Tolerance Puzzles

Abstract

This chapter provides a general schema for regimenting a broad family of puzzles of modal variation. These puzzles begin with a ‘Tolerance’ premise according to which an objects (or a certain kind of object) can differ in any small way along a certain parameter. This is supplemented with a ‘Non-contingency’ premise according to which the Tolerance premise is necessarily true if true at all, an ‘Iteration’ premise according to which anything possibly possible is possible, and a ‘Persistent Closeness’ premise according to which what counts as a ‘small difference’ is modally constant. These premises jointly imply the conclusion, ‘Hypertolerance’, that the object or objects in question can differ arbitrarily along the relevant parameter. We show how this schema is general enough to subsume puzzles involving time or objective chance, and discuss some difficulties that arise in trying to formulate compelling instantiations of the schema involving variation in originating matter.