  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 and 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 $\mathsf{RCA}_0$, while the formalization of (2) is equivalent to
$\mathsf{ACA}_0$ over $\mathsf{RCA}_0$. Thus, in a certain precise sense, the
approach of (1) is more constructive than that of (2).
