Is there a good epistemological argument against platonism?

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Abstract

One important disagreement within the philosophy of mathematics is over the existence of mathematical objects such as numbers. Platonists assert that mathematical objects exist, whereas nominalists deny their existence. According to platonists, mathematical objects are abstract: in other words, platonists think of mathematical objects as neither causally active nor spatially located. Nominalists tend to agree that if there were mathematical objects, then they would be abstract. But they claim that there are no mathematical objects. Nominalists have various ways of arguing against platonism. For instance, they can try to provide nominalist accounts of mathematics which provide better explanations of the phenomena than the platonist competition. Nominalists also argue against platonism more directly. Of recent direct attacks on platonism, Hartry Field’s (1988, 1989) is perhaps the strongest, and has certainly been the most-discussed. 1 As we shall see, it is – broadly speaking – epistemological in character. In their recent article ‘Nominalism reconsidered’ (2005: 520–23), John Burgess and Gideon Rosen contend that there is no good epistemological argument against platonism. They propose a dilemma, claiming that epistemological arguments against platonism either (i) rely on a dubious epistemology, or (ii) resemble a dubious sceptical argument concerning perceptual knowledge. I take it that impalement on either horn of the dilemma would seriously weaken Field’s argument. In what follows, I will defend Field’s argument by showing that it escapes both horns. I begin by reviewing Field’s argument; then I take on (i) and (ii) in turn.
Original languageEnglish
Pages (from-to)135-141
Number of pages7
JournalAnalysis
Volume66
Issue number2
DOIs
Publication statusPublished - Apr 2006

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