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The uncanny accuracy of God's mathematical beliefs

Published online by Cambridge University Press:  04 June 2019

ROBERT KNOWLES Open the ORCID record for ROBERT KNOWLES [Opens in a new window]
ROBERT KNOWLES*
Affiliation:
School of Philosophy, Religion, and History of Science, University of Leeds, Leeds, LS2 9JT, UK
*
e-mail: r.knowles@leeds.ac.uk
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Abstract

I show how mathematical platonism combined with belief in the God of classical theism can respond to Field's epistemological objection. I defend an account of divine mathematical knowledge by showing that it falls out of an independently motivated general account of divine knowledge. I use this to explain the accuracy of God's mathematical beliefs, which in turn explains the accuracy of our own. My arguments provide good news for theistic platonists, while also shedding new light on Field's influential objection.

Type
Original Article
Information
Religious Studies , Volume 57 , Issue 2 , June 2021 , pp. 333 - 352
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Copyright
Copyright © Cambridge University Press 2019

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References

Achinstein, P. (1983) The Nature of Explanation (Oxford: Oxford University Press).Google Scholar
Adams, R. M. (1983) ‘Divine necessity’, Journal of Philosophy, 80, 741–752.CrossRefGoogle Scholar
Alston, W. (1986) ‘Does God have beliefs?’, Religious Studies, 22, 287–306.CrossRefGoogle Scholar
Asay, J. (2016) ‘The facts about truthmaking: an argument for truthmaker necessitarianism’, Ergo, 3, 493–500.Google Scholar
Baker, A. (2005) ‘Are there genuine mathematical explanations of physical phenomena?’, Mind, 114, 223–238.CrossRefGoogle Scholar
Baker, A. (2016a) ‘Mathematics and explanatory generality’, Philosophia Mathematica, 25, 194–209.Google Scholar
Baker, A. (2016b) ‘Parsimony and inference to the best explanation’, Synthese, 193, 333–350.CrossRefGoogle Scholar
Baker, A. & Colyvan, M. (2011) ‘Indexing and mathematical explanation’, Philosophia Mathematica, 19, 323–334.CrossRefGoogle Scholar
Bangu, S. (2013) ‘Indispensability and explanation’, Journal for the Philosophy of Science, 64, 255–277.CrossRefGoogle Scholar
Baras, D. (2017) ‘A reliability challenge to theistic platonism’, Analysis, 77, 479–487.CrossRefGoogle Scholar
Baron, S. (2014) ‘Optimisation and mathematical explanation: doing the Levy walk’, Synthese, 191, 459–479.CrossRefGoogle Scholar
Baron, S., Colyvan, M., & Ripley, D. (2017) ‘How mathematics can make a difference’, Philosophers’ Imprint, 17, 1–29.Google Scholar
Benacerraf, P. (1973) ‘Mathematical truth’, Journal of Philosophy, 70, 661–679.CrossRefGoogle Scholar
BonJour, L. (2003) ‘A version of internalist foundationalism’, in BonJour, L. & Sosa, E. (eds) Epistemic Justification: Internalism vs. Externalism, Foundations vs. Virtues (Malden MA: Blackwell), 3–96.Google Scholar
Brown, J. R. (2012) Platonism, Naturalism, and Mathematical Knowledge (New York: Routledge).Google Scholar
Cameron, R. P. (2008) ‘Truthmakers, realism, and ontology’, Philosophy, 83, 107–128.Google Scholar
Carter, J. A. & Gordon, E. C. (2014) ‘Objectual understanding and the value problem’, American Philosophical Quarterly, 51, 1–13.Google Scholar
Clarke-Doane, J. (2016) ‘What is the Benacerraf problem?’, in Pataut, F. (ed.) Truth, Objects, Infinity: New Perspectives on the Philosophy of Paul Benacerraf (Dordrecht: Springer), 17–43.CrossRefGoogle Scholar
Colyvan, M. (2002) ‘Mathematics and aesthetic considerations in science’, Mind, 111, 69–74.CrossRefGoogle Scholar
Colyvan, M. (2010) ‘There is no easy road to nominalism’, Mind, 119, 285–306.CrossRefGoogle Scholar
Colyvan, M. (2012) ‘Road work ahead: heavy machinery on the easy road’, Mind, 121, 1031–1046.CrossRefGoogle Scholar
de Regt, H. W. (2017) Understanding Scientific Understanding (Oxford: Oxford University Press).CrossRefGoogle Scholar
Dickinson, T. M. (2019) ‘God knows: acquaintance and the nature of divine knowledge’, Religious Studies, 55, 1–16.CrossRefGoogle Scholar
Earman, J. (2000) Hume's Abject Failure: The Argument against Miracles (Oxford: Oxford University Press).CrossRefGoogle Scholar
Evans, C. S. (2013) God and Moral Obligation (Oxford: Oxford University Press).CrossRefGoogle Scholar
Field, H. (1980) Science without Numbers (Oxford: Blackwell).Google Scholar
Field, H. (1989) Realism, Mathematics, and Modality (Oxford: Blackwell).Google Scholar
Field, H. (2001) Truth and the Absence of Fact (Oxford: Oxford University Press).CrossRefGoogle Scholar
