Phil Corkum
University of Alberta
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: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
On What Grounds What.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
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Citations of this work BETA

Fictionalism in the Philosophy of Mathematics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.
Aristotle on Geometrical Potentialities.Naoya Iwata - 2021 - Journal of the History of Philosophy 59 (3):371-397.

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