Is ‘Congruence’ A Peculiar Predicate?

Abstract

The logical status of spatial and temporal congruence has been much debated. Recently the topic of debate has shifted from the alleged conventionality of congruence to the alleged eccentricity of congruence predicates. For example, espousing a point of view suggested to him by Nuel Belnap, Adolf Grunbaum has recently remarked that the predicate ‘x is (spatially) congruent to y’ deviates from the ‘classical account’ of the interrelations between the intensional and extensional components of the meaning of a predicate. By the classical account (hereafter CA), Grunbaum means the rather common view that the extension of a predicate is completely determined by its intension. Contrary to CA, Grunbaum maintains that “the fact that ‘being spatially congruent’ means sustaining the relation of spatial equality does not suffice at all to determine its extension uniquely in the class of spatial intervals.”1 Rather, he states, the “term ‘spatially congruent’ has the same (nonclassical) intension and only a different extension in the context of alternative space metrics.”2 (The parenthetical ‘nonclassical’ is meant only to underscore the allegation that ‘x is congruent to y’ deviates from CA.)