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- Title
A NOTE ON THE REVERSE MATHEMATICS OF THE SORITES.
- Authors
DZHAFAROV, DAMIR D.
- Abstract
Sorites is an ancient piece of paradoxical reasoning pertaining to sets with the following properties: (Supervenience) elements of the set are mapped into some set of "attributes"; (Tolerance) if an element has a given attribute then so are the elements in some vicinity of this element; and (Connectedness) such vicinities can be arranged into pairwise overlapping finite chains connecting two elements with different attributes. Obviously, if Superveneince is assumed, then (1) Tolerance implies lack of Connectedness, and (2) Connectedness implies lack of Tolerance. Using a very general but precise definition of "vicinity", Dzhafarov & Dzhafarov (2010) offered two formalizations of these mutual contrapositions. Mathematically, the formalizations are equally valid, but in this paper, we offer a different basis by which to compare them. Namely, we show that the formalizations have different proof-theoretic strengths when measured in the framework of reverse mathematics: the formalization of (1) is provable in RCA0, while the formalization of (2) is equivalent to ACA0 over RCA0. Thus, in a certain precise sense, the approach of (1) is more constructive than that of (2).
- Subjects
SORITES paradox; QUALITY (Aesthetics); TOLERATION; MATHEMATICS; FORMALIZATION (Philosophy)
- Publication
Review of Symbolic Logic, 2019, Vol 12, Issue 1, p30
- ISSN
1755-0203
- Publication type
Article
- DOI
10.1017/S1755020318000461