We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on ?The Philosophy of Logical Atomism? truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig (...) Wittgenstein. It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John Shosky. An unpublished manuscript by Peirce identified as having been composed in 1883?1884 in connection with the composition of Peirce's ?On the Algebra of Logic: A Contribution to the Philosophy of Notation? that appeared in the American Journal of Mathematics in 1885 includes an example of an indirect truth table for the conditional. (shrink)

My purpose here is purely historical. It is not an attempt to resolve the question as to whether Russell did or did not countenance nonclassical logics, and if so, which nonclassical logics, and still less to demonstrate whether he himself contributed, in any manner, to the development of nonclassical logic. Rather, I want merely to explore and insofar as possible document, whether, and to what extent, if any, Russell interacted with the various, either the various candidates or their, ideas that (...) Dejnožka and others have proposed as potentially influential in Russell’s intellectual reactions to nonclassical logic or to the philosophical concepts that might contribute to his reactions to nonclassical logics. (shrink)

A survey is provided of the Soviet-Russian logician and historian Sof'ja A. Janovskaya (1896?1966). She wrote survey articles on logic, and also historical and philosophical essays on logic and on mathematics. A selected bibliography of her writings is appended.

We consider the history of logic in pre-Petrine. Petrine. and immediate post-Pctrine Russia (from the 15th to the mid-18th centuries) and especially of the Petrine era from the late 17th to early 18th century. Throughout much of this time, the clergy evinced strong hostility towards logic. Nevertheless, a small number of academics and clerics such as Stefan Iavorskii and Fcofan Prokopovich kept Aristotelian logic alive during this period and provided the foundation for its development in the modern era.

Les contributions à la logique de MacColl et Charles Sanders Peirce (1839-1914) ont été les deux plus profondes influences sur le travail de Ernst Schröder (1841-1902) en logique algébrique. Dans son Vorlesungen über dieAlgebra der Logik, Schröder a cité MacColl comme l’un de ses précurseurs les plus importants. Schröder a comparé les travaux de Peirce avec les premières parties de la série d’articles intitulés « The calculus of equivalent statements » que MacColl publie entre 1877 et 1880. Schröder a attribué (...) la priorité à MacColl pour avoir anticipé les résultats de Peirce. Pour Schröder, MacColl était une phase préliminaire à l’algèbre de la logique de Peirce. (shrink)