Field, H. (2005) ‘Recent debates in the a priori’, in T. Gendler & J. Hawthorne (eds) Oxford Studies in Epistemology, I (Oxford: Clarendon Press), 69–88.Google Scholar
Fumerton, R. (1995) Metaepistemology and Skepticism (Lanham MD: Rowman & Littlefield).Google Scholar
Fumerton, R. (2001) ‘Classical foundationalism’, in De Paul, M. R. (ed.) Resurrecting Old-Fashioned Foundationalism (Lanham MD: Rowman & Littlefield), 3–20.Google Scholar
Goff, P. (2010) ‘Orthodox truthmaker theory cannot be defended by cost/benefit analysis’ Analysis, 70, 45–50.CrossRefGoogle Scholar
Grimm, S. (2006) ‘Is understanding a species of knowledge?’, British Journal for the Philosophy of Science, 57, 515–535.CrossRefGoogle Scholar
Hasan, A. & Fumerton, R. (2017) ‘Knowledge by acquaintance vs. description’, in Zalta, E. N. (ed.) The Stanford Encyclopedia of Philosophy.Google Scholar
Kitcher, P. (2002) ‘Scientific knowledge’, in Moser, P. (ed.) The Oxford Handbook of Epistemology (New York: Oxford University Press), 385–408.CrossRefGoogle Scholar
Kvanvig, J. (2003) The Value of Knowledge and the Pursuit of Understanding (New York: Cambridge University Press).CrossRefGoogle Scholar
Lange, M. (2017) Because Without Cause: Non-Causal Explanations in Science and Mathematics (Oxford: Oxford University Press).Google Scholar
Leng, M. (2010) Mathematics and Reality (Oxford: Oxford University Press).CrossRefGoogle Scholar
Leng, M. (2012) ‘Taking it easy: a response to Colyvan’, Mind, 121, 983–995.CrossRefGoogle Scholar
Liggins, D. (2018) ‘The reality of Field's epistemological challenge to platonism’, Erkenntnis, 83, 1027–1031.CrossRefGoogle Scholar
Linnebo, Ø. (2018) ‘Platonism in the philosophy of mathematics’, in Zalta, E. N. (ed.) The Stanford Encyclopedia of Philosophy.Google Scholar
Lipton, P. (2004) Inference to the Best Explanation, 2nd edn (New York: Routledge).Google Scholar
Lyon, A. (2012) ‘Mathematical explanations of empirical facts, and mathematical realism’, Australasian Journal of Philosophy, 90, 559–578.CrossRefGoogle Scholar
Lyon, A. & Colyvan, M. (2008) ‘The explanatory power of phase spaces’, Philosophia Mathematica, 16, 227–243.CrossRefGoogle Scholar
MacBride, F. (1999) ‘Listening to fictions: a study of Fieldian nominalism’, British Journal for the Philosophy of Science, 50: 431–455.CrossRefGoogle Scholar
Melia, J. (2000) ‘Weaseling away the indispensability argument’, Mind, 109, 455–479.CrossRefGoogle Scholar
Merricks, T. (2007) Truth and Ontology (Clarendon Press).CrossRefGoogle Scholar
Murat, A. (2013) ‘Pain’, in Zalta, E. N. (ed.) The Stanford Encyclopedia of Philosophy.Google Scholar
Pincock, C. (2015) ‘Abstract explanations in science’, British Journal for the Philosophy of Science, 66, 857–882.CrossRefGoogle Scholar
Pritchard, D. (2016) ‘Seeing it for oneself: perceptual knowledge, understanding, and intellectual autonomy’, Episteme, 13, 29–42.CrossRefGoogle Scholar
Putnam, H. (1971) Philosophy of Logic (New York: Harper).Google Scholar
Quine, W. V. O. (1948) ‘On what there is’, The Review of Metaphysics, 2, 21–38.Google Scholar
Rogers, K. A. (2008) ‘Evidence for God from certainty’, Faith and Philosoph y, 25, 31–46.CrossRefGoogle Scholar
Salmon, W. (1989) ‘Four decades of scientific explanation’, in Kitcher, P. & Salmon, W. (eds) Scientific Explanation: Minnesota Studies in the Philosophy of Science, XIII (Minneapolis: University of Minnesota Press), 3–219.Google Scholar
Schaffer, J. (2008) ‘Truthmaker commitments’, Philosophical Studies, 141, 7–19.CrossRefGoogle Scholar
Schindler, S. (2018) Theoretical Virtues in Science: Uncovering Reality through Theory (Cambridge: Cambridge University Press).CrossRefGoogle Scholar
Shapiro, S. (2000) Thinking about Mathematics (New York: Oxford University Press).Google Scholar
Thurow, J. C. (2013) ‘The defeater version of Benacerraf's problem for a priori knowledge’, Synthese, 190, 1587–1603.CrossRefGoogle Scholar
Warren, J. (2017) ‘Epistemology versus non-causal realism’, Synthese, 194, 1643–1662.CrossRefGoogle Scholar
Woodward, J. (2003) Making Things Happen: A Theory of Causal Explanation (New York: Oxford University of Press).Google Scholar
Yablo, S. (2012) ‘Explanation, extrapolation, and existence’, Mind, 121, 1007–1029.CrossRefGoogle Scholar
Ylikoski, P. & Kuorikoski, J. (2010) ‘Dissecting explanatory power’, Philosophical Studies, 148, 201–219.CrossRefGoogle Scholar
Zagzebski, L. (2001) ‘Recovering understanding’, in Steup, M. (ed.) Knowledge, Truth, and Duty: Essays on Epistemic Justification, Responsibility, and Virtue (New York: Oxford University Press), 235–252.CrossRefGoogle Scholar