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Books that Laid the Foundation for AIImportant Books in the History of Thought AITopics > Overview | History > Classic Books > Foundation Books Some of the classics in philosophy, linguistics, science fiction and other fields that have influenced the thinking of AI scientists. Detailed summaries from online catalogues courtesy of Bernard Quaritch Antiquarian Books. ASIMOV, Isaac. iRobot first published in 1950; introduced Robbie the robot. BABBAGE, Charles. Table of the Logarithms of the Natural Numbers, from 1 to 108000 … Stereotyped. – Second Edition. London, for B. Fellowes, 1831.Tall 8vo, pp. xx, 201, [1] First published by Mawman in London in 1827, the tables were reprinted, without corrections, in 1829 by the publishers of our edition. ‘Computational aids began to haunt Babbage’s mind the day he realized that existing mathematical tables were peppered with errors whose complete eradication was all but infeasable. As a creature of his era – the machine-power revolution – he asked himself, at first only half in earnest, why a table of, say, sines could not be produced by steam. Then he went on to reflect that maybe it could. He was at the time enthusiastic about the application of the method of differences to tablemaking, and was indeed using it to compile logarithms. His finished table of eight-figure logarithms for the first 108,000 natural numbers is among the best ever made. While still engaged in this work, Babbage turned to the planning of a machine that would not only calculate functions but also print out the results’ (DSB). ‘Babbage designed his Difference Engine no. I to mechanize production of mathematical tables such as these. However, when Babbage undertook the production of these tables in 1826 he had only a small model of the machine. Babbage did not have a working portion of the Difference Engine no. I until 1832, and even that was insufficient to compute mathematical tables. Because of his inability to mechanize table production Babbage did not attempt to compute new tables. Instead, to assure the greatest accuracy possible, the proofs of these tables were checked a total of nine times against the tables of Callet, Hutton, Vega, Briggs, Gardiner, and Taylor, with the result that only nine errors were found in the first edition. These were corrected in the second edition of 1831, and no further errors were found in the tables in any of the later editions. To insure maximum legibility and ease of use, Babbage gave careful consideration to the tables’ typography, printing several test sheets on different colors of paper to discover which was least fatiguing to the eye’ (Origins of Cyberspace 50, on the 1834 edition). The Crawford Library catalogue lists experimental printings of this edition in various colours of paper and ink. Provenance: William Peck, who was observer at the private observatory of Robert
Cox at Murrayfield. In 1896 he was to become the first ‘City Astronomer’ of
Edinburgh and director of Calton Hill Observatory. Although no further corrections
were made to the later editions, this copy contains several corrections in pencil on the
final 13 pages. BECHER, Johann Joachim. Character, pro Notitia Linguarum Universali. Inventum steganographicum hactenus inauditum quo quilibet suam Legendo vernaculam diversas imò omnes Linguas, unius etiam diei informatione, explicare ac intelligere potest. Frankfurt, Johann Georg Spörlin for Johann Wilhelm Ammon and Wilhelm Serlin, 1661. ‘For each item in Becher’s dictionary there is an Arabic number: the city of Zürich, for example, is designated by the number 10283. A second Arabic number refers the user to grammatical tables which supply verbal endings, the endings for the comparative and superlative forms of adjectives, or adverbial endings. A third number refers to case endings. The dedication “Inventum Eminentissimo Principi” is written 4442. 2770:169:3. 6753:3, that is, “(My) Invention (to the) Eminent + superlative + dative singular, Prince + dative singular”. ‘Unfortunately Becher was afraid that his system might prove difficult for peoples who did not know the Arabic numbers; he therefore thought up a system of his own for the direct visual representation of numbers. The system is atrociously complicated and almost totally illegible. Some authors have imagined that it is somehow akin to Chinese. This is hardly true. What we have, in fact, is a basic graphical structure where little lines and dots at various points on the figure represent different numbers ... [However, Gaspar Schott’s Technica curiosa (1664), and Becher’s system have been seen] as tentative models for future practices of computer translation. In fact, it is sufficient to think of Becher’s pseudo-ideograms as instructions for electronic circuits, prescribing to a machine which path to follow through the memory in order to retrieve a given linguistic term, and we have a procedure for a word-for-word translation (with all the obvious inconveniences of such a merely mechanical program)’ (Umberto Eco, The Search for the Perfect Language, pp. 201–3). Galland pp. 19-20 (‘among other things the work contains a numeral code of 10,000 Latin words’); STC German B489; Stojan 39 and 41; OCLC locates only four copies, Library of Congress, Washington, Princeton, and Cornell. BERTRAND, Joseph Louis François. Calcul des probabilités. Paris, Gauthier-Villars, 1889. (FIRST PRINTING, 1888). BOOLE, George et al. The Cambridge Mathematical Journal [vols. 1-4]. [continued as:] The Cambridge and Dublin Mathematical Journal [vols. 1-9, i.e. 5-13 of the preceding]. Cambridge, Macmillan, Barclay, Whittaker, et al, 1841-1854. ‘Boole’s first published work, Researches in the theory of analytical transformations, appeared in the Cambridge Mathematical Journal of November 1839 [printed in vol. II of the journal, with the general title dated 1841]. Eighteen months later, Thomson’s first publication, On Fourier's expansions of function in trigonometrical series (signed simply ‘P.Q.R.’), appeared in the same journal, and in 1845 Thomson became editor of the Journal under its new title of Cambridge and Dublin Mathematical Journal’ (online article on George Boole by University of Glasgow, Special collections). ‘In papers in the Cambridge Mathematical Journal in 1841 and 1843, Boole dealt with linear transformations ... This was the starting point of the theory of invariants ... Other papers dealt with differential equations, and the majority of those published after 1850 studies the theory of probability, closely connected with Boole’s work on mathematical logic’ (DSB). BORGHI, Pietro. Qui comenza la nobel opera de arithmethica ne la qual se tracta tute cosse amercantia pertinente facta ... [Colophon:] Venice, Erhard Ratdolt, 2 August, 1484. ‘This work is more elaborate than the Treviso arithmetic, and had a far greater influence on education. More than any other book it set a standard for the arithmetics of the sixteenth century, and none of the early textbooks deserves more careful study. Borghi first treats of notation, carrying his numbers as far as “numero de million de million de million”‚ and making no mention whatever of the Roman numerals. In the same spirit he eliminates all of the medieval theory of numbers, asserting that he does this because he is preparing a practical book for the use of merchants’ (Smith). ‘The boys (there is no record of any girls attending these schools) began their training in the abacus schools around the age of 10 or 11, usually immediately after two years in an elementary grammar school where they learned the basic skills of reading and writing. They generally stayed in the abacus schools for about two years and were taught the basic principles of arithmetic and practical mathematics: how to write the numbers, how to multiply and divide, how to deal with fractions, and how to solve the basic mathematical problems. Sections of the course were also devoted to understanding the complex Florentine monetary system. The school even followed a familiar routine of lessons, exercises, recitations and even an occasional holiday party. It appears that nearly all the educated men of the Renaissance gained their basic understanding of mathematics in schools such as these, including, for example, such notables as Leonardo da Vinci and Niccolò Machiavelli. When grouped with the earlier schools of reading and writing, higher schools of Latin grammar, and the educational apex of the university, it is apparent that the abacus schools were an integral part of an educational system’ (van Egmond, pp. 8-9). BMC V 289; Goff B1034; Poggendorff I, col. 241; Smith pp. 19-20 and ‘The first great commercial arithmetic’ Isis 8 (1926) pp. 41-49; Stillwell 151; Van Egmond, p. 293. CAPEK, Karel. R.U.R. (Rossum's Universal Robots). (1921).
