Month: November 2022

On the reverse philosophy of the sorites paradox

Walter Dean

The goal of this talk is to use the sorites paradox to illustrate the methodology of “reverse philosophy”—i.e. the application of methods from reverse mathematics to study the mathematical involvement of recognized arguments in analytic philosophy. After briefly motivating such a program, I will focus on the following: 1) the role of measurement and representation theorems in the linguistic formulation of various forms of the sorites; 2) the role of a weak form of Hölder’s Theorem in the formulation of the conditional sorites for predicates such as “tall”; 3) the role of a stronger form of Hölder’s Theorem in the formulation of the so-called continuous sorites for predicates such as “red” of Weber & Colyvan 2010/Weber 2021. Contrasts will be drawn between the constructivity of the weaker form (as observed by Krantz 1968 and formalized in RCA_0 by Solomon 1998) and the non-constructivity of the latter form (due to its apparent dependence on Arithmetical Comprehension).

Neopragmatism About Logic

Lionel Shapiro

I’ll propose an application to logic of the “neopragmatist” program. Neopragmatists argue that inquiry into the nature of what we think and talk about can be fruitfully replaced by inquiry into the functions of concepts and expressions. Logical vocabulary can serve as a particular target for neopragmatist theorizing, but it has also been taken to pose obstacles to neopragmatist accounts more generally. I’ll argue that a neopragmatist approach to logical relations (such as logical consequence), as well as to ascriptions of content, undermines two constraints on neopragmatist accounts of logical connectives (such as “and”, “or”, and “not”). Freed from these constraints, I’ll sketch a simple version of such an account, on which logical connectives express dialectical attitudes. The resulting approach is deflationary in two ways: it’s based on deflationism about logical relations and it aims to deflate some of neopragmatists’ usual theoretical ambitions.