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Consistency, Models, and Soundness

Axiomathes 20 (2):153-207 (2010)

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  1. Studien Zu Frege = Studies on Frege.Matthias Schirn - 1976
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  • Frege in Perspective. [REVIEW]Michael D. Resnik - 1992 - Philosophical Review 101 (4):893-895.
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  • Hilbert's Finitism and the Notion of Infinity.Karl-Georg Niebergall & Matthias Schirn - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press.
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  • Kurt Godel. Collected Works. Volume IV: Selected Correspondence AG; Volume V: Selected Correspondence HZ.W. W. Tait - 2006 - Philosophia Mathematica 14 (1):76.
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  • Finitism and intuitive knowledge.Charles Parsons - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 249--270.
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  • The incompleteness theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 821 -- 865.
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  • Nachgelassene Schriften.R. H. Stoothoff - 1971 - Philosophical Quarterly 21 (82):77.
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  • Grundlagen der Arithmetik: Studienausgabe mit dem Text der Centenarausgabe.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner Verlag.
    Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.
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  • Models of Peano Arithmetic.Richard Kaye - 1991 - Clarendon Press.
    An introduction to the developments of nonstandard models. Beginning with Godel's incompleteness theorem, it covers the prime models, cofinal extensions, and extensions, Gaifman's construction of a definable type, Tennenbaum's theorem and Friedman's theorem on indicators, ending with a chapter on recursive saturation and resplendency.
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  • On a Consistent Subsystem of Frege's Grundgesetze.John P. Burgess - 1998 - Notre Dame Journal of Formal Logic 39 (2):274-278.
    Parsons has given a (nonconstructive) proof that the first-order fragment of the system of Frege's Grundgesetze is consistent. Here a constructive proof of the same result is presented.
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  • On the consistency of the first-order portion of Frege's logical system.Terence Parsons - 1987 - Notre Dame Journal of Formal Logic 28 (1):161-168.
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  • Frege and the philosophy of mathematics.Michael D. Resnik - 1980 - Ithaca, N.Y.: Cornell University Press.
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  • Gottlob Frege.Hans Dietrich Sluga - 1980 - New York: Routledge.
    This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.
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  • Frege: importance and legacy.Matthias Schirn (ed.) - 1996 - New York: Walter de Gruyter.
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  • Frege, an introduction to his philosophy.Gregory Currie - 1982 - Totowa, NJ: Barnes & Noble.
    Studie over het werk van de Duitse wijsgeer Friedrich Ludwig Gottlob Frege (1848-1925).
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  • Remarks on finitism.William Tait - manuscript
    The background of these remarks is that in 1967, in ‘’Constructive reasoning” [27], I sketched an argument that finitist arithmetic coincides with primitive recursive arithmetic, P RA; and in 1981, in “Finitism” [28], I expanded on the argument. But some recent discussions and some of the more recent literature on the subject lead me to think that a few further remarks would be useful.
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  • Consistent fragments of grundgesetze and the existence of non-logical objects.Kai F. Wehmeier - 1999 - Synthese 121 (3):309-328.
    In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T (...)
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  • Deflationism and the gödel phenomena: Reply to Ketland.Neil Tennant - 2005 - Mind 114 (453):89-96.
    I am not a deflationist. I believe that truth and falsity are substantial. The truth of a proposition consists in its having a constructive proof, or truthmaker. The falsity of a proposition consists in its having a constructive disproof, or falsitymaker. Such proofs and disproofs will need to be given modulo acceptable premisses. The choice of these premisses will depend on the discourse in question.
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  • Partial realizations of Hilbert's program.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (2):349-363.
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  • Hume’s Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters.Matthias Schirn - 2006 - Synthese 148 (1):171 - 227.
    In this paper, I shall discuss several topics related to Frege’s paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege’s notion of evidence and its interpretation by Jeshion, the introduction (...)
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  • On the philosophical significance of consistency proofs.Michael D. Resnik - 1974 - Journal of Philosophical Logic 3 (1/2):133 - 147.
    We have seen that despite Feferman's results Gödel's second theorem vitiates the use of Hilbert-type epistemological programs and consistency proofs as a response to mathematical skepticism. Thus consistency proofs fail to have the philosophical significance often attributed to them.This does not mean that consistency proofs are of no interest to philosophers. We know that a ‘non-pathological’ consistency proof for a system S will use methods which are not available in S. When S is as strong a system as we are (...)
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