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  1. Axioms in Mathematical Practice.Dirk Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
    On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...)
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  • Towards an Institutional Account of the Objectivity, Necessity, and Atemporality of Mathematics.Julian C. Cole - 2013 - Philosophia Mathematica 21 (1):9-36.
    I contend that mathematical domains are freestanding institutional entities that, at least typically, are introduced to serve representational functions. In this paper, I outline an account of institutional reality and a supporting metaontological perspective that clarify the content of this thesis. I also argue that a philosophy of mathematics that has this thesis as its central tenet can account for the objectivity, necessity, and atemporality of mathematics.
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  • Believing the axioms. I.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (2):481-511.
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  • What are Implicit Definitions?Eduardo N. Giovannini & Georg Schiemer - 2019 - Erkenntnis 86 (6):1661-1691.
    The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such “structural definitions” can be semantically understood in two different ways, namely as specifications of the meaning of the primitive terms of a theory and as definitions of higher-order mathematical concepts or structures. We analyze these (...)
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  • (1 other version)Speech Acts: An Essay in the Philosophy of Language.John Searle - 1969 - Philosophy and Rhetoric 4 (1):59-61.
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  • Expression and Meaning: Studies in the Theory of Speech Acts.John R. Searle - 1979 - Philosophy 56 (216):270-271.
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  • We hold these truths to be self-evident: But what do we mean by that?: We hold these truths to be self-evident.Stewart Shapiro - 2009 - Review of Symbolic Logic 2 (1):175-207.
    At the beginning of Die Grundlagen der Arithmetik [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both (...)
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  • The Foundations of Illocutionary Logic.J. R. Searle & Daniel Vanderveken - 1989 - Linguistics and Philosophy 12 (6):745-748.
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  • Constitutive Rules, Language, and Ontology.Frank Hindriks - 2009 - Erkenntnis 71 (2):253-275.
    It is a commonplace within philosophy that the ontology of institutions can be captured in terms of constitutive rules. What exactly such rules are, however, is not well understood. They are usually contrasted to regulative rules: constitutive rules (such as the rules of chess) make institutional actions possible, whereas regulative rules (such as the rules of etiquette) pertain to actions that can be performed independently of such rules. Some, however, maintain that the distinction between regulative and constitutive rules is merely (...)
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  • (1 other version)How to define theoretical terms.David Lewis - 1970 - Journal of Philosophy 67 (13):427-446.
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  • Posthumous Writings.Gottlob Frege - 1982 - Revue Philosophique de la France Et de l'Etranger 172 (1):101-103.
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  • (2 other versions)The Construction of Social Reality. Anthony Freeman in conversation with John Searle.J. Searle & A. Freeman - 1995 - Journal of Consciousness Studies 2 (2):180-189.
    John Searle began to discuss his recently published book `The Construction of Social Reality' with Anthony Freeman, and they ended up talking about God. The book itself and part of their conversation are introduced and briefly reflected upon by Anthony Freeman. Many familiar social facts -- like money and marriage and monarchy -- are only facts by human agreement. They exist only because we believe them to exist. That is the thesis, at once startling yet obvious, that philosopher John Searle (...)
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  • Logic as calculus and logic as language.Jean Heijenoort - 1967 - Synthese 17 (1):324 - 330.
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  • Dedekind and Wolffian Deductive Method.José Ferreirós & Abel Lassalle-Casanave - 2022 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (4):345-365.
    Dedekind’s methodology, in his classic booklet on the foundations of arithmetic, has been the topic of some debate. While some authors make it closely analogue to Hilbert’s early axiomatics, others emphasize its idiosyncratic features, most importantly the fact that no axioms are stated and its careful deductive structure apparently rests on definitions alone. In particular, the so-called Dedekind “axioms” of arithmetic are presented by him as “characteristic conditions” in the _definition_ of the complex concept of a _simply infinite_ system. Making (...)
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  • On Certain Mathematical Terms in Aristotle's Logic: Part I.Benedict Einarson - 1936 - American Journal of Philology 57 (1):33.
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  • (2 other versions)Introduction to Logic and to the Methodology of Deductive Sciences.Alfred Tarski & Olaf Helmer - 1944 - Philosophy 19 (72):90-91.
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  • Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics.Stewart Shapiro - 2005 - Philosophia Mathematica 13 (1):61-77.
    There is a parallel between the debate between Gottlob Frege and David Hilbert at the turn of the twentieth century and at least some aspects of the current controversy over whether category theory provides the proper framework for structuralism in the philosophy of mathematics. The main issue, I think, concerns the place and interpretation of meta-mathematics in an algebraic or structuralist approach to mathematics. Can meta-mathematics itself be understood in algebraic or structural terms? Or is it an exception to the (...)
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  • Responses to Critics of The Construction of Social Reality.David-Hillel Ruben - 1997 - Philosophy and Phenomenological Research 57 (2):449-458.
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  • Logic as Calculus and Logic as Language.Jean Van Heijenoort - 1967 - Synthese 17 (1):324-330.
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  • Alfred Tarski. Introduction to logic and to the methodology of deductive sciences. Third edition of VI 30. Oxford University Press, New York1965, viii + 252 pp.Ann M. Singleterry - 1966 - Journal of Symbolic Logic 31 (4):674.
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  • The informal logic of mathematical proof.Andrew Aberdein - 2006 - In Reuben Hersh (ed.), 18 Unconventional Essays on the Nature of Mathematics. Springer. pp. 56-70.
    Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of (...)
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  • Proofs and refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.
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  • (4 other versions)The Object of Morality.G. J. Warnock - 1971 - Tijdschrift Voor Filosofie 35 (1):209-211.
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  • Constitutive rules and speech-act analysis.Joseph Ransdell - 1971 - Journal of Philosophy 68 (13):385-400.
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  • Basic laws of arithmetic.Gottlob Frege - 1893 - In Basic Laws of Arithmetic. Oxford, U.K.: Oxford University Press.
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  • Completeness and the Ends of Axiomatization.Michael Detlefsen - 2014 - In Juliette Kennedy (ed.), Interpreting Gödel: Critical Essays. Cambridge: Cambridge University Press. pp. 59-77.
    The type of completeness Whitehead and Russell aimed for in their Principia Mathematica was what I call descriptive completeness. This is completeness with respect to the propositions that have been proved in traditional mathematics. The notion of completeness addressed by Gödel in his famous work of 1930 and 1931 was completeness with respect to the truths expressible in a given language. What are the relative significances of these different conceptions of completeness for traditional mathematics? What, if any, effects does incompleteness (...)
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