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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. L. Luna & W. Taylor (forthcoming). Taming the Indefinitely Extensible Definable Universe. Philosophia Mathematica:nkt044.
    In previous work in 2010 we have dealt with the problems arising from Cantor's theorem and the Richard paradox in a definable universe. We proposed indefinite extensibility as a solution. Now we address another definability paradox, the Berry paradox, and explore how Hartogs's cardinality theorem would behave in an indefinitely extensible definable universe where all sets are countable.
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  3. Charles 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. Jessica Carter (forthcoming). Mathematics Dealing with 'Hypothetical States of Things'. Philosophia Mathematica:nkt040.
    This paper takes as a starting point certain notions from Peirce's writings and uses them to propose a picture of the part of mathematical practice that consists of hypothesis formation. In particular, three processes of hypothesis formation are considered: abstraction, generalisation, and an abductive-like inference. In addition Peirce's pragmatic conception of truth and existence in terms of higher-order concepts are used in order to obtain a kind of pragmatic realist picture of mathematics.
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  6. Joachim Frans & Erik Weber (forthcoming). Mechanistic Explanation and Explanatory Proofs in Mathematics. Philosophia Mathematica:nku003.
    Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist (...)
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  7. Mihai Ganea (forthcoming). Finitistic Arithmetic and Classical Logic. Philosophia Mathematica:nkt042.
    It can be argued that only the equational theories of some sub-elementary function algebras are finitistic or intuitive according to a certain interpretation of Hilbert's conception of intuition. The purpose of this paper is to investigate the relation of those restricted forms of equational reasoning to classical quantifier logic in arithmetic. The conclusion reached is that Edward Nelson's ‘predicative arithmetic’ program, which makes essential use of classical quantifier logic, cannot be justified finitistically and thus requires a different philosophical foundation, possibly (...)
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  8. B. Larvor (forthcoming). The Growth of Mathematical Knowledge. Philosophia Mathematica.
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  9. André Lebel (forthcoming). Jean-Michel Salanskis. Philosophie des Mathématiques. Problèmes & Controverses. Paris: Vrin, 2008. ISBN 978-2-7116-1988-7. Pp. 304. [REVIEW] Philosophia Mathematica:nku001.
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  10. 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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  11. 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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  12. 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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