Abstract
On some accounts of vagueness, predicates like “is a heap” are tolerant. That is, their correct application tolerates sufficiently small changes in the objects to which they are applied. (So, according to tolerant views, if a given object is a heap, it will necessarily remain a heap after one grain of sand is removed.) Of course, such views face the sorites paradox, and various solutions have been proposed. One proposed solution involves banning repeated appeals to tolerance, while affirming tolerance in any individual case. (So, you may always remove one grain of sand safely, but you mustn’t make a habit of it.) In effect, this solution rejects the reasoning (rather than the premises) of the sorites argument. This paper discusses a thorny problem afflicting this approach to vagueness. In particular, it is shown that, on the foregoing view, whether an object is a heap will sometimes depend on factors extrinsic to that object, such as whether its components came from other heaps. More generally, the paper raises the issue of how to count heaps in a tolerance-friendly framework.
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Notes
Gaifman uses “Sorites conditional” in place of “tolerance principle.”
This supposition is purely presentational.
It should be noted that Gaifman’s (2010) contextualist view is safe from this problem. On his view, a vague predicate “loses its tolerance” in contexts like that posed by the staircase (see his p. 17). The challenge presented is most pressing for views that regard tolerance principles as true without qualification.
For constructive feedback and suggestions, I would like to thank Anna Brinkerhoff, David Christensen, Jamie Dreier, Kelly Gaus, Yongming Han, Richard Heck, Han Li, Matthew Mandelkern, Josh Schechter, Brett Topey, Leo Yan and three anonymous referees at Synthese. Many thanks.
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