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Philosophia Mathematica 15 (3):357-365 (2007)

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  1. Mathematics and Metaphilosophy.Justin Clarke-Doane - 2022 - Cambridge: Cambridge University Press.
    This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the problem of explaining the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the problem of explaining their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book shows that mathematical facts are not, in general, empirically accessible, contra Quine, (...)
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  • For Better and for Worse. Abstractionism, Good Company, and Pluralism.Andrea Sereni, Maria Paola Sforza Fogliani & Luca Zanetti - 2023 - Review of Symbolic Logic 16 (1):268-297.
    A thriving literature has developed over logical and mathematical pluralism – i.e. the views that several rival logical and mathematical theories can be equally correct. These have unfortunately grown separate; instead, they both could gain a great deal by a closer interaction. Our aim is thus to present some novel forms of abstractionist mathematical pluralism which can be modeled on parallel ways of substantiating logical pluralism (also in connection with logical anti-exceptionalism). To do this, we start by discussing the Good (...)
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  • Fundamentality physicalism.Gabriel Oak Rabin - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy (1):77-116.
    ABSTRACT This essay has three goals. The first is to introduce the notion of fundamentality and to argue that physicalism can usefully be conceived of as a thesis about fundamentality. The second is to argue for the advantages of fundamentality physicalism over modal formulations and that fundamentality physicalism is what many who endorse modal formulations of physicalism had in mind all along. Third, I describe what I take to be the main obstacle for a fundamentality-oriented formulation of physicalism: ‘the problem (...)
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  • (1 other version)Mathematical platonism meets ontological pluralism?Matteo Plebani - 2017 - Inquiry: An Interdisciplinary Journal of Philosophy:1-19.
    Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for...
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  • (1 other version)Mathematical platonism meets ontological pluralism?Matteo Plebani - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):655-673.
    Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for plural platonism, the view that results from combining mathematical platonism and ontological pluralism. I will argue that some forms of platonism are in harmony with ontological pluralism, while other forms of platonism are in tension with it. This shows that there are some interesting connections between the platonism–antiplatonism dispute and recent debates over (...)
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