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  1. Logic, Metalogic and Neutrality.Timothy Williamson - 2013 - Erkenntnis 79 (Suppl 2):211-231.
    The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were (...)
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  • Completeness and categoricity: Frege, gödel and model theory.Stephen Read - 1997 - History and Philosophy of Logic 18 (2):79-93.
    Frege’s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel’s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ‘complete’ it is clear from Dedekind’s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical or (...)
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  • Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-first-Century Semantics.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (2):77-94.
    This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
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  • Sets and Abstracts – Discussion.Stewart Shapiro - 2005 - Philosophical Studies 122 (3):315-332.
  • Do not claim too much: Second-order logic and first-order logic.Stewart Shapiro - 1999 - Philosophia Mathematica 7 (1):42-64.
    The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.
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  • The grounds for the model-theoretic account of the logical properties.Manuel García-Carpintero Sánchez-Miguel - 1992 - Notre Dame Journal of Formal Logic 34 (1):107-131.
  • Logical constants.John MacFarlane - 2008 - Mind.
    Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...)
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  • Remarks on Second-Order Consequence.Ignacio Jané - 2010 - Theoria 18 (2):179-187.
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  • Second-order Logic and the Power Set.Ethan Brauer - 2018 - Journal of Philosophical Logic 47 (1):123-142.
    Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from a logic, but rather must (...)
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  • On How Logic Became First-Order.Matti Eklund - 1996 - Nordic Journal of Philosophical Logic 1 (2):147-67.
    Added by a category editor--not an official abstract. -/- Discusses the history (and reasons for the history) implicit in the title, as well as the author's view on same.
     
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  • INVENTING LOGIC: THE LÖWENHEIM-SKOLEM THEOREM AND FIRST- AND SECOND-ORDER LOGIC.Valérie Lynn Therrien - 2012 - Pensées Canadiennes 10.
  • Dependencia e indeterminación en la lógica de segundo orden.Lucas Rosenblatt - 2011 - Cuadernos de Filosofía 57:31-50.
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