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Logicism, structuralism and objectivity

Topoi 20 (1):79-95 (2001)

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  1. (1 other version)Truth.Michael Dummett - 1959 - Proceedings of the Aristotelian Society 59 (1):141-62.
    Michael Dummett; VIII.—Truth, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 141–162, https://doi.org/10.1093/aristotelian/59.1.
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  • The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
    In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...
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  • Frege and the philosophy of mathematics.Michael D. Resnik - 1980 - Ithaca, N.Y.: Cornell University Press.
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  • The philosophy of mathematics.Wilbur Dyre Hart (ed.) - 1996 - New York: Oxford University Press.
    This volume offers a selection of the most interesting and important work from recent years in the philosophy of mathematics, which has always been closely linked to, and has exerted a significant influence upon, the main stream of analytical philosophy. The issues discussed are of interest throughout philosophy, and no mathematical expertise is required of the reader. Contributors include W.V. Quine, W.D. Hart, Michael Dummett, Charles Parsons, Paul Benacerraf, Penelope Maddy, W.W. Tait, Hilary Putnam, George Boolos, Daniel Isaacson, Stewart Shapiro, (...)
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  • (1 other version)Origins of analytical philosophy.Michael Dummett - 1993 - Cambridge: Harvard University Press.
    When contrasted with "Continental" philosophy, analytical philosophy is often called "Anglo-American." Dummett argues that "Anglo-Austrian" would be a more accurate label. By re-examining the similar origins of the two traditions, we can come to understand why they later diverged so widely, and thus take the first step toward reconciliation.
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  • Kant and the exact sciences.Michael Friedman - 1992 - Cambridge: Harvard University Press.
    In this new book, Michael Friedman argues that Kant's continuing efforts to find a metaphysics that could provide a foundation for the sciences is of the utmost ...
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  • (2 other versions)Empiricism, Semantics and Ontology.Rudolf Carnap - 1950 - Revue Internationale de Philosophie 4 (11):20-40.
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  • Space, number and structure: A tale of two debates.Stewart Shapiro - 1996 - Philosophia Mathematica 4 (2):148-173.
    Around the turn of the century, Poincare and Hilbert each published an account of geometry that took the discipline to be an implicit definition of its concepts. The terms ‘point’, ‘line’, and ‘plane’ can be applied to any system of objects that satisfies the axioms. Each mathematician found spirited opposition from a different logicist—Russell against Poincare' and Frege against Hilbert— who maintained the dying view that geometry essentially concerns space or spatial intuition. The debates illustrate the emerging idea of mathematics (...)
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  • Mathematics as a science of patterns: Ontology and reference.Michael Resnik - 1981 - Noûs 15 (4):529-550.
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  • What is required of a foundation for mathematics?John Mayberry - 1994 - Philosophia Mathematica 2 (1):16-35.
    The business of mathematics is definition and proof, and its foundations comprise the principles which govern them. Modern mathematics is founded upon set theory. In particular, both the axiomatic method and mathematical logic belong, by their very natures, to the theory of sets. Accordingly, foundational set theory is not, and cannot logically be, an axiomatic theory. Failure to grasp this point leads obly to confusion. The idea of a set is that of an extensional plurality, limited and definite in size, (...)
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  • Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
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  • (3 other versions)Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
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  • Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
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  • Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.
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  • The logical structure of the world.Rudolf Carnap - 1967 - Berkeley,: University of California Press. Edited by Rudolf Carnap.
    Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle.
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  • Category theory: The language of mathematics.Elaine Landry - 1999 - Philosophy of Science 66 (3):27.
    In this paper I argue that category theory ought to be seen as providing the language for mathematical discourse. Against foundational approaches, I argue that there is no need to reduce either the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories. I assign category theory the role of organizing what we say about the content and structure of both mathematical concepts and theories. Insofar, then, as the (...)
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  • Structure in mathematics and logic: A categorical perspective.S. Awodey - 1996 - Philosophia Mathematica 4 (3):209-237.
