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Forthcoming articles
  1. Santos Gonçalo (forthcoming). Numbers and Everything. Philosophia Mathematica.
    I begin by drawing a parallel between the intuitionistic understanding of quantification over all natural numbers and the generality relativist understanding of quantification over absolutely everything. I then argue that adoption of an intuitionistic reading of relativism not only provides an immediate reply to the absolutist's charge of incoherence but it also throws a new light on the debates surrounding absolute generality.
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  2. Russell Marcus (forthcoming). How Not to Enhance the Indispensability Argument. Philosophia Mathematica:nku004.
    The new explanatory or enhanced indispensability argument alleges that our mathematical beliefs are justified by their indispensable appearances in scientific explanations. This argument differs from the standard indispensability argument which focuses on the uses of mathematics in scientific theories. I argue that the new argument depends for its plausibility on an equivocation between two senses of explanation. On one sense the new argument is an oblique restatement of the standard argument. On the other sense, it is vulnerable to an instrumentalist (...)
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  3. C. McCarty (forthcoming). Structuralism and Isomorphism. Philosophia Mathematica:nkt024.
    If structuralism is a true view of mathematics on which the statements of mathematicians are taken ‘at face value’, then there are both structures on which (1) classical second-order arithmetic is a correct report, and structures on which (2) intuitionistic second-order arithmetic is correct. An argument due to Dedekind then proves that structures (1) and structures (2) are isomorphic. Consequently, first- and second-order statements true in structures (1) must hold in (2), and conversely. Since instances of the general law of (...)
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  4. Andrea Sereni (forthcoming). Frege, Indispensability, and the Compatibilist Heresy. Philosophia Mathematica:nkt046.
    In Grundgesetze, Vol. II, §91, Frege argues that ‘it is applicability alone which elevates arithmetic from a game to the rank of a science’. Many view this as an in nuce statement of the indispensability argument (IA) later championed by Quine. Garavaso has questioned this attribution. I argue that even though Frege's applicability argument is not a version of IA, it facilitates acceptance of suitable formulations of IA. The prospects for making the empiricist IA compatible with a rationalist Fregean framework (...)
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  5. Roy T. Cook (forthcoming). B. Jack Copeland, Carl J. Posy, and Oron Shagrir, Eds, Computability: Turing, Gödel, Church, and Beyond. Cambridge, Mass.: MIT Press, 2013. ISBN 978-0-262-01899-9. Pp. X + 362. [REVIEW] Philosophia Mathematica:nku016.
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  6. Thomas Forster (forthcoming). Mathematical Objects Arising From Equivalence Relations and Their Implementation in Quine's NF. Philosophia Mathematica:nku005.
    Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted aussonderung but there are set theories (e.g., NF and Church's CUS) which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for “low” sets, and thus, for example, a set of all (low) ordinals. However, that set has an ordinal in turn which is not a member (...)
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  7. Donald Gillies (forthcoming). Timothy Childers. Philosophy and Probability. Oxford: Oxford University Press, 2013. ISBN: 978-0-19-966182-4 (Hbk); 978-0-19-966183-1 (Pbk). Pp. Xviii + 194. [REVIEW] Philosophia Mathematica:nku017.
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  8. Matthew Inglis & Andrew Aberdein (forthcoming). Beauty Is Not Simplicity: An Analysis of Mathematicians' Proof Appraisals. Philosophia Mathematica:nku014.
    What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
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  9. B. Larvor (forthcoming). The Growth of Mathematical Knowledge. Philosophia Mathematica.
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  10. Gianluigi Oliveri (forthcoming). Book Review.'I Fondamenti della Matematica nel Logicismo di Bertrand Russell'. Stefano Donati. Firenze (Firenze Atheneum). 2003. ISBN: 88-7255-204-4. 988 pages.€ 39.00. [REVIEW] Philosophia Mathematica.
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  11. Christopher Pincock (forthcoming). Sorin Bangu. The Applicability of Mathematics in Science: Indispensability and Ontology. Basingstoke: Palgrave Macmillan, 2012. ISBN 978-0-230-28520-0 (Hbk). Pp. Xiii + 252. [REVIEW] Philosophia Mathematica:nku018.
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  12. Agustín Rayo (forthcoming). Nominalism, Trivialism, Logicism. Philosophia Mathematica:nku013.
    This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...)
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  13. Daniël F. M. Strauss (forthcoming). The On to Log I Cal Sta Tus of the Prin Ci Ple of the Ex Cluded Mid Dle. Philosophia Mathematica.
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  14. Neil Tennant (forthcoming). Logic, Mathematics, and the A Priori, Part I: A Problem for Realism. Philosophia Mathematica:nku006.
    This is Part I of a two-part study of the foundations of mathematics through the lenses of (i) apriority and analyticity, and (ii) the resources supplied by Core Logic. Here we explain what is meant by apriority, as the notion applies to knowledge and possibly also to truths in general. We distinguish grounds for knowledge from grounds of truth, in light of our recent work on truthmakers. We then examine the role of apriority in the realism/anti-realism debate. We raise a (...)
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  15. Neil Tennant (forthcoming). Logic, Mathematics, and the A Priori, Part II: Core Logic as Analytic, and as the Basis for Natural Logicism. Philosophia Mathematica:nku009.
    We examine the sense in which logic is a priori, and explain how mathematical theories can be dichotomized non-trivially into analytic and synthetic portions. We argue that Core Logic contains exactly the a-priori-because-analytically-valid deductive principles. We introduce the reader to Core Logic by explaining its relationship to other logical systems, and stating its rules of inference. Important metatheorems about Core Logic are reported, and its important features noted. Core Logic can serve as the basis for a foundational program that could (...)
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  16. Robert Trueman (forthcoming). A Dilemma for Neo-Fregeanism. Philosophia Mathematica:nku012.
    Neo-Fregeans need their stipulation of Hume's Principle — $NxFx=NxGx \leftrightarrow \exists R (Fx \,1\hbox {-}1_R\, Gx)$ — to do two things. First, it must implicitly define the term-forming operator ‘Nx…x…’, and second it must guarantee that Hume's Principle as a whole is true. I distinguish two senses in which the neo-Fregeans might ‘stipulate’ Hume's Principle, and argue that while one sort of stipulation fixes a meaning for ‘Nx…x…’ and the other guarantees the truth of Hume's Principle, neither does both.
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