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Identity and Modality

Oxford University Press (2006)

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  1. Bad Company and Neo-Fregean Philosophy.Matti Eklund - 2009 - Synthese 170 (3):393-414.
    A central element in neo-Fregean philosophy of mathematics is the focus on abstraction principles, and the use of abstraction principles to ground various areas of mathematics. But as is well known, not all abstraction principles are in good standing. Various proposals for singling out the acceptable abstraction principles have been presented. Here I investigate what philosophical underpinnings can be provided for these proposals; specifically, underpinnings that fit the neo-Fregean's general outlook. Among the philosophical ideas I consider are: general views on (...)
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  • Realistic Structuralism's Identity Crisis: A Hybrid Solution.Tim Button - 2006 - Analysis 66 (3):216–222.
    Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly the same (...)
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  • Rayo’s Metametaphysics.Matti Eklund - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (4):483-497.
    In his important book The Construction of Logical Space, Agustín Rayo lays out a distinctive metametaphysical view and applies it fruitfully to disputes concerning ontology and concerning modality. In this article, I present a number of criticisms of the view developed, mostly focusing on the underlying metametaphysics and Rayo’s claims on its behalf.
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  • 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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  • An “I” for an I: Singular Terms, Uniqueness, and Reference.Stewart Shapiro - 2012 - Review of Symbolic Logic 5 (3):380-415.
    There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and (...)
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