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  1. (2 other versions)Philosophy of Logic.W. V. Quine - 2005-01-01 - In José Medina & David Wood (eds.), Truth. Blackwell.
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  • Essai d'une théorie algébrique des nombres entiers, précédé d’une Introduction logique à une theorie déductive quelconque.Alessandro Padoa - 1901 - Bibliothèque du Congrès International de Philosophie 3:309-365.
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  • (1 other version)Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
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  • (4 other versions)Principles of mathematics.Bertrand Russell - 1931 - New York,: W.W. Norton & Company.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
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  • (1 other version)Undecidable Theories.Alfred Tarski, Andrzej Mostowski & Raphael M. Robinson - 1953 - Philosophy 30 (114):278-279.
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  • Afterword.[author unknown] - 2007 - Mediaevalia 28 (Special Issue):187-188.
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  • (2 other versions)Introduction to Logic and to the Methodology of the Deductive Sciences. [REVIEW]Alfred Tarski - 1942 - Modern Schoolman 20 (1):56-56.
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  • (5 other versions)The Cambridge Dictionary of Philosophy.Robert Audi (ed.) - 1995 - New York City: Cambridge University Press.
    Widely acclaimed as the most authoritative and accessible one-volume dictionary available in English this second edition offers an even richer, more comprehensive, and more up-to-date survey of ideas and thinkers written by an international team of 436 contributors. Includes the most comprehensive entries on major philosophers, 400 new entries including over 50 on preeminent contemporary philosophers, extensive coverage of rapidly developing fields such as the philosophy of mind and applied ethics, more entries on non-Western philosophy than any comparable volume, and (...)
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  • Mathematical Logic.Morton G. White & Willard Van Orman Quine - 1942 - Philosophical Review 51 (1):74.
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  • (2 other versions)Philosophy of Logic.Michael Jubien & W. V. Quine - 1988 - Journal of Symbolic Logic 53 (1):303.
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  • The Limits of Logic: Higher-order Logic and the Löwenheim-Skolem Theorem.Stewart Shapiro - 1996 - Routledge.
    The articles in this volume represent a part of the philosophical literature on higher-order logic and the Skolem paradox. They ask the question what is second-order logic? and examine various interpretations of the Lowenheim-Skolem theorem.
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  • A Formalization of Set Theory Without Variables.István Németi - 1988 - American Mathematical Soc..
    Completed in 1983, this work culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. Written in collaboration with Steven Givant, the book appeals to a very broad audience, and requires only a familiarity with first-order logic. It is of great interest to logicians and mathematicians interested in the foundations of mathematics, but also to philosophers interested in logic, semantics, algebraic logic, or the methodology of the deductive sciences, and to (...)
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  • (5 other versions)The Cambridge Dictionary of Philosophy.Robert Audi (ed.) - 1995 - New York City: Cambridge University Press.
    This is the leading, full-scale comprehensive dictionary of philosophical terms and thinkers to appear in English in more than half a century. Written by a team of more than 550 experts and now widely translated, it contains approximately 5,000 entries ranging from short definitions to longer articles. It is designed to facilitate the understanding of philosophy at all levels and in all fields. Key features of this third edition include: • 500 new entries covering Eastern as well as Western philosophy, (...)
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  • Fixed- versus Variable-domain Interpretations of Tarski’s Account of Logical Consequence.Paolo Mancosu - 2010 - Philosophy Compass 5 (9):745-759.
    In this article I describe and evaluate the debate that surrounds the proper interpretation of Tarski’s account of logical consequence given in his classic 1936 article ‘On the concept of logical consequence’. In the late 1980s Etchemendy argued that the familiar model theoretic account of logical consequence is not to be found in Tarski’s original article. Whereas the contemporary account of logical consequence is a variable‐domain conception – in that it calls for a reinterpretation of the domain of variation of (...)
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  • A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...)
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  • Tarski on Logical Consequence.Mario Gómez-Torrente - 1996 - Notre Dame Journal of Formal Logic 37 (1):125-151.
    This paper examines from a historical perspective Tarski's 1936 essay, "On the concept of logical consequence." I focus on two main aims. The primary aim is to show how Tarski's definition of logical consequence satisfies two desiderata he himself sets forth for it: (1) it must declare logically correct certain formalizations of the -rule and (2) it must allow for variation of the individual domain in the test for logical consequence. My arguments provide a refutation of some interpreters of Tarski, (...)
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  • Domains of Sciences, Universes of Discourse and Omega Arguments.Jose M. Saguillo - 1999 - History and Philosophy of Logic 20 (3-4):267-290.
    Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...)
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  • (1 other version)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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  • (1 other version)Mathematical logic.Willard Van Orman Quine - 1951 - Cambridge,: Harvard University Press.
    INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...
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  • Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
    I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...
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  • Symbolic logic.Clarence Irving Lewis - 1932 - [New York]: Dover Publications. Edited by Cooper Harold Langford.
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  • Undecidable theories.Alfred Tarski - 1953 - Amsterdam,: North-Holland Pub. Co.. Edited by Andrzej Mostowski & Raphael M. Robinson.
