Attempts to resolve the sorites paradox typically require
restrictions, revisions, or rejection of either classical logic or common
sense. The only exception to this generalization is the epistemological
approach developed by James Cargile and Richmond Campbell in [3] and
[4]. They claim that vagueness is due to ignorance; although there is a
sharp division point between, say, short and nonshort men, we do not
know where the division point is. The main objection to this view is that
Cargile and Campbell have not given a positive explanation of the source
of this ignorance and they have not explained how vague predicates could
have the unlimited sensitivity necessary to possess sharp division points.
This paper is intended to lend support to the epistemological approach by
providing criticisms of rival strategies and by showing how the
explanatory gap can be filled by an appeal to "blurry" predicates.
The paradoxes of vagueness can be traced back to Eubulides'
paradox of the heap. Eubulides' paradox has the form of a mathematical induction. The base step of the induction is the claim that a collection of
sand containing, say, one million grains of sand, is a heap. The induction
step is the thesis that any heap remains a heap if only one grain of sand
is removed from it. Classical logic allows us to validly infer from these two
propositions that a collection of sand containing one grain of sand is a
heap.