    A precise notion of ‘mathematical structure’ other than that given by model theory may prove fruitful in the philosophy of mathematics. It is shown how the language and methods of category theory provide such a notion, having developed out of a structural approach in modern mathematical practice. As an example, it is then shown how the categorical notion of a topos provides a characterization of ‘logical structure’, and an alternative to the Pregean approach to logic which is continuous with the (...)
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  • (4 other versions)Two Dogmas of Empiricism.W. V. O. Quine - 2011 - In Robert B. Talisse & Scott F. Aikin (eds.), The Pragmatism Reader: From Peirce Through the Present. Princeton University Press. pp. 202-220.
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  • The Philosophy of Logical Atomism.Bertrand Russell - 1918 - The Monist 29 (3):345-380.
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  • The Philosophy of Logical Atomism.Bertrand Russell - 1918 - In ¸ Iterussell1986. Open Court. pp. 193-210..
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  • The Logical Syntax of Language.Rudolph Carnap - 1936 - Philosophical Review 46 (5):549-553.
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  • (1 other version)Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of science today. New York: Oxford University Press.
    Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
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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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  • From absolute to local mathematics.J. L. Bell - 1986 - Synthese 69 (3):409 - 426.
    In this paper (a sequel to [4]) I put forward a "local" interpretation of mathematical concepts based on notions derived from category theory. The fundamental idea is to abandon the unique absolute universe of sets central to the orthodox set-theoretic account of the foundations of mathematics, replacing it by a plurality of local mathematical frameworks - elementary toposes - defined in category-theoretic terms.
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  • Numbers can be just what they have to.Colin McLarty - 1993 - Noûs 27 (4):487-498.
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  • Frege's Conception of Logic.Warren Goldfarb - 2001 - In Juliet Floyd & Sanford Shieh (eds.), Future pasts: the analytic tradition in twentieth-century philosophy. New York: Oxford University Press. pp. 25-41.
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  • (2 other versions)Principia Mathematica.A. N. Whitehead & B. Russell - 1927 - Annalen der Philosophie Und Philosophischen Kritik 2 (1):73-75.
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  • Frege's Theory of Sense and Reference: Its Origin and Scope.Wolfgang Carl - 1994 - New York: Cambridge University Press.
    Gottlob Frege has exerted an enormous influence on the evolution of twentieth-century philosophy, yet the real significance of that influence is still very much a matter of debate. This book provides a completely new and systematic account of Frege's philosophy by focusing on its cornerstone: the theory of sense and reference. Two features distinguish this study from other books on Frege. First, sense and reference are placed absolutely at the core of Frege's work; the author shows that no adequate account (...)
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  • Structural relativity.Michael Resnik - 1996 - Philosophia Mathematica 4 (2):83-99.
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  • (2 other versions)The Basic Laws of Arithmetic. [REVIEW]Aaron Sloman - 1966 - British Journal for the Philosophy of Science 17 (3):249-253.
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  • The Semantic Tradition From Kant to Carnap: To the Vienna Station.J. Alberto Coffa - 1991 - New York: Cambridge University Press. Edited by Linda Wessels.
    This major publication is a history of the semantic tradition in philosophy from the early nineteenth century through its incarnation in the work of the Vienna Circle, the group of logical positivists that emerged in the years 1925–1935 in Vienna who were characterised by a strong commitment to empiricism, a high regard for science, and a conviction that modern logic is the primary tool of analytic philosophy. In the first part of the book, Alberto Coffa traces the roots of logical (...)
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  • (1 other version)Carnap's Construction of the World (Review). [REVIEW]Robert Hanna - 1999 - Philosophical Books 40 (3):89-101.
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  • (1 other version)The basic laws of arithmetic.Gottlob Frege - 1893 - Berkeley,: University of California Press. Edited by Montgomery Furth.
    ... as 'logicism') that the content expressed by true propositions of arithmetic and analysis is not something of an irreducibly mathematical character, ...
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  • Truth and proof: The platonism of mathematics.W. W. Tait - 1986 - Synthese 69 (3):341 - 370.
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