Hyperintensional Questions

Abstract

It has been known for decades that Montague’s (1974 [1970]) possible-worlds semantics, which follows Kripke 1963 in treating worlds as unanalyzed primitives and propositions as sets of worlds, does not provide enough meaning distinctions to make correct predictions about a wide range of natural-language entailment patterns. This granularity problem, as it has come to be known, has many dimensions, of which the best known is that two declarative sentences which entail each other must express the same proposition. This is because entailment is modelled by the subset inclusion relation on the powerset of the set of propositions, and that relation is irretrievably antisymmetric. The most notorious consequence of this antisymmetry of entailment is the so-called logical omniscience problem, that (assuming knowledge is a relation between individuals and propositions) anyone who knows at least one necessary truth (e.g. that s/he is self-identical, or that two is even) must know every necessary truth, even an unresolved mathematical conjecture or its denial (whichever is true). Thus, e.g. if Paris Hilton knows that Paris Hilton is Paris Hilton, then she must also know that every nontrivial zero of the zeta-function has real part 1/2, if that is indeed the case, or else she must know that this is not the case, if indeed it is not. In short, it seems to be a consequence of MS that a celebrity hotel heiress devoted to parties and shopping knows whether the Riemann Hypothesis is true. This is just one of the unsavory consequences of MS.