personal prejudices. What, then, is so strange about the Gorgias'! At first glance, nothing. Socrates, in his familiar role of master dialectician, tries to make the famous rhetorician Gorgias give an account of his occupation. When, after a period of Socratic questioning, Gorgias becomes ashamed of certain unpleasant facets of rhetoric, he is quickly caught up in contradictions. His disciple, Polus, takes up the argument. He too is refuted after he becomes ashamed of some of the beliefs necessary to a rhetorician. Then yet another, Callicles, breaks into the conversation, angrily denouncing Socrates and his dialectic, and almost as angrily deploring the shame of Gorgias and Polus. The question-and-answer begins again, Callicles makes a few ad~issions, and the last objector is reduced to a petulant silence. Socrates goes on to defend his calling, ending with a myth and a plea for the practice of virtue. That was the first glance. At second glance, some rather strange aspects of the dialogue come to light. The chief of these is the answer to a simple question : "Who is Socrates?" One member of the seminar provided a memorable image when he suggested that all the characters were masked but that Socrates wore the strangest mask of all: himself. Socrates gives a rhetorical formulation to what are sometimes considered his favorite doctrines. He engages in long speeches and a long myth while restricting the professed rhetoricians to short answers to his questions. Those questions take advantage of the shame of a man, rather than of facts that must be admitted by all men. He advertises dialectic with glowing words, which would seem unnecessary in view of his statement that truth can never be refuted. 1 In short, Socrates, the hero of dialectic, vanquishes rhetoricians on a dialectical question (the good of an.object)-by means of rhetoric! This Socrates surely is not the "master dialectician" referred to earlier. Who then is he? The dialogue is not simple; neither are the characters. Socrates' first question of Gorgias is to ask him who he is. And through questions and answers, silence and expostulations, the person of Gorgias as well as those of the others emerges. Gorgias himself is a virtuoso rhetorician and probably somewhat of an innovator; but he does not realize that his new rhetoric is antithetical to common values. He seems a decent sort. Polus, his disciple, is really just a camp follower. He has imbibed the system whole, substituting it for common values, but he seems not to have considered what he has accepted. As is usual in such cases, he has written a book on the subject. Callicles is of hardier stuff. He is quite aware of the implications of rhetoric, and he will not shrink from them. Socrates says Callicles is a touchstone against which he can test the mettle of his own soul. 2 Although there is, of course, no way of telling when Socrates is serious, so subtle and allpervading is his irony, nonetheless I would contend that this estimation of Callicles' worth is made in all earnestness. Then one can conclude that the two large figures in the dialogue are Socrates and Callicles. The others can be found between the poles created by these two. 1 Gorgias, 473 B. 2 Ibid., 486 D. Socrates gives a clue to the dissimilarity between himself and Callicles even before the latter bursts into the argument. Socrates tells Polus that rhetoric is not an art ( rtxv71) but a flattery ( KoAaK£[a). He sets up four flatteries : cooking, clothing, rhetoric, and sophistry; and he then gives the corresponding arts of medicine, gymnastic, justice, and legislation. Socrates, who has introduced the terms "art" and "flattery" to the argument as contradictories, must then define these terms. He says he will not call any irrational ( O'.A.oyov) thing an art. It seems fairly safe to define "flattery" Socratically as an irrational undertaking which aims at the pleasant and "art" as a rational undertaking which aims at the good. 3 In other words, Socrates' "flatteries" are phenomena of aesthetics, his "arts" phenomena of ethics. (One might term the difference that between fine and liberal arts.) The musical orgies of a Wagner are, Socratically speaking, flatteries, which find their counterpart in the art of mathematical music best exemplified by Pythagoras. In the same way one can set Michelangelo, who shaped matter into pleasing form, against Lavoisier, who analyzed matter in its essence. And the problem is no more "just" that of rhetoric versus dialectic· for the giant question of ethics versus aesthetics has been introduced. It is on such a question that men can well divide. And he who holds to either ethics or aesthetics wholeheartedly has grasped no small thing. He has assumed a truly polar position-naturally to the exclusion of the other pole. Socrates is plainly on the side of his rational art and ethics. Callicles, on the other hand, seeks pleasure. The flattery of rhetoric is useful to him in seeking advancement in the state; and for him even the state evidently exists for the pleasure (or lack of pain) of man. The Socratic state aims at the good; its features are justice and order-in a word, rationality. The Calliclean state, on the other hand, is a disordered complex through which a man flatters and advances. It aims at pleasure. So, it is plain, does Callicles. The only question is how steadfastly Callicles will hold to his aesthetics. A bit of word-play might be interesting here. As a seeker of pleasure, Callicles as a conscious man would be a seeker of beauty. Then as beauty ( kalon) is to good ( agathon), so is Callicles to Agathocles. And who is this Agathocles, who goes with good as Callicles goes with beauty? Agathocles is the given name of Plato. One is left with the question of whether this is mere wordplay or whether it might possibly be a significant hint dropped by the author of the Gorgias. With Plato, as with Socrates, one is never quite sure what is seriously intended. With the word "beauty," just as with "art" and "flattery," Socrates has given a definition before Callicles even enters the rhetorical arena. Socrates calls beauty a mixture of pleasure and good4 (to which Polus, with his usual perspicacity, agrees!). This gives Socrates the right to make comparisons in beauty between two objects, for good is a dialectical term and admits of degrees, even though pleasure is an irrational. That is, Socrates, once Polus has admitted that doing injustice is less beautiful than suffering it and that physical pain in the former case is no more than in the latter forces the conclusion that doing injustice must be les~ good than suffering it. 5 If Polus had admitted the last statement and the minor premise, Socrates likewise could have forced admission of the first-that in terms of beauty. But Callicles is at a disadvantage here, for he can admit no absolute good admitting of degrees. He must judge beauty, as Socrates has flattery, to be an irrational without standard of comparison. Otherwise, he would admit the primacy of rationality and be fair meat for the dialectical appetite of a Socrates. Callicles, in short, is helpless in rational argumenteven in questions of beauty. For he can make no statements of comparison and back them up rationally. He can say that a is fouler than b-but cannot back up his assertion nor break down a contrary assertion by Socrates. He can speak of the "better" people-but cannot give an inclusive definition. From the moment he enters the argument-indeed, from the fact that he enters the argument-he has been almost fated to lose. Is there then no utility in aesthetics ? Where does Callicles triumph over Socrates? Possibly, just possibly, in the state. Socrates, the "artist," saw the state as "art" and himself consequently as the only true statesman. Callicles, on the other hand, saw the state as a "flattery." Socrates' Apology to the Athenian state is an attempt to touch a rationale in that state-to find in it a form of his republic, no matter how degenerate. Historically, the apology failed: Socrates was put to death. It would seem that, as far as Athens is concerned, Callicles had his triumph. What is this strange pseudo-dialectic going on between the two poles of the dialogue, Callicles and Soc- "Ibid., 464 B-466 A, for references in this paragraph. •Ibid., 474 D. •Ibid., 475 D. �Charles rates? It is first a Socratic probing for C;i.llicles' weak-. nesses, an attempt to pierce Callicles' aesthetic armor. If Callicles ever goes along with the argument, he· is lost. He does not, and so he is not. He gives his only· possible response to a demonstration: "Nonsense!" Even Plato's editors can see the results. At the head of one page of his translation:; Benjamin Jowett puts the heading "Socrates grows more and more· ironical." 6 Socrates, the ethical man, has ·a relationship ~mly in irony to the man of aesthetics, Callicles. Not that the relation involves contempt! Socrates evidently reserved his contempt for such wishy-washy, unconscious people as Polus. Callicles is rather the touchstone and thus worthy of respect. But what ·is the itonic relationship? Irony implies a duality, a hidden struggle within words. The relation itself is then an immense ethical concern for Callicles as existing individual, coupled with an immense ethical lack of concern for Callicles' aesthetic!>. Because Callicles' beliefs are so far from his own, and in fact differ in kind, Socrates can dismiss them-for, as an ethical man, he must, of course, support the primacy of ethics. But as for· Callicles himself, Socrates must, again as an ethical man, recognize another fully;conscibus human being with which he must be passionately concerned. Andthe by-play between immense concern and immense lack of concern in Socrates' 'words is the duality in words known as irony. Dialectic has broken down completely with Callicles, who cannot be convinced. The most he can say is that the statements of Socrates seem right but unbelievable. What is left to Socrates but rhetoric-rhetoric for the. good ! This would seem to be. Socrates' attempt to make beauty-to poetize-after his own principles. For what is he doing but synthesizing the· good and the· pleasurable? And this synthesis is defined by him as beauty, as has been said. And the dialogue ends with a myth-a beautiful myth. One translator says that many students flocked to Plato after he published the Gorgias7-many pe'ople evidently were convinced of reason by irrationality. A strange story, this. Plato in writing the dialogue acts as does Socrates inside: both weave rhetorical nets to capture men for the sake of dialectic. Plato had his irony, as did Socrates. One can picture the author of the Gorgias welcoming, yet secretly laughing at the young men passionately convinced by Socratic rhetoric of the value of dialectic. One can also imagine Plato laughing in limbo at this paper. And here the masks enter once more. About the Gorgias one can do almost anything-in conjecture. All that is sure is that the figures are hooded: Gorgias, Callicles, Socrates-yes, and Plato. 6 7 Jowett, Dialogues of Plato, Vol. I., p. 551_, Random House. Lamb, Intr. to Gorgias, Loeb Class1cal Library, p. 250. l t· 1 G. Bell • Poetry and Madness . : . the modern abstract has been the expression of man reduced from humanity to function or confronted with that reduction, of nature desiccated out of organic interplay to symbolic paradigm. In this exploration the first and greatest found triumphant calling. The followers pursued where they could not lead, beginning in the void where they were born. That was n;iore and more the smart place to reside. They also talked of new directions and called themselves leaders. It was Golaud offering guidance to Melisande: "Venez avec moi. . . ." "Ou allezvous ?" And he: "J e ne sais pas .... J e suis perdu aussi. ... " The paradox of the lost guide. Cassandra mad to reveal and her revelation mad. . . . Most of our poets, it is clear, have felt they were living in a lost age, a time of disruption and despair, that life in such a period was fever and disease, that their own fragmentations, fixations, auto-eroticisms, what else, were somehow expressive-provided they were obscured and subtilized to the level of the symbolic .abstract-of the general fragmentation and neurosis .... But the time of reversal is at hand. We have had enough snivelling and retreat and aesthetic elaboration of despair. Armageddon has always waited around the corner; whether for the individual or culture, the earth or solar system, or an assumed world of matter crouched before Judgment-what difference? Death is. the universal death, spirit the eternal protagonist. The problem is to live in this stress with integrity. Our wars have not altered the situation. The film over the meaningless and void is no thinner than ever, the spectacle of life on that film grander than before. The spiritual malady of our time i's mostly of faint heart-a kind of green-sickness in girls .... Against currents of pettiness and obstacles of specialized jealousy, the Western mind gropes through the new sciences and organic history toward the philosophic synthesis its destiny requires. Against the incredible meanness of the pulp-literate masses .and the modish anaemia of the literary reviews, the 'vVestetn tongue awakes to the splendor of its singing task, the celebration of this culminant human adventure. Let those who teach and edit and print know this for their charge, the vision they must encourage. Not that it will therefore be a popular thing, or will save W, estern society or depend on that salvation. Had t~e achievement of Plato hinged on restoring the Greek city state, we would not know the meaning of the ·sl}adows on the wall of the cave. Of course in one sense the spirit of a new poetry is also the spirit of renewed freedom, being the wisdom and will to live affirmatively in the highest drama of mind. But the fruit of this spirit may spring in "a garden enclosed," in the private life, not in the public. And it may be difficult of q.ccess, as much so as the fashionable obscurities of today. Its complications, however, will be those of responsible profundity, opening to reason, involving the explicit and affirmative core. Such is the fruit that will appear, ftnd its token and sign will be wholeness. · That is the close of an article I once wrote, called "Modern Poetry and the Pursuit of Sense," 1 in which I demonstrated too well that I am not addicted to the magic of the irrational. But truth evades one-way for~u­ lation, requires that we catch it in the protean field of its ambiguity. Hence the fecundity of paradox, of Mystery, th.e ·great whore seated on the beast, to whom all the poets of the earth. have bowed, even the writer of those Revelations in which she stands condemned. As I read that essay now, its rhetoric does not move me as it once did. I even blush a little, as if I had offended against the dithyrambic god; I resolve to write another on poetry as madness, poetry as drunken release. For it is not a new consideration. It did not begin with Mallarme's formulation: "To name an object is to .do away with three1iluarters of the enjoyment of the poem," nor with ni9g~rn or the romantic cult of the unconscious. Of cour~e it is appropriate that Freud should have quoted Schiller in this connection: "In the case of a creative. mind, it seems to me, the intellect has withdrawn its watchers from the gates, and the ideas rush in pell-mell, and only then does it review and inspect the multitude. You worthy critics ... are ashamed or afraid of the passing madness found in all true creators .... Hence your complaints of unfruitfulness." 2 But the concept is older than Freud or Schiller. Diogenes 10, 1955. Method of Dream Interpretation, Freud quoting from a letter of Dec. 1, 1788, from Schiller to Korner. 1 2 �The inebriating water of the Muse has flowed down to us, as Milton loved to emphasize, from the mountains of Sinai and Parnassus, and the bloom of prophetic and poetic madness has its roots in both traditions. When I was a boy we were staying at Eureka Springs in the Ozarks, and there was a convention of Holy Rollers. I watched in amazement as they rolled over the green, gabbling in unintelligible sounds. It was said they were talking in tongues, and that the spirit of God was on them. We had read the Bible enough in my family for me to know the reference: the flame-like descent of the Pentecost, when it was spoken of the disciples: "These men are drunk with new wine." But I did not remember Paul's judgment on such rhapsodists, or suspect how it might apply to the poetry of our time: For he that speaketh in an unknown tongue speaketh not unto men but unto God ; for no man understandeth him; howbeit in the spirit he speaketh mysteries .... But he that prophesieth speaketh unto men to edification, and exhortation, and comfort. . . . Wherefore let him that speaketh in an unknown tongue pray that he may interpret. . . . I will sing with the spirit, and I will sing with the understanding also.3 Paul naturally did not deny that the gabble of inspiration might be the truth of God. How could one who was both Christian and Hebrew forget it? If the Apocalypse was not before him, Isaiah and Ezekiel were, prophetic voices crying in the wilderness, establishing a model for the Christian poet, for Dante, Milton, Blake, even Yeats and Eliot, for the poet as visionary, as seer. Also in the Classical world, where poetry may have seemed more a courtly entertainment, it went beyond that. Virgil is a poignant reminder of the power of the other obligation, the sense that the poet must be a mythmaker, inspired herald of tribal truth, of tradition and the v6µ.oi. Inspired-because to fulfill such a role one must go beyond oneself; like sibyl and oracle, Ibicus, Pindar, Homer had to be possessed. Thus Plato says in the Phaedrus4 that "the madness of those who are possessed by the Muses" is one of the madnesses which are divine gifts, and that "he who, having no touch of the Muses' madness in his soul, comes to the door and thinks he will get into the temple by the help of arthe, I say, and his poetry are not admitted; the sane man disappears and is nowhere when he enters into rivalry with the madman." With Plato, of course, the word "madness" cuts two ways. At its profoundest it suggests possession by the love of Wisdom, the drunkenness of the soul sprouting wings. Taken lightly, it means that the rhapsode cannot give an account of his trade. He is like one who speaks in tongues. And the Platonic request might not be unlike Paul's, that the poet not only speak mysteries, but turn around and clarify them, that he be philosopher and poet in one. But that poetry springs from some sort of divine possession, Plato did not question. There is a whole drift of critics who have emphasized the surgical precision of the trade of words, deprecating the W ordsworthian abandonment to nature : And should the guide I choose Be nothing better than a wandering cloud, I cannot miss my way; or that of Whitman : Not words, not music or rhyme I want-not custom or lecture, not even the best : Only the lull I like, the hum of your valved voice. -implying that this very dependence somehow makes Wordsworth and Whitman sloppy poets. The fact remains that Shakespeare's invention is said to have flowed with such celerity he could not stop it, and so surely that he scarcely blotted a line; that Milton would wake from sleep to dictate long passages of spontaneous utterance; that Blake claimed to have received his poetry and pictures by spiritual mediation ("I have written this Poem from immediate Dictation . . . sometimes twenty or thirty lines at a time without Premeditation & even against my Will ... & an immense Poem Exists which seems to be the Labour of a long Life, all produc'd without Labour or Study. . . . My heart is full of futurity . . . " 5 ) ; that Wordsworth's greatest poem, the "Tintern Abbey," came to him, as he says, while he was walking down the Wye valley, that he kept it in his head through the day, and wrote the whole thing down that evening in Chepstow, without alteration or revision; that Coleridge received in an opium dream a narrative poem in its entirety, of which the recorded fragment, "Kubla Khan" is perhaps his most pregnant poem ; that Goethe would never force or strain his talent in any way, but insisted that everything must form itself, like the foliage and fruit to which his analogies returned; that Yeats, for all his revision and laborSometimes a line will take us hours maybe, But if it does not seem a moment's thought, Our stitching and unstitching has been naught. I Corinthians, XIV, 2, 13, 15. Phaedrus, 245A. 5 Letter to Butts, April 25, 1803. 