Discourse Contextualism: A Framework for Contextualist Semantics and Pragmatics

representations of contexts, recall, assign specific values to variables (§3.3.6). This includes the standards variable s. Hence the inductive premise is false given any abstract context c. (For instance, if we assume a context c1 such that sc1(rich) = 100, then n = 99 provides a counterinstance: x99’s degree of wealth isn’t at least as great as the degree standard of richness in c1, but x100’s is.) So, for any abstract context c, the argument is valid but unsound. Our formal semantics locates the problem with the sorites argument in the inductive premise. This result is of little comfort, however. If the inductive premise is false in any context, why do we find it so plausible? Why are we so inclined to accept it if, no matter what context we might be in, it is false? If saying that the inductive premise is false in any context is sufficient to dissolve the paradox, what should we say about the fact that the premise’s classical equivalent— the “sharp boundaries claim” in (20)— is true in any context?11 (20) Sharp boundaries a. There is an n such that xn isn’t rich and xn+1 is rich. 10See Hyde 2014 for various formulations of the paradox. 11Cf. Wright’s (2003: 97–98) “misconceived conditional”: ∃xn[Fxn ∧ ¬Fxn+1]→ F is not vague.