Conjoining mathematical empiricism with mathematical realism: Maddy's account of set perception revisited

Synthese 145 (3):425 - 448 (2005)
Abstract
Penelope Maddy’s original solution to the dilemma posed by Benacerraf in his (1973) ‘Mathematical Truth’ was to reconcile mathematical empiricism with mathematical realism by arguing that we can perceive realistically construed sets. Though her hypothesis has attracted considerable critical attention, much of it, in my view, misses the point. In this paper I vigorously defend Maddy’s (1990) account against published criticisms, not because I think it is true, but because these criticisms have functioned to obscure a more fundamental issue that is well worth addressing: in general – and not only in the mathematical domain – empiricism and realism simply cannot be reconciled by means of an account of perception anything like Maddy’s. But because Maddy’s account of perception is so plausible, this conclusion raises the specter of the broader incompatibility of realism and empiricism, which contemporary philosophers are frequently at pains to forget.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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DOI 10.1007/s11229-005-6202-5
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Is Justified True Belief Knowledge?Edmund Gettier - 1963 - Analysis 23 (6):121-123.
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford University Press.
Realism in Mathematics.Penelope Maddy - 1990 - Oxford University Prress.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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