Les contributions à la logique de MacColl et Charles Sanders Peirce (1839-1914) ont été les deux plus profondes influences sur le travail de Ernst Schröder (1841-1902) en logique algébrique. Dans son Vorlesungen über dieAlgebra der Logik, Schröder a cité MacColl comme l’un de ses précurseurs les plus importants. Schröder a comparé les travaux de Peirce avec les premières parties de la série d’articles intitulés « The calculus of equivalent statements » que MacColl publie entre 1877 et 1880. Schröder a attribué (...) la priorité à MacColl pour avoir anticipé les résultats de Peirce. Pour Schröder, MacColl était une phase préliminaire à l’algèbre de la logique de Peirce. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Logic Pamphlets of Charles Lutwidge Dodgson and Related PiecesIrving H. AnellisFrancine F. Abeles, editor. The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces. The Pamphlets of Lewis Carroll, 4. New York-Charlottesville-London: Lewis Carroll Society of North America-University Press of Virginia, 2010. Pp. xx + 271. Cloth, $75.00.Until William Bartley’s rediscovery and reconstruction of Dodgson’s lost Part II of Symbolic Logic, Lewis Carroll’s reputation in logic, when (...) taken seriously, rested upon his few published articles on logical paradoxes and puzzles, while his published books, The Game of Logic and Symbolic Logic, were regarded as suitable perhaps as pedagogical tools, but dismissed otherwise as amusements, on a par with the Alice works. Richard Braithwaite asserted (“Lewis Carroll as Logician”) that “Carroll regarded formal and symbolic logic not as a corpus of systematic knowledge about valid thought nor yet as an art for teaching a person to think correctly.” He suggested that Dodgson used his pseudonym for his popular and whimsical writings, reserving his legal name only for his serious mathematical products. Philosophers practicing linguistic analysis in their assault on nonsense deriving from misuse of language meanwhile developed an interest in Carroll (e.g. George Pitcher, “Wittgenstein, Nonsense, and Lewis Carroll”). Abeles, on the contrary, stresses the seriousness of Dodgson’s pedagogical and popularizing mission (195–99).Bartley’s discovery opened the door for reevaluating Dodgson as a serious logician, and Abeles has been in the forefront of that reevaluation. Her general introduction and introductions to the main divisions of this collection of Carroll’s publications (and additional material from his Nachlass and a handful of publications of others, composed in response to Carroll’s published articles) place his serious logical work and its significance in historical perspective, providing a deeper, more sophisticated view than found in Bartley’s “Editor’s Introduction” to Lewis Carroll’s Symbolic Logic. Abeles also offers brief introductions to the individual entries, which describe their physical characteristics and circumstances of composition.Dodgson aligned with the majority of those British logicians of his day, starting with George Boole, who understood formal logic to be Aristotelian syllogistic, and symbolic logic to be syllogistic logic expressed algebraically. His notational innovation was employing indices to terms so that, independently of the arrangement of terms, propositions could easily be read; thus, “xy0” can be read as “no x are y” or “no y are x” and “x1y0” as “all x are not y” or “no x are y”. In dealing with the classical elimination problem in the class calculus—to determine the maximum information, without duplications, obtainable from a given set of premises—Dodgson in his later work and unpublished letters anticipated several concepts of automated theorem proving.Central to both geometry and to formal logic are the rules of logical inference that establish the validity of arguments and guarantee that conclusions inferred from true [End Page 506] premises are true. The modern analytic tableaux, or tree method, is a fundamental tool in this regard, both for deriving theorems and for determining the validity or invalidity of the proofs for propositional calculus and first-order predicate calculus.Introducing his reconstruction of Part II of Symbolic Logic, Bartley noted that, along with the logic diagrams that Carroll devised, he also devised a tableau method that strongly resembled Beth’s semantic tableaux. Abeles went more deeply and convincingly into that resemblance in her earlier research. Beth’s tableaux, together with Hintikka’s model sets, were the direct ancestors of Smullyan’s analytic tableaux, which in turn are the theoretical basis for the Robinson resolution method that continues to be central to much work in programming logic.Abeles has also shown that the work in Studies in Logic by Charles Peirce and his logic students at Johns Hopkins University served as a source of inspiration for Dodgson. More critically, she demonstrated that Dodgson devised and employed the tree method for carrying out proofs of syllogisms and chains of syllogisms, or soriteses, in Part II of Symbolic Logic (see her “Lewis Carroll’s Method of Trees: Its Origins in Studies in Logic,” Modern Logic 1 [1990]: 25–34). The tree... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviews 105 NEW RUSSIAN WORK ON RUSSELL IRVING H. ANELLIS Modern Logic Publishing I Box 1036, Welch Ave. Station Ames, JA 5°010-1036, USA A. S. Kolesnikov. cI»HJIOCOcPHJl BepTPaHa PacceJIa [Filosofija Bertrana Rassela]. Leningrad: Izdatel'srvo Leningradskogo Universiteta, 1991. Pp. 232. 3 rub. 30 kop.. Anatolii Sergeevich Kolesnikov is a relatively new name in Russell studies,.r1.a1though his book shows a deep knowledge of the material available on Russell in (...) Russian and a wide acquaintance with Russell's publications in English and in Russian translation.1 In this work, which translates as The Philosophy ofBertrand Russel~ Kolesnikov traces the evolution of Russell's "world-view", while presenting a traditional Soviet interpretation of Russell's place in "bourgeois" philosophy. This monograph presents for the first time in Russian a thorough analysis of the evolution of Russell's philosophy as the outstanding representation of contemporary bourgeois philosophy, and is the first major study on Russell's philosophy in Russian since the appearance in'1962 ofSoviet philosopher 1. S. Narskii's The Philosophy ofBertrand Russell2 Russell himself is viewed by Kolesnikov as the best representative of the bourgeois humanist, philosopher, and mathematician. The author seeks a critical understanding of the historical and philosophical sources of Russell's ideas and conceptions and of the influence which these exercised and continue to exercise on contemporary Western philosophy and science. The author's aim is to "uncover" the neo-realist empiricist direction of Russell's philosophy as it manifested itself as a condition of his scientific and epistemological thinking. As had been usual for Soviet studies of Western "bourgeois" philosophers and their philosophies, Lenin and his empiriocriticism serves as a foil for the elucidation of Russell's thought and its development. Probably the most famous example of the dialectical attack on anaI Kolesnikov is also the author of The Freethought ofBertrand Russell [Svobodomyslie Bertrana Rassela] (Moscow: Mysl', 1978). 2 The Philosophy ofBertrand Russell: Lectures for Students in the University Philosophy Faculty [Filosofija Bertrana Rassela: lekcija dlja studentovfilosofikih fakul'tov universitetov] (Moscow: 1962). In the first footnote (on p. 60) to his translation of the article on "Bertrand Russell in the Great Soviet Encyclopedia: Translation from Russian", Russel~ nos. 23-4 (1976): 60-2, Charles Haynes wrote that "Narskiy... appears to be a leading Soviet writet on Russell's philosophy." In fact Narskii wrote extensively on philosophy of logic, for which work he is bcst known. 106 Reviews lytic philosophy revolved around the rather rough treatment accorded to A. J. Ayer when he lectured at Moscow State University in 1962. This methodology for criticizing "bourgeois idealism" has declined in recent years as a consequence of perestroika; from as early as 1987 Soviet philosophers have managed to refrain from employing this tactic in their writings (as one may readily see, e.g., from Zinaida Sokuler's recent paper on "Wirrgenstein on the Contradictions in Logic and in the Foundations of Mathematics"3). Kolesnikov's discussion of political-ideological, social and moral issues is limited to the Preface, which also presents a brief sketch of Russell's life, especially his education and the earliest of the philosophical influences at Cambridge, of course Russell's visit in 1920 to Soviet Russia and the writings that derived from that trip, especially his book The Practice and Theory of Bolshevism, and of his travels in China. Here Kolesnikov notes Russell's ties to the Fabian socialists and names in particular the Webbs, H. G. Wells and "other members representative of the bourgeois intelligentsia" (p. 5). Mention is also made here of his activism for nuclear disarmament and against the American war in Indochina, and of the essay "Why I Am Not a Christian". We are told at the very outset (p. 3) that "the name of this philosopher is widely known in our country." The remainder of the book is concerned with Russell's technical philosophy, i.e. with his work in philosophy of mathematics, logic, philosophy of language, metaphysics and epistemology. Kolesnikov divides Russell's philosophical evolution into three stages (p. 22). The "early" period (1894-1910) is the developmental stage, characterized by the influence ofneo-Hegelianism and neo-Kantianism and by the development of the conception of... (shrink)

