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  1. Concepts and Axioms.A. S. Troelstra - 1998 - Philosophia Mathematica 6 (2):195-208.
    The paper discusses the transition from informal concepts to mathematically precise notions; examples are given, and in some detail the case of lawless sequences, a concept of intuitionistic mathematics, is discussed. A final section comments on philosophical discussions concerning intuitionistic logic in connection with a ‘theory of meaning’.
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  • How to Live Without Identity—And Why.Kai F. Wehmeier - 2012 - Australasian Journal of Philosophy 90 (4):761 - 777.
    Identity, we're told, is the binary relation that every object bears to itself, and to itself only. But how can a relation be binary if it never relates two objects? This puzzled Russell and led Wittgenstein to declare that identity is not a relation between objects. The now standard view is that Wittgenstein's position is untenable, and that worries regarding the relational status of identity are the result of confusion. I argue that the rejection of identity as a binary relation (...)
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  • A Logical Approach to Philosophy: Essays in Memory of Graham Solomon.David DeVidi & Tim Kenyon (eds.) - 2006 - Dordrecht, Netherland: Springer.
    Graham Solomon, to whom this collection is dedicated, went into hospital for antibiotic treatment of pneumonia in Oc- ber, 2001. Three days later, on Nov. 1, he died of a massive stroke, at the age of 44. Solomon was well liked by those who got the chance to know him—it was a revelation to?nd out, when helping to sort out his a?airs after his death, how many “friends” he had whom he had actually never met, as his email included correspondence (...)
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  • (1 other version)The Foundations of Geometry.David Hilbert - 1899 - Open Court Company (This Edition Published 1921).
    §30. Significance of Desargues's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 CHAPTER VI. PASCAL'S THEOREM. §31. ...
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  • The Philosophical Basis of Intuitionistic Logic.Michael Dummett - 1978 - In Truth and other enigmas. Cambridge: Harvard University Press. pp. 215--247.
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  • (1 other version)On the Experience of Time.Bertrand Russell - 1915 - The Monist 25 (2):212-233.
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  • (1 other version)Les fondements des mathématiques: intuitionnisme, théorie de la démonstration.Arend Heyting - 1955 - Paris,: E. Nauwelaerts.
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  • A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.
    Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...)
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  • Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.
    This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.
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  • Truth and Pluralism: Current Debates.Nikolaj Jang Lee Linding Pedersen & Cory Wright (eds.) - 2012 - Oxford, England: Oxford University Press.
    The relative merits and demerits of historically prominent views such as the correspondence theory, coherentism, pragmatism, verificationism, and instrumentalism have been subject to much attention in the truth literature and have fueled the long-lived debate over which of these views is the most plausible one. While diverging in their specific philosophical commitments, adherents of these historically prominent views agree in at least one fundamental respect. They are all alethic monists. They all endorse the thesis that there is only one property (...)
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  • Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
    Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...)
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  • The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
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  • From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
    The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for ...
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  • Reference and generality.P. T. Geach - 1962 - Ithaca, N.Y.,: Cornell University Press. Edited by Michael C. Rea.
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  • Mathematical logic and Hilbert's & symbol.A. C. Leisenring - 1969 - London,: Macdonald Technical & Scientific.
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  • Individuals: An Essay in Descriptive Metaphysics.Peter F. Strawson - 1959 - London, England: Routledge. Edited by Wenfang Wang.
    The classic, influential essay in 'descriptive metaphysics' by the distinguished English philosopher.
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  • Frege: Philosophy of Language.Michael Dummett - 1973 - London: Duckworth.
    This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...
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  • The collected papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam,: North-Holland Pub. Co.. Edited by M. E. Szabo.
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  • The foundations of arithmetic: a logico-mathematical enquiry into the concept of number.Gottlob Frege - 1974 - Evanston, Ill.: Northwestern University Press. Edited by J. L. Austin.
    § i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...
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  • Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • Collected works.Kurt Gödel - 1986 - New York: Oxford University Press. Edited by Solomon Feferman.
    Kurt Godel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's (...)
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  • Plotinus.Lloyd P. Gerson - 1994 - New York: Routledge.
    This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.
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  • Introduction to logic.Patrick Suppes - 1957 - Mineola, N.Y.: Dover Publications.
    Coherent, well organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition; Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories in both discussion and exercises. Ideal for undergraduates; no background in math or philosophy required.
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  • (1 other version)From Brouwer to Hilbert: the debate on the foundations of mathematics in the 1920s.Paolo Mancosu (ed.) - 1998 - New York: Oxford University Press.
    From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. (...)
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  • Truth and objectivity.Crispin Wright - 1992 - Cambridge: Harvard University Press.
    Recasting important questions about truth and objectivity in new and helpful terms, his book will become a focus in the contemporary debates over realism, and ...
