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).

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