CARDANO, Girolamo. Artis magnae, sive de regulis algebraicis Lib. unus. Qui & totius operis de Arithmetica, quod opus perfectum inscripsit, est in ordine decimus. [Colophon:] Nuremberg, Johann Petri, 1545. ‘Notable was also Cardano’s research into approximate solutions of a numerical equation by the method of proportional parts and the observation that, with repeated operations, one could obtain roots always closer to the true ones. Before Cardano, only the solution of an equation was sought. Cardano, however, also observed the relations between the roots and the coefficients of the equation and between the succession of the signs of the terms and the signs of the roots; thus HE IS JUSTLY CONSIDERED THE ORIGINATOR OF THE THEORY OF ALGEBRAIC EQUATIONS’ (DSB). Cardano’s Ars magna was ‘the most important contribution to algebra in the 1500s, [and included] the solution for cubic equations taken from Tartaglia’ (Dibner). Adams C651; Dibner 103; Milestones of Science 35; Norman 400; Parkinson pp. 39- 40; Poggendorff I, col. 376; Source Books in the History of Mathematics 16; NUC locates copies at Harvard, Columbia University, Burndy Library, Yale, and Mount Holyoke College, South Hadley; OCLC adds locations at the Smithsonian Institute, Linda Hall Library, Buffalo and Erie County Public Library, Illinois, and Brown University. CARNAP, Rudolf. The logical syntax of language. London, Kegan Paul, 1937. 8vo, pp. xvi, 352, 20. This work develops the distinction between object language and meta-language that was characteristic of Hilbert’s formalism. It also introduces Carnap’s distinction between language used in the material mode and in the formal mode. In the material mode, sentences which appear to be about things in the world are in fact syntactical, formal sentences about language. ‘One purpose of this book, in opposition to the view attributed to Wittgenstein, was to show that a language could significantly be used to express its own syntax. Another was to make good Carnap’s claim that philosophy, to the extent that it could be a cognitive discipline, had to consist in the logic of science, which was itself identified with the logical syntax of a scientific language’ (A. J. Ayer). DAVYS, John, and John WALLIS. An Essay on the Art of Decyphering. In which is inserted a Discourse of Dr. Wallis. Now first publish’d from his original Manuscript in the Publick Library at Oxford. London, for Lawton Gilliver and John Clarke, 1737. ‘His solutions – nearly all nomenclators, a few monoalphabetics – had a considerable impact on current events. In the summer of 1689, he solved the correspondence between Louis XIV and his ambassadors in Poland’ (Kahn p. 168). Wallis was very successful in pointing out to his employers how important cryptography was and managed to convince them to grant him substantial pay-rises. ESTC t010607; Galland p. 53. DE MORGAN, Augustus. An Essay on Probabilities, and on their application to Life Contingencies and Insurance Offices. London, Longman, Brown, Green, & Longmans, [1838]. DESCARTES, René. Discours de la Methode pour bien conduire sa raison, & chercher la verité dans les sciences … Leiden, Jan Maire, 1637. ‘This celebrated work is remarkable for a number of things: for its autobiographical
tone, for its very compressed exposition of the foundations of the Cartesian system,
and for the fact that it was written in French … The French style that Descartes
developed for this purpose has always been regarded as a model for the expressions of
abstract thought in that language’ (Encyclopedia of Philosophy). DESCARTES, Réné. Specimina Philosophiae: seu Dissertatio de Methodo rectè regendae rationis, & veritatis in scientiis investigandae: Dioptrice et Meteora. Ex Gallico translate, & ab Auctore perlecta, variisque in locis emendata. Amsterdam, Louis Elzevir, 1644. I. This is the first Latin edition of the Discours de la Methode, Descartes’s ‘outline of the Cartesian scientific method, summed up in the famous Four Rules presented in Book 2, together with scientific treatises to illustrate the methods range’ (Norman). ENCRYPTION MACHINE. A type T-D ‘NEMA’ Enigma enciphering machine. Switzerland, Zellweger AG, c. 1948. THIS IS THE VERY LAST ‘NEMA’ OF ENIGMA-MACHINE FORMAT PRODUCED, ONE OF THE FEW SURVIVING EXAMPLES INTENDED FOR MILITARY USE AND COMPLETE WITH THE INSTRUCTION MANUAL. Only 640 such machines, numbered from 100 to 740, were built. They were manufactured in number order, numbers 100 to 640 being strictly for training purposes and those numbered from 641 to 740 being reserved for use in time of war. The training model and the service or military model were designed to be incompatible with each other. The present machine, number 740, therefore differs from the majority of extant machines. Between 1938 and 1940, Germany had supplied Switzerland with a number of commercial Enigma machines. Correctly suspecting that both the Germans and the Allies were able to read their Enigma-coded traffic, the Swiss modified these machines, creating what has come to be known as the ‘Swiss Enigma K’. However, security doubts persisted, leading the Swiss to develop a completely new enciphering machine. This machine, called ‘Nema’ (an acronym derived from ‘Neue Maschine’), was designated ‘T-D’ (‘Tasten-Drücker’ or ‘key-printer’). It works on the same principle as Enigma, but the ‘scrambler’ component contains ten wheels, as compared with the four or five normal for a standard Enigma machine. These, arranged to work as four pairs plus a reflector rotor and a special ‘red’ rotor, result in a code security combination of at least 15,000,000,000,000,000,000,000,000. There is no settable input wheel as in the Swiss Enigma K machines, nor are there any Steckers (used to swap pairs of letters) as in the German service machines. The principle innovation lies in the irregular motion of the wheels, which are configured in a way which is intended to prevent the isolation of the fast wheel, as happened with the Enigma machines. FIBONACCI, Leonardo [or LEONARDO OF PISA]. [Liber abbaci, chapters 14 and 15]. [?Venice, c. 1480]. ‘An encyclopedic work treating much of the known mathematics of the thirteenth century on arithmetic, algebra, and problem solving’ (Sigler, Fibonacci’s Liber Abaci p. 4), it was instrumental in introducing the Hindu-Arabic numerals, thus revolutionizing both Western mathematics and commerce. ‘Italian merchants carried the new mathematics and its methods wherever they went in the Mediterranean world. The new mathematics also spread into Germany, where it was propagated by the cossists (a corruption of the Italian cosa, or thing, the unknown of algebra)’ (Sigler, ibid.). Divided into fifteen chapters, sections of the work, especially the advanced mathematics in chapters 14 and 15, survive as separate manuscripts. Ours is the manuscript from the collection of Baldassare Boncompagni who, based on a complete copy preserved at the Biblioteca Nazionale Centrale, Florence (Codice Magliabechiano Conv. Sopp. C.1. no. 2616), published the first modern edition of the Liber Abbaci in 1857. ‘Leonardo of Pisa, also known as Fibonacci, [composed] his Liber Abbaci in 1202, and again in revised form in 1228. He is most widely known because of a relatively insignificant problem in Liber Abbaci which gives rise to the Fibonacci sequence. However, Liber Abbaci has also been recognised as an important step in the development of algebra in medieval Europe. For example, Leonardo is seen as a pioneer in the development of systematic methods for solving linear equations in several unknowns and