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  1. (1 other version)Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Revue Philosophique de la France Et de l'Etranger 89:465-466.
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  • A Mathematical Introduction to Logic.Herbert Enderton - 2001 - Bulletin of Symbolic Logic 9 (3):406-407.
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  • (3 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)Aristotle's Posterior Analytics.Jonathan Barnes - 1978 - Mind 87 (345):128-129.
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  • INFORMATION-THEORETIC LOGIC.John Corcoran - 1998 - In C. Martínez U. Rivas & L. Villegas-Forero (eds.), Truth in Perspective edited by C. Martínez, U. Rivas, L. Villegas-Forero, Ashgate Publishing Limited, Aldershot, England (1998) 113-135. ASHGATE. pp. 113-135.
    Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and (...)
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  • The Problem of Meaning in Linguistics.W. V. O. Quine - 1953 - In Willard Van Orman Quine (ed.), From a Logical Point of View. Cambridge: Harvard University Press. pp. 47-64.
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  • On the Syllogism and Other Logical Writings.Augustus De Morgan & Peter Lauchlan Heath - 1966 - New Haven, CT, USA: Routledge and Kegan Paul.
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  • An Investigation of the Laws of Thought: On Which Are Founded the Mathematical Theories of Logic and Probabilities.George Boole - 2009 - [New York]: Cambridge University Press.
    Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a (...)
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  • The Logical Form of Quantifier Phrases: Quantifier-sortalvariable.John Corcoran - 1999 - Bulletin of Symbolic Logic 5:418-419.
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  • Translations From the Philosophical Writings of Gottlob Frege.Peter Geach & Max Black - 1952 - Philosophical Library.
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  • The logical syntax of language.Rudolf Carnap - 1937 - London,: K. Paul, Trench, Trubner & co.. Edited by Amethe Smeaton.
    Available for the first time in 20 years, here is the Rudolf Carnap's famous principle of tolerance by which everyone is free to mix and match the rules of ...
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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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  • 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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  • Mathematical logic.Joseph Robert Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.
    8.3 The consistency proof -- 8.4 Applications of the consistency proof -- 8.5 Second-order arithmetic -- Problems -- Chapter 9: Set Theory -- 9.1 Axioms for sets -- 9.2 Development of set theory -- 9.3 Ordinals -- 9.4 Cardinals -- 9.5 Interpretations of set theory -- 9.6 Constructible sets -- 9.7 The axiom of constructibility -- 9.8 Forcing -- 9.9 The independence proofs -- 9.10 Large cardinals -- Problems -- Appendix The Word Problem -- Index.
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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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  • Categoricity.John Corcoran - 1980 - History and Philosophy of Logic 1 (1):187-207.
    After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...)
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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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  • From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
    Several of these essays have been printed whole in journals; others are in varying degrees new. Two main themes run through them. One is the problem of meaning, particularly as involved in the notion of an analytic statement. The other is the notion of ontological, commitment, particularly as involved in the problem of universals.
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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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  • Meanings of Implication.John Corcoran - 1973 - Diálogos. Revista de Filosofía de la Universidad de Puerto Rico 9 (24):59-76.
    Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is (...)
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  • A mathematical introduction to logic.Herbert Bruce Enderton - 1972 - New York,: Academic Press.
    A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional (...)
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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 Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions.Martin Davis (ed.) - 1965 - Hewlett, NY, USA: Dover Publication.
    "A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by (...)
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  • Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
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  • Aristotle.Jonathan Barnes - 1982 - In Richard Mervyn Hare, Jonathan Barnes & Henry Chadwick (eds.), Founders of thought. New York: Oxford University Press.
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  • (1 other version)The problem of interpreting modal logic.W. V. Quine - 1947 - Journal of Symbolic Logic 12 (2):43-48.
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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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  • 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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  • Foundations of Logic and Mathematics.Rudolf Carnap - 1937 - Chicago, IL, USA: U. Of Chicago P.
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  • (1 other version)Foundations of Geometery.David Hilbert & Paul Bernays - 1971 - Open Court.
    The material contained in the following translation was given in substance by Professor Hilbertas a course of lectures on euclidean geometry at the University of G]ottingen during the wintersemester of 1898-1899. The results of his investigation were re-arranged and put into the formin which they appear here as a memorial address published in connection with the celebration atthe unveiling of the Gauss-Weber monument at G]ottingen, in June, 1899. In the French edition, which appeared soon after, Professor Hilbert made some additions, (...)
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  • Logic, Semantics, Metamathematics.Atwell Turquette - 1958 - Philosophical Review 67 (1):113.
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  • Aristotle's Posterior Analytics. [REVIEW]Dorothea Frede - 1978 - Philosophical Review 87 (2):288-291.
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  • Information-theoretic logic and transformation-theoretic logic,.John Corcoran - 1999 - In R. A. M. M. (ed.), Fragments in Science,. World Scientific Publishing Company,. pp. 25-35.
    Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. This (...)
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  • Gaps between logical theory and mathematical practice.John Corcoran - 1973 - In Mario Bunge (ed.), The methodological unity of science. Boston,: Reidel. pp. 23--50.
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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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  • (1 other version)Undecidable theories.Alfred Tarski - 1968 - 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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  • (1 other version)Information recovery problems.John Corcoran - 1995 - Theoria 10 (3):55-78.
    An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and it develops (...)
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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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  • 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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  • On ω-inconsistency and a so-called axiom of infinity.W. V. Quine - 1953 - Journal of Symbolic Logic 18 (2):119-124.
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  • (1 other version)Completeness in the theory of types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
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  • Foundations of Logic and Mathematics.Rudolf Carnap - 1938 - In Otto Neurath, Rudolf Carnap & Charles William Morris (eds.), International Encyclopedia of Unified Science: Foundations of the unity of science... University Press. pp. 139--213.
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  • (1 other version)Aristotle's Posterior Analytics.Jonathan Barnes - 1977 - Zeitschrift für Philosophische Forschung 31 (2):316-320.
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  • Validez y semantica representacional.José Miguel Sagüillo - 1995 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 10 (3):103-120.
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  • Logic as Calculus and Logic as Language.Jean Van Heijenoort - 1967 - Synthese 17 (1):324-330.
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  • Selected Essays.Jean Van Heijenoort - 1985 - Edited by C. Cellucci, M. Mugnai, A. Maierù & F. Schupp.
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  • The Logical Syntax of Language.Rudolf Carnap & Amethe Smeaton - 1938 - Philosophy 13 (52):485-486.
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  • (1 other version)Information Recovery Problems.John Corcoran - 1995 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 10 (3):55-78.
    An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and it develops (...)
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  • A Philosophical Companion to First-order Logic.R. I. G. Hughes (ed.) - 1993 - Indianapolis and Cambridge: Hackett Publishing.
    This volume of recent writings, some previously unpublished, follows the sequence of a typical intermediate or upper-level logic course and allows teachers to enrich their presentations of formal methods and results with readings on corresponding questions in philosophical logic.
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  • The discovery of my completeness proofs.Leon Henkin - 1996 - Bulletin of Symbolic Logic 2 (2):127-158.
    §1. Introduction. This paper deals with aspects of my doctoral dissertation which contributed to the early development of model theory. What was of use to later workers was less the results of my thesis, than the method by which I proved the completeness of first-order logic—a result established by Kurt Gödel in his doctoral thesis 18 years before.The ideas that fed my discovery of this proof were mostly those I found in the teachings and writings of Alonzo Church. This may (...)
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