3 4 -tells how he heard his poems first as a rhythmic pulse, a tune or melody, and would listen attentively until the generative music filled itself with words; that Rilke, finally, wrote a good part of his masterpiece, the Duinese Elegien along with the Sonnets to Orpheus (a kind of overflow) in a single trance-like spell of several days, when, as he said in letters, he hardly knew what he was about: "a nameless storm, a hurricane in my mind," "the most enigmatic dictation I have ever held through and achieved . . . a single breathless act of obedience ... without one word being doubtful or having to be changed." So despite all emphasis on the watchmaking control of verse, it has commonly appeared as a release, a drowning of the individual in something larger or deeper, above or below him, a suspension of the waking for some kind of creative and associative sleep. We do not have to say what powers these are that take over, though surely the old notion of possession by a god, or demon, meets with the experience and with the precursive power of what is bestowed, more adequately than the account of school psychology that the consciousness must be by-passed for the subliminal to flow -unless the subliminal is made a myth-forming matrix of world-energies-which is only to bring back the gods under new names. But so far we have dealt only with the process, how the poets gets hold of the poem, as if he did not will it, but received it from some creative fountain. But this is not to say much about the quality of the poem itself, nor is it to deny that the conscious will, through the entire life of the poet, may have established channels for that release. When Rilke abandoned himself to the poetic impulse, if he wrote grammatically, it was because he had been drilled in grammar from childhood; if he used allusions to classical and modern literature, it was because he had studied these things; if the poems are permeated with philosophy and religion it means his conscious and unconscious mind had been thus impregnated; if he wrote in sonnets, it is because he had memorized sonnets until he could even have dreamed them. No waking discipline is entirely lost, it stamps itself on the unconscious; the creative outbreak may occur in the context of a life of dedicated control. Does not the fact of musical improvisation put the whole problem before us? Imagine Bach improvising an organ fugue on a theme given him by Frederick the Great. Where does the reason, the conscious mind, or the will, enter? If the fingers were not trained to an unthinking precision and the soul to flame out in those formal rhythms and chords, how could the man sit there, without meditation, a type of the possessed poet, yielding to the creative fountain? But what pours out is the mathematical order and volitional triumph of the four part fugue. Even in the airy soarings of Beethoven's last piano sonata, in variations that seem improvised, though they were painstakingly elaborated, what strata of rhythmic and harmonic discipline underlie the seeming abandonment ! It is not enough to say that all such release takes place in the field of energy, where release itself, even the frenzy of flame, is instinct with rhythm and form. Because, despite the example of Bach, this most disturbing question remains: Granted the poet has to be somehow possessed or mad, what about his poem? Is the fruit of his abandon clarity? Can the artist be mad and what he produces sane? Or does the madness spill over into the product as well? Poetry and the arts would not constitute such a problem at St. John's if we could once and for all shout from the housetops that the answer to this question is the former. But it is just the suspicion of some complicity between art and unreason, poetry and ambiguity, tragedy and immorality, metaphor and mistake, which leads us to the central mystery: What is it that madness can reveal? What is the nature of mind and experience that enables the shadowy inscape to reach beyond definition? Why should the holocaust of sense provide the flash in which sense itself is more prophetically. revealed? Here the problem of madness has gone beyond mere obscurity or the veilings of the modern oblique. If a man says he is going to bomb the city of New York and destroy that hideous Gomorrah once and for all, we understand very well what he is saying. We may even sense the poetic appropriateness of it. But we would still call him a madman. He is a madman because he is ready to tear the texture of articulated civilization. Like Ahab he has given himself to the god of fire. But that is exactly what tragic poets have done from the beginning. They have thrillingly entrained us in the adventure of destruction; they have celebrated it as somehow the noblest way, the way in which values strangely inhere. How does this thing come about? The imagery I have used already hints at my notion. I would say the matter can best be clarified (and this is not entirely poetic love of mystery) by putting it into the context of nature. We are part of a universe so ambivalent that energy itself must be characterized under the antithetical �20 I I 11 [, i 'I I' ii I'11 'I 11 II 11 1\ !, poles of leaf and flame-the entropic fire-urge to run down hill, the plant-urge of anti-entropy to buttress against decay. And as always with any primary ambivalence, we cannot escape some Hegelian identity of opposites: that the plant-urge only realized itself as an over-pattern by using and riding all particular fire-leaps of sunlight and chemical change; while the fire-urge, on the contrary, is validated for temporal manifestation by the buttressings without which it would always burri itself out of being. As our words up and down imply, this is not a pure or symmetrical ambivalence, in fact no such can exist in the human consciousness, which means, as far as one can tell,· in the organizing universe. There is no perfect parity; the poles have rank, like differentiations of a one in which they blend. So the centr~I drive of energy is entropic, the drive of flame. That gives it its character, its life, though strangely enough it is also a death-urge. While that which by containing energy makes it linger, assuring it a temporal being, is what binds and prevents its operation, its pall of ·death. To die in freedom or be buried alive. That alternative is at the heart of the madness cif the arts. For we are ultimate forms of an energy which, under the .woven ambiguities, spirit is. We manifest its po~ larities ; we are washed on the tides of the fire-oceari from which we spring. That is why, in the context of poetry, the tragic has possessed the soul more fiercely than the comic, has more flamingly taken it beyond itself. And that is why in the Oresteia, Oedipus, and Antigone, or with Shakespeare, Milton, Blake, Dostoievsky, Flaubert, Melville, Conrad, Faulkner, sense has so often seemed limited, morality stuffy, marriage a bore, convention and law the protections of the prude, tradition with all its artifice the jail to be broken. That is why the rational Republic can never be formulated so that the mere blood of nature will not in the end traii-' scend it; why Plato, who hated the phenomenon, so glowingly describes the "fair and spangled" state, the free society on its road to ruin; why in his conscious and Socratic capacity, he had to expel, in effect to exorcise, from the body politic all that poetry he must have poignantly admired. For Plato does not like to admit (that is his peculiar triumph) how far he and the world are cloven. The ambivalent mystery and power of the universe, which poets had always fed on and early philosophers and mythmakers hinted at, was first in Christian culture to be made the paradoxical cele- · bration of reason. Though that was bound to happen, since reason, like morality-like energy itself-is in- 21 ternally at war. It arrives at its peaks of insight by its own abandonment-a thing which Plato, the greatest poet of reason, could hardly fail to exemplify, though it did not serve his turn to admit the fact. If Western science, under the guise and discipline of reason, has been a submission to "brute fact;'' an apotheosis though the Passion of nature, is it any wonder that our poetry has more and more given itself to the wave of mystery-as if it had sensed from the first that its destiny was Dionysian, to yield to the impulse : "Gefiihl, Gefiihl ist alles," to Nietzsche's and George's Rausch and Traum, ("-it is precisely the growing dominance of evil that one desires, the growth of power, so as to make use of the most powerful forces in nature, the emotions ... "), to Joyce's unconscious, (. . . Can't hear with the waters of. The chittering waters of. Flittering bats, fieldmice bawk talk. Ho ! Are you not gone ahome? What Tom Malone? Can't hear with bawk of bats, all the liffeying waters of. Ho, talk save us! My foos won't moos. I feel as old as yonder elm. A tale told of Shaun or Shem? All Livia's daughtersons. Dark hawks hear us. Night! Night! My ho head halls; I fell as heavy as yonder stone . . . Beside the rivering waters of, hitherandthithering waters of. Night !6 ) Pound's mere chunks of material, documents, letters, the ravings that come to hand, (1335. 3 lire 15 groats to stone for making a lion. 1340. Council of the lords noble, Marc Erizio Nie. Speranzo, Tomasso Gradonico; that the hall be new built over the room of the night watch and over the columns toward the canal where the '.walk is . . . ... because of the stink of the dungeons. 1334.) ·-through all this, to become in madness a medium for some drunken god. Nor is the word "madness" any longer metaphorical. The greatest German lyric poetry is produced, with Holderlin, on the verge of that abyss ; one feels the power and i:nystery simultaneously increased, like ad- · vancing a psychic throttle, until the fabric breaks in.· sch~zophrenic.despair. While with Rimbaud, the most revolutionary French modern, whose works grew from the perverse frenzy· of his youth, before he broke into another sort of aberration and silence, the program was deliberate: "d'arriver a l'inconnu par le dereglement des sens"-to arrive at the unknown by the derangement of the senses; an end to which he espoused all liquors, dopes, dream-producing drugs. And without 6 James Joyce, Finnegans Wake. making a roll call of the poets writing in America today one may become aware that of those in their forties, five or' more of the best regarded are manic depressives with clinical interludes. But why should one go to such pains to prove what must be evident to all? Even readers of Life magazine are aware that the one passionately proclaimed poetic movement in America now is the most drunken. The Beatniks have shown again, what one might have hoped was out of date, that madness is still the road you can get a mob of people to traipse on with you. Even the petty-bourgeois will follow you to a fire.· Or to put it in a grimmer metaphor there is no surer way to produce something big than to go on opening the phy.sical, moral, and poetic sphincter to the flux. So what should the poet do but let go? Bring on the marijuana, bring on the sex. The Western orgy has hardly begun. "Hieronymo's mad againe ... Why, then Ile fit you." And there I stop, drawn up, blushing again, this time almost with shame. Hurling myself into the rout of Dionysos, I have betrayed the other god, Apollo, of clear forms and luminous knowledge. The pursuit of poetry as release, has taught us what we should have known before, .that we are dealing with a field-construction; we are navigating between poles. No doubt there are passages in Shakespeare so obscure that no one can tell whether they are misprints or what the poet intended, but so incredibly moving that, right or wrong, they could not be changed. Such is Cleopatra's cry: 0 sun, Burn the great sphere thou movest in! Darkling stand The varying shore o' the world. It may illustrate the evocative power of the ambiguous. But these moments are accents in a paraphraseable texture. There is no doubt also that the tragic disruption of morality draws us in its wake, fills us with a Faustian glory, as when a forest burns. But in great literature this frenzy too occurs in the frame of its opposite. As nature has used the fire-urge to buttress a position against that terror, o.i- as music has used dissonance to celebrate harmony, poetry employs madness for the clarification of form. And perhaps the noblest program for a work of art would be, as the old commonplace ran: "to hold the mirror up to nature"-but to that nature from which, in the ambivalence of cell and flame, man has arisen, and of which. he remains a living part. And one might even say that this has been done supremely by Homer, Dante, Shakespeare, Goethe, the very authors we would have wanted, at ·St. John's, to get on our side. They are safe allies, being almost established now; Rimbaud and Pound may prove the upstart darlings of one age. For ages vary. Perhaps our leaning as far as we have towards the poetry of Rausch and Traum is a reflection of a time intoxicated with fire, too perilously carried in ·the rush where nature destroys its own. The bottom may fall out of the market for derangement ; in the long run, constructions in the field should hold their own. So I think we can stake our capital on Homer, Dante, Shakespeare, the poets most truly mad-and sane. And I hope the time will come when St. John's College will not only allow this as a critical judgement, but will be so infected by it as a creative obligation, that it will aspire to produce in its midst writers mad enough to take these mad ones as models for their productive aim. �E'yvind l{onquist* 22 23 THE FIRST How should I know? Someone who had this morsel to bestow. THE SECOND Prologue to Antigone! But I know. 0 we of little faith! What luck 0 sister, that our brother has come back! THE FIRST Bertolt Brecht 20 The delivery of the narration must be simple and in the manner of a fable, not as if the narrator stood under the impact of what happened, but as if she had been asked to report the event many times before. On this point the narrator must also be attentive that her report not be loaded emotionally in the acted parts. The performance must clearly have the character of a demonstration. Before the Antigone set stands a partition with a door and a wardrobe. A table, two chairs. And we hugged one another and were glad Our brother was at war and things weren't bad. And we cut into the bacon and ate of the bread That he had brought here for our bodies' need. Take more, they drive you at the factory. A board with the inscription "BERLIN. APRIL 1945. DAYBREAK." is lowered. A stagehand, right forward, strikes the alarm once, and the TWO SISTERS go up from the orchestra. No, go ahead. THE SECOND It is not as hard for me, cut deep. THE FIRST Not me. THE SECOND How could he come? THE FIRST SISTER Then as we came out of the air raid shelterAnd the house was not destroyed, and it was brighter Because of fire than the dawn-it was My sister who the thing first saw. THE FIRST With the soldiers. THE SECOND A ROAR FROM WITHOUT. Now. Where may he be? THE SECOND SISTER Sister, why is it that our door is open wide? THE FIRST Where the fighting i8. THE FIRST The wind of the fire has reached it from outside. THE SECOND Oh. THE SECOND THE FIRST Sister, why came the footprint in the dust there? But we could hear from battle no alarms. THE FIRST THE SECOND Of course from someone who went up the stairs. I should not have asked. THE SECOND THE FIRST Sister, the corner there, what is that sack? I meant no harm. And as we sat there silent, to our ears arose A noise from just outside the door that our blood froze. THE FIRST Yes, something is here like something that we lack. TWO SISTERS GO TO THE SACK AND LOOK THEREIN. THE SECOND THE SECOND A whole bacon, sister, a loaf of bread. Sister, let us go look; that was a scream. THE FIRST THE SECOND Sister, who was here then? TWO SISTERS RESUME THEIR PLAYING. THE FIRST ITALICIZED LINES ARE SPOKEN TO THE AUDIENCE. This is not anything of which to dread. TWO SISTERS GO TO THE TABLE AND SIT. THE SECOND TWO SISTERS COME OUT OF AN AIR RAID SHELTER BACK TO THEIR DWELLING. 10 ' THE FIRST 30 Stay seated; he who wants to see is seen. So we did not go through the door and saw none Of the things which outside there were going on. A ROAR FROM WITHOUT. �Sister, sister, do not go out. Our brother is outside the house. He is there not without reason though, He hangs on a meathook, oh. My sister went then from the house, And from herself a scream she thrust out. Yet we ate nothing further, and we faced No more each other and stood up and made FROM HERE ON WHAT THE VERSE DESCRIBES IS GONE THROUGH. 40 Ourselves ready for work like any other day, And my sister took away the dishes, and I Remembered and carried brother's sack up to the closet Where his old clothes were kept. And there it was my heart beat as in shock, His uniform was hung there on a hook. Sister, he is not in the battle, He has made off from all of that, He is no longer in the war. THE SECOND 70 SECOND SISTER FOLLOWS TO THE WARDROBE. FIRST SISTER SHOWS SECOND THE UNIFORM. THE SECOND He is not, yet others are. SECOND SISTER RUNS TO THE TABLE, FOLLOWED BY FIRST. Sister, do not take the knife; You will not hence get him alive. If they see us with him stand, We shall feel as he their ·hand. They have to death commanded him. THE SECOND He however cheated them. THE SECOND THE FIRST 80 For there was a little hole THE SECOND Let me, I am too long detained, , Though they have left him for us hanged. THE FIRST And it was that from which he stole. And as she meant to leave the door, An SS-man stepped before. THE FIRST He is not where others are. SS MAN That is he, and who may you be? Out of your door he came to me. So in conclusion I surmise That peoples' traitor you might recognize. THE SECOND He is no longer in the war. Sister, they hanged him, which is why He had to us made loud outcry. Give me the knife, give here the knife to me, That I may cut him down and he go free. That I may drag his body in And rub it back to life again. THE FIRST THE FIRST 50 SECOND SISTER LOOKS OUT THE DOOR, TURNS BACK. . ,THE UNIFORM IS HUNG UP AGAIN IN THE WARDROBE. THE FIRST And we laughed, because we felt so glad Our brother was not in the war, and things weren't bad. As we stood there then, to our ears arose A noise, that our blood froze. THE FIRST Dear sir, let not with us your judgment stand, For we do not know the man. A ROAR FROM WITHOUT. SS MAN THE SECOND Why has she then a knife with her? Sister, who screams outside? THE FIRST THE FIRST 90 Again they torture people in their pride. THE SECOND Sister, should we go out to see? Then looked I closely at my sister. At pain of her own death should she Yet go to set our brother free? He 111,ight not yet be dead, you see. THE FIRST 60 Stay in, who wants to see is seen. We waited thus a while and so saw none Of the things which outside there were going on. We had to go to work then, and for me It was what was before the door to see. The stage is placed in half light. The partition for the prologue is raised. Stage workers take away the table and chairs. , TWO SISTERS GO TO THE TABLE AND TAKE UP THE TWO SISTERS go to rear to give their costumes to the wardrobe mistresses. At the same time the actors come from the right and left of the orchestra and they go to their benches in the rear. Full light fills the acting space, which is set up amid posts with the skulls of horses. DISHES. THEN FIRST SISTER GOES OUT THE DOOR, LOOKS, AND TURNS BACK TO SECOND. *Translator (First Translation Into English) 1 Suhrkamp Verlag Frankfort, Main, Germany \-\Tith the permission of Mrs. Helene Weigel. �I! CCheodore Barnes Stinchecum Three Short Speeches I It is so obvious that it hardly seems worth stating that intelligent men are not necessarily philosophica!. Nevertheless, in an era of confusion and speed this truism, with radical effect, goes poorly represented. The time of the Weimar Republic was in no way an exception to the rule; indeed, a more active intelligentsia cannot be imagined. One need only call to mind such phenomena as the Bauhaus if he ~eed a concrete representation of the intellectual energies of those days ~e­ fore the abyss of Nazism opened and those energies were absorbed exiled or murdered by a nation gone mad with History.' The communists, the socialists and the nationalists fought against each other in the streets b~t in their hearts a certain alliance existed, namely, a dedication to the exterior and inexorable laws of historical process and a consequent immolati~n of t~e se_lf_ to t~at process. The intelligentsia acted as if the ?i~toncist view of the world were true and History obhgmgly cooperated. Haste is anathema to reflection; leisure is the calm, questioning sister of philosophy. The intelligentsia of pre-Hitler Germany were men in a terribly great hu~ry: the automobiles sped, the cinema whirled, the machmes gyrated, and a favorite "style" evolved. The truth had to be got at quickly and History seemed more than ever in that precipitous time between Great Wars the Grand Calculator which promised to give not only answers but a method for finding those answers quickly. In short, this was to become a time of "final solutions" ; intelligent men rushed at what seemed to be light and were wounded by fire and were not illuminated, and also the world was darkened. The figure to seize is, I think, Dante's: the Weimar time looks like that place of Futiles running restlessly after a whirling standard. It is into this Vestibule of Hell that Bertolt Brecht came, bringing within him~elf a clear and great contradiction, the one between passion and reason, a fit subject for self-reflection in a time of leisure. But in Berlin the plague was on and Brecht fell ill from History and haste. The Marxist dialectic, _truly an unstatic standard, was seized by him as the mtellectual basis of a new methodical rhetoric for the theatre. For Brecht the theatre was henceforward to have an explicitly Marxist "political" purpose, the one pu:pose which seems best to contradict the maxim of Longmus: "The effect of genius is not to persuade or convince the audience but rather to transport them out of themse1v es . .'