he gives one of the earliest accounts of the algebraic methods of al-Khwārizmī and Abū-Kāmil for solving quadratic equations … Chapter 14 is about calculation with square and cube roots, either using approximations or in the style of Euclid’s Elements X. Finally, Chapter 15 has three sections, one dealing with advanced proportion, another with (geometric or abstract) squares and cubes, and the last one dealing with the algebra of al-Khwārizmī’ (John Hannah, False Position in Leonardo of Pisa’s Liber Abbaci, pp. 1-2). ‘The Liber Abbaci was, for centuries, one of the storehouses from which authors got material for works on arithmetic and algebra. In it are set forth the most perfect methods of calculation with integers and fractions, known at the time; the square and cube root are explained, cube root not having been considered in the Christian occident before; equations of the first and second degree leading to problems, either determinate or indeterminate, are solved by the methods of “single” or “double position,” and also by real algebra. He recognised that the quadratic x2 + c = bx may be satisfied by two values of x’ (Cajori, A History of Mathematics p. 123). ‘Leonardo Fibonacci, the first great mathematician of the Christian West, was a member of a family named Bonacci, whose presence in Pisa since the eleventh century is documented … His father, as a secretary of the Republic of Pisa, was entrusted in 1192 with the direction of the Pisan trading colony in Bugia (now Bougie), Algeria. He soon brought his son there to have him learn the art of calculating, since he expected Leonardo to become a merchant. It was there that he learned methods “with the new Indian numerals,” and he received excellent instruction. On the business trips on which his father evidently soon sent him and which took him to Egypt, Syria, Greece (Byzantium), Sicily, and Provence, he acquainted himself with the methods in use there through zealous study and in disputations with native scholars. All these methods, however – so he reports – as well as “algorismus” and the “arcs of Pythagoras” (apparently the abacus of Gerbert) appeared to him as in “error” in comparison with the Indian methods. It is quite unclear what Leonardo means here by the “algorismus” he rejects; for those writings through which the Indian methods became known, especially after Sacrobosco, a younger contemporary of Leonardo, bear that name … Around the turn of the century, Leonardo returned to Pisa. Here for the next twenty-five years he composed works in which he presented not only calculations with Indian numerals and methods and their application in all areas of commercial activity, but also much of what he had learned of algebraic and geometrical problems. His inclusion of the latter in his own writings shows that while the instruction of his countrymen in the solution of problems posed by everyday life was indeed his chief concern, he nevertheless also wished to provide material on theoretical arithmetic and geometry for those in more advanced questions. He even speaks once of wanting to add the “subtleties of Euclid’s geometry”; these are the propositions from books II and X of the Elements, which he offers to the reader not only in proofs, in Euclid’s manner, but in numerical form as well. His most important original accomplishments were in indeterminate analysis and number theory, in which he went far beyond his predecessors. ‘The word abacus in the title does not refer to the old abacus, the sand board; rather it means computation in general, as was true later with the Italian masters of computation, the maestri d’abbaco. Of the second treatment of 1228, to which “new material has been added and from which superfluous removed,” there exist twelve manuscript copies from the thirteenth through the fifteenth centuries; but only three of these from the thirteenth and the beginning of the fourteenth centuries are complete. Leonardo divided this extensive work, which is dedicated to Michael Scotus, into fifteen chapters … ‘[In chapters 14 and 15 of the Liber abbaci] Leonardo shows himself to be a master in the application of algebraic methods and an outstanding student of Euclid. Chapter 14, which is devoted to calculations with radicals, begins with a few formulas of general arithmetic. Called “keys” (claves), they are taken from book II of Euclid’s Elements. Leonardo explicitly says that he is forgoing any demonstrations of his own since they are all proved there. The fifth and sixth propositions of book II are especially important; from them, he said, one could derive all the problems of the Aliebra and the Almuchabala [the title of al- Khwārizmī’s treatise]. Square and cube roots are taught numerically according to the Indian-Arabic algorithm, which in fact corresponds to the modern one. Leonardo also knew the procedure of adding zeros to the radicands in order to obtain greater exactness … Next, examples are given that are illustrative of the ancient methods of approximation … The chapter then goes on systematically to carry out complete operations with Euclidean irrationals … The proof, which is never lacking, of the correctness of the calculation is presented geometrically … At the end of chapter 15, which is divided into three sections, one sees particularly clearly what complete control Leonardo had over the geometrical as well as the algebraic methods for solving quadratic equations and with what skill he could use them in applied problems. The first section is concerned with proportions, and their multifarious transformations … The second section first presents applications of the Pythagorean theorem, such as the ancient Babylonian problem of a pole leaning against a wall and the Indian problem of two towers of different heights. On the given line joining them (i.e., their bases) there is a spring which shall be equally distant from the top of the towers … The third section contains algebraic quadratic problems (questiones secundum modum algebra). First, with reference made to “Maumeht,” i.e. to al-Khwārizmī, the six normal forms ax2 = bx, ax2 = c, bx = c, ax2 + bx = c, ax2 + c = bx (here Leonardo is acquainted with both solutions), and ax2 = bx + c are introduced; they are then exactly computed in numerous, sometimes complicated, examples ... Leonardo also includes equations of higher degrees that can be reduced to quadratics. For example it is given that (1) y = 10/x; (2) z = y2/x; and (3) z2 = x2 + y2. This leads to x8 + 100x4 = 10,000. The numerical examples are taken from the algebra of al-Khwārizmī and al-Karajī, frequently even with the same numerical values. In this fourth section of the Liber abbaci there also appear further names of the powers of the unknowns … ‘With Leonardo a new epoch in Western mathematics began; however, not all of his ideas were immediately taken up. Direct influence was exerted only by those portions of the Liber abbaci and of the Practica that served to introduce Indian- Arabic numerals and contributed to the mastering of the problems of daily life. Here Leonardo became the teacher of the masters of computation (the maestri d’abbaco) and of the surveyors, as one learns from the Summa of Luca Pacioli, who often refers to Leonardo. These two chief works were copied from the fourteenth to the sixteenth centuries … Leonardo was also the teacher of the “Cossists,” who took their name from the word causa, which was used for the first time in the West by Leonardo in place of res or radix. His alphabetical designation for the general number or coefficient was first improved by Viète (1591), who used consonants for the known quantities and vowels for the unknown. Many of the problems treated in the liber abbaci, especially some of the puzzle problems of recreational arithmetic, reappeared in manuscripts, and then in arithmetics of later times … Cardano, in his Artis arithmeticae tractatus de integris, mentions appreciatively Leonardo’s achievements when he speaks of Pacioli’s Summa. One may suppose, he states, that all our knowledge of non-Greek mathematics owes its existence to Leonardo, who, long before Pacioli, took it from the Indians and Arabs’ (Kurt Vogel in DSB). Imbedded in one of the mathematical puzzles contained in an earlier chapter of the work, the Fibonacci sequence has found application in stochastic processes, Fibonacci retracement, Fibonacci Vector Geometry (FVG), ‘a relatively modern branch of computational geometry which studies geometric objects that can be sequentially generated using Fibonacci-type recurrences’ (Sukanto Bhattacharya, ‘A Computational Exploration of the Efficacy of Fibonacci Sequences in Technical Analysis and Trading’ in Annals of Economics and Finance 1, p. 220), etc., and the Golden ratio found in it is observed in plant life, music, art, and architecture. Regarding his contribution to the history of financial mathematics it was recently suggested that Fibonacci was ‘the first to develop present value analysis for comparing the economic value of alternative contractual cash flows [and] he also developed a general method for expressing investment returns, and solved a wide range of complex interest rate problems … Stimulated by the commercial revolution in the Mediterranean during his lifetime … his discoveries significantly influenced the evolution of capitalist enterprise and public finance in Europe in the centuries that followed. Fibonacci’s discount rates were more culturally influential than his famous series’ (William N. Goetzmann, Fibonacci and the Financial Revolution, NBER GÖDEL, Kurt. On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Translated by B. Meltzer … with Introduction by R. B. Braithwaite. Edinburgh and London, Oliver & Boyd, [1962]. ‘Gödel’s paper is a milestone in the history of modern logic … As Hermann Weyl (1885–1955), a leading mathematician of the recent era, put it, “If the game of mathematics is actually consistent, then the formula of consistency cannot be proved within this game.” Gödel’s incompleteness theorems dealt a mortal blow to the final objective of Hilbert’s career, a formalized version of all classical mathematics’ (Burton, p. 581). Indeed, it is reported that ‘when Hilbert first learned about Gödel’s work from Bernays, he was “somewhat angry”’ (Reid p. 198). Gödel’s proof is often considered the most important contribution to logic since Aristotle. ‘He presented mathematicians with the astounding and melancholy conclusion that the axiomatic method [as presented in Russell and Whitehead’s Principia Mathematica] has certain inherent limitations, which rule out the possibility that even the ordinary arithmetic of the integers can ever be fully axiomatized’ (Nagel and Newman, Gödel’s Proof, p. 6). Here was proof that ‘a system like Principia Mathematica – or indeed any system rich enough to contain arithmetic within it – must contain certain propositions which are not “provable” within that system. It was clear, now, why the formalists [led by Hilbert] had encountered such difficulty in proving the consistency of arithmetic; this task, as they had envisaged it, can never, by its very nature, be brought to completion’ (Passmore p. 395). When Gödel wrote his paper at the age of only 25, ‘the notion of formal system, introduced by Frege in 1879, had become by then the accepted standard of precision in the foundation of mathematics. It seemed to embody the Aristotelian ideal of a perfect deduction from first principles. Gödel’s results, by showing that mathematics cannot be completely and consistently formalized in one system, shattered this ideal. The bounds of mathematics cannot be those of one formal system. Since mathematics had often been regarded as the standard of rational knowledge that other sciences should strive to attain, Gödel’s theorems seem to acquire significance for the whole body of human knowledge …’ (The Encyclopedia of Philosophy III, p. 356). HARRIS, James. Hermes: or, a Philosophical Inquiry concerning Language and Universal Grammar … By J. H. London, H. Woodfall for J. Nourse and P. Vaillant, 1751. ‘Harris said that he had learnt everything he knew about grammar not from English or French works but from the rationalist grammar of the Spanish grammarian Sanctius, whose Sanctii Minerva, seu de causis linguae Latinae was published in Salamanca in 1578… His general theory is that language, both spoken and written, and the thought processes it reflects, reveal a universality found not only in language but in Nature itself’ (Dictionary of Eighteenth-Century British Philosophers Vol. I, p. 402). Harris was an anti-Lockean, and distinguished sharply between the faculties of sensation and reflection. Language, for him, is associated primarily with reflection, and, although it can be used to express thoughts about the objects of sensation, this is inessential to it. His idea of a universal grammar has naturally led to comparisons with Saussure and Chomsky. HILBERT, David. Grundlagen der Geometrie. [Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, I Theil]. Leipzig, B.G. Teubner, 1899. In Grundlagen der Geometrie, David Hilbert presents the first widely recognized purely deductive development of Euclidean concepts, proceeding from undefined terms and unproved axioms to carefully derived propositions, with the possibility existing that such undefined terms as “point” and “line” can have representations other than those normally considered. Hilbert reconstructs Euclidean geometry in the algebraic framework of Cartesian coordinates and proceeds to show that if algebra is consistent then so are the Euclidean postulates. The work sparks renewed interest in Euclidean geometry, convincing a large number of mathematicians that geometry can be treated essentially as an abstract, purely formal system’ (Parkinson). ‘Hilbert’s goals in axiomatics were consistency and independence. Both problems
had been tackled before him. Non-Euclidean geometry was invented to show the
independence of the axiom of parallel lines, and models of non-Euclidean geometry
within Euclidean geometry proved its relative consistency. Hilbert’s approach was at
least partially different; his skilfully used tool was algebraization. Algebraic models
and countermodels were invoked to prove consistency and independence … In
Hilbert’s work and long afterward, algebraization of geometries has proved an
important force in creating new algebraic structures. Isolation and interplay of
incidence axioms and continuity axioms are reflected by analogous phenomena in the
algebraic models. In Hilbert’s work they led to structures which foreshadow the ideas
of field and skew field, on the one hand, and topological space, on the other, as well
as various mixtures of both. Indeed, Hilbert taught the mathematicians how to
axiomatize and what to do with an axiomatic system’ (DSB). HILBERT, David and Wilhelm ACKERMANN. Grundzüge der theoretischen Logik. Berlin, Julius Springer, 1928. A positive answer to the latter was expected, and was obtained the following year in
the doctoral dissertation of Kurt Gödel (published, in somewhat revised form, as
Gödel 1930)’ (The Cambridge History of Philosophy. 1870-1945, pp. 594-595).
