Aristotle on Mathematical Truth

Abstract
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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References found in this work BETA
Science Without Numbers.Hartry Field - 1980 - Princeton University Press.
Realism in Mathematics.Penelope Maddy - 1990 - Oxford University Prress.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Aristotle's First Principles.Terence Irwin - 1988 - Oxford University Press.

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