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Hartry Field (1993). The Conceptual Contingency of Mathematical Objects.

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  1.  45
    Abstraction Reconceived.J. P. Studd - 2016 - British Journal for the Philosophy of Science 67 (2):579-615.
    Neologicists have sought to ground mathematical knowledge in abstraction. One especially obstinate problem for this account is the bad company problem. The leading neologicist strategy for resolving this problem is to attempt to sift the good abstraction principles from the bad. This response faces a dilemma: the system of ‘good’ abstraction principles either falls foul of the Scylla of inconsistency or the Charybdis of being unable to recover a modest portion of Zermelo–Fraenkel set theory with its intended generality. This article (...)
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  2.  50
    The Holistic Presumptions of the Indispensability Argument.Russell Marcus - 2014 - Synthese 191 (15):3575-3594.
    The indispensability argument is sometimes seen as weakened by its reliance on a controversial premise of confirmation holism. Recently, some philosophers working on the indispensability argument have developed versions of the argument which, they claim, do not rely on holism. Some of these writers even claim to have strengthened the argument by eliminating the controversial premise. I argue that the apparent removal of holism leaves a lacuna in the argument. Without the holistic premise, or some other premise which facilitates the (...)
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  3. A Truthmaker Indispensability Argument.Sam Baron - 2013 - Synthese 190 (12):2413-2427.
    Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of (...)
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  4.  85
    Explanation, Extrapolation, and Existence.Stephen Yablo - 2012 - Mind 121 (484):1007-1029.
    Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s (...)
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  5. Contingentism in Metaphysics.Kristie Miller - 2010 - Philosophy Compass 5 (11):965-977.
    In a lot of domains in metaphysics the tacit assumption has been that whichever metaphysical principles turn out to be true, these will be necessarily true. Let us call necessitarianism about some domain the thesis that the right metaphysics of that domain is necessary. Necessitarianism has flourished. This paper considers why this is so and considers domains in which contingentism has been defended.
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  6. Defending Contingentism in Metaphysics.Kristie Miller - 2009 - Dialectica 63 (1):23-49.
    Metaphysics is supposed to tell us about the metaphysical nature of our world: under what conditions composition occurs; how objects persist through time; whether properties are universals or tropes. It is near orthodoxy that whichever of these sorts of metaphysical claims is true is necessarily true. This paper looks at the debate between that orthodox view and a recently emerging view that claims like these are contingent, by focusing on the metaphysical debate between monists and pluralists about concrete particulars. This (...)
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  7. Defending Contingentism in Metaphysics.Kristie Miller - 2009 - Dialectica 63 (1):23-49.
    Metaphysics is supposed to tell us about the metaphysical nature of our world: under what conditions composition occurs; how objects persist through time; whether properties are universals or tropes. It is near orthodoxy that whichever of these sorts of metaphysical claims is true is necessarily true. This paper looks at the debate between that orthodox view and a recently emerging view that claims like these are contingent, by focusing on the metaphysical debate between monists and pluralists about concrete particulars. This (...)
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  8. Epistemicism and Nihilism About Vagueness: What’s the Difference?David Enoch - 2007 - Philosophical Studies 133 (2):285-311.
    In this paper I argue, first, that the only difference between Epistemicism and Nihilism about vagueness is semantic rather than ontological, and second, that once it is clear what the difference between these views is, Nihilism is a much more plausible view of vagueness than Epistemicism. Given the current popularity of certain epistemicist views, this result is, I think, of interest.
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  9. Abstraction and Identity.Roy T. Cook & Philip A. Ebert - 2005 - Dialectica 59 (2):121–139.
    A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.
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    Conceptual Contingency and Abstract Existence.Mark Colyvan - 2000 - Philosophical Quarterly 50 (198):87-91.
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    Existence Claims and Causality.Colin Cheyne - 1998 - Australasian Journal of Philosophy 76 (1):34 – 47.
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