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_Mathematics and Metaphilosophy_

Cambridge: Cambridge University Press (2022)

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  1. Two epistemological challenges regarding hypothetical modeling.Peter Tan - 2022 - Synthese 200 (6).
    Sometimes, scientific models are either intended to or plausibly interpreted as representing nonactual but possible targets. Call this “hypothetical modeling”. This paper raises two epistemological challenges concerning hypothetical modeling. To begin with, I observe that given common philosophical assumptions about the scope of objective possibility, hypothetical models are fallible with respect to what is objectively possible. There is thus a need to distinguish between accurate and inaccurate hypothetical modeling. The first epistemological challenge is that no account of the epistemology of (...)
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  • Mathematical platonism and the causal relevance of abstracta.Barbara Gail Montero - 2022 - Synthese 200 (6):1-18.
    Many mathematicians are platonists: they believe that the axioms of mathematics are true because they express the structure of a nonspatiotemporal, mind independent, realm. But platonism is plagued by a philosophical worry: it is unclear how we could have knowledge of an abstract, realm, unclear how nonspatiotemporal objects could causally affect our spatiotemporal cognitive faculties. Here I aim to make room in our metaphysical picture of the world for the causal relevance of abstracta.
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  • Replies to Rosen, Leiter, and Dutilh Novaes.Justin Clarke-Doane - 2023 - Philosophy and Phenomenological Research 107 (3):817-837.
    Gideon Rosen, Brian Leiter, and Catarina Dutilh Novaes raise deep questions about the arguments in Morality and Mathematics (M&M). Their objections bear on practical deliberation, the formulation of mathematical pluralism, the problem of universals, the argument from moral disagreement, moral ‘perception’, the contingency of our mathematical practices, and the purpose of proof. In this response, I address their objections, and the broader issues that they raise.
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  • Pragmatic accounts of justification, epistemic analyticity, and other routes to easy knowledge of abstracta.Brett Topey - forthcoming - In Xavier de Donato-Rodríguez, José Falguera & Concha Martínez-Vidal (eds.), Deflationist Conceptions of Abstract Objects. Springer.
    One common attitude toward abstract objects is a kind of platonism: a view on which those objects are mind-independent and causally inert. But there's an epistemological problem here: given any naturalistically respectable understanding of how our minds work, we can't be in any sort of contact with mind-independent, causally inert objects. So platonists, in order to avoid skepticism, tend to endorse epistemological theories on which knowledge is easy, in the sense that it requires no such contact—appeals to Boghossian’s notion of (...)
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  • What is Logical Monism?Justin Clarke-Doane - forthcoming - In Christopher Peacocke & Paul Boghossian (eds.), Normative Realism. Oxford University Press.
    Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...)
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