This work ‘is considered the first elementary text clearly grounded in the formalism
now known as first-order logic (FOL). Hilbert and Ackermann also formalized FOL
in a way that subsequently achieved canonical status. FOL is now the core formalism
of all mathematical logic, and is presupposed by contemporary treatments of Peano
arithmetic and nearly all treatments of axiomatic set theory. The 1928 edition
included a clear statement of the Entscheidungsproblem (decision problem) for FOL,
and also asked whether that logic was complete (i.e., whether all semantic truths of
FOL were theorems derivable from the FOL axioms and rules). The first problem
was answered in the negative by Alonzo Church in 1936. The second was answered
affirmatively by Kurt Gödel in 1929. The text also touched on set theory and
relational algebra as ways of going beyond FOL. Contemporary notation for logic
owes more to this text than it does to the notation of Principia Mathematica, long
popular in the English speaking world’ (Wikipedia article on Principles of theoretical
logic). JEVONS, William Stanley. Pure logic and other minor works ... edited by Robert Adamson … and Harriet A. Jevons with a preface by Professor Adamson. London, Macmillan & Co., 1890. KEMPELEN, Wolfgang von. Mechanismus der menschlichen Sprache nebst der Beschreibung seiner sprechenden Maschine. Vienna, J. V. Degen, 1791. This work ‘stands alone as a milestone on the way to the phonograph. This talkingmachine, invented by de Kempelen, is based on an elaborate study of the human voice, and the first few plates illustrate physiologically how the vowels and consonants are sounded, reference being made to Helmont’s Alphabeti naturalis Hebraici delineation, 1667. The author then goes on to show how these sounds may be produced mechanically, and so arrives at the full description and illustration (on many plates) of his machine. It is based on a wind-instrument, the air is supplied by a bellows, and he claims in the end that by the use of various stops etc., he is able to make the machine talk easily in French, Italian and Latin; German, however, is more difficult. Though his machine differs from the phonograph, in that it does not reproduce the human voice from recorded sound vibrations, yet the inventor’s study of the voice and his method of reproducing it based on scientific principle prepared the way for others to follow.’ (Weil, Cat. 2, item 231). Goethe heard the machine perform and reported that it was ‘able to say some childish words very nicely’. Kempelen (1734–1804) later built a chess-playing automaton called ‘the Turk’ which won games against Benjamin Franklin and Napoleon. LEIBNIZ, Gottfried Wilhelm. Oeuvres philosophiques latines & françoises de feu. Tirées de ses manuscrits qui se conservent dans la bibliotheque royale a Hanovre et publiées par Mr. Rud. Eric Raspe. Avec une Préface de Mr. Kaestner. Amsterdam et Leipzig, J. Schreuder, 1765. [bound with:] [SIGORGNE, Pierre, or Louis DUTENS, attributed authors]. Institutions Leibnitiennes, ou précis de la monadologie. Lyon, Périsse, 1767. Leibniz refers to this work in a letter of 1714, and clarifies that, having written it in 1704- 5, he had renounced going to press, unwilling to publish a radical refutation of a recently dead author. In his introduction Raspe surmises that reasons of prudence and unwillingness to be distracted from the dominant controversies on calculus and on metaphysics might have prevented Leibniz from entering another contest. The publication of the Nouveaux essais in this 1765 edition were momentous and influential, and informed Hume’s and Kant’s reading of Leibniz. Aarsleff (op. cit., passim) has shown that the Nouveaux essais mark a pivotal moment in the philosophy of language. Scant evidence of sources and background is provided in Locke’s Essay, while Leibniz in his seriatim refutation offers a reconstruction of the ideal building blocks used by his opponent, as well as those employed by himself to defend the notion of a natural language, to reveal the protagonists, arguments and folds of the seventeenth-century discussion on Adamitic language and the possibility of organized knowledge of the world as it actually is. On inviting and prefacing the German translation of Monboddo’s anti-Lockean work on language, which had been received largely with lukewarm consideration, when not outright scorn, in a milieu strongly dominated by the Lockean tradition, Herder correctly predicts better chances of recognition and success for the Scottish philosopher in Germany, where the anti-Lockean perspective had been rendered more than acceptable by the diffusion of the Nouveaux essays. This edition also prints Leibniz’s other works concerning language, including those addressing the sign-based quality of the universal language which ought to be adopted by philosophy (‘Dialogus de connexione inter res & verba’, ‘Difficultates quaedam Logicae’ and ‘Historia & commendatio charactericae universalis quae simul fit ars inveniendi’), and also includes the ‘Examen du sentiment du P. Malebranche que nous voyons tout en Dieu’, and ‘Discours touchant la methode de la certitude & de l’art d’inventer’. The Leibniz is bound with a beautiful copy of the first edition of the anonymously published Institutions Leibnitiennes, also issued in octavo in the same year. It is ‘an accurate but critical account of Leibniz’s cosmological theories’ (DSB), attributed to Pierre Sigorgne, the author of the Instutions Newtoniennes, or sometimes to Louis Dutens; the text refers to an edition of Leibniz’ works being prepared by the same editor, and Dutens oversaw the publication of the Geneva Opera omnia that came out in 1768. The Institutions lay out the content of Leibniz’ exchanges with professor Canz of Tübingen on the topic of the monad. LEIBNIZ, Gottfried Wilhelm. Explication de l’Arithmetique binaire, qui se sert des seuls caracteres 0 & 1; avec des remarques sur son utilité, & sur ce qu’elle donne le sens des anciens figues Chinoises de Fohy. [with:] [FONTANELLE, Bernard le Bouyer]. Nouvelle arithmétique binaire. [contained in:] Histoire de l’Académie Royale des Sciences Année MDCCIII. Avec les Mémoires de Mathématiques & de Physique, pour la même Année. Paris, Jean Boudot, 1705. ‘Explication de l’arithmétique binaire’ by Leibniz appeared in the 1703 volume of the Mémoires de l’Académie Royale des Sciences [printed in 1705] on pages 85-89. This explanation of binary arithmetic was the first publication on this topic to result in a significant impact on the scientific community’ (Glaser, History of Binary and other Nondecimal Numeration p. 39). This is the second of Leibniz’s great trilogy of works on mathematics and computation, following Nova methodus pro maximis et minimis (1684), his independent invention of calculus, and preceding Brevis descriptio machinae arithmeticae (1710), his (decimal) mechanical calculating machine. Leibniz had conceived of a Machina Arithmeticae Dyadicae based on the binary system as early as 1679, but this was never constructed. Leibniz had been in possession of his ideas concerning binary arithmetic since the early 1670s, but seems first to have made them public in 1679 on his appointment to the court of Ernst August, Duke of Hanover. Outlining his plans to the Duke, he described a design for a calculating machine to operate the four rules in binary arithmetic. He recognised that the development of such a machine would not be easy: a much greater number of wheels would be needed than for the ordinary calculating machine (which had been constructed in 1671), with the consequent problems related to friction and smooth movement; but the greatest difficulty would be the mechanical conversion of ordinary numbers into binary and the binary answers into ordinary numbers. Perhaps it was on account of these seemingly insuperable obstacles that