Van Heijenoort’s account of the historical development of modern logic was composed in 1974 and first published in 1992 with an introduction by his former student. What follows is a new edition with a revised and expanded introduction and additional notes.

I use van Heijenoort’s published writings and manuscript materials to provide a comprehensive overview of his conception of modern logic as a first-order functional calculus and of the historical developments which led to this conception of mathematical logic, its defining characteristics, and in particular to provide an integral account, from his most important publications as well as his unpublished notes and scattered shorter historico-philosophical articles, of how and why the mathematical logic, whose he traced to Frege and the culmination of (...) its formative period in the incompleteness results of Gödel, became modern logic, as distinct from the traditional logic of Aristotle, and why and how the logistic tradition that led from Frege through Russell, rather than the algebraic tradition that led from De Morgan and Boole through Peirce and Schröder, came, in his view, to define modern logic. (shrink)

Abstract:I begin by asking whether there was a Fregean revolution in logic, and, if so, in what did it consist. I then ask whether, and if so, to what extent, Russell played a decisive role in carrying through the Fregean revolution, and, if so, how. A subsidiary question is whether it was primarily the influence of The Principles of Mathematics or Principia Mathematica, or perhaps both, that stimulated and helped consummate the Fregean revolution. Finally, I examine cases in which logicians (...) sought, in the years immediately following publication of the Principles and Principia, to integrate traditional logic into the Fregean paradigm, focusing on the case of Henry Bradford Smith. My proposed conclusion is that there were different means adopted for rewriting the syllogism, in terms of the logic of relations, in terms of the propositional calculus, or as formulas of the monadic predicate calculus. This suggests that the changes implemented as a result of the adoption of the Russello-Fregean conception of logic could more accurately be called by Grattan-Guinness’s term convolution, rather than revolution. (shrink)

(No abstract is available for this citation).

Jean van Heijenoort was best known for his editorial work in the history of mathematical logic. I survey his contributions to model-theoretic proof theory, and in particular to the falsifiability tree method. This work of van Heijenoort’s is not widely known, and much of it remains unpublished. A complete list of van Heijenoort’s unpublished writings on tableaux methods and related work in proof theory is appended.

Writing the biography of an intellectual or cultural figure, in which there are few if any familiar historical signposts, can be extremely daunting. Unlike the celebrity or the military or political personality, there are few if any incidents of action to recount. Rather, there are primarily ideas to describe, and the biographical subject’s thought processes and interactions, insofar as these have been recorded, to explain and to evaluate. Thus, one must depend in large part upon the background and knowledge of (...) the reader to assist in making sense of the movement of the biographee’s thought. There are, of course, exceptions. Albert Einstein might be one, if only because he became a public figure and his upending .. (shrink)