On nominalism

Geoffrey Hellman
University of Minnesota
Probably there is no position in Goodman’s corpus that has generated greater perplexity and criticism than Goodman’s “nominalism”. As is abundantly clear from Goodman’s writings, it is not “abstract entities” generally that he questions—indeed, he takes sensory qualia as “basic” in his Carnap-inspired constructional system in Structure—but rather just those abstracta that are so crystal clear in their identity conditions, so fundamental to our thought, so prevalent and seemingly unavoidable in our discourse and theorizing that they have come to form the generally accepted framework for the most time-honored, exact, sophisticated, refined, central, and secure branch of human knowledge yet devised, mathematics itself! Of all the abstracta to question, why sets? Of course, Goodman gave his “reasons”, the unintelligibility of “generating” an infinitude of “constructed objects” automatically from any given object or objects. But critics have been quick to point out that set theory is intended not as a theory of what can be “generated” or “constructed” from given objects in any literal sense but rather as a theory of a certain realm of objects independently existing in their own right. “Construction” is a metaphor.
Keywords nominalism   mathematics   platonism   Burgess   Rosen   toread
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ISBN(s) 0031-8205
DOI 10.1111/j.1933-1592.2001.tb00086.x
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References found in this work BETA

Parts of Classes.David LEWIS - 1991 - Blackwell.
Meaning and Necessity.Rudolf Carnap - 1947 - University of Chicago Press.
Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.

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Plural Quantification and Classes.Gabriel Uzquiano - 2003 - Philosophia Mathematica 11 (1):67-81.

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