Leibniz never constructed the binary calculating machine, indeed never even mentioned it in his correspondence. The publication of the Explication was provoked by his correspondence with Joachim Bouvet, a member of the Jesuit Mission in China. Early in life Leibniz had developed an interest in China, and in April 1697 he edited a collection of letters and essays by members of the Mission, entitled Novissima Sinica. A copy of this came into the hands of Bouvet, who wrote to Leibniz on 18 October 1697 expressing his commendation of the work. Thus began an extended correspondence between the two men which proved to be very important for the dissemination of Leibniz’s ideas about binary arithmetic. The crucial exchange began on 15 February 1701, when Leibniz wrote to Bouvet describing for his correspondent the principles of his binary arithmetic, including the analogy of the formation of all the numbers from 0 and 1 with the creation of the world by God out of nothing. Bouvet immediately recognised the relationship between the hexagrams of the I ching and the binary numbers and he communicated his discovery in a letter written in Peking on 4 November 1701. This reached Leibniz, after a detour through England, on 1 April 1703. With this letter, Bouvet enclosed a woodcut of the arrangement of the hexagrams attributed to Fu-Hsi, the mythical founder of Chinese culture, which holds the key to the identification. Within a week of receiving Bouvet’s letter, Leibniz had sent to Abbé Bignon for publication in the Mémoires of the Paris Academy his Explication de l’Arithmetique binaire, … & sur ce qu’elle donne le sens des anciens figues Chinoises de Fohy. Ten days later he sent a brief account to Hans Sloane, the Secretary of the Royal Society. Leibniz viewed binary arithmetic less as a computational tool than as a means of discovering mathematical, philosophical and even theological truths. He remarked to Tschirnhaus in 1682 that he anticipated from the use of binary numbers discoveries in number theory that other progressions could not reveal. It was at the same time a candidate for the characteristica generalis, his long sought-for alphabet of human thought. With base 2 numeration Leibniz witnessed a confluence of several intellectual strands in his world view, including theological and mystical ideas of order, harmony and creation. ‘In the domain of mathematics, Leibniz regarded binary notation as intrinsically superior to decimal notation. Over and above this advantage, however, he believed that it contained the key to resolving both the problem of conceptual primitives and the problem of adequate characters. If it could be established, as Leibniz speculated from about 1679 onwards, that the only truly primitive concepts were those of God and Nothingness (or Being and Privation), then the symbols 1 and 0 would form the basis for an adequate characteristic, whose simplest signs would stand in an immediate relation to the two conceptual primitives’ (The Cambridge Companion to Leibniz pp. 236-7). Bernard Le Boyer de Fontenelle’s Nouvelle Arithmétique is contained on pages 58-63 of the part Histoire, written as secretary of the academy. ‘His unsigned article constituted an editorial comment on the Explication of Leibniz … Fontenelle pointed out the need that ten need not be the base of our arithmetic, and that indeed certain other bases would have advantages over it. Base 12, for example, would simplify dealing with certain fractions such as 1/3 and 1/4. He also noted that numbers have two sorts of properties, essential ones and those dependent on the manner of expressing them. As an example of the former he cited the property that the sum of the first n odd numbers equals n2, and of the latter that a number divisible by 9 has a digit sum also divisible by 9. This same property would hold for 11 in the case of base 12. He reported that Leibniz had worked with the simplest of all possible bases, base two. This base was not recommended for common use because of the excessive length of its number representation, but Leibniz considered it particularly suitable for difficult research and as possessing advantages absent from other bases. Fontenelle reported further that Leibniz had communicated this binary arithmetic in 1702, but had asked that no mention of it be made in the Histoire until he could supply an application. This application eventually came forth in the binary interpretation of the Figures of Fohy’ (Glaser, ibid., p.44). LOCKE, John.] An Essay concerning humane understanding. In four books. London, Tho. Basset, 1690. MOIVRE, Abraham de. The Doctrine of Chances: or, a Method of calculating the probability of Events in Play ... London: Printed by W. Pearson, for the Author, 1718. ‘De Moivre’s scientific immortality rests on chance, for his fame is securely founded in three books upon differing mathematical aspects of that subject, The Doctrine of Chances (1718, 1738, 1756), Annuities upon Lives (1725, and several later editions), and Miscellanea Analytica de Seriebus et Quadraturis (1730). ‘De Moivre’s earliest book on probability, the first edition of The Doctrine of Chances, was an expansion of a long (fifty-two pages) memoir he had published in Latin in the Philosophical Transactions of the Royal Society in 1711 under the title “De Mensura Sortis” (literally, “On the measurement of sorts”)’ (Stigler p. 71). ‘Also included in The Doctrine of Chances are great advances in problems concerning the duration of play; a clearer formulation of combinatorial problems about chances; the use of difference equations and their solutions using recurring series; and, as is illustrated by the work on the normal approximation, the use of generating functions, which, by the time of Laplace, came to play a fundamental role in probability mathematics’ (DSB). ‘The Theory of Probability owes more to [de Moivre] than to any other mathematician, with the sole exception of Laplace’ (Todhunter p. 193). Landmark Writings in Western Mathematics pp. 105-120; Norman 1529; Parkinson p. 143; Poggendorff II, col. 173; Tomash M 114. MOIVRE, Abraham de. Miscellanea analytica de seriebus et quadraturis. London, J. Tonson and J. Watts, 1730. ‘The most memorable of De Moivre’s discoveries emerged only slowly. This is his approximation to the binomial probability distribution, which, as the normal, or Gaussian, distribution, became the most fruitful single instrument of discovery used in probability theory and statistics for the next two centuries … ‘With his approximation of n! De Moivre was able, for example, to sum the terms of the binomial from any point up to the central term. This summation is equivalent to the modern normal approximation and is, indeed, the first occurrence of the normal probability integral. He even appears to have perceived, although he did not name, the parameter now called the standard deviation σ’ (DSB). ESTC t096683; Norman 1531; Parkinson pp. 148-149; Poggendorff II, col. 173. RIESE, Adam. Rechenung nach der lenge, auff den Linihen und Feder. Darzu forteil vnd behendigkeit durch die Proportiones, Practica genannt, Mit grüntlichem vnterricht des visierens. Leipzig: Jacob Berwalt, 1550. ‘The first forty-six folios contain the treatise “auff den Linihen,” the counter reckoning. This is followed (ff. 47-105) by that “auff der Feder,” the common algorism. The third part is the “Practica,” and the fourth the “Visieren” or gauging. The book represents the culmination of Riese’s work, and is the best exponent of the practical arithmetic of the middle of the century in Germany’ (Smith p. 252). The greatest of all the Rechenmeister of the sixteenth century, ‘Ries wrote his first two books while at Erfurt: Rechnung auff der linihen (1518), of which no copy of the first edition is known, and Rechenung auff der linihen vnd federn (1522), which had gone through more than 108 