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  1. A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography.Karin Usadi Katz & Mikhail G. Katz - 2012 - Foundations of Science 17 (1):51-89.
    We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.
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  • Malament–Hogarth Machines and Tait’s Axiomatic Conception of Mathematics.Sharon Berry - 2014 - Erkenntnis 79 (4):893-907.
    In this paper I will argue that Tait’s axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experience which would justify acceptance of a mathematical statement without justifying belief that this statement is provable.
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  • Warum die Mathematik keine ontologische Grundlegung braucht.Simon Friederich - 2014 - Wittgenstein-Studien 5 (1).
    Einer weit verbreiteten Auffassung zufolge ist es eine zentrale Aufgabe der Philosophie der Mathematik, eine ontologische Grundlegung der Mathematik zu formulieren: eine philosophische Theorie darüber, ob mathematische Sätze wirklich wahr sind und ob mathematischen Gegenstände wirklich existieren. Der vorliegende Text entwickelt eine Sichtweise, der zufolge diese Auffassung auf einem Missverständnis beruht. Hierzu wird zunächst der Grundgedanke der Hilbert'schen axiomatischen Methode orgestellt, die Axiome als implizite Definitionen der in ihnen enthaltenen Begriffe zu behandeln. Anschließend wird in Anlehnung an einen Wittgenstein'schen Gedanken (...)
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  • Godel's Unpublished Papers on Foundations of Mathematics.W. W. Tatt - 2001 - Philosophia Mathematica 9 (1):87-126.
  • Mathematics and Fiction II: Analogy.Robert Thomas - 2002 - Logique Et Analyse 45:185-228.
    The object of this paper is to study the analogy, drawn both positively and negatively, between mathematics and fiction. The analogy is more subtle and interesting than fictionalism, which was discussed in part I. Because analogy is not common coin among philosophers, this particular analogy has been discussed or mentioned for the most part just in terms of specific similarities that writers have noticed and thought worth mentioning without much attention's being paid to the larger picture. I intend with this (...)
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  • Objects and Objectivity : Alternatives to Mathematical Realism.Ebba Gullberg - 2011 - Dissertation, Umeå Universitet
    This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes (...)
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  • Essay Review. [REVIEW][author unknown] - 2008 - History and Philosophy of Logic 29 (2):183-193.
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