Frege and Vagueness

Whoever undertakes to scrutinize logical arguments conducted outside mathematics cannot but wince at the flightly conduct of words. Their meanings have no exact lines of demarcation. What an adjective conveys may depend on the noun that follows (’white wine’). We often have difficulty in grasping the exact meaning of a verb if we do not know its subject and complement(s). When we look up a word in a dictionary, we see how the word’s uses have come to diverge ever more from its primary meaning and have branched out in many directions. Metaphors lose their sparkle and, like dead stars, come to lead an obscure existence (‘source of grief’). Words in ordinary language are far from having neat definitions, like that of ‘even’ in arithmetic. Every predicate is vague, in the sense that there are individuals for which it is intrinsically indeterminate whether the predicate holds or not.