The Eleatic and the Indispensabilist

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THEORIA. An International Journal for Theory, History and Foundations of Science, ISSN: 0495-4548, Vol: 30, Issue: 3, Page: 415-429

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Marcus, Russell
UPV/EHU Press; Euskal Herriko Unibertsitatea / Universidad del PaĆ­s Vasco
Arts and Humanities
article description
The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe to exist. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan's recent defenses of Quine's indispensability argument present an intriguing attempt to provide reasons to favor the indispensabilist's criterion against some contemporary eleatics. I show that Colyvan's argument is not decisive against the eleatic and then sketch a way to capture some of the important intuitions behind both views.