Abstract
ABSTRACT: This paper offers a generic revenge-proof solution to the Sorites paradox that is compatible
with several philosophical approaches to vagueness, including epistemicism,
supervaluationism, psychological contextualism and intuitionism. The solution is
traditional in that it rejects the Sorites conditional and proposes a modally expressed
weakened conditional instead. The modalities are defined by the first-order logic
QS4M+FIN. (This logic is a modal companion to the intermediate logic QH+KF,
which places the solution between intuitionistic and classical logic.) Borderlineness
is introduced modally as usual. The solution is innovative in that its modal system
brings out the semi-determinability of vagueness. Whether something is borderline
and whether a predicate is vague or precise is only semi-determinable: higher-order
vagueness is columnar. Finally, the solution is based entirely on two assumptions.
(1) It rejects the Sorites conditional. (2) It maintains that if one specifies borderlineness
in terms of the ‒suitably interpreted‒ modal logic QS4M+FIN, then one can
explain why the Sorites appears paradoxical. From (1)+(2) it results that one can tell
neither where exactly in a Sorites series the borderline zone starts and ends nor what
its extension is. Accordingly, the solution is also called agnostic.