. . The obj" ect of poetry is to enthrall." The proof of the pudding, however, was in the plays themselves and some of the plays were carried beyond the purposes of the new rhetoric (Epic Theatre, if we must have a neat methodic nomenclature) by a movement which can have no other name but inspiration. II Of current ways of looking at works of .a.rt, th_ree seem to gather the most attention from the cntics. First (and this view is the one most talked about by tho~e contemporary critics who have been nurtured Roma~tl­ cally), one can consider a work of art as the express~on of its maker. The artist somehow squeezes out of himself something into the thing made or don~. The ?est possible reaction to such a trivial theory is, I thmk, to shrug "So what?" It is, of course, true that whatever we do bears the stamp of ourselves ; that stamp will be more or less ordered and interesting as we are more or less ordered and interesting. Second (and this occupies the central position in Classical theory) , the work of art can be held to be a revelation of a spiritual realm and, consequent!~, the exhibition of the essential character of the particular object represented. So run the th~ories :Which revolve about the notion of imitation, theories which, when the! are stated in this way, seem to require the further addition of some sort of inspiration from above. (That a singular conception of the nature of reality underlies these theories can only be noted, unfortunately, in passing.) Attacks on art usually proceed from a more limited idea of imitation, namely, that the artist represents not what is essential in the object but what is accidental or, put in a simpler way, that he merely makes a copy of what is already a copy. Third, there are critics who demand that art must have some social purpose, either as simple propaganda for a cause (usually explicitly partisan) or as highly developed works, sentimental or otherwise, which are made according to methods derived from socio-historical truths or which aim to persuade the onlooker of or to demonstrate those truths, the most representative being those critics and artists named "socialist-realists." For the Marxist critic and for the Marxist artist, a work must reflect the opposition of forces leading toward the goal of the general dialectic of History. Dialectical materialism directs the attention of the artist and the critic to the fact that nothing is static. It is therefore necessary to deal with any subject as developing in time. A work of art for the Marxist is a product which is good to the extent that it is a faithful representation of the reality dealt with : reality is dialectical in the sense that any period or subject is moving into its future through a series of oppositions. Works of art truly reflecting these processes are necessarily optimistic ; the aesthetic is, therefore, colored by a species of revolutionary romanticism. The Marxist is explicitly uninterested in works (except in so far as they are historical facts) which are simply the "expressions" of individuals. Photographic representations of reality are meaningless for socialist-realist critics since stasis is exactly what is unrepresentative of the world as interpreted by them; that the artist might be inspired is, furthermore, contraindicated; that he is stimulated by current forces in the historical process is, on the other hand, upheld, and it is this which justifies a study of the history of art. It is necessary to add some remarks on the difference between stimulation and inspiration. That both concepts require the artist to be a passive agent has to a great extent led many critics and artists to confuse the two. The problem is made even more difficult by the easily made observation that many artists seem to suffer from an abundance of sensitivity to things below and at the same time make images which bear the stamp, infused from above, of a divinity. That any discussion of what makes a work of art a good work of art must inevitably go beyond simple historical analysis (and I mean both biographical history and history in the broadest sense) or the investigation of the technics of imitation toward a discussion of the theological implications of inspiration is not generally accepted and is a thesis which I am not here prepared to defend. I think that it may be important, however, to point out in this connection that inspiration might be experienced as an intolerable burden, and that, furthermore, to seek stimulation by Dionysus is, perhaps, a flight from and denial of the genuinely divine breath of Apollo. III Arthur Rimbaud ended his short and turbulent literary career at the age of nineteen. It would be impossible to imagine a poet less like the theorizing, dialectical seeker of a rational rhetoric, Bertolt Brecht. It is true that certain earlier works of Brecht bear a striking relation in language and subject to Rimbaud, but it must come as something of a shock to those who know Brecht not through his verse and plays but through the unreliable reputation of his "theory" that this wild French child can have had any influence on him. Rimbaud stands as a paradigm of the poet driven and eventually destroyed as poet by the opposition of stimulus and inspiration. To discover that Brecht found this poet in some way attractive is, I think, to discover something of importance about what has been noted by many critics: the contradictory nature of Brecht's most interesting plays. That Brecht did not pursue his attraction for Rimbaud speaks not for the fact that Brecht was less "poetic" but that he was more intelligent. That Brecht was not, also, more philosophical is, I think, explained by the fact that he consistently ignored the possibility of inspiration, that, in short, he denied the possibility of philosophy and turned, instead, in the direction of intellectual methodology. That he failed consistently to deny his gift is the testimony of the plays. Brecht perceived that a work of art cannot be intelligible if it proceeds from simple stimulation ; that is, he, like all artist-intellectuals, is interested not only in moving the passions of men but in holding the attention of their minds. The contradiction in the plays is, in effect, the reflection of his failure to find a philosophical position adequate to the task he sets himself, one might almost say a failure even to seek that position. Bertolt Brecht can be seen as standing somewhere between the failure of Rimbaud to go on speaking and the great Platonic achievement which is once and for all the paradigm of the proper uses of speech. �R.._obert Koff The Relationship Between Analysis and Performance Formal analysis which is valuable to a performer differs from analysis which is aimed at instructing a composer or theorist. It is unimportant to account for the derivation of each phrase related to an obscure germ motive unless a simultaneous decision can be made as to the mode of performance. For the performer, this must begin with some contact with the performance practices of every style of music. . The first step is to determine the value, importance, and accuracy of tradition. Since a performance style can undergo extreme changes over a period of time, every composer's intention can best be investigated through his own music (using unedited editions and original manuscripts) and through the comments and criticisms of his own contemporaries. Such an important and excellent performer as Joachim is of great value in understanding the music of Brahms, as Brahms intended it. However, his edition of the Bach solo violin sonatas is of questionable value as a model of the performance as is revealed by other sources. Many questions occur that demand answer~. Are Beethoven metronome indications to be taken seriously? Many artists are unaware that they exist. Sho~ld Moza~t be performed on a nine-foot concert-grand piano, or 1s an instrument that more closely approximates the sonority of the Stein or Walter pianos used by ~oza:t to be preferred? Is Bach to be performed on a pi~no m the manner of a Busoni transcription or on a harpsichord and a clavichord? Has the modern violin and bow certain disadvantages when compared to a violin with the original adjustments (low, flat bridge; unwoun.d gut strings, etc.) and a pre-Tourte bow? Can the madequately schooled fiddler of our gene~ation at~emp~ to recreate the improvisations of Corelli and Vivaldi so that some semblance of their music as originally conceived be preserved? Should this music be performed without the mandatory ornamentation, or perhaps not at all? Is the performance of music to be categorized, and allotted to the various specialists whose fields of concentration do not cross? Can one performer gain sufficient knowledge and instrumental technic to perform adequately the music of all periods? The approach which might offer some of the answ~rs to these problems can best be indicated by presentmg a functional analysis with some comments on the ways in which three composers, each one demanding a somewhat different style, intended their works to be performed. A modest knowledge of the execution of the ornaments is a basic prerequisite but hardly serves to i~lu­ minate the performance style of Bach. The most important way to begin must be by obtaining some ~c­ quaintance with the music of the French and Italian school of the early eighteenth century. Some contact with the declamatory, improvisatory, florid, highly expressive and dramatic music of Corelli and Vivaldi is essential in order to experience this influence as found in various places in the music of this peri~d, and ~o ~ive a clue, not only to the technic of free impro~isat10n, but also to the expressive character of the music. In order to appreciate the rhythmic freedom ( e~­ pressive rubato alterations) that must be employed 111 the performance of this music, it is ~ost .helpful to ref:r to the harpsichord. Here, the special kmd of dynamic variation that is possible on this instrument (numerous timbre registration and octave and keyboard couplings) should be transcribed to the modern piano. This process will force certain pianistic devices to be changed or eliminated, such as note to note dynamic variation and the use of the sustaining pedal. This must be replaced by more emphasis on touch, dynamic regi~tration, and expressive rubato. In this way the phrasmg and dynamics will be better associated with the architectural structure of the music. The excellent examples of music well edited by Bach can serve to guide the performer when studying the vast amount that is unedited. An adequate acquaintance with original material will orient one's personal taste in determining the choice of countless dynamic, tempo, and phrasing possibilities. Schweitzer's invaluable study of Bach is an excellent aid to the solution of the performer's most pressing problem. From what he says in reference to the cantatas, a few basic principles are evolved that can be applied to the instrumental compositions. The most important principle is that the pictorial image expressed by constantly repeated leitniotiv figurations must be housed in a single emotional expression, coupled with a single dynamic framework which does not change. The harpsichord (or piano) registration is chosen at the beginning of the composition to establish the mood and dynamic level desired. While having the freedom of modest dynamic flexibility, the string instruments, in like manner, never break the format that has been chosen. Except when the structure of the music calls for terraced dynamics, this approach must continue without alteration until there is evoked a new figuration, a new motive, a new pictorial image. There are a few instances where a single movement of Bach's music will contain more than two basic contrasting sections. A formal analysis of the structural materials is helpful as an aid to the performer's understanding only when coupled with the above suggestions. This gives a clue to the basic kinds of emotional expression in the music of Bach and that of Mozart, Beethoven and the numerous Romantics. In the first kind there is chosen a single subject, identified with a specific character, and an exploration is made around this motive germ core. In contrast, the other kind uses constant and rapid changes of material and mood, travels from pathos to good humor, from serious drama to light comedy; all within a single sonata-allegro or rondo format. An example might be cited briefly to illustrate. The Sonata #3 in E Major for violin and harpsichord contains four movements. The first, in an Italian improvisatory, through-composed style, contains an accompanying figuration in the harpsichord part which never alters its pulse nor loses its identity. The violin voice expresses a series of flexible through~composed musical sentences, each beginning with the same motive. There are many choices of tempo, mood, and dynamic framework possible for this movement, according to the instinct of the performer. However, once the basic image has been chosen, there is no need to change registration or dynamics in the harpsichord part. The performer of the solo violin aria can explore every phase of the subject, but need not indulge in nineteenth-century emotional extremes. Rather, his object should be to explore the many facets of the same expression. As each motive is extended in various ways, the underlying harmony gives the clue to the quality of the presentation of each sentence within the chosen framework. The violin solo can implement the rubato freedom with the constantly shifting dynamics indigenous to a bowed string instrument. However, once again, if the image appears to express a quiet mood, the dynamic range must remain constant and avoid any extreme oscillation. The third movement, also quiet and slow, requires the same unified treatment as above. New, contrasted sections occur in each of the two quick movements of this sonata. When the second motive appears, a new registration, different dynamics, and a new mood may be presented. If a harpsichord, violin, and bow similar to the instruments used in the first half of the eighteenth century can be used, the sonority and quality of sound require some readjustments for the listener. However, once intoxicated by the experience, one is reluctant to return to the more modern hammer-klavier and metal strung violin. An approach to the functional analysis of the music of Mozart must take two directions. The first is to det~rmine whether th~ operative bel-canto style, or an architectonic-harmonic motivic treatment is to be emphasized. In a sonata-allegro form, Mozart moves freely from one style to the other and it is the performer's first task to isolate these two qualities. In general, the steps to take are as follows. The tempo must be determined by the Italian tempo directions (the number of harmonic changes per measure or measures can be a deciding factor) . The slower the harmonic rhythms change, the faster the tempo may be taken .. Mozart's own wish, as clearly stated in his correspondence, suggests that the left hand maintains a strict tempo while the right hand takes whatever expressive rubato is needed. Here a "hands not together" approach is indicated which is more in the character of the late nineteenth century performance practices. To performers or listeners who have been conditioned to prefer a style ·"pure like Mozart's," this will appear to be a strong contradiction. Chopin made a similar comment regarding strict rhythm and rubato playing. Having established a tempo, the second step is to determine the direction of each measure and phrase. Within the restriction of a constant metronomic pulse, the license of tempo rubato allows three possibilities. One-a measure or phrase can have a forward, accelerated direction. Two-the phrase can remain static or stationary to coincide exactly with the metronomic pulse. Three-the phrase can relax or retard slightly. �'Che R._everend Charles Edward Berger 30 Each antecedent and consequent phrase will normally have a point of greatest emphasis (or phrase accent). This will be determined by the harmony, the rhythmic forces, melodic contour, etc. However, in the music which is not influenced by the bet-canto style, the melodic high point is seldom the same as the phrase accent. Conversely, when the bel-canto predominates, the contour alone, rather than harmonic forces, will determine the expressive rubato. In this case the performer can sustain the longest, highest note in the best tradition of the art of Italian singing. The same structure present in all the operas of Mozart can be found in a condensed form in his instrumental works. The implication here suggests the distribution of the component parts of a sonata-allegro movement between tutti and solo voices or instruments. Creating an implied orchestration in a solo sonata or chamber music composition will be most helpful in determining the performance characteristics. An example of this treatment can be shown by referring to K. 304 Sonata in E Minor for violin and clavier. The opening eight measures of the first movement are played in unison octave by both instruments, and serve as an orchestral tutti introduction. The absence of any phrasing indications in an Urtext edition does not imply that it is to remain unedited. The performer is obliged, as when studying Bach, to refer to many good examples among Mozart's compositions which have been well edited by the composer. By becoming acquainted with his mannerisms, his principles can be applied to the unedited music. The phrase directions of the opening tutti of K. 304 must be determined and housed in a relatively impersonal framework. This is changed a few bars later when the solo violin, as it is accompanied by a clavier figuration, has more expressive freedom. The neutral direction of the implied full orchestration of the opening is contrasted to the more cantabile solo instrumental interludes, as in an opera format. In contrast to the motivic-harmonic treatment of the tutti material, the bel-canto quality is present in the second section of the exposition where a maximum tempo rnbato is desired. Every phrase, regardless of its compositional motivation, must have its direction of movement clearly understood and projected. The antecedent and consequent phrases (if the music is so constructed) each might have a phrase accent, with the parts balanced so that one predominates over the other. This is determined by the objective analysis of the performer. He must not only recognize all the compositional devices but recreate the music according to the style of performance in Mozart's time. He must give some direction to every measure, playing the role of opera stage-director, orchestra-conductor, vocal soloist, music editor and instrumentalist. He must recreate in an instrumental composition the same scope of dramatic intensity that ranges from the awesome terror of the Ghost, the vindictive power of the Queen of the Night, the virile, seductive loves of Don Giovanni, the coquetry of Zerlina, and the humor of Papageno. There is no place for the inhibited performer when dealing with the realities of life-in-the-raw as it is spoken by this supreme, articulate master through the language of music. The performance-analysis of the music of Beethoven must take into consideration all of the eccentricities peculiar to this composer. The problem of tempo must be solved in relation to the importance of the newly invented Maelzel metronome. A study must be made of the manner of composition as is revealed in his sketch books. Adequate investigation must be made of the performance practices of Beethoven, the virtuoso pianist. Here is a new kind of music to be performed in a manner quite different from that of Mozart. The phrase directions, the dynamic and articulation indications have another meaning. The basic concept of a constant pulse tempo rubato must be changed to one of constantly shifting pulse, one where each measure might be played in a new tempo. The language of music, which is so personal to each composer, is equally so to the performer. As he recreates the composition from blueprint of the manuscript, colors it with his own personality, accepts, alters, or denies tradition, isolates the performance practices of one composer from another, trains like an athlete; the fleeting moments of all his efforts as presented to an audience are soon over. It is my hope that some of these suggestions may prove helpful to both performer and audience as they continue to grow and change in their understanding of performance practices. 