David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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British Journal for the History of Philosophy 20 (6):1057-1076 (2012)
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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Hartry Field (1980). Science Without Numbers. Princeton University Press.
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
Charles S. Chihara (1990). Constructibility and Mathematical Existence. Oxford University Press.
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