Vagueness, Logic, and Ontology

Remember the story of the most-most? It’s the story of that club in New York where people are the most of every type. There is the hairiest bald man and the baldest hairy man; the shortest giant and the tallest dwarf; the smartest idiot and the stupidest wise man. They are all there, including honest thieves and crippled acrobats. On Saturday night they have a party, eat, drink, dance. Then they have a contest. “And if you can tell the hairiest bald man from the baldest hairy man—we are told—you get a prize.” The story is from Saul Bellow’s Herzog, a novel published almost forty years ago but still very modern in its philosophical provocations. It is a funny and provoking story because so is the idea of a contest like that of the most-most. There is no sharp boundary demarcating the category of bald men, no precise number of hairs separating the bald from the hairy. Hence it makes no sense to suppose that one can identify the hairiest bald man. It does not even make sense to suppose that such a person exists, as if the difficulty were merely epistemic. Some people are clearly bald and some are clearly hairy, but between these two sorts of people there exist a variety of borderline cases: baldish guys, men wearing toupees, hirsute beatniks with a shiny spot on the top of their heads. Our concept of baldness and our linguistic practices do not specify any precise, general criterion for saying in each case whether we are dealing with a bald man or with a hairy one. ‘Bald’ and ‘hairy’ are vague concepts and their ranges of application have vague boundaries. Shall we distinguish three categories, then? Some people are clearly bald (Picasso), some are clearly hairy (the count of Montecristo), and some are borderline cases. That’s a third category of its own, and we may suppose that the New York club includes the most of each of these three categories. Unfortunately things are not so easy. Two boundaries aren’t any better than one. And if it is impossible to identify the hairiest bald man (i.e., to draw a boundary