Paradox

QUINE’S QUESTION MARK 361co-authored a defense of nominalism with Nelson Goodman.Nominalists reject abstract entities—they think that everythinghas a position in space or time. Their diet is aimedagainst philosophical excesses such as Plato’s forms. However,nominalism also winds up prohibiting entities thatscientists help themselves to—numbers, geometrical points,sets, etc.Quine soon felt the pinch. He became persuaded that setsare indispensable for mathematics. To retain mathematics,he relented and swallowed sets. Quine is a pragmatist. Setsearned their way into Quine’s metaphysics by being useful.Principia Mathematica teaches that sets plus logic are enoughto reconstruct all of mathematics. In turn, mathematics isessential to theoretical physics. Science and mathematics setthe standard for rationality, so Quine feels entitled to believein whatever is indispensably postulated by scientists. ForQuine, metaphysics is an afterthought of science.Meanwhile, Nelson Goodman kept sharpening the knifeof nominalism. In 1951 he published The Structure of Appearances.This book contains a logic of parts and wholes. Goodmandenies that there are sets. Instead, there are fusions builtup from smaller things. Unlike a set, a fusion has a positionin space and time. You can touch a fusion. I’m a fusion. So areyou. Goodman’s “calculus of individuals” says that there areonly finitely many atomic individuals and that any combinationof atoms is an individual. Objects do not need to have alltheir parts connected, for instance, Alaska and Hawaii areparts of the United States of America. Goodman does not lethuman intuition dictate what counts as an object; he alsothinks that there is the fusion of his ear and the moon.In a seminar Goodman taught at the University ofPennsylvania around 1965, John Robison pointed out that