editions by 1656 … In 1525 Ries married Anna Leuber, by whom he had eight children. He then purchased his own home and became a citizen of Annaberg. He held important positions in the ducal mining administration: Rezessschreiber (recorder of mine yields, from 1525), Gegenschreiber (recorder of ownership of mining shares from 1532), and Zehnter auf dem Geyer (calculator of ducal tithes, 1533-1539). While fulfilling his official responsibilities he still found time to continue teaching arithmetic. He ran a highly regarded school, and improved and revised his books. During this period he wrote a comprehensive work, Rechenung nach der lenge, auff den Linihen vnd Feder, which far surpassed his books written at Erfurt, especially in the number of examples. Most of the work had been completed by 1525; but it was not published until 1550, after elector Maurice of Saxony had advanced the printing costs. Because the expense was so great, the book was reprinted only once, in 1616. ‘In all his arithmetic books (but with greatest detail in the one of 1550) Ries described how the computations were done, both on the abacus and with the new Indian methods. He employed the rule of three to solve many problems encountered in everyday life … Ries … furnish[ed] the student with a great number of exercises. The steps to be followed were presented in detail, and the reader could check the correctness of answers by following the procedure used to obtain them. Ries surpassed his predecessors in the presentation of his material: it was clear and orderly, and proceeded methodically from the simpler to the more difficult. ‘Besides the section on gauging, the Rechenung nach der lenge contains an extensive section entitled “Practica,” in which Ries solves problems according to the “Welsh practice” through the use of proportional parts. In addition he treats problems taken from recreational mathematics, solving them according to the regula falsi. Particularly noteworthy is the fact that in his table of square roots the fractions are repeated in a manner that prepared the way for the use of decimal fractions. ‘Ries did more than any previous author to spread knowledge of arithmetic, the branch of mathematics most useful in arts and trade. He was a pioneer in the use of Indian numerals. Ries soon became synonymous with “arithmetic”; to this day, “nach Adam SHANNON, Claude Elwood. Communication Theory of Secrecy Systems. New York, American Telephone and Telegraph Company, October, 1949. 8vo, pp. 656-715, contained in The Bell System Technical Journal, Vol. XXVIII, No. 4. ‘Claude Elwood Shannon was born in Petoskey, Michigan, on April 30, 1916, and was raised in nearby Gaylord, a small town in the north-central portion of Michigan’s southern peninsula. He majored in electrical engineering and mathematics at the University of Michigan and there developed an interest in communications and cryptology. At the Massachusetts Institute of Technology, where in 1940 he was awarded a Ph.D. in mathematics, he wrote a master’s thesis of such originality that it had an immediate impact on the designing of telephone systems. After a year at the Institute for Advanced Study in Princeton, he joined the staff of the Bell Telephone Laboratories. ‘There he built a maze-solving mouse, used to study circuitry for logic machines, and worked on a chess-playing machine, which may be regarded as the first step in the construction of computers for evaluating military situations and deciding the best move … “During World War II,” he has said, “Bell Labs were working on secrecy systems. I’d worked on communication systems and I was appointed to some of the committees studying cryptanalytic techniques. The work on both the mathematical theory of communications and the cryptology went forward concurrently from about 1941. I worked on both of them together and I had some of the ideas while working on the other. I wouldn’t say one came before the other – they were so close together you couldn’t separate them.” Though the work on both was substantially complete by about 1944, he continued polishing them until their publication as separate papers in the abstruse Bell System Technical Journal in 1948 and 1949. ‘Both articles – “A Mathematical Theory of Communication” and “Communication Theory of Secrecy Systems” – present their ideas in densely mathematical form … but Shannon’s terse and incisive style breathes life into them. The first paper is on information theory; the second dealt with cryptology in information-theory terms’ (Kahn pp. 743-744). SILVESTRI, Giacopo. Opus novum, praefectis arcium, imperatoribus exercituum, exploratoribus, patriae defensoribus, peregrinis, mercatoribus, militibus, architectis, ac omnis industriae & litteraturae studiosis, principibus maxime utilissimum pro cipharis, lingua Latina, Greca, Italica, & quavis alia multi formiter de scribentibus, interpretandisque. Opera nuova utilissima a signori mercatanti & ad ogni altra qualita di persone ... La qual opera e scritta in lingua Latina & replicata in lingua volgar. [colophon:] Rome, [Marcello Silber], 1526. ‘The little quarto-volume, published in Rome, 1526, by the Florentine Silvestri is an important precursor of the universal language systems of Kircher, Becher, and of the only recently identified Spanish Jesuit Pedro Bermudo. Silvestri’s work deserves thorough investigation. Opus novum is apparently the only work by Silvestri, who, in a biography of Florentine writers of the year 1722 is called an “Uomo d’Ingegno” ... Mentioned rarely in the cryptologic literature, this work is known as the first book which – although written in Latin – contains extensive summaries in Italian ... Starting from ideas similar to Trithemius’, but not influenced by him, Silvestri proposes to work out a method of encrypting, which anticipates the first code-books for telegraphic communication in the 1850s. Silvestri refers to handbooks with alphabetical lists of words, such as Tortelli’s Commentariorum grammaticorum ... which had to be agreed on by the two correspondents. The words of two copies of the same issue had to be fitted with identical numbers or other symbols by the sender and recipient of secret messages. This method, which resembles very much the use of modern code-books ... is extensively described’ (translated from Gerhard F. Strasser, Lingua Universalis, Kryptologie und Theorie der Universalsprachen im 16. und 17. Jahrhundert, Wolfenbütteler Forschungen, vol. XXXVIII, pp. 64-5). Silvestri does not restrict this method to words in the nominative case, singular, or
infinitive alone. Further symbols, added to the code for the word denote its
grammatical position – an important step towards a universal language, and at the
same time towards an artificial, machine-readable and computable language. VON NEUMANN, John. Theory of self-reproducing automata … edited and completed by Arthur W. Burks. Urbana and London, University of Illinois Press, 1966. ‘It had usually been assumed by thinkers on inanimate devices that their outputs must necessarily be less complex than themselves, and indeed this notion seems quite reasonable. Certainly all machines we can think of in the past had this quality. It was therefore not obvious that von Neumann’s question as to whether there exist selfreproductive automata would have a positive answer. In fact it did. ‘In June 1948 von Neumann gave a few lectures to a small group of us on the subject. These lectures were anticipatory to his paper for the Hixon Symposium, but they were quite detailed and indicated that he had progressed very far in his thinking. In fact there was no doubt that he already that spring saw in principle his way to the end. At the time he was thinking about a device which was in Burks’ terms “a kinematic model” as contrasted with his later construct which was a “cellular model.” All these things are beautifully presented by Burks in his completion of von Neumann’s work. ‘In his Hixon Symposium von Neumann presented his kinematic model and said that it was “feasible, and the principle on which it can be based is closely related to Turing’s principle …” He further discussed the fundamental notion of complication and surmised that automata whose complexity is below a certain level can only produce less complicated offspring, whereas those above a certain level can reproduce themselves “or even construct higher entities.” It is interesting to conjecture what would have been the effect on von Neumann’s work if he had known about DNA and RNA. He clearly stated in his writings and conversations on automata that the copying mechanism was performing “the fundamental act of reproduction, the duplication of the genetic material”’ (Herman H. Goldstine, The Computer from Pascal to Neumann p. 276). VON NEUMANN, John, and Oskar MORGENSTERN. Theory of games and economic behavior. Princeton, Princeton University Press, 1944. 8vo, pp. xviii, 625, [3] ‘Had it merely called to our attention the existence and exact nature of certain
