Knowledge and reality

Abstract

objects. What might the nominalist say in reply? The most plausible reply open to the nominalist seems to me to be along the following lines. My platonist critic is certainly a very literal-minded fellow. I didn’t mean the ‘some’ in the open sentence ‘x is like y in some anatomically relevant ways’ to be taken as a quantifier: I didn’t mean this sentence to be read ‘∃z (z is a way in which a thing can be like a thing and z is anatomical and x is like y in z)’. That’s absurd. One might as well read ‘There’s more than one way to skin a cat’ as ‘∃x ∃y (x is a way of skinning a cat and y is a way of skinning a cat and x y)’. I meant this open sentence to have no internal logical structure, or none beyond that implied by the statement that two variables are free in it. It’s just a form of words we learn to use by comparing various pairs of objects in the ordinary business of life. And here is the rejoinder to this reply: If you take that line you confront problems it would be better not to have to confront. Consider the sentence ‘x is like y in some physiologically relevant ways’. Surely there is some logical or structural or syntactical 20 Peter van Inwagen relation between this sentence and ‘x is like y in some anatomically relevant ways’? One way to explain the relation between these two sentences is to read the former as ‘∃z (z is a way in which a thing can be like a thing and z is physiological and x is like y in z)’ and the latter as ‘∃z (z is a way in which a thing can be like a thing and z is anatomical and x is like y in z)’. How would you explain it? Or how would you explain the relation between the sentences ‘x is like y in some anatomically relevant ways’ (which you say has no logical structure) and ‘x is like y in all anatomically relevant ways’? If neither of these sentences has a logical structure, how do you account for the obvious validity of the argument Either of two female spiders of the same species is like the other in all anatomically relevant ways. Hence, an insect that is like a given female spider in some anatomically relevant ways is like any female spider of the same species in some anatomically relevant ways? If the premise and conclusion of this argument are read as having the logical structure their syntax suggests, the validity of this argument is easily demonstrable in textbook quantifier logic. If one insists that they have no logical structure, one will find it difficult to account for the validity of this argument. That is one of those problems I alluded to, one of those problems it would be better not to have to confront. (One of thousands of such problems.) I suggest that we can learn a lesson from this little exchange between an imaginary nominalist and an imaginary platonist: that one should accept the following condition of adequacy on philosophical paraphrases. Paraphrases must not be such as to leave us without an account of the logical relations between predicates that are obviously logically related. Essentially the same constraint on paraphrase can be put in these words: A paraphrase must not leave us without an account of the validity of any obviously valid argument. Accepting this constraint has, I believe, a significant consequence. This consequence requires a rather lengthy statement. Apparent quantification over properties pervades our discourse. In the end, one can avoid quantifying over properties only by quantifying over other sorts of abstract object—”ways in which a thing can be like a thing,” for example. But most philosophers, if forced to chose between quantifying over properties and quantifying over these other objects