Aristotle on Mathematical Truth

Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism also faces a difficult challenge: there is evidence that Aristotle would deny the fictionalist position that mathematics is false. I argue that, in Aristotle's view, the fiction of mathematics is not to treat what does not exist as if existing but to treat mathematical objects with an ontological status they lack. This form of fictionalism is consistent with holding that mathematics is true
Keywords Aristotle  fictionalism  philosophy of mathematics
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DOI 10.1080/09608788.2012.731230
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Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.

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Jean De Groot (2006). A Husserlian Perspective on Empirical Mathematics in Aristotle. Proceedings of the American Catholic Philosophical Association 80:91-99.
Chris John Daly (2008). Fictionalism and the Attitudes. Philosophical Studies 139 (3):423 - 440.

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