fundamental gaps in economic theory, the Theory of games and economic Behaviour
… would have been a book of outstanding importance. But it does more than that. It
is essentially constructive: where existing theory is considered to be inadequate, the
authors put in its place a highly novel analytical apparatus designed to cope with the
problem. It would be doing the authors an injustice to say that theirs is a contribution
to economics only. The scope of the book is much broader. The techniques applied
by the authors in tackling economic problems are of sufficient generality to be valid in
political science, sociology, or even military strategy. The applicability to games
proper (chess and poker) is obvious from the title. Moreover, the book is of
considerable interest from a purely mathematical point of view … The appearance of
a book of the caliber of the Theory of Games is indeed a rare event’ (Leonid Hurwicz
in The World of Mathematics II, pp. 1267–1284). WITTGENSTEIN, Ludwig Josef Johann. Logisch-philosophische Abhandlung. [in:] Annalen der Natur- und Kulturphilosophie XIV, 3/4. Leipzig, Unesma, 1921. ‘The move to thought, and thereafter to language, is perpetrated with the use of Wittgenstein’s famous idea that thoughts, and propositions, are pictures - “the picture is a model of reality” (TLP 2.12). Pictures are made up of elements that together constitute the picture. Each element represents an object, and the combination of objects in the picture represents the combination of objects in a state of affairs. The logical structure of the picture, whether in thought or in language, is isomorphic with the logical structure of the state of affairs which it pictures. More subtle is Wittgenstein’s insight that the possibility of this structure being shared by the picture (the thought, the proposition) and the state of affairs is the pictorial form. “That is how a picture is attached to reality; it reaches right out to it” (TLP 2.1511). This leads to an understanding of what the picture can picture; but also what it cannot - its own pictorial form. ‘While “the logical picture of the facts is the thought”, in the move to language Wittgenstein continues to investigate the possibilities of significance for propositions. Logical analysis, in the spirit of Frege and Russell, guides the work, with Wittgenstein using the logical calculus to carry out the construction of his system. Explaining that “Only the proposition has sense; only in the context of a proposition has a name meaning” (TLP 3.3), he provides the reader with the two conditions for sensical language. First, the structure of the proposition must conform with the constraints of logical form, and second, the elements of the proposition must have reference (Bedeutung). These conditions have far-reaching implications. The analysis must culminate with a name being a primitive symbol, and this is manifested by the very abstract character of both names and (simple) objects. Moreover, logic itself gives us the structure and limits of what can be said at all’ (A. Biletzki, in the Stanford Encyclopedia of Philosophy). Wittgenstein had completed the present work in August 1918, whilst serving as a volunteer in the Austrian army, and still had the manuscript with him when he was taken prisoner by the Italians in November. ‘From his prison camp near Monte Cassino he wrote to Russell, to whom the manuscript was subsequently delivered by diplomatic courier through the offices of a mutual friend, J. M. Keynes … Wittgenstein was anxious to have his book, Logisch-philosophische Abhandlung, published immediately. Shortly after his release from imprisonment and his return to Vienna, in August 1919, he offered it to a publisher. He believed that his book finally solved the problems with which he and Russell had struggled. From Russell’s letter, however, he concluded that Russell had not understood his main ideas, and he feared that no one would. He and Russell met in Holland in December 1919 to discuss the book. Russell undertook to write an introduction for it, but the following May, Wittgenstein wrote to Russell that the introduction contained much misunderstanding and he could not let it be printed with his book. Subsequently the publisher with whom he had been negotiating rejected the book. Wittgenstein wrote to Russell, in July 1920, that he would take no further steps to have it published and that Russell could do with it as he wished. The German text was published in 1921 in Wilhelm Ostwald’s Annalen der Naturphilosophie. The following year it was published in London with a parallel English translation, under the title Tractatus Logicophilosophicus’ WITTGENSTEIN, Ludwig. Philosophische Untersuchungen / Philosophical Investigations. Translated by G. E. M. Anscombe. Oxford, Basil Blackwell, 1953. ‘The Philosophical Investigations was published in 1953 in two parts. Part I was written in the period 1936–1945 and Part II between 1947 and 1949 … Wittgenstein believed that the Investigations could be better understood if one saw it against the background of the Tractatus [Logico-Philosophicus (1922), the only book of his published in his lifetime]. A considerable part of the Investigations is an attack, either explicit or implicit, on the earlier work. This development is probably unique in the history of philosophy – a thinker producing, at different periods of his life, two highly original systems of thought, each system the result of many years of intensive labors, each expressed in an elegant and powerful style, each greatly influencing contemporary philosophy, and the second being a criticism of the first’ (The Encyclopedia of Philosophy VIII, 334). ‘The idea of a private language was made famous in philosophy by Ludwig Wittgenstein, who in §243 of his book Philosophical Investigations explained it thus: “The words of this language are to refer to what can be known only to the speaker; to his immediate, private, sensations. So another cannot understand the language”. … What Wittgenstein had in mind is a language conceived as necessarily comprehensible only to its single originator because the things which define its vocabulary are necessarily inaccessible to others. ‘Immediately after introducing the idea, Wittgenstein goes on to argue that there cannot be such a language. The importance of drawing philosophers’ attention to a largely unheard-of notion and then arguing that it is unrealizable lies in the fact that an unformulated reliance on the possibility of a private language is arguably essential to mainstream epistemology, philosophy of mind and metaphysics from Descartes to versions of the representational theory of mind which became prominent in late twentieth century cognitive science’ |