    This book is well known for its proof that many mathematical systems - including lattice theory and closure algebras - are undecidable. It consists of three treatises from one of the greatest logicians of all time: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups.".
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  • Rereading Tarski on logical consequence.Mario Gómez-Torrente - 2009 - Review of Symbolic Logic 2 (2):249-297.
    I argue that recent defenses of the view that in 1936 Tarski required all interpretations of a language to share one same domain of quantification are based on misinterpretations of Tarski’s texts. In particular, I rebut some criticisms of my earlier attack on the fixed-domain exegesis and I offer a more detailed report of the textual evidence on the issue than in my earlier work. I also offer new considerations on subsisting issues of interpretation concerning Tarski’s views on the logical (...)
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  • REVIEW OF Alfred Tarski, Collected Papers, vols. 1-4 (1986) edited by Steven Givant and Ralph McKenzie. [REVIEW]John Corcoran - 1991 - MATHEMATICAL REVIEWS 91 (h):01101-4.
    Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about logic, whereas (...)
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  • What are logical notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
    In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.
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  • The concept of truth in formalized languages.Alfred Tarski - 1956 - In Logic, semantics, metamathematics. Oxford,: Clarendon Press. pp. 152--278.
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  • Ancient logic and its modern interpretations.John Corcoran (ed.) - 1974 - Boston,: Reidel.
    This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...)
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  • The concept of logical consequence.John Etchemendy - 1990 - Cambridge: Harvard University Press.
    Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR.
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  • (1 other version)Philosophy of logic.Willard Van Orman Quine - 1986 - Cambridge: Harvard University Press. Edited by Simon Blackburn & Keith Simmons.
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  • (1 other version)Aristotle's Prior Analytics and Boole's Laws of thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...)
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  • Logic in the twenties: The nature of the quantifier.Warren D. Goldfarb - 1979 - Journal of Symbolic Logic 44 (3):351-368.
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  • String theory.John Corcoran, William Frank & Michael Maloney - 1974 - Journal of Symbolic Logic 39 (4):625-637.
    For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...)
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  • Conceptual structure of classical logic.John Corcoran - 1972 - Philosophy and Phenomenological Research 33 (1):25-47.
    One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...)
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  • (1 other version)On Tarski on models.Timothy Bays - 2001 - Journal of Symbolic Logic 66 (4):1701-1726.
    This paper concerns Tarski’s use of the term “model” in his 1936 paper “On the Concept of Logical Consequence.” Against several of Tarski’s recent defenders, I argue that Tarski employed a non-standard conception of models in that paper. Against Tarski’s detractors, I argue that this non-standard conception is more philosophically plausible than it may appear. Finally, I make a few comments concerning the traditionally puzzling case of Tarski’s ω-rule example.
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  • (2 other versions)The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
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  • (5 other versions)Review: John Etchemendy, The Concept of Logical Consequence. [REVIEW]Vann Mcgee - 1992 - Journal of Symbolic Logic 57 (1):254-255.
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  • The Concept of Logical Consequence.W. D. Hart - 1991 - Philosophical Quarterly 41 (165):488-493.
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  • Review of Robert Audi: The Cambridge Dictionary of Philosophy[REVIEW]Stanley Bates - 1997 - Ethics 107 (2):381-383.
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  • (1 other version)Who were the American Postulate Theorists?Michael Scanlan - 1991 - Journal of Symbolic Logic 56 (3):981-1002.
    Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency.
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  • (1 other version)Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects (...)
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  • Aristotle's natural deduction system.John Corcoran - 1974 - In Ancient logic and its modern interpretations. Boston,: Reidel. pp. 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
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  • (1 other version)Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton 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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  • Argumentations and Logic.John Corcoran - 1989 - ARGUMENTAION 3 (1):17-43.
    Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...)
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  • The logic of common nouns: an investigation in quantified modal logic.Anil Gupta - 1980 - New Haven: Yale University Press.
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  • The Architecture of Modern Mathematics: Essays in History and Philosophy.José Ferreirós Domínguez & Jeremy Gray (eds.) - 2006 - Oxford, England: Oxford University Press.
    This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.
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  • (1 other version)Introduction to logic and to the methodology of the deductive sciences.Alfred Tarski - 1963 - New York: Oxford University Press. Edited by Jan Tarski.
    Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic. The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw (...)
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  • (2 other versions)Philosophy of Logic.Leslie Stevenson - 1972 - Philosophical Quarterly 22 (86):80.
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  • The Essential Peirce: Selected Philosophical Writings Vol. 1.Charles Peirce, Christian S. & Nathan House J. W. Kloesel - 1992 - Bloomington: Indiana University Press.
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  • The Work of John Corcoran: An Appreciation.Stewart Shapiro & Michael Scanlan - 1999 - History and Philosophy of Logic 20 (3-4):149-158.
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  • (3 other versions)Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 1980 - New York: Cambridge University Press. Edited by John P. Burgess & Richard C. Jeffrey.
    Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a (...)
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