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- W3216281435 abstract "Abstract This paper outlines an account of numbers based on the numerical equivalence schema (NES), which consists of all sentences of the form ‘#x.Fx=n if and only if ∃nx Fx’, where # is the number-of operator and ∃n is defined in standard Russellian fashion. In the first part of the paper, I point out some analogies between the NES and the T-schema for truth. In light of these analogies, I formulate a minimalist account of numbers, based on the NES, which strongly parallels the minimalist (deflationary) account of truth. One may be tempted to develop the minimalist account in a fictionalist direction, according to which arithmetic is useful but untrue, if taken at face value. In the second part, I argue that this suggestion is not as attractive as it may first appear. The NES suffers from a similar problem to the T-schema: it is deductively weak and does not enable the derivation of any non-trivial generalizations. In the third part of the paper, I explore some strategies to deal with the generalization problem, again drawing inspiration from the literature on truth. In closing this paper, I briefly compare the minimalist to some other accounts of numbers." @default.
- W3216281435 created "2021-12-06" @default.
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- W3216281435 date "2021-11-13" @default.
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- W3216281435 title "Steps Towards a Minimalist Account of Numbers" @default.
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- W3216281435 doi "https://doi.org/10.1093/mind/fzab060" @default.
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