Possible predicates and actual properties

Abstract

In "Properties and the Interpretation of Second-Order Logic" (Hale, Philos Math 21:133-156, 2013) Bob Hale develops and defends a deflationary conception of properties where a property with particular satisfaction conditions actually (and in fact necessarily) exists if and only if it is possible that a predicate with those same satisfaction conditions exists. He argues further that, since our languages are finitary, there are at most countably infinitely many properties and, as a result, the account fails to underwrite the standard semantics for second-order logic. Here a more lenient version of the view is explored, which allows for the possibility of countably infinite predicates understood as the product of linguistic supertasks. This enriched deflationist account of properties-the Infinitary Deflationary Conception of Existence-supports the standard semantics for models with countable first-order domains, and allows one to prove the categoricity of the second-order Peano axioms. The deflationary account of propertiesIn "Properties and the Interpretation of Second-order Logic" (Hale 2013), Bob Hale defends a 'deflationary' conception 1 of properties that can be used to legitimate the 1 Hale equates his deflationary approach to properties with so-called abundant conceptions, but prefers the former terminology since it emphasizes the existence conditions for properties rather than their profusion. Further, as we shall see, Hale's reading the deflationist conception (as well as the alternative development R. T. Cook (B)

Does everything resemble everything else to the same degree?

“…Atoms are akin toSider's "profiles" (1993, p. 50); see alsoDorr and Hawthorne (2013, p. 23). 11 In contrast to predicates in the infinitary languages discussed byCook (2019).…”

“…For discussion of whether there are infinite sentences in natural language see, for example, Langendoen and Postal (1986),Collins (2010) andBlumson (2014a).13 See especiallyCook (2019Cook ( , pp. 2572Cook ( -2581.…”