31 On Preaching Although I can make no claim to expertness on the subject, I am glad to accede to the request of the editors and try to set down some of my thoughts concerning what for many is a high art, and for most a highly Christian art. It is not accidental that popularly the Christian clergy are often described as "preachers" ; for preaching is among the most important of the many duties of a clergyman. So far as I have been able to determine, preaching belongs in great measure if not entirely to the Judaeo-Christian tradition. My impression is that it has always been more closely identified with the Christian rather than the Jewish tradition. To be sure, the early prophets were the first preachers ; but the prophetic tradition itself later became more a writing than a preaching tradition, while Christianity has never lost its association with preaching. Its distinction from the Jewish tradition began with the proclamation of what the early Christians took to be the truth about Jesus : that He had been raised up from the dead ; and His resurrection disclosed not only His identity as Lord and Christ, but also that He headed a great new movement which would usher in a new set of relationships between God and man. Such proclamations constituted the burden of early Christian preaching; they also disclose what preaching essentially is. One fact is immediately apparent from the discussion of the preaching tradition: the sermon is spoken. Great cathedrals adorned with images in stained glass and sculpture are sometimes called "sermons in stone" because of their attempt to portray and proclaim the Christian story. Also, there are, to be sure, many books of sermons. But the sermon itself is spoken. So far as it is literature, it is oral literature. It is no accident that many preachers who become highly skilled at writing for preaching do not excel at writing for reading. They come to depend upon voice inflections for emphasis, and upon all sorts of things which the human voice makes possible but which remain impossible for type. A sermon must employ all linguistic arts and techniques ; a man who lacks rudimentary knowledge of the use of language will not be transformed overnight into a great preacher, even though he experience a conversion like that of St. Paul or of St. Augustine. Preaching may be described as the effort so to state the truth about God as to demand some sort of verdict from the hearer. It is by no means the simple declaration of truth. That the sum of two and two is four would never be the burden of a sermon, nor would the truth that God is good be a subject for a sermon. There would have to be a "therefore" following the proclamation that God is good: "God is good; therefore His people ought to be good"; or "therefore, we who are not good are threatened by His judgment." And before the demands of proper sermon structure could be satisfied, it would be necessary to cast the "therefore" in moving terms, resulting in a definite decision by the hearers to will and strive for goodness, or to make ready for the judgment. Unlike lecturing, which strives simply to illumine a subject and inform hearers, preaching attempts something radically different, for it attempts to persuade. It seeks to induce hearers to change their position and to adopt the point of view of the preacher. Some would say that preaching attempts to take people who are here and move them over there. This was certainly what the earliest Christian preachers attempted as they addressed entirely Jewish audiences and sought to persuade them to accept the beliefs about Jes us which are now called "Christian" and which mark the differences which exist between Christians and Jews. They did not, for example, preach on the theme that God is the Creator, for the Jews already believed that. What these early preachers did try to do was to lead other Jews to believe that through the resurrection God had initiated a new order of the creation with which it was possible, through baptism, to become identified. There was no point in the early Christians' trying to persuade the Jews that some day there would be a general resurrection, for this seems to have been a tenet of belief of �Paul Priest 32 most Jews of that time. What they sought to persuade hearers to believe was that Jesus himself would be the author of that general resurrection, which serves to explain why the Gospels ascribe several resurrections to Jesus. Nothing that I have written should be construed to mean that a sermon may not endeavor to inform, or that if a sermon does inform hearers, it is to that extent not a sermon but a lecture. Most sermons contain some information new to many of those who hear it, and the expository sermon is almost completely given over to informing hearers. (Incidentally, such sermons are among the most difficult to prepare and preach.) But not even the expository sermon may merely inform. It must also move or attempt to persuade, striving for a decision by the hearer resulting in a new act of will. It must also have to do with God. However eloquent it might be, no effort of a salesman to persuade and move us to buy his product could rightly be called a sermon, for the inducement must always have to do with God. From the foregoing considerations, we can construct a tentative definition of a sermon. Such a definition would run as follows : a sermon is a reasoned discourse which attempts to proclaim what the preacher regards as a truth about God, and which endeavors to persuade hearers to accept and act upon that truth. However, just as the experience of a conversion without linguistic skill is not a sufficient condition for producing a great preacher, without conversion and its attendant conviction, not even the finest speaker can hope to become art effective preacher. Preaching and conviction about God go together· just· as hand and glove-with the difference being that although hand may be withdrawn from glove, preaching and conviction cannot be separated. Preaching has been called "truth mediated through personality" ; and as this bears on conviction, it means that the person who lacks genuine conviction and commitment will as surely communicate this, if he should ever attempt to preach, as would a person aflame with conviction communicate his conviction if he assayed preaching. Precisely because it is so personal an activity, preaching always reveals something-if only the ineptitude of the preacher. All too often, preaching reveals a splendid knowledge of language and literature but a profound ignorance of proper structure of sermons, or the sermon may reveal gross ignorance of human nature and of the ability or inability of people to accept propositions. I have often had to suffer through sermons (and doubtless have caused many others to suffer through sermons) which were so poorly organized and presented that profit to the listener seemed impossible. Because preaching aims at commitment and at stirring the wills of hearers with a view to effecting godly transformation, in a profound sense the only Christian preacher may be said to be Jesus. His Gospel is the Gospel of transformation. It is the good news that this poor, weak, sinful, inept persort can be transformed or is being transformed into a facsimile of a son of God. Wherever we meet a man or woman who has quite evidently been transformed into a: child of God, there we may observe the effect of one of Jesus' sermons. The effort of Christian preachers is therefore simply to aid Jesus in effecting the process of transformation. Their sermons are sermons to the extent that they help Him in this work. 33 Delight lll the Given: Plainsong as a Paradign1 of Pure Art cy 71~~~71·~:: ;:'.i1i!=filJ~z@.gz;Q:~~ 1)e, ~ o "- 111 - ver- sa. ter- The "plainness" we may feel in plainsong is no part of its name, which translates the Latin "cantus planus," literally "flat song," all in one plane, without the perspective or sense of depth that would be given by an accompanying voice. Indeed, the melody seems to be some sort of plane figure, a curving line that one sees all at once, even though he hears it happen in time. The line rises into space and somehow is there; it is not moving toward a destination. Therefore we may consider it static or, in English, "plain." The Jubilate Deo above seems to fix itself thus for us in space by quickly outlining its working limits: "Jubilate" frames the fifth from D to A, and "Deo" then fills out the fifth from C back down to F. This fifth then controls the following melody on "universa terra," like a persisting pair of parallel lines within which the melodic curve goes back and forth, exploring possibilities. Later, in the second "Jubilate," the higher fifth from A up to E comes to dominate ; and taken together, these three fifths form the scaffolding of the entire piece. The clarity and firmness of this structure in fifths, giving the melody a sense of security, gives it also a r-a. .... sense of freedom and independence. The melody (we are given to feel) may flow where it will; it is not going to lose the fixed lines or unbalance them by its weight and so need to be pulled back. An excellent illustration is the C at the very beginning. If it were a C sharpthat is, a leading-tone-it would merely slide up into the D ; but instead it hangs from the base of the fifth, almost counterbalancing it, aloof and proud, opening a whole new range of musical view. This sense of a melody's being different (and so, in a sense, free) from the structure in which it moves is rare in most of our harmonic music. In such music melodies carry the feeling of the harmonies that underlie them, whether these melodies form chords or move through them. The way in which the Gregorian melody moves through this essentially static medium of tones, structured in fifths-its dynamic or rhythmic aspect-begins, somewhat as in the case of the fifths, with a strong controlling limitation: all the notes are approximately of the same time value. But given this initial security, they are free to move in groups of two or three (either one may be used at any time). These groups are not like �34 the regular foursquare measures of recurrent beats that mark off our music. Rather, they are little impulses of breath which build upon each other the way a gust of wind in the pines enforces the previous gust. They sometimes tread on one another's heels, as shown where the curves of grouping (above the notes) overlap. (A long note-double the basic value-always gives the impression of starting a new group.) This jamming, called a "pressus," seems to compress energy, giving a sense of tension and vigor somewhat as syncopation does in more modern music. It also, like syncopation, gives a surprise ; so does the apparently rough and irregular alternation of groups of two and three. But syncopation displaces the beat, and here there is no beat; the movement is in the groupings, the impulses. That is why the basic note value is free to vary slightly at times, speeded up or lingered upon, like the first A in "Jubilate." Now I suggest that what binds this free rhythmic movement to its structured medium of tones and intervals is a sense of enjoyment or delight in the tones themselves, their relations, and the movements these relations make possible, such as pausing to relish a single tone, vibrating between two tones a second apart or a third; or building an ascent, with increasing momentum, as if feeling out or appreciating the qualities of each note on the way, as in the second "Jubilate"; then repeating, with emphasis, the previous pattern on "Deo universa," and about to make an orderly close on "terra" -but suddenly unable to restrain itself the melody frolics away in rising thirds through a raised B natural to C, and then plays through different intervals that hang from C. And it seems no diminution of the strong, adult power of this music to express the emotion in its text, that its movements also contain something like the play of children, leaping and gliding. Some of the most sublime instants in modern music seem to be expressing a similar childlike delight in the music simply as something given, something that is just there, the medium or material. In Beethoven's violin concerto, for example, the second subject in the first movement is a mere running up of a scale : 35 Of course, this moment has a complex and artful preparation, by contrast with which only, perhaps, it exists; but the moments which open such windows are so rare (and no doubt also somewhat different for every listener) that one might feel they too had to be "given." We think of Mozart as one into whose mind melodies dropped ready-made; and yet even his finest things suggest a very perfect ordering of forms and emotions, rather than the free and artless spiration of a spirit. Ars est celare artem, but nobody can quite do it: I doubt that anyone has managed by taking thought to give an impression of spontaneity. That seems, when it comes, to find its own perfect form. Tradition holds that the Gregorian Chant came by direct inspiration of the Holy Spirit; and Mozart is reported to have said that he would give his whole production to have written one line of it. same glance why tragedy is considered the highest form of poetry, since it spans the broadest arc between delight and sorrow, and why poetry that is called "rhetorical," that seems to be using its art to persuade us of some idea without having assimilated the idea to its art, is considered inferior. What then of the idea of which the Jubilate Dea is trying to persuade us? "Exult unto God, all the earth." "Make a joyful noise." But this is almost the only idea that has no conflict whatever with the claims of art. ~eligious delight differs from artistic only in intensifymg the sense of givenness ; and since it too does not come whenever we will (and any attempts to imitate it produce the most horrible disasters), we fill our lives as our art with technique and discipline, to enable ourselves the better to wait for the much desired gift. "The wise in heart shall be called prudent, but the sweet of tongue shall find greater things." Proverbs, I :21 But this sense of delight in the given seems close to the essence of all art. Art cannot merely present the given, for then it would be a scientific demonstration; there must also be a purely human sense of delight in the given. It is asked whether a painting tells us about its subject or about its painter. About both, of course; but the painting principally reveals aspects of the subject and medium, and relationships between these, in which the artist takes delight. Therefore it is art. Delight is the essential artistic emotion, to use the term in the broadest way; it is what we feel when terrible grief, dread, wickedness, or even disgust has been enclosed in an artistic ordering. And yet this would not attract us, I think, had not the artist found something somewhere in the given that was beautiful or comical or otherwise pleasing. If this is so, we can see in the �Book Review James CCaylor Artifice and Accidents I Igor Stravinsky's Poetics of Music1 is an English translation of six lectures the composer delivered at Harvard about twenty years ago now available in a paperback. It is a book well worth getting, if only because so few first-rate composers seem inclined to talk about their art, outside of professional shoptalk. I know that anyone who likes music will want to read this if he hasn't already, but the book should be particularly interesting to the people who are anxiously concerned about the "ontological status" of music and who keep searching for a rationale to explain and encompass this upsetting and "irrational" phenomenon. Not that Stravinsky's book offers any such thing. It is by turns fascinating and irritating, a strange mixture of insights, prejudices, sententious epigrams, semantic quibbles, oracular pronouncements, anecdotes, fingerpointings, and metaphysical flights. One immediate problem is to get past the ghostly image of Igor Stravinsky, world's greatest living composer, laying down the Word for party-liners to pick up and parrot. That such an image exists is no more Stravinsky's fault than it is Ernest Hemingway's, or T. S. Eliot's, or Pablo Picasso's, or Martin Heidegger's, or any other public figure's with the same kind of authority and eminence, but that image is an obstacle all the same. You have to put up also with such Dr. Johnson-like utterances as "Modern man is progressively losing his values and his sense of proportions," with lengthy tirades against Wagner and music drama, and with a detailed historical criticism of Russian music that takes, I think, a fair amount of special knowledge to really grapple with. But beyond these superficial barriers the book is a moving and revealing human document. Stravinsky calls these lectures "confessions,"-not the emotional spectaculars the word suggests, but findings that emerge from an apparently involuntary and habitual process of self-examination. Certainly these findings are as "objective" as you could reasonably demand, and I guess Stravinsky is justified in saying that what he has observed in himself as a musician is generally true of composing and playing music. In this sense, the title of the book becomes clearer : this is a highly personal "poetics," but the introspection that produced it was profound and thorough enough to get beyond the purely personal level. What the reader finds is the revelation of a personality which makes itself known in the form of a disposition towards music. It is this disposition which holds together the lectures with all their digressions, obscurities, and inconsistencies. A lot of what Stravinsky says about music is familiar. We enjoy natural sounds like the breeze in the leaves and the song of birds, but these are only the raw materials of music, materials which must be organized by a conscious exercise of human artifice. Our proper enjoyment of music comes from participation in an act of intelligence made articulate in sound; the making of music is, to start with, "a will moving first in an abstract realm with the object of giving shape to something concrete." This is a recognizably ancient doctrine of the Western tradition, and it has probably been the implicit attitude of European composers from the time of the Renaissance on. This attitude leads Stravinsky to invest music with the highest degree of intellectual dignity, which in turn has certain consequences. For one thing, on this basis he would defend composers from being compromised or tyrannized by political doctrine or by the self-preserving interests of an entrenched bureaucracy, as Stravinsky claims is the case in the Soviet Union. Furthermore, since composers are working on a level of such high seriousness, they have a responsibility to maintain good order within their own house, not to be willfully revolutionary or capricious or egotistic in their handling of the musical materials. They have an equally great responsibility to remain alive to the possibilities within 1 Poetics of Music, Igor Stravinsky, © 1947 Harvard College, reprinted 1959 Vintage Press. 