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Mathematical objects and the object of theology

Published online by Cambridge University Press:  18 October 2016

VICTORIA S. HARRISON
VICTORIA S. HARRISON*
Affiliation:
Philosophy and Religious Studies Program, Room 4101a, Humanities and Social Sciences Building (E21), University of Macau, Avenida da Universidade, Taipa, Macau, China
*
e-mail: [email protected]
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Abstract

This article brings mathematical realism and theological realism into conversation. It outlines a realist ontology that characterizes abstract mathematical objects as inaccessible to the senses, non-spatiotemporal, and acausal. Mathematical realists are challenged to explain how we can know such objects. The article reviews some promising responses to this challenge before considering the view that the object of theology also possesses the three characteristic features of abstract objects, and consequently may be known through the same methods that yield knowledge of mathematical objects.

Type
Articles
Information
Religious Studies , Volume 53 , Issue 4 , December 2017 , pp. 479 - 496
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Copyright
Copyright © Cambridge University Press 2016 

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References

Balaguer, M. (1998) Platonism and Anti-Platonism in Mathematics (New York & Oxford: Oxford University Press).CrossRefGoogle Scholar
Balthasar, H. U. von (1982) The Glory of the Lord: A Theological Aesthetics, I: Seeing the Form (Edinburgh: T. & T. Clark).Google Scholar
Beall, Jc. (2001) ‘Existential claims and platonism’, Philosophia Mathematica, 9, 80–86.CrossRefGoogle Scholar
Benacerraf, P. (1973) ‘Mathematical truth’, Journal of Philosophy, 70, 661–679.Google Scholar
Brouwer, L. E. J. (1912) Intuitionisme en formalisme (Groningen: Noordhoof).Google Scholar
Brown, J. R. (1990) ‘π in the sky’, in Irvine, A. D. (ed.) Physicalism in Mathematics (Dordrecht: Kluwer Academic), 95–120.CrossRefGoogle Scholar
Burgess, J. P. & Rosen, G. (1997) A Subject with no Object (Oxford: Clarendon Press).Google Scholar
Cheyne, C. (2001) Knowledge, Cause, and Abstract Objects (Dordrecht: Kluwer Academic).CrossRefGoogle Scholar
Chihara, C. (1990) Constructibility and Mathematical Existence (Oxford: Oxford University Press).Google Scholar
Dummett, M. (1973) Frege: Philosophy of Language (London: Duckworth).Google Scholar
Field, H. (1980) Science without Numbers (Princeton: Princeton University Press).Google Scholar
Gödel, K. (1983 [1964]) ‘What is Cantor's continuum problem?’, repr. in Benacerraf, P. & Putnam, H. (eds) Philosophy of Mathematics, 2nd edn (Cambridge: Cambridge University Press), 470–485.Google Scholar
Hale, B. (1987) Abstract Objects (Oxford: Basil Blackwell).Google Scholar
Katz, J. (1981) Language and Other Abstract Objects (Totowa NJ: Rowman & Littlefield).Google Scholar
Katz, J. (1998) Realistic Rationalism (Cambridge MA: MIT Press).Google Scholar
Koetsier, T. & Bergmans, L. (eds) (2005) Mathematics and the Divine: A Historical Study (Amsterdam: Elsevier).Google Scholar
Maddy, P. (1997) Naturalism in Mathematics (Oxford: Oxford University Press).Google Scholar
Mill, J. S. (1843) A System of Logic (London: Longmans Green, & Company).Google Scholar
Moore, A. & Scott, M. (eds) (2007) Realism and Religion (Aldershot: Ashgate).Google Scholar
Parsons, C. (1979) ‘Mathematical intuition’, Proceedings of the Aristotelian Society, 80, 142–168.Google Scholar
Poincaré, H. (1913) The Foundations of Science (Lancaster PA: The Science Press).Google Scholar
Putnam, H. (1979) ‘What is mathematical truth?’, in Putnam, H., Mathematics, Matter and Method: Philosophical Papers, I, 2nd edn (Cambridge: Cambridge University Press), 60–78.CrossRefGoogle Scholar
Quine, W. V. O. (1983 [1976]) ‘Carnap and logical truth’, reprinted in Benacerraf, P. & Putnam, H. (eds) Philosophy of Mathematics, 2nd edn (Cambridge: Cambridge University Press), 355–376.Google Scholar
Shapiro, S. (2011) Thinking about Mathematics (Oxford: Oxford University Press).Google Scholar
Stein, E. (2002) The Science of the Cross, Koeppel, J. O.C.D. (tr.), The Collected Works of Edith Stein, VI (Washington DC: ICS Publications).Google Scholar
Tait, W. W. (1986) ‘Truth and proof: the platonism of mathematics’, Synthese, 69, 331–370.CrossRefGoogle Scholar
Tieszen, R. L. (1989) Mathematical Intuition (Dordrecht: Kluwer Academic).CrossRefGoogle Scholar