Non-uniqueness as a non-problem
Philosophia Mathematica 6 (1):63-84 (1998)
| Abstract | A response is given here to Benacerraf's (1965) non-uniqueness (or multiple-reductions) objection to mathematical platonism. It is argued that non-uniqueness is simply not a problem for platonism; more specifically, it is argued that platonists can simply embrace non-uniqueness—i.e., that one can endorse the thesis that our mathematical theories truly describe collections of abstract mathematical objects while rejecting the thesis that such theories truly describe unique collections of such objects. I also argue that part of the motivation for this stance is that it dovetails with the correct response to Benacerraf's other objection to platonism, i.e., his (1973) epistemological objection. | |||||||||
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Colin Cheyne (1999). Problems with Profligate Platonism. Philosophia Mathematica 7 (2):164-177.
Nancy R. Howell (2008). Uniqueness in Context. Zygon 43 (2):493-503.
Jonathan Matheson (2011). The Case for Rational Uniqueness. Logic and Episteme 2 (3):359-373.
Mark Balaguer (1994). Against (Maddian) Naturalized Platonism. Philosophia Mathematica 2 (2):97-108.
Mark Balaguer (1998). Platonism and Anti-Platonism in Mathematics. Oxford University Press.
Brent Mundy (1991). Embedding and Uniqueness in Relationist Theories. Philosophy of Science 58 (1):102-124.
Mark Balaguer (1995). A Platonist Epistemology. Synthese 103 (3):303 - 325.
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