37 the materials and not to succumb to sterile academic formulas. It may seem paradoxical at first that Stravinsky of all people should make such a fuss about the word "revolutionary," which means all kinds of bad things to him. In fact, in his lectures and in other published writings he has bent over backwards to assure us that he is the soul of propriety, dignity, order and decorum, all of which makes him sound like a stuffy, humorless pedant. But he's not that way at all in his music. "Revolutionary" or not, The Rite of Spring startled, bewildered, and shocked an awful lot of people when it was first performed in 1912. And in the three decades after that, his successive scores were a major part of the body of "modern" concert music considered avant-garde, futuristic, controversial, "far out," and so on. Similar things were happening in poetry, painting, theater, psychology, and physics at the time, of course. Today many Stravinsky scores are concert program staples; nearly all of them have been recorded, and the composer holds a kind of grand master's position in his profession. Stravinsky insists he is not a revolutionist because he has always sought to maintain tonal order and not to impair it or overthrow it, and he has never striven after novelty for novelty's sake. Philosophically that is an important point, and I am willing to take his word for it. All the same, it's undeniable that Stravinsky's works sounded new when they appeared, and they still do. Listening to The Soldier's Tale ( 1918) recently, I was amazed by its freshness and its up-to-date, right-now quality. Mozart sounds fresh too, but there is a difference: he is classic; Stravinsky is still modern. It is not within the scope of this review or my own knowledge to give a full account of this difference, but I can try to sketch it m somewhat. Practically all of the standard concert repertory of European music from the late seventeenth to the early twentieth centuries was based on the diatonic system : melodies were drawn from two modes, major and minor, which could begin on any one of twelve tones within the octave; harmonies were drawn from the triads built on successive scale tones. Also metric groupings were usually fixed and regular, with two, three, four, or six beats to each measure. Of course, this is a theoretical reconstruction. Composers were not consciously following a "system"; they put down the music that came to them, but that music happened to fall within these limits. Considering the infinite variety of tonal materials available, this diatonic system is extremely limited, but it was quite adequate at the time, and it is still pretty much entrenched in our own jazz and pop music as well as in most of our hymn tunes. But by the early 1900's it was becoming clear to an increasing number of composers that the old diatonic frame, canonized in textbooks and conservatories, was getting to be cramped and confining, like an outgrown suit of clothes. It was time to pioneer, to discover and to exploit new resources of harmony, tonality, and rhythm. In different ways, Arnold Schoenberg, Bela Bart6k, Joseph Schillinger, and Stravinsky attacked the problem and offered solutions in their musical works and theoretical writings. Schoenberg and Schillinger (a mathematician rather than a composer) came up with systematic disciplines, while Bart6k and Stravinsky worked at the problem directly in their compositions. One of Stravinsky's innovations was rhythmic: the accents in his music are often shifting and nominally irregular-less like the accents of rhyming verse, more like those of spoken prose. This has a lot to do with the peculiarly modern sound of his music. As for tonality, he describes his own attitude with the term "polarity"; that is, he keeps the idea of a tonal center, as in diatonic music, the center being a single tone towards which other tones converge or from which they radiate, depending on how you hear it. Finding the center of a group of tones already in the air or starting with a center and setting up tones in relation to it results in the solution of the basic musical problem represented by any work in progress. This is still highly theoretical. Stravinsky's account of a composer at work is refreshingly matter-of-fact. He prefers the term "inventor of music" to "composer," and for him the business of inventing music is one of "grubbing about" with tonal materials-lines, chords, sonorities, rhythms, patterns, cadences-until they fall into order. And this order satisfies an original appetite stirred up by the commissioning of the work. This appetite is a kind of expectation of what the work will be like, but with nothing really certain to go on. I think anyone who has ever done anything "creative" (and that includes just about all of us) will recognize the truth of Stravinsky's subjective description: you start out with a cloudy anticipation, and get underway with some scrap of an idea that comes mysteriously from somewhere. Then after suffering varying degrees of �39 progress and frustration, you come out with a finished job and say, "Yes, that's what it is." This is that mysterious "creative process," a mystery like music itself because as a phenomenon it is so complete and self-defining. II One professional secret that Stravinsky lets out is the importance of accidental discoveries. Speaking of "the true creator" he says, "The least accident holds his interest and guides his operations. If his finger slips he will notice it; on occasion, he may draw profit from something unforeseen that a momentary lapse reveals to him." It seems to me that only an "inventor" of music could make that statement. It is quite possible for a hack composer to grind out music strictly by formula, working on paper without any reference to an instrument, and come up with something that sounds respectable. A lot of movie and television scores, I gather, are manufactured this way, through the Schillinger system. This is serviceable commodity music, but it's not serious, and because it's not serious it's dull. A Stravinskyan inventor is always alert, ready to make the best of whatever is lying around, including slips of his fingers. There is a legend, for example, that the theme for a fugue by Domenico Scarlatti was taken from a sequence of tones the composer's cat made strolling up the keyboard. Sometimes, when I'm listening to something by Stravinsky, I can't help playing detective and trying to identify the origin of this or that fragment. In Oedipus Rex, for example, I hear things that remind me of Handel, Verdi, Bach and Moussorgsky; I can also hear automobile horns honking and telephones ringing. Some of his ballet scores use music by other composers, for instance Pergolesi and Tchaikovsky-music that he has torn apart, shaken up, turned inside out, and thoroughly Stravinskyized. Stravinsky's music sometimes reminds me of Chinese cooking, in which some of the most incongruous ingredients, still whole and recognizable, not all boiled down, turn out to go with each other perfectly. One consequence of this grubbing, puttering, do-ityourself kind of "inventing" is that Stravinsky has a unique personal sound in his music that would be very hard to imitate. He uses a lot of musical effects that I imagine no composer ever thought of using before : the ragged intervals and choppy phrases that give his lines such a peculiar shape; the pungent, odd, differentsounding chords; the unusual instrumental voicings. Of course they are not as startling now as they once were, but that is the evidence of Stravinsky's success. Now other composers are beginning to exploit some of his discoveries, and I don't see how a contemporary composer can help but feel grateful for Stravinsky's spadework. This business about accidents has some interesting consequences. Accidents of any kind are something of a scandal in the drawing room of traditional philosophy, because there is just no way to account for them. They frustrate our intelligence and spoil the pattern of an otherwise well-ordered universe. The civil law tries to work out some kind of justice for people who get hurt in automobile accidents, using notions such as "contributory negligence" and "reasonable care." But, it is obvious all the same that plain old accidents will happen; it is often completely arbitrary to assign blame or liability to any of the parties involved. However, I gather that in modern physics accidents are being regarded as more than a nuisance. Physicists agree that we can make predictions about the behavior of things and can count on these predictions to have a high degree of probability, but we can't expect any more than that. There remains the area of accidents, sports, monsters, freaks, unlikely coincidences, and surprises in general. I think Stravinsky's willingness to incorporate accidents into his compositions is, like the disposition of modern physics, an indication of a coming new image of the world-an image which has been shaping itself over the last few generations. More about accidents: there have been other "inventors" of music besides Stravinsky : take, for example, the American jazz composer and pianist, Thelonious Monk. Monk operates unmistakeably within the traditions of the jazz idiom, and his tunes are the usual 32 or 12 bar structures; but there is a difference. His playing, which sounds at first awkward and uncouth to ears used to the fleet muscular grace of the player-athletes, has stock elements; but it is also odd and unpredictable. I have never listened to Monk when he didn't fool me at least once coming out of a turn of phrase. Frankly, I am sure that when Monk drops those hammer-heavy hands on the keyboard during an improvised chorus, he doesn't always know what keys he is going to hit, it's not all thought out in the way that even improvising musicians will pre-think their choruses by a split second. Like Stravinsky, Monk keeps a tonal center going, but he lets a certain amount of chance enter in the actual content of a chord er phrase, g1vmg the whole chorus enough of a general shape that the chance material falls into place and sounds right. In a way, Monk goes one step further than Stravinsky, who can erase and rewrite; an improvised chorus is a thing of the moment that falls just as it is on the listener's ear or the recording tape. To flirt with chance under these precarious conditions is daring, but Monk, who is no "revolutionary" either, can do it successfully. What Monk does seems weird now, but I suspect our music will probably go more and more in this direction. If that is the case, we will have to review and reconsider the venerable form-and-matter theory as applied to music. III In the final lecture Stravinsky discusses the performance of music. Much of the lecture is polemical, consisting of a fierce onslaught on "interpreters," that is, performers who project their own egos into music at the expense of the composer's intentions. Stravinsky undoubtedly has heard some horrible mutilations of his scores at the hands of vain, stupid, or insensitive conductors and soloists-he is certainly entitled to a little public spleen on that account. I don't think anyone with any musical taste and judgment is taken in for long by the muscle-bound, tin-eared virtuosos, publicity hounds, personality freaks, and ubiquitous phonies who infest the music business. But on the matter of literal and strict adherence to the score, I'd say Stravinsky goes far out on a limb. He calls for another small semantic reform, distinguishing between "executants" and "interpreters." Executants are the virtuous performers who stick to the letter of the score and fill in the gaps and ambiguities with properly cultivated taste and intuition. Interpreters, of course, are the others. That seems to be a legitimate distinction, but how far can you carry it in practice? Stravinsky makes a point of ridiculing the "naive impudence" of symphony conductors who speak of their Fifth, their Seventh, and so on. But why shouldn't they? Musical scores are at best only a kind of shorthand as far as performance is concerned, because the notation presently in use is inadequate to be any more than that. Actually, until the nineteenth century, instrumentalists and singers were expected to make their own embellishments ad libitum, according to standard and current conventions. Stravinsky apparently wants to rule out the ad lib factor. But how else can a conductor (for example) bring a score to life and give it the inflection and nuance and rhythmic drive it needs, if not by interpreting it through the grain of his own personal, musical being? Standards of taste and disciplines of musical intuition may rule out whimsical or bizarre affectations, but even these have their limits. You can go into a record store and listen to Toscanini's Seventh, and \i\Talter's, and Klemperer's, and Reiner's and J ochum's-they are all quite different. And these conductors are all musicians of the highest integrity. Each one of them must pour himself into the music, just as he permits Beethoven to pour into him; the result has to be a unique compound. You buy the one you like best. Stravinsky has conducted many of his own scores on records ; I happen to prefer Leonard Bernstein's version in one instance, and you might prefer Ansermet's or Monteux's-or Stravinsky's. As long as there is such a split in function between composer and performer, this situation is bound to exist. Parents may claim to know their children better than anyone else, but their knowledge is partial and limited because they are parents. This distinction between performer and composer is a thing limited to concert music. Composers of pop music provide material to be processed by arrangers and performers, and by the producers and engineers at the recording studios. A pop composer usually is not too fussy about how his material is performed-just as long as the record sells and he gets his royalties. If he is lucky enough to turn out a hit that becomes a standard, he may be delighted or dismayed by the variety of renditions he may chance to hear; but his dismay is, again, eased somewhat by the royalty checks. Jazz composers are almost invariably performing musicians themselves, and they write their tunes for themselves or their own groups to play. Duke Ellington, for example, writes for his own orchestra, keeping in mind the personalities, capabilities, and limitations of his men. As a result, the finished work is more like a collaboration between himself and the band. After the piece has been played in performance for a while it starts to take on seasoning and character; it may go through a whole life cycle this way. \i\Then other groups play Ellington tunes, the tunes lose some of their Ellington flavor, of course, but another group may also come up with an equally authentic version of their own. The virtue of a good jazz composition is this durability and adaptability which keeps it alive in a variety of styles and �41 interpretations, often far from what the composer had in mind. The point is that he's got no complaint coming. If he doesn't like the way someone else plays his tune, that's tough. True democracy: all interpreters, no executants. Along the frontiers of jazz, some musicians are working on more formal set compositions, but invariably they leave room for improvising somewhere. It's far from ..clear that the element of improvisation will inevitably die out, as it apparently did in European music during the nineteenth century; it may or it may not. If it doesn't, we may look at the decline of improvisation in European music as a temporary aberration which may have been related to a grand metaphysical desire to wipe out chance and accident from human enterprises, a desire that may have come about by pushing the conscious-will-organizing-and-informing-matter theory to a dead end. To bring things into a good perspective, I think we should remember that people making music is just as much a natural phenomenon, just as mysterious, wonderful and unaccountable as the song of birds or the breeze in the leaves. "We are not to suppose that when certain rhetoricians pour ridicule upon that which they are quite incapable of refuting, without any attempt at argument, their words are really thereby constituted rhetoric.'· For rhetoric proceeds by persuasive reasoning; words without reasoning are buffoonery rather than rhetoric." Galen, On the Natural Faculties, I, 16 "As for the argument that speech ought not to be the exponent of action, the man who uses it must be either senseless or interested; senseless if he believes it possible to treat of the uncertain future through any other medium; interested if, wishing to carry a disgraceful measure and doubting his ability to speak ~ell in a bad cause, he thinks to frighten opponents and hearers by well-aimed calumny." Thucydides, Peloponnesian War, Bk. III, par. 42 1~<~·;: ~,------------------------1 II Jr 11, "A rhetorician of times past said, that to make little things appear great was his profession. They would in Sparta have sent such a fellow to be whipped for making profession of a tricky and deceitful art ; and I fancy that Archidamus, who was king of that country, was a little surpris~d at the answer of Thucydides, when inquiring of him, which was the better wrestler, Pericles or he, he replied, that it was hard to affirm; for when I have thrown him, said he, he always persuades the spectators that he had no fall and carries away the prize." Montaigne, Essays, I, 51 �Contributors Jacob Klein Douglas Allanbrook Student, St. John's College Charles G. Bell Tutor, St. John's College Eyvind Ronquist Student, St. John's College Theodore Barnes Stinchecum Student, St. John's College Robert Koff Member, Juilliard String Quartet, 1946-1958; Lecturer and Performer, St. John's College (J uilliard String Quartet); Faculty Member: Juilliard School of Music; Tanglewood Music School; Aspen · Music School;' Adjunct Associate Professor and Director of Performing Activities in Music, Brandeis University, 1958- The Reverend Charles Edward Berger Member, Board of Visitors and Governors, St. John's College; Rector, All Saints Church, Chevy Chase, Maryland Paul Priest Tutor, St. John's College James Taylor I Tutor, St. John's College James Forrester .. Tutor, St. John's College Alumnus, St. John's College; A.B. , 1955 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The Bulletin of St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Description An account of the resource <em>The Bulletin of St. John's College</em> was published quarterly by St. John's College from 1932 to 1968. It was distributed to alumni, faculty, and staff. Some issues include the Report of the President, the official statement of the St. John's program, the Catalogue, the Polity of the college, or the Dean's Statement.<br /><br />The publication was continued by <a href="https://digitalarchives.sjc.edu/collections/show/12" title="The College (1969-1981)"><em>The College</em> (1969-1981)</a>.<br /><br />Click on <strong><a title="The Bulletin" href="http://digitalarchives.sjc.edu/items/browse?collection=37&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in The Bulletin of St. John's College Collection</a></strong> to view and sort all items in the collection. Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Page numeration Number of pages in the original item. 42 pages Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context Bulletin January 1961-Vol XIII No.1-Rhetoric Title A name given to the resource Bulletin, St. John's College, January 1961 Description An account of the resource Volume XIII, No. 1 of the Bulletin, St. John's College, Rhetoric. Published in January 1961. Date A point or period of time associated with an event in the lifecycle of the resource 1961-01 Creator An entity primarily responsible for making the resource Sheppard, Harrison J. (Editor-in-Chief) Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Rights Information about rights held in and over the resource St. John's College owns the rights to this publication. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/0fbdbd6ae291bd77ff7b14deafd651fd.jpg fd98e9d5d8a99ee6ec8506a671150906 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Physical Dimensions The actual physical size of the original image 20.5 x 25.5 cm. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data Photograph Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-1094 Title A name given to the resource Burning Notes for Senior Papers in Common Room Fireplace, Annapolis, Maryland Description An account of the resource 1 photographic print : b&w Date A point or period of time associated with an event in the lifecycle of the resource 1974-04 Creator An entity primarily responsible for making the resource Unknown Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Type The nature or genre of the resource Still Image Format The file format, physical medium, or dimensions of the resource jpeg Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/de70041b425026adf3cf8581e7f67f62.jpg c18e71de25bf02f60f11e246bfda2467 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data photograph Physical Dimensions The actual physical size of the original image 25.5 x 20.5 cm Resolution Resolution of the image in dpi. 600 dpi Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-0092 Title A name given to the resource Burt Thoms Speaking at Commencement under the Liberty Tree, St. John's College, Annapolis, Maryland Description An account of the resource 1 photographic print : b&w Creator An entity primarily responsible for making the resource Unknown Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1949-1958 [circa] Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Type The nature or genre of the resource still image Format The file format, physical medium, or dimensions of the resource jpeg Subject The topic of the resource Commencement (St. John's College, Annapolis, MD) Baccalaureate addresses Thoms, Burt Klein, Jacob, 1899-1978 Cleveland, Richard F. Commencement Liberty tree https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/9b1ea8652d86aa80e64448e53b5581d9.jpeg 2886a91a4c252229887339e17a79845f Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data photograph Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource BVG Chairman Ronald H. Fielding (A70) presents President Mark Roosevelt with the St. John's chain of office and college seal, St. John's College, Santa Fe, New Mexico Description An account of the resource photograph : color Creator An entity primarily responsible for making the resource Dowlatshahi, Babak Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Santa Fe, NM Date A point or period of time associated with an event in the lifecycle of the resource 2016-09-16 Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Type The nature or genre of the resource still image Format The file format, physical medium, or dimensions of the resource jpeg Subject The topic of the resource Roosevelt, Mark Fielding, Ronald H. Identifier An unambiguous reference to the resource within a given context Roosevelt, M. Fielding, R. Inauguration 2016 Inauguration Presidents https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/b9e321d1f28cff64fb242b0d1e75b941.jpg 2da0dc4f64a3f2bfe216d5427534e424 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Physical Dimensions The actual physical size of the original image 25.5 x 20.5 cm. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data Photograph Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-0838 Title A name given to the resource C. Robert Sutton Speaking into a Microphone before Placing a Record on a Phonograph in the Great Hall in McDowell Hall, St. John's College, Annapolis, Maryland Description An account of the resource 1 photographic print : b&w Date A point or period of time associated with an event in the lifecycle of the resource 1942 [circa] Creator An entity primarily responsible for making the resource Unknown Subject The topic of the resource St. John's College (Annapolis, Md.). -- Students. Phonograph Sutton, Robert C. Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Type The nature or genre of the resource Still Image Format The file format, physical medium, or dimensions of the resource jpeg Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Alumni McDowell Hall https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/1ebd03dc7ffa2e52436d7654e0f7c622.mp3 ee3f50efed1ba6f0a46d3973746d95d3 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiocassette Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:56:09 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Caesars: From Plutarch to Shakespeare—and Beyond Description An account of the resource Audio recording of a lecture delivered on March 22, 2002, by Christopher Pelling as part of the Formal Lecture Series. Dr. Pelling is Regius Professor of Greek emeritus at the University of Oxford. Note: the recording started slightly after Dr. Pelling began speaking. This lecture is also part of the Steiner Lecture Series. The Andrew Steiner Memorial Lecture fund was created by the family and friends of Mr. Steiner, an alumnus (class of 1963) of St. John’s College, Annapolis. It was established to attract scholars from different disciplines and worlds, recognizing Andrew’s great intellectual versatility. Creator An entity primarily responsible for making the resource Pelling, C. B. R. Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 2002-03-22 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Subject The topic of the resource Shakespeare, William, 1564-1616. Julius Caesar Plutarch. Caesar Plutarch--Influence. Caesar, Julius--In literature. Rome--In literature. Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Pelling_Christopher_2002-03-22_ac Friday night lecture Steiner lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/a750e33a1cad4235ae601e22819f9821.pdf 472b3820a62b938da44bfd8fe905ba99 PDF Text Text Can Taxes Be Fair? Should They Be? Lecture to be delivered at St. John's College, Annapolis, October 11, 2013 By William S. Peirce Professor Emeritus of Economics, Case Western Reserve University, wsp@cwru.edu Abstract: The concept of "fairness" is so frequent in modern discussions of taxation that the absence of the term in ancient and medieval discussions of taxation may seem surprising. The older literature uses such terms as "intolerable" and "confiscatory," as well as "old" and "new." Fairness seems to have entered the tax discussion in the literature on natural rights that held sway in the era of the U.S. and French revolutions. Despite the ubiquity of fairness as a criterion in the discussion, it has not led to agreement in the design of taxes. The flaws are fundamental; the concept cannot be perfected. The economic concept of "opportunity cost" is more basic, and this leads directly to the choice of the land value tax. This offers a way out of the swamp of fairness in the design of a tax system. We hear references to fairness and taxation all the time. The President calls on the rich to pay their fair share. Organizations actively promote the "Fair Tax." If you study Public Finance you will hear much about specific versions of fairness in the form of horizontal equity (that equals should be treated equally) and vertical equity (that unequals should be treated in an appropriately unequal way). Although vertical equity has some echoes of Aristotle (bk.5, ch.3), the juxtaposition of the concepts of fairness and taxation is a recent phenomenon, beginning in the late 18th century—the intellectual climate that gave us Adam Smith, the American Revolution, and the French Revolution. That climate was, of course, the culmination of centuries of development of parliamentary control of the sovereign, as well as the evolution of Judeo-Christian concepts of natural law and individual rights. My topic is already impossibly large, but I want to sketch out an earlier view of taxation that explains why the pre-Enlightenment references to "fairness" are so scarce. Lacking the time and knowledge to review the facts of ancient history, and in the spirit of Adam Smith and the Scottish Enlightenment, I will engage in some "theoretical or conjectural history" inspired by Mancur Olson (2000, pp.3-12): Imagine yourself in a squalid village surrounded by wilderness a thousand or so years ago. You and your neighbors are engaged in the daily struggle to scrape together dinner. A cloud of dust appears on the horizon, followed by the thunder of galloping hooves. The villagers scramble to hide from the gang of roving bandits who kill or rape anyone they see, steal whatever they can carry, set fire to the rest, and gallop off. The surviving villagers crawl out of their hiding places and try to piece together their squalid life before winter sets in, knowing that the next gang of bandits may gallop in at any time. 1 �Now put yourself in the position of the roving bandits. (History is written by the winners.) You ride for days through the wilderness, risk the perils of attacking and plundering, and have very little to show for the effort because squalid villages provide scant booty. Eventually, the more perceptive roving bandits realize that by settling in a village as stationary bandits and protecting the inhabitants from other marauders, they can induce the villagers to work harder, accumulate capital, produce more, and provide them with more loot than they could extract by plunder. The stationary bandits can evolve into government by providing internal order, judging disputes, defending property rights, converting indiscriminate looting into predictable taxes, and providing the public goods that increase production and, hence, tax revenues—roads, bridges, irrigation, training in useful skills, etc. Although the villagers were safer and more comfortable when the roving bandits evolved into stable government, there was no doubt that the government was an alien power extracting surplus from the people. Taxes were not described as "fair" or "unfair." but rather as "tolerable" or "oppressive." A "good king" was someone who understood that arbitrary exactions and high tax rates did not yield him as much revenue as more moderate and predictable rates that allowed his subjects to prosper. The story with which you are probably more familiar is from I Samuel 8:5-18. Samuel judged Israel, but when he was old and his sons were corrupt, the people requested a king "like all the nations." Samuel explained what kings were like: "He will take your sons, and appoint them for himself, for his chariots, and to be his horsemen; and some shall run before his chariots. And he will appoint him captains over thousands, and captains over fifties; and will set them to ear his ground , and to reap his harvest, and to make his instruments of war, and instruments of his chariots. And he will take your daughters to be confectionaries, and to be cooks, and to be bakers. And he will take your fields, and your vineyards, and your oliveyards, even the best of them, and give them to his servants. And he will take the tenth of your seed, and of your vineyards, and give to his officers, and to his servants. And he will take your menservants and your maidservants, and your goodliest young men, and your asses, and put them to his work. He will take the tenth of your sheep: and ye shall be his servants." Again, the picture is that of an outsider who takes whatever he wants from his subjects. Fairness is not an issue. The alien power did not always settle in the subject territory. The Roman empire, and many others, extracted tribute from weaker nations. Often local agents (the hated "publicans" of the Bible) would be granted the tax franchise for a particular area. Each agent was responsible for paying the contractual amount to the government, but could keep whatever he could squeeze out of the populace. This ancient device of "tax farming" persisted in some form for many centuries, which suggests the value of using someone with local and particular knowledge to estimate what the government could extract from taxpayers. The problems with authorizing an agent of government to squeeze an arbitrary amount from the taxpayer have led most commentators to condemn any practice that seems to put revenue agents on commission. The details of the taxes and forms of government varied from place to place and time to time, but from the viewpoint of the mass of mankind the differences were not great. The masses could expect that nearly all of the surplus above subsistence would be extracted from them either as taxes or as rents to a landlord. When taxes became intolerable, the masses were squeezed to the point where 2 �population would actually be decreasing from malnutrition or because people fled from the high tax civilization to refuge with the barbarians. Even before the great invasions of Rome in the 5th century, central control of the Empire had weakened. As taxes on farmland were raised to the point where small farmers abandoned their plots, the large landowners absorbed the smaller plots and became the feudal lords who contended with each other and with kings for power and taxes throughout the Middle Ages. Much of the political history focusses on barons, dukes, princes, and kings, but the maneuverings of these folks for land and revenue made little difference to the mass of mankind. Nevertheless, the concept of justice in taxation was developing and property rights and contracts retained their force. The teachings of the Church became increasingly important. "God will certainly punish anyone who reinstitutes an old tax…" (Pope Gregory,c. 600,quoted in Adams, p. 137). New taxes, also, were forbidden by the Edict of Paris (614 ) and it was expected that an exactio inaudita (unheard-of tax) would provoke divine retribution. Kings would often have to ask the barons for special assistance to fund wars. This was generally granted for defensive wars, but not for offensive expeditions, which were expected to be self-financing through plunder and tribute. Montesquieu (Bk. XXX) cites a number of contracts between kings and cities or particular populations setting , among other matters, the taxes that could be levied on the city or group. These examples are from 7th – 12th centuries in western Europe when the king, however limited the geographic extent of his kingdom, was the highest earthly power until usurped or conquered. Yet kings did feel bound by their contracts. Whether this was evidence of a fear of eternal retribution, some innate feeling of ethics, or a pragmatic calculation of the value of being known to keep one's word, or some combination of these, the result was strengthen an ideal of justice in taxation that involved stability, predictability, and appropriateness. Today, "just" is often used as a synonym for "fair," but the medieval concept is more closely related to the idea of being fitting, proper, and lawful. In Plato's Republic (p.112, "The Guardians' Duties"), the potter should not be paid either too much or too little because only the optimum pay would result in the maximum production of high quality pots. This is purely an efficiency rule. It has nothing to do with fairness. Aristotle (Ethics, Bk.4, ch.2) described the contributions that a man should make to his community. They should reflect his wealth and station in life, being neither too cheap and tawdry nor too extravagant. For example, a very rich man might present a well-equipped naval vessel to his city. Someone with less wealth could offer a good banquet to the poor of the city. By the time that Aquinas [1225-1274] brought the later works of Aristotle into the mainstream of western scholarship, that version of justice in taxation was firmly established. That is, the individual's contribution to the community should be somehow proportionate to the wealth and standing of the individual, but there was no thought of using taxes to change the wealth of one person relative to another. King Louis the 14th of France [1638-1715] is reputed to have responded to reports that the people were complaining about high taxes by stating, "It is all mine anyway, I can take whatever I want." Whether he actually said that is irrelevant. The statement is a throwback to the view that taxing power is just the continuation of the plunder by the roving bandits that is justified by the power of the government. In stark contrast, the roughly contemporaneous words of John Locke (1690) define the new intellectual atmosphere: "…every man has a property in his own person; this nobody has any right 3 �to but himself. The labor of his body and the work of his hands, we may say, are properly his" (The Second Treatise of Government, para. 27). That leaves no room for slavery or feudalism and room only for those taxes to which he has consented. At this stage, reached in different countries at different times, it becomes possible and seemingly useful to speak of "fairness" in taxation. The concept presupposes the existence of a surplus above subsistence for the masses—a surplus that is not considered to be rightfully the property of landowners or governments, but rather belongs to the individuals who create it by their labor. This rough and impressionistic notion of a real divide in the way intellectuals perceived the world is borne out by a careful study by Alfani and Frigeni (2013). They analyzed manuscripts and printed documents from about 1100 to 1830 centering on Italy. They found that people were aware of the vast disparities in wealth throughout that period, but in the earlier years considered it acceptable and a natural part of a natural or God-given order. This is consistent with Aristotle, Augustine, and Aquinas. Beginning in the 16th century, they find signs of "jus naturalism" or individuals in a State of Nature with freedom and equality. This is consistent with Grotius, Hobbes, and Locke. The concept of the State of Nature reflects an abandonment of the Medieval (and earlier) concept of a natural hierarchical order. A key word count confirms the shift: "aequalitas" occurs 17 times from 1700-1785, and 334 times from 1789-1830; whereas "aequitas", which was common prior to the French revolution declined afterwards. To put it bluntly, the atmosphere shifted from the regal, "Why do they complain about taxes, it is all mine?" to the individualistic "What right do those bandits have to plunder any of my hard earned wealth?" Regardless of shifts in intellectual climate, the practical administrators needed to raise tax revenue, especially in times of war with the increasing cost of a professional military establishment. The traditional land taxes, tariffs, tolls, and excises had been stretched to the point where everyone recognized their weaknesses. By the beginning of the 19th century, many practical tax specialists thought that "capacity" or "faculty" to earn income was the appropriate tax base. It was commonly held that property was a good measure of faculty in a primitive economy, but that it had become progressively less comprehensive as an increasing proportion of income seemed to be generated without involving much visible property. When the British Prime Minister William Pitt was scrambling for revenue to fight the war against Napoleon, he proposed a "property tax" that was, in fact, an income tax. It was adopted in 1806. It relied heavily on "stoppage" (withholding at the source), but there were many difficulties in compliance in that era when the few written records were considered strictly confidential. One device was to establish committees of men in the same occupation and city who were charged with estimating the income for each of their competitors. The British tax was so thoroughly reviled, especially for its highly intrusive implementation, that when the wars ended and the budget stabilized in 1816 the tax was abolished and Parliament voted to destroy all of the records, as had been done with the income tax of 1404. Despite the public bonfire of destruction, the income tax administrator secretly retained a duplicate set (Adams, p.347). 