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Coincidence Avoidance and Formulating the Access Problem

Published online by Cambridge University Press:  14 May 2020

Sharon E. Berry Open the ORCID record for Sharon E. Berry [Opens in a new window]
Sharon E. Berry*
Affiliation:
Philosophy Department, Oakland University, Rochester, MI, USA
*
Email: [email protected]
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Abstract

In this article, I discuss a trivialization worry for Hartry Field’s official formulation of the access problem for mathematical realists, which was pointed out by Øystein Linnebo (and has recently been made much of by Justin Clarke-Doane). I argue that various attempted reformulations of the Benacerraf problem fail to block trivialization, but that access worriers can better defend themselves by sticking closer to Hartry Field’s initial informal characterization of the access problem in terms of (something like) general epistemic norms of coincidence avoidance.

Keywords

access problemBenacerraf problemcoincidenceHartry Field
Type
Article
Information
Canadian Journal of Philosophy , Volume 50 , Issue 6 , August 2020 , pp. 687 - 701
Copyright
© The Author(s) 2020. Published by Canadian Journal of Philosophy

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References

Baker, Alan. 2009. “Mathematical Accidents and the End of Explanation.” In New Waves in Philosophy of Mathematics, edited by Bueno, Otávio and Linnebo, Øystein, 137–59. Basingstoke, UK: Palgrave Macmillan.CrossRefGoogle Scholar
Benacerraf, Paul. 1973. “Mathematical Truth.” Journal of Philosophy 70: 661–80.CrossRefGoogle Scholar
Berry, Sharon. 2018. Not Companions in Guilt. Philosophical Studies 175 (9): 2285–308.CrossRefGoogle Scholar
Berry, Sharon. Forthcoming. “The Residual Access Problem.”Google Scholar
Bhogal, Harjit. Forthcoming. “Coincidences and the Grain of Explanation.” Philosophy and Phenomenological Research.Google Scholar
Clarke-Doane, Justin. 2014. “Moral Epistemology: The Mathematics Analogy.” Nous 48 (2): 238–55.CrossRefGoogle Scholar
Clarke-Doane, Justin. 2017. “What Is the Benacerraf Problem?” In Truth, Objects, Infinity: New Perspectives on the Philosophy of Paul Benacerraf, 2nd ed., edited by Pataut, Fabrice. Switz.: Springer International.Google Scholar
Donaldson, Thomas Mark Eden. 2014. “If There Were No Numbers, What Would You Think?” Thought: A Journal of Philosophy 3 (4): 283–87.Google Scholar
Enoch, David. 2010. “The Epistemological Challenge to Metanormative Realism: How Best to Understand It, and How to Cope with It.” Philosophical Studies 148 (3): 413–38.10.1007/s11098-009-9333-6CrossRefGoogle Scholar
Field, Hartry. 1980. Science without Numbers: A Defense of Nominalism. Princeton, NJ: Princeton University Press.Google Scholar
Field, Hartry. 1989. Realism, Mathematics, and Modality. Oxford: Blackwell.Google Scholar
Gödel, Kurt. 1947. “What Is Cantor’s Continuum Problem?” In Kurt Gödel: Collected Works, Vol. II, edited by Feferman, Solomonet al., 176–87. Oxford: Oxford University Press.Google Scholar
Goldman, Alvin, and Beddor, Bob. 2016 (Winter). “Reliabilist Epistemology.” In The Stanford Encyclopedia of Philosophy, edited by Zalta, Edward N..Google Scholar
Hellman, Geoffrey. 1994. Mathematics without Numbers. New York: Oxford University Press.Google Scholar
Hirsch, Eli. 2010. Quantifier Variance and Realism: Essays in Metaontology. New York: Oxford University Press.Google Scholar
Hume, David. 2007. An Enquiry Concerning Human Understanding and Other Writings. Cambridge: Cambridge University Press.Google Scholar
Kitcher, Philip. 1981. “Explanatory Unification.” Philosophy of Science 48 (4): 507–31.10.1086/289019CrossRefGoogle Scholar
Klarreich, Erica. 2017. Mathematicians Chase Moonshine’s Shadow. In The Best Writing on Mathematics 2016, edited by Pitici, Mircea. Princeton, NJ: Princeton University Press.Google Scholar
Kunen, Kenneth. 2017. Set Theory: An Introduction to Independence Proofs, Vol. 102. Amsterdam: Elsevier.Google Scholar
Lando, Tamar. 2016. Coincidence and Common Cause. Noûs 51 (1): 132–51.CrossRefGoogle Scholar
Lange, Marc. 2010. “What Are Mathematical Coincidences (and Why Does It Matter)?” Mind 119 (474): 307.CrossRefGoogle Scholar
Lewis, David K. 1986a. “Causal Explanation.” In Philosophical Papers, Vol. II, 214–40. New York: Oxford University Press.Google Scholar
Lewis, David K. 1986b. On the Plurality of Worlds. Malden, MA: Blackwell Publishers.Google Scholar
Linnebo, Øystein. 2006. “Epistemological Challenges to Mathematical Platonism.” Philosophical Studies 129 (3): 545–74.CrossRefGoogle Scholar
Nolan, Daniel. 1997. “Impossible Worlds: A Modest Approach.” Notre Dame Journal of Formal Logic 38 (4): 535–72.Google Scholar
Wikipedia. “Planets Beyond Neptune.” Accessed October 27, 2016. https://en.wikipedia.org/wiki/Planets_beyond_Neptune.Google Scholar
Wright, Crispin. 1983. Frege’s Conception of Numbers as Objects. Scotland: Aberdeen University Press.Google Scholar