How structuralism can solve the ‘access’ problem
DOI:
https://doi.org/10.15448/1984-6746.2016.1.23296Keywords:
Mathematical Epistemology. Ontology. Platonism. Structuralism.Abstract
According to mathematical structuralism, the subject matter of mathematics is not the study of mathematical objects, but of mathematical structures. By moving away from objects, the structuralist claims to be in a position to solve the ‘access’ problem: structuralism explains the possibility of mathematical knowledge without requiring any access to mathematical objects. Fraser MacBride has challenged the structuralist response, and argued that the structuralist faces a dilemma in the attempt to solve that problem (MacBride, 2004). In the present paper, I argue that MacBride’s dilemma can be resisted, and that, particularly in the version articulated by Michael Resnik (Resnik, 1997), structuralism can solve the ‘access’ problem. I show exactly how MacBride’s dilemma fails, and argue that this failure provides an opportunity to highlight a significant feature of structuralism: the way in which it articulates a fundamentally different picture of mathematical epistemology than traditional epistemology would suggest.
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Azzouni, J. Metaphysical Myths, Mathematical Practice. Cambridge: Cambridge University Press, 1994 . DOI: https://doi.org/10.1017/CBO9780511551291
Benac erraf, P. “Mathematical Truth”. Journal of Philosophy, 70 (1973), p. 661-679. DOI: https://doi.org/10.2307/2025075
da Costa , N.C.A.; French, S. Science and Partial Truth. New York: Oxford University Press, 2003. DOI: https://doi.org/10.1093/019515651X.001.0001
Field, H. Realism, Mathematics and Modality. Oxford: Basil Blackwell, 1989.
French, S. The Structure of the World: Metaphysics and Representation. Oxford: Oxford University Press, 2014. DOI: https://doi.org/10.1093/acprof:oso/9780199684847.001.0001
MacBride, F. “Can Structuralism Solve the ‘Access’ Problem?”. Analysis, 64 (2004), p. 309-317. DOI: https://doi.org/10.1093/analys/64.4.309
Resnik, M. Mathematics as a Science of Patterns. Oxford: Clarendon Press, 1997.
Shapiro, S. Philosophy of Mathematics: Structure and Ontology. New York: Oxford University Press, 1997.
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