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. (shrink)

In order to re-contextualize the otherwise ontologically privileged meaning of metaphysical debates into a more insubstantial form, metaphysical deflationism runs the risk of having to adopt potentially unwanted anti-realist tendencies. This tension between deflationism and anti-realism can be expressed as follows: in order to claim truthfully that something exists, how can deflationism avoid the anti-realist feature of construing such claims singularly in an analytical fashion? One may choose to adopt a Yablovian fallibilism about existential claims, but other approaches can be (...) appealed to as well. Amie Thomasson's Easy Ontology is one such approach, whereby the interaction of empirical as well as analytic features within the construction of its ontological theory affords a role for analytical rules without forsaking a link with empirical reality. The development of these analytical and empirical features has resulted in significant critiques regarding, one, potential reference failure of easy-ontological claims, and two, a circularity in how easy ontology explains the relation between its analytical rules and existential claims. This essay offers a response by showcasing how an easy ontological deflationism can reject these criticisms without succumbing to, one, the anti-realism of pure analyticism, and two, a further critique of wholesale referential indeterminacy in its referring terms. (shrink)