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  • (1 other version)Theory of knowledge: the 1913 manuscript.Bertrand Russell - 1913/1992 - New York: Routledge. Edited by Elizabeth Ramsden Eames & Kenneth Blackwell.
    First published in 1984 as part of The Collected Papers of Bertrand Russell , Theory of Knowledge represents an important addition to our knowledge of Russell's thought. In this work Russell attempts to flesh out the sketch implicit in The Problems of Philosophy . It was conceived by Russell as his next major project after Principia Mathematica and was intended to provide the epistemological foundations for his work. Russell's subsequent difficulties in presenting his theory of knowledge, brought on by what (...)
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  • The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge: Harvard University Press.
    Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...
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  • (2 other versions)Introduction to Logic.J. Dopp - 1957 - Journal of Symbolic Logic 22 (4):353-354.
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  • Completeness of indexed varepsilon -calculus.G. E. Mints & Darko Sarenac - 2003 - Archive for Mathematical Logic 42 (7):617--625.
    Epsilon terms indexed by contexts were used by K. von Heusinger to represent definite and indefinite noun phrases as well as some other constructs of natural language. We provide a language and a complete first order system allowing to formalize basic aspects of this representation. The main axiom says that for any finite collection S 1,…,S k of distinct definable sets and elements a 1,…,a k of these sets there exists a choice function assigning a i to S i for (...)
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  • (2 other versions)Introduction to Metamathematics.Ann Singleterry Ferebee - 1968 - Journal of Symbolic Logic 33 (2):290-291.
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  • (1 other version)Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • The practice of finitism: Epsilon calculus and consistency proofs in Hilbert's program.Richard Zach - 2003 - Synthese 137 (1-2):211 - 259.
    After a brief flirtation with logicism around 1917, David Hilbertproposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays andWilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the development of axiomatic systems for everstronger and more comprehensive areas of mathematics, and finitisticproofs of consistency of these systems. Early advances in these areaswere made by Hilbert (and Bernays) in a series of lecture courses atthe (...)
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  • Die intuitionistische grundlegung der mathematik.Arend Heyting - 1931 - Erkenntnis 2 (1):106-115.
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  • (2 other versions)Georg Cantor, His Mathematics and Philosophy of the Infinite.Arnold Oberschelp - 1982 - Journal of Symbolic Logic 47 (2):456-457.
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  • Completeness before Post: Bernays, Hilbert, and the development of propositional logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...)
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  • Choice functions and the scopal semantics of indefinites.Yoad Winter - 1997 - Linguistics and Philosophy 20 (4):399-467.
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  • (1 other version)Mr. Strawson on referring.Bertrand Russell - 1957 - Mind 66 (263):385-389.
    Leaving detail aside, I think we may sum up Mr. Strawson's argument and my reply to it as follows: There are two problems, that of descriptions and that of egocentricity. Mr. Strawson thinks they are one and the same problem, but it is obvious from his discussion that he has not considered as many kinds of descriptive phrases as are relevant to the argument. Having confused the two problems, he asserts dogmatically that it is only the egocentric problem that needs (...)
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  • Quantifier scope: How labor is divided between QR and choice functions. [REVIEW]Tanya Reinhart - 1997 - Linguistics and Philosophy 20 (4):335-397.
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  • Hilbert's program then and now.Richard Zach - 2002 - In Dale Jacquette (ed.), Philosophy of Logic. Malden, Mass.: North Holland. pp. 411–447.
    Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...)
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  • (1 other version)Filozofia matematyki: antologia tekstów klasycznych.Roman Murawski (ed.) - 1986 - Poznań: Uniwersytet im. Adama Mickiewicza w Poznaniu.
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  • Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
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  • On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
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  • Origins of Analytical Philosophy.Michael Dummett - 1994 - Philosophy 69 (268):246-248.
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  • (2 other versions)Michael Dummett, Frege: Philosophy of Language. [REVIEW]Hidé Ishiguro - 1974 - Philosophy 49 (190):438-442.
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  • (1 other version)Steps Toward a Constructive Nominalism.Nelson Goodman & W. V. Quine - 1947 - Journal of Symbolic Logic 13 (1):49-50.
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  • (2 other versions)The Collected Papers of Gerhard Gentzen.K. Schütte - 1972 - Journal of Symbolic Logic 37 (4):752-753.
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  • (1 other version)Logic, Semantics, Metamathematics: Papers from 1923 to 1938.I. Grattan-Guinness - 1956 - Journal of Symbolic Logic 54 (1):281-282.
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  • (1 other version)The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
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  • The Principles of Logic.F. H. Bradley - 1923 - Mind 32 (127):352-356.
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  • (2 other versions)Introduction to Semantics.Rudolf Carnap - 1942 - Philosophy of Science 9 (3):281-282.
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