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|
|Categories||categorize this paper)|
References found in this work BETA
Citations of this work BETA
Critical Notice of Michail Peramatzis, Priority in Aristotle’s Metaphysics, Oxford University Press, 2011.Phil Corkum - 2013 - Canadian Journal of Philosophy 43 (1):136-156.
Similar books and articles
Fictionalism in the Philosophy of Mathematics.Mark Colyvan - 2011 - In E. J. Craig (ed.), Routledge Encyclopedia of Philosophy.
Why Pragmaticism is Neither Mathematical Structuralism nor Fictionalism.AhtiVeikko Pietarinen - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:19-25.
What Mathematicians' Claims Mean : In Defense of Hermeneutic Fictionalism.Gábor Forrai - 2010 - Hungarian Philosophical Review 54 (4):191-203.
Fictionalism in the Philosophy of Mathematics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.
A Husserlian Perspective on Empirical Mathematics in Aristotle.Jean De Groot - 2006 - Proceedings of the American Catholic Philosophical Association 80:91-99.
Aristotle's Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities.Paola Cantù - 2010 - Synthese 174 (2):225 - 235.
Handling Mathematical Objects: Representations and Context.Jessica Carter - 2013 - Synthese 190 (17):3983-3999.
Aristotle and Modern Mathematical Theories of the Continuum.Anne Newstead - 2001 - In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang.
New Directions for Nominalist Philosophers of Mathematics.Charles Chihara - 2010 - Synthese 176 (2):153 - 175.
Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics.John J. Cleary - 1995 - E.J. Brill.
Added to index2010-11-05
Total downloads145 ( #30,611 of 2,146,802 )
Recent downloads (6 months)6 ( #120,194 of 2,146,802 )
How can I increase my downloads?
There are no threads in this forum
Nothing in this forum yet.