4 �In 1842 Prime Minister Robert Peel persuaded Parliament to reinstate the income tax temporarily until the budget was in balance. It never was repealed, nor was the initial 3% flat rate maintained (Seligman, p. 132; Adams, p. 349). The top rate on earned income peaked at 83% before 1979, with a surcharge of 15% on investment income above 7,100 pounds (Pechman, p.298). The U.S. had a top rate in excess of 90% in the 1950s. So much for the assertions of Seligman, the great champion of the income tax for the U.S., that, "…the moderate rate [less than or equal to 6%] has been an important factor in the success of the income tax [in Great Britain]"(p. 216) and, with respect to Italy, "Obviously an income tax running up to twenty per cent, to which all manner of other kinds of local taxes are to be added, would indeed be unendurable if enforced to the hilt" (p. 353). The U.S. adopted an income tax to finance the Civil War in 1863. The rate was 3% on income exceeding $600 with a 5% rate above $10,000. Soon, the 5% rate was raised to 10%. The tax expired in 1872 when the revenue was no longer needed (Seligman, p. 437). Still, pressure was building for a permanent income tax. Enormous accumulations of wealth during the rapid growth of the post-civil war boom stirred the ire of reformers. Moreover, Lough (2013) stresses the growth of the free trade movement. If the tariffs that had traditionally supported the government, and aided northern manufacturers, were reduced, some substitute tax was necessary. Not least, the Progressive Movement, with its enthusiasm for direct government action and control of individual behavior, contributed to the pressure. An Income tax was passed in 1894 but declared unconstitutional. When the 16th Amendment was ratified in 1913, that obstacle was removed and the income tax soon followed because "wealth is escaping its due share of taxation" (Seligman, p.675). The rates were graduated, with a tax of 1% of the first taxable $20,000 and then increasing by 1% steps to 7% over $500,000 (equivalent to $11.7 million today). When Justice Oliver Wendell Holmes, Jr., opined in 1904 that "taxes are what we pay for a civilized society" he was living in a world of 1% tax rates. Is a 40% rate 40 times as civilized? The progressive rates of the new law were immediately challenged in court as a denial of "equality," but the Supreme Court allowed the law to stand. This was a significant change because legal theory and popular opinion had long supported the idea that taxing everyone an equal proportion of income (the Biblical "tithe" or 10%) was the just way to share the cost of government. In order to understand the sudden prominence of progressive taxation, it is necessary to look at what the economic theorists had been writing. Adam Smith's Wealth of Nations provides a compendium of the best economic thinking circa 1776. His four Maxims of Taxation are frequently cited: "I. The subjects of every state ought to contribute towards the support of the government, as nearly as possible, in proportion to their respective abilities; that is, in proportion to the revenue which they respectively enjoy under the protection of the state." "II. The tax which each individual is bound to pay ought to be certain, and not arbitrary." "III. Every tax ought to be levied at the time, or in the manner, in which it is most likely to be convenient for the contributor to pay it." 5 �"IV. Every tax ought to be so contrived as both to take out and to keep out of the pockets of the people as little as possible, over and above what it brings into the public treasury of the state." (summarized from book V, chapter II, Part II, pp. 777-779) Smith's advice and discussion have held up remarkably well for more than two centuries, but note that in Maxim I he slurred over the distinction between taxes as a price for the benefits received from government by the taxpayer (the benefit principle) and taxes as a measure of the ability of the individual to pay or the sacrifice that is inflicted on the taxpayer (ability-to-pay principle). He papers over the distinction by assuming that both approaches point to taxes proportional to income, although in other passages Smith suggests that additional taxes on luxury goods are acceptable because they fall only on the rich for goods they need only to display their status. A great deal of public finance literature since Wicksell (1896) has dealt with the benefit principle. Presumably, it is fair, and certainly efficient, to charge for services that can be directly or indirectly priced; e.g., charge tolls on limited access highways and finance construction of roads with a gasoline tax. After exhausting the cases where fees for service are technically feasible and politically acceptable, however, governments usually have a lot of bills to pay (e.g., the military budget and other aspects of foreign affairs, interest on the debt). This is where "ability to pay" usually becomes the standard. Instead of making the tax strictly proportional to income, the amount of income necessary for subsistence could be exempted, with a flat rate above that. This is sometimes called a digressive tax. For example, you pay 0% on the first $20,000 and 25% on everything above that. The marginal rate is 25% for everyone above the exemption level, but the average rate never quite gets to 25% although it approaches it for the very rich. [This is the concept underlying the "Flat Tax" advocated by Hall and Rabushka (1983).] Even this modest departure from strict proportionality raised warnings from those who forecast class warfare over the amount to be exempted. The strong support for progressive taxes in the economic mainstream originates in two separate, but highly interrelated, developments in economic theory during the century following the publication of the Wealth of Nations. The first of these is "utilitarianism" and the second is the dominance of marginal analysis. Jeremy Bentham (1748-1832) coined the "utilitarian" term and adopted the slogan, "the Greatest Happiness of the Greatest Number." Bentham was a lawyer, but wrote voluminously in many fields including the design of legislation. His work influenced economics directly through writings and also through his sometime coauthor, economist James Mill (1773-1836) and participation in the education of John Stuart Mill (1806-1873), son of James. While the slogan suggests a mathematically impossible double maximization, it does convey the sentiment that has motivated much of the subsequent analysis of taxation and public expenditures, including modern cost/benefit analysis. Although he did not use the modern words, Bentham wrote his utilitarian analyses under the assumption that the marginal utility of income is declining (see Robbins. 1965, p.62). This view starts with the plausible proposition that a dollar more or less makes a lot less difference to the rich person than does a dollar more or less to the person who has very few dollars. The extra dollar that allows the 6 �beggar to buy a crust of bread increases his welfare (or happiness or utility) more than a decrease of a dollar would decrease the utility of Warren Buffet. Decreasing marginal utility is usually assumed in economics for most ordinary goods and services. You may value one bag of carrots or professional tooth-cleaning, but the second one that month is worth less to you and the third even less than that. But is that true for income in general? Most economists ceased to ask that question after the "Marginal Revolution" of 1870. At about the same moment, William Stanley Jevons (1835-1882), writing in English, Leon Walras (1834-1910), writing in French, and Carl Menger (1840-1921), writing in German, adopted a form of analysis that a cynic described as "the reinvention of a crude form of differential calculus a couple of centuries after Newton and Leibniz." Nevertheless, this "marginal analysis" soon came to dominate economics and made the concept of decreasing marginal utility of income almost automatic for economists. If we assume that successive units of income have less value, and we assume that everyone is equal with respect to capacity to enjoy income, then the tax implications can be quite dramatic. If the objective is to collect the required tax revenue while imposing the minimum total sacrifice on society, the appropriate tax is zero up to a certain point and then 100% after that. That is, depending on the revenue requirements, the government would set one annual income, for example, $100,000. If you have less than that, you pay no tax. Anything you earn above that is sent directly to the Treasury. Of course, most people realized that this was not going to work well—at least not for long. A few extreme socialists and utopians wanted to believe in it, and even such a clever economic theorist as Edgeworth (1897) had difficulty in abandoning the spirit of it. Indeed, if one accepts the goal not just of minimizing the sacrifice of taxation, but of maximizing the utility of society, why would you not advocate continuing the leveling by transferring money from rich to poor until everyone had the same income? A clever socialist, George Bernard Shaw (1928, p.470) put it this way: "Socialism means equality of income or nothing, and that under Socialism you would not be allowed to be poor. You would be forcibly fed, clothed, lodged, taught, and employed whether you liked it or not. If it were discovered that you had not character and industry enough to be worth all this trouble, you might possibly be executed in a kindly manner; but whilst you were permitted to live you would have to live well." Faced with this logic, most economists retreated slightly to the goal, not of maximum utility or minimum sacrifice, but rather to the notion that everyone should endure the same proportional sacrifice of income. Opposition to progressivity was the common position even among the liberal utilitarians of the 19th century (Hutchison, 52). The opposition was based in part on the fear that progressivity would diminish incentives to work and invest and hence hobble the engine of economic growth that was essential for raising the laboring poor to a more comfortable level. Another factor was the fear that breaking the rule of proportionality would lead to continuing efforts to shift all tax burdens to the small minority of the very rich. (Adams, ch. 31). It is interesting that the economists , in general, were more caught up in the utilitarian notion that the happiness of society would be enhanced by reducing the burdens on the poor, while the lawyers retained the tradition from history and political philosophy that, in the absence of firm rules (such as proportional taxation), the problems of "faction" as discussed by Madison in Federalist 10 would tear the republic apart or turn it into a tyranny. 7 �But John Stuart Mill, who had grown up with utilitarianism, added this caution: "For what reason ought equality to be the rule in matters of taxation? For the reason that it ought to be so in all affairs of government. A government ought to make no distinction of persons or classes in the strength of their claims on it. If any one bears less than his fair share of the burden, some other person must suffer more than his share. Equality of taxation, therefore, as a maxim of politics, means equality of sacrifice." (Book V, Ch.I, section 2, p. 539). Despite the emphasis on sacrifice, "To tax the larger incomes at a higher percentage than the smaller is to lay a tax on industry and economy; to impose a penalty on people for having worked harder and saved more than their neighbors. It is not the fortunes which are earned, but those which are unearned, that it is for the public good to place under limitation." (pp.541-542) . Moreover, the income tax relies on self-reporting of income and, thus, "…is, in practice, unequal in one of the worst ways, falling heaviest on the most conscientious." (p. 556). Mill's comments provide a hint of the way out of the morass, but before we follow that trail, let us dig ourselves in deeper. If one accepts the view that the marginal utility of income is diminishing, and one accepts the goal that everyone should sacrifice an equal proportion of his total utility to pay for government, then it is easy to see that rich people should pay more dollars in taxes than should poor people. Does that require a progressive tax on income? It is easy to lapse into that conclusion, but it is incorrect, as was demonstrated cogently by Cohen-Stewart in 1889. [Also see Blum & Kalven. 1953]. Briefly, if the loss of a dollar is as painful to a rich man as to a poor, then equal sacrifice would call for equal dollar taxation. That is, a lump sum tax or a head tax—each person must pay a tax of, e.g., $1,000/year. That is the extreme of regressivity, unless one considers extremely decadent societies such as the strange world of pre-revolutionary France where, "One will hardly believe that in order to become noble it is sufficient to become rich; and to cease to pay taxes it is sufficient to become a noble. So there is only one way of escaping taxation and that is to make a fortune." [Pierre-Samuel Du Pont de Nemours, as quoted in Adams, p.218]. How quickly would the marginal utility of income have to decrease before equal sacrifice resulted in proportional taxation? The answer seems to be that proportional taxation is appropriate if, and only it, the marginal utility of income curve is a rectangular hyperbola! [See Musgrave, 1959, pp. 98-102] That is a wonderfully precise answer, but none of the assumptions can be observed to be met. We have no way to observe utility, let alone the shape of the marginal utility curve. Moreover, does anyone believe that the relationship between income and happiness is the same for everyone, or even for anyone throughout a lifetime? And we have not even inquired about the relationship between the happiness of one person and what he observes of his neighbors. In particular, if Mr. Smith is altruistic, deriving pleasure from observing that Mr. Knight is wealthy, and Mr. Knight is envious, deriving pleasure from the poverty of his neighbors, the way to improve the total happiness of society is to tax the altruist Smith and give the money to the mean-spirited Knight. Most of us would probably not vote for such a tax, even if it could be designed and administered. Yet, the prevailing economic definition of fairness leans on such weak reeds. In the modern public finance literature, fairness (and, perhaps, efficiency), depends on horizontal equity and vertical equity. Vertical equity depends on the degree of progressivity, as discussed above. Horizontal equity requires that "equals be treated equally," but, equals in respect to what? Academic tax specialists and 8 �reformers in the U.S. have usually begun with a bias toward a comprehensive definition of income as developed by Henry Simons (1950) and others. This amounts to whatever the person consumed during the year plus the net increase in wealth. Thus, it is the power to consume without decreasing wealth. In the purest form, consumption plus the net amount added to the accounts would be taxable income. That includes, for example, wages, interest, dividends, capital gains, rents (including the rent that an owner occupier could have received from his own house), gifts (of cash, securities, goods, and services). It would not matter where the power to consume came from or how it was used. The British debate, however, often favored the notion that wage and salary income should be discounted 25% relative to investment income because wages and salaries end when the recipient dies or loses his job. It is interesting that Andrew Mellon (1934, pp. 56-57), wealthy investor, Secretary of Treasury for Harding and Coolidge, and considered an arch conservative, stated, "The fairness of taxing more lightly incomes from wages, salaries and professional services than the income from business or from investments is beyond question." The actual tax law, of course, is a jumble of special treatment of particular sources and uses of income. Ownership of real estate is heavily favored, as is any investment that generates capital gains. Similarly on the uses side, medical expenses, gifts to charities, child care expenses, historic preservation, energy conservation, electric cars, and saving for education and retirement are among the favored expenditures. Which is fairer, the comprehensive definition or the tax law definition? Each exception to the comprehensive base for particular sources or uses of income is defended in the name of "fairness" by its beneficiaries. It matters because it is (roughly) taxable income, rather than comprehensive income, that determines who is treated as an equal of whom. In recent years an effort has emerged to consider consumption, rather than income, as the tax base and, thus, the fair basis for defining equality. The classical reasoning for this is that consumption measures what a person uses up from the product of the economy, whereas income should be a better measure of what he produces. John Stuart Mill arrived at consumption as the preferred tax base by an alternate route. In his view, the lower tax on earned income would allow the wage earner to accumulate savings for the years when his earning capacity had diminished. The modern pressure for consumption taxation is driven in part by belief that saving and investment should be encouraged. Some versions of consumption taxation also promise less intrusive administration (Zodrow and Mieszkowski, 2002). Some of these problems seemed remote prior to 1930 when the federal government took less than 5% of GDP, but with total government spending now exceeding one-third of GDP, including massive redistribution, the warnings about control of a dominant faction to prevent exploitation of the rest of society become more pertinent. In the modern era, economists have continued to analyze the effects of taxation on incentives to earn income and balance these against changes in social utility, defined in some unmeasurable way. The philosopher Rawls (1971) added the twist of assuming that only the income of the person with the lowest income needed to be a concern of public policy. But economists and philosophers of the Rawlsian type do not stop to consider the Madisonian question of what will happen to a tax bill of the most sophisticated design when it is submitted to Congress. Nor do they 9 �consider the possibility that the sovereign is a revenue maximizing entity at war with his subjects; i.e., a stationary bandit. Because of the impossibility of defining a "fair" tax, it is worthwhile searching for a different approach. The comment by Mill, "It is not the fortunes that are earned, but the fortunes that are unearned..." provides the starting point. Of course, an income tax becomes totally arbitrary and capricious if the IRS agent has to review your return to judge each receipt for its "worthy earnedness." Spare us that intrusion! In fact, it is possible to make a distinction between earned and unearned if we are willing to give up the idea of taxing the individual on his income and turn, instead, to a tax levied on the source of the unearned income. This does require giving up progressivity as it is usually defined because the concept applies only to people. The specific alternative to consider is the land value tax (LVT) as developed with great vigor and insight by Henry George in his best-selling book, Progress and Poverty (1879). LVT had antecedents in both practice and theory, including the Physiocrats, Smith, Ricardo, and Mill, but George and those inspired by George have worked out the details most fully. To put the matter in its simplest form, the LVT would replace other taxes with a single levy on the market value of the land that each person claims title to. Thus, the mechanics are similar to the existing real estate tax used by most local governments and school districts in the U.S. The difference is that the tax would apply only to the value of the land. All buildings and other improvements would be exempt. The market value of land reflects the income you could receive just from holding title to the land. Thus, if you happened to inherit a block of vacant land in the middle of Manhattan, or any other thriving city, you could easily lease it to a developer who would do the work of arranging for a building to be built and rented out and managed. The developer would be compensated for his work, but you could just sit back and enjoy the lease payments. Those payments would be described by an economist as "economic rent." The proposed LVT would be designed to take a substantial portion (e.g., 90%) of the economic rent, but it would be levied as a percentage of the market price of the land, so that you could not avoid it by leaving the land idle. You would have a strong incentive to put the land to work at the optimum moment. If you think of imposing a LVT today while dropping all other taxes it may seem unfair to those who have just invested their hard-earned savings into a piece of land. That is the transition problem that arises with any change in the tax law—there are winners and losers, and sometimes special transition rules can be adopted to ease the pain. Most parcels of land in the city already have buildings on them, so the taxpayer would save by eliminating the building tax while paying more for the land. The most important point is that the LVT would, over time, make the whole economy, especially the cities, function more efficiently. The LVT is easier to justify if we think of starting with a blank slate, before anyone has laid claim to land. The words of John Locke are the starting point for the analysis of property by many in the classical liberal tradition: 10 �26. God, who has given the world to men in common, has also given them reason to make use of it to the best advantage of life and convenience. The earth and all that is therein is given to men for the support and comfort of their being. And though all the fruits it naturally produces and beasts it feeds belong to mankind in common, as they are produced by the spontaneous hand of nature; and nobody has originally a private dominion exclusive of the rest of mankind in any of them, as they are thus in their natural state; yet, being given for the use of men, there must of necessity be a means to appropriate them some way or other before they can be of any use or at all beneficial to any particular man. The fruit or venison which nourishes the wild Indian, who knows no enclosure and is still a tenant in common, must be his, and so his, i.e., a part of him, that another can no longer have any right to it before it can do him any good for the support of his life. 27. Though the earth and all inferior creatures be common to all men, yet every man has a property in his own person; this nobody has any right to but himself. The labor of his body and the work of his hands, we may say, are properly his. Whatsoever then he removes out of the state that nature has provided and left it in, he has mixed his own labor with, and joined to it something that is his own, and thereby makes it his property. It being by him removed from the common state nature has placed it in, it has by this labor something annexed to it that excludes the common right of other men. For this labor being the unquestionable property of the laborer, no man but he can have a right to what that is once joined to, at least where there is enough and as good left in common for others. (John Locke. 1690. The Second Treatise of Government). This analysis has a powerful appeal for the situation where land is a free good. Locke, himself, noted that significant restriction in the famous closing phrase of the quote, “where there is enough and as good left in common for others.” Although Locke tried to make the case that the world had enough good unclaimed land that men might enclose and homestead, few would try to argue that proposition today. When land of a particular quality is no longer a free good, unregulated markets will readily generate annual rental rates for particular parcels, and those annual rents can readily be capitalized into sales prices for parcels that change hands and appraised values for parcels that do not. Land rents, like other prices, can serve to allocate inputs to their most productive uses. The rents are an opportunity cost that must be paid by the user of the land if the economy is to operate efficiently. But who should receive that rent? Henry George argued that the rent should belong to society because it either measures the natural advantage of a parcel; e.g., superior fertility of soil or location on a natural trade route, or the efforts of other people; e.g., highways, ports, and other public infrastructure, the activities of neighbors that attract business to your block, and the growth of population of the community. The opposition to LVT often cites the unfairness of taking nearly all the rent, and hence, nearly all the value, of property in land. Most holders of land today have acquired it in legal and morally 11 �defensible ways. That is correct and is a serious concern, but there are two sets of counterarguments. Georgists often claim that even a fully legal land title still leaves the buyer of land as the holder of stolen property. After all, British titles date to a roving bandit, "a French bastard landing with an armed banditti," as Thomas Paine (1776, p.16) so gently expressed it. U.S. titles generally date to a grant by a European monarch of land that belonged to someone else. Even in the rare case when a title does not originate in "force or fraud," --even if it originates in Locke's enclosure from the state of nature—why should that historical accident contribute to the inequality of fortunes today? The set of arguments that I find more convincing, however, relate to the comparison of the LVT with nearly all other feasible taxes. If the LVT is theft, it is a one-time problem. The income tax robs people every year of the fruit of their labors. When this moral case is combined with the efficiency and privacy advantages of the LVT, the case, to me, seems overwhelming. So, rather than arguing about fairness or justice in taxation, let's shift the focus toward the one tax base that has a well-defined market value based on opportunity cost; i.e., what the market determines to be the rent of the land. The focus can then shift away from the utilitarian pseudo-science of minimizing unobservable "sacrifices" and maximizing unseen "utilities" or pretending that we can say anything about the "fairness" of taking from one person to give to another. To quote Frank Chowderov (1946, p.267), "Taxation is highwaymanry made respectable by custom, thievery made moral by law," while the LVT just allows the community to reclaim the value that it has produced. References Adams, Charles. 1993. For Good and Evil: The Impact of Taxes on the Course of Civilization. Lanham, Maryland: Madison Books. Alfani, Guido, and Roberta Frigeni. 2013. "Inequality (un)perceived: The emergence of a discourse on economic inequality from the Middle Ages to the Age of Revolutions." Dondena Working Papers, No. 58. Milan: Carlo F. Dondena Centre for Research on Social Dynamics, Univ. Bocconi. Aristotle. c. 330 B.C. The Ethics of Aristotle, translated by J.A.K. Thomson. London: Penguin Books, 1955. Backhaus, Juergen, and Richard E. Wagner. 1987. "The Cameralists: A Public Choice Perspective." Public Choice 53 (No.1): 3-20. Blum, Walter J., and Harry Kalven, Jr. 1953. The Uneasy Case for Progressive Taxation. Chicago: University of Chicago Press. Buchan, James. 2003. Crowded with Genius; The Scottish Enlightenment: Edinburgh's Moment of the Mind. New York: HarperCollins. 12 �Chodorov, Frank. 1946. "Socialism via Taxation." In Fugitive Essays: Selected Writings of Frank Chodorov. Compiled, Edited, and with an Introduction by Charles H. Hamilton. Indianapolis: Liberty Fund, 1980. Cohen-Stuart, Arnold Jacob. 1889. "On Progressive Taxation." Musgrave and Peacock, pp.48-71. Edgeworth, Francis Ysidro. 1897. "The Pure Theory of Taxation." Musgrave and Peacock, pp.119-136. George, Henry. 1879. Progress and Poverty: An Inquiry into the Cause of Industrial Depressions and of Increase of Want with Increase of Wealth. The Remedy. Garden City, NY: twenty-fifth anniversary edition, Doubleday, Page & Company, 1911. Hall, Robert E. and Alvin Rabushka. 1983. Low Tax, Simple Tax, Flat Tax. New York: McGraw-Hill, 1983. Holmes, Oliver Wendell, Jr. 1904. Compania de Tabacos v. Collector, 275 U.S.87, 100. Hutchison, T.W. 1953. A Review of Economic Doctrines, 1870-1929. Oxford: The University Press, 1962. Locke, John. 1690. The Second Treatise of Government. New York: The Liberal Arts Press, 1952. Lough, Alexandra Wagner. 2013. "The Federal Income Tax and the Georgist Movement." Pittsburgh: Lecture presented to the meeting of the Council of Georgist Organizations, August 8, 2013. Mellon, Andrew W. 1934. Taxation: The People's Business. New York: Macmillan Company. Mill, John Stuart. 1848. Principles of Political Economy. Abridged by J. Laurence Laughlin. New York: D. Appleton and Company, 1884. Montesquieu, Baron de. 1748. The Spirit of Laws. Thomas Nugent, trans. New York: The Colonial Press, rev.ed., 1900. Musgrave, Richard A. 1959. The Theory of Public Finance. New York: McGraw-Hill. Musgrave, Richard A. and Alan T. Peacock. 1967. Classics in the Theory of Public Finance. New York: St. Martin's Press. Olson, Mancur. 2000. Power and Prosperity: Outgrowing Communist and Capitalist Dictatorships. New York: Basic Books. Paine, Thomas. 1776. Common Sense. In Basic Writings of Thomas Paine.New York: Willey Book Company, 1942. Pechman, Joseph A. 1987. Comparative Tax Systems: Europe, Canada, and Japan. Arlington, VA: Tax Analysts. Plato. c. 380 B.C. The Republic of Plato. Cornford translation. New York: Oxford University Press, 1945. Rawls, J.A. 1971. A Theory of Justice. Cambridge, MA: Belknap Press. 13 �Robbins, Lionel. 1965. The Theory of Economic Policy in English Classical Political Economy. London: Macmillan & Co. Seligman, E.R.A. 1914. The Income Tax: A Study of the History, Theory, and Practice of Income Taxation at Home and Abroad. New York: Macmillan, 2nd ed. 1914. Shaw, Bernard. 1928. The Intelligent Woman's Guide to Socialism and Capitalism. New York: Brentano's Publishers. Simons, Henry C. 1950. Federal Tax Reform. Chicago: The University of Chicago Press. Smith, Adam. 1776. An Inquiry into the Nature and Causes of the Wealth of Nations. New York: Modern Library. 1937. Wicksell, Knut. 1896. "A New Principle of Just Taxation." Musgrave and Peacock, pp.72-118. Zodrow, George R. and Peter Mieszkowski. 2002. United States Tax Reform in the 21st Century. New York: Cambridge University Press. 14 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Page numeration Number of pages in the original item. 14 pages Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Creator An entity primarily responsible for making the resource Peirce, William Spangar Title A name given to the resource Can taxes be fair? : Should they be? Date A point or period of time associated with an event in the lifecycle of the resource 2013-10-11 Format The file format, physical medium, or dimensions of the resource pdf Description An account of the resource Typescript of a lecture delivered on October 11, 2013 by William Peirce as part of the Formal Lecture Series. Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Rights Information about rights held in and over the resource A signed permission form has been received stating, "I hereby grant St. John's College permission to: Make an audio recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audio recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online." Type The nature or genre of the resource text Subject The topic of the resource Taxation Fairness. Economic aspects. Language A language of the resource English Identifier An unambiguous reference to the resource within a given context Bib # 80998 Relation A related resource <p><a title="Audio recording" href="http://digitalarchives.sjc.edu/items/show/45">Audio recording</a></p> Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/1a240f1a567f64d9a88d16b3932ef4a7.mp3 5e88a97280a7d1ce8613931a0744545b Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:51:44 Original Format The type of object, such as painting, sculpture, paper, photo, and additional data wav Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Creator An entity primarily responsible for making the resource Peirce, William Spangar Title A name given to the resource Can taxes be fair? : Should they be? Date A point or period of time associated with an event in the lifecycle of the resource 2013-10-11 Format The file format, physical medium, or dimensions of the resource mp3 Description An account of the resource Audio recording of a lecture delivered on October 11, 2013 by William Peirce as part of the Formal Lecture Series. Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Rights Information about rights held in and over the resource A signed permission form has been received stating, "I hereby grant St. John's College permission to: Make an audio recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audio recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online." Type The nature or genre of the resource sound Subject The topic of the resource Taxation Fairness. Economic aspects. Language A language of the resource English Identifier An unambiguous reference to the resource within a given context Bib # 81119 Relation A related resource <a title="Typescript" href="http://digitalarchives.sjc.edu/items/show/44">Typescript</a> Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/8cfca53db9011a2ff7f54d3551f59a70.jpg b64e299f6aa8889fc23d20b3cc18581f Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Physical Dimensions The actual physical size of the original image 25.5 x 20.5 cm. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data Photograph Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-1646 Title A name given to the resource Carol Angell, of Mount Holyoak College Talks with Edwin J. Delattre and Mrs. Delattre after the Inauguration Ceremony for Edwin J. Delattre, Annapolis, Maryland, Fall 1980 Description An account of the resource 1 photographic print : b&w Date A point or period of time associated with an event in the lifecycle of the resource 1980-09 Creator An entity primarily responsible for making the resource Unknown Subject The topic of the resource Delattre, Edwin J. Angell, Carol Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Type The nature or genre of the resource Still Image Format The file format, physical medium, or dimensions of the resource jpeg Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Inauguration Presidents https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/3417d4c84320f169ff4b75a9cb79b8e1.jpg e512842407016b3a58dfe7ef087a703d Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Physical Dimensions The actual physical size of the original image 25.5 x 20.5 cm. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data Photograph Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-1779 Title A name given to the resource Carolyn J. Howard, Barbara Leonard, Marilyn Mylander Standing outside during the Inauguration Luncheon for Edwin J. Delattre, Annapolis, Maryland, Fall 1980 Description An account of the resource 1 photographic print : b&w Date A point or period of time associated with an event in the lifecycle of the resource 1980-09 Creator An entity primarily responsible for making the resource Unknown Subject The topic of the resource Howard, Carolyn J. Leonard, Barbara Hopkins Mylander, Marilyn Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Type The nature or genre of the resource Still Image Format The file format, physical medium, or dimensions of the resource jpeg Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Alumni Deans Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/794018d8790e2e2c50c6273acf541285.jpg 0b082ab3f46718b7977991afab5e729d Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Physical Dimensions The actual physical size of the original image 25.5 x 20.5 cm. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data Photograph Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-1780 Title A name given to the resource Carolyn J. Howard, Barbara Leonard, Marilyn Mylander Standing outside during the Inauguration Luncheon for Edwin J. Delattre, Annapolis, Maryland, Fall 1980 Description An account of the resource 1 photographic print : b&w Date A point or period of time associated with an event in the lifecycle of the resource 1980-09 Creator An entity primarily responsible for making the resource Unknown Subject The topic of the resource Howard, Carolyn J. Leonard, Barbara Hopkins Mylander, Marilyn Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Type The nature or genre of the resource Still Image Format The file format, physical medium, or dimensions of the resource jpeg Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2a21be450eacf0ff5389e23457fa035e.jpg 2f3f5a9c670456d24b9bb90e561dd2f3 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Physical Dimensions The actual physical size of the original image 25.5 x 20.5 cm. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data Photograph Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-0473 Title A name given to the resource Carpenters Rebuilding a Staircase in Pinkney Hall, St. John's College, Annapolis, Maryland Description An account of the resource 1 photographic print : b&w Date A point or period of time associated with an event in the lifecycle of the resource 1942 [circa] Creator An entity primarily responsible for making the resource Unknown Subject The topic of the resource Pinkney Hall (St. John's College, Annapolis, MD) 1940-1950. Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Type The nature or genre of the resource Still Image Format The file format, physical medium, or dimensions of the resource jpeg Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Pinkney Hall https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/54c4e17a88bc39e73df7beb0aa19a12f.jpg 878412308d13093179d7b3b985eaca68 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Physical Dimensions The actual physical size of the original image 25.5 x 20.5 cm. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data photograph Resolution Resolution of the image in dpi. 600 dpi Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-2224 Title A name given to the resource Carroll-Barrister House, St. John's College, Annapolis, Maryland Description An account of the resource 1 photographic print : b&w Creator An entity primarily responsible for making the resource Warren, M. E. Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1940-1960 [circa] Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Type The nature or genre of the resource still image Format The file format, physical medium, or dimensions of the resource jpeg Carroll Barrister House https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/8b651a21d35fe61381a296383111e927.pdf 6fe021b1a25896ff88038036e5e15d71 PDF Text Text ����������������������������� Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource St. John's College Lecture Transcripts—Santa Fe Contributor An entity responsible for making contributions to the resource St. John's College Meem Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Santa Fe, NM Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College at the Santa Fe, NM campus. Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Page numeration Number of pages in the original item. 29 pages Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Cartesian certainty, or awakening from the dreams of a slave Description An account of the resource Transcript of a lecture given on September 15, 2006 by Janet Dougherty as part of the Dean's Lecture and Concert Series. Creator An entity primarily responsible for making the resource Dougherty, Janet Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Santa Fe, NM Date A point or period of time associated with an event in the lifecycle of the resource 2006-09-15 Rights Information about rights held in and over the resource Meem Library has been given permission to make this item available online. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Subject The topic of the resource Descartes, René, 1596-1650. Plato. Meno. Language A language of the resource English Identifier An unambiguous reference to the resource within a given context 24003551 Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/5a889798d4054d3fde4566a33fbd53e2.jpg 349f85051b839d13c7c95e025fdea951 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Image Collection—Annapolis Description An account of the resource <p>The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. </p> To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the <strong><a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener">Library’s Image Collection Use Policy</a></strong>.<br /><br />Click on <strong><a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7">Items in the Image Collection—Annapolis Collection</a></strong> to view and sort all items in the collection. Publisher An entity responsible for making the resource available St. John's College Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Identifier An unambiguous reference to the resource within a given context imagecollectionannapolis Still Image A static visual representation. Examples include paintings, drawings, graphic designs, plans and maps. Recommended best practice is to assign the type Text to images of textual materials. Physical Dimensions The actual physical size of the original image 12.5 x 18 cm. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data black and white photograph, Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Identifier An unambiguous reference to the resource within a given context SJC-P-0731 Title A name given to the resource Cary Stickney wearing a toga and laurel wreath and carrying a torch in the street at the Real Olympics, Annapolis, Maryland Description An account of the resource Cary Stickney wearing a toga and laurel wreath and carrying a torch in the street at the Real Olympics, Annapolis, Maryland, circa 1970s. Date A point or period of time associated with an event in the lifecycle of the resource circa 1970s Creator An entity primarily responsible for making the resource Unidentified Subject The topic of the resource Real Olympics (St. John's College, Annapolis, MD). St. John's College (Annapolis, Md.) -- Students. Stickney, Cary Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Type The nature or genre of the resource still image Format The file format, physical medium, or dimensions of the resource jpeg Rights Information about rights held in and over the resource St. John's College owns the rights to this photograph. Alumni Real Olympics Reality