ABSTRACT
I shall discuss is to be found in the section of his Philosophy of Logic2 called “Set Theo ry in Sheep’s Clothing.** M uch of th is section is devoted to dispelling two confusions which we can easily agree w ith
Quine in dep lo ring : th a t of supposing th a t and ‘(F ) ’ say th a t some (all) p red icates (i.e., predicate-expressions) are th u s and so, and th a t of supposing th a t quan tification over a ttr ib u te s has rele v a n t ontological advan tages over quan tifica tion over sets. W ha t I wish to d ispu te is his assertion th a t the use of p red ica te le tte rs as quan tifiab le variab les is to be deplored, even when the values of those variab les are sets, on the g round th a t p red icates are no t names of th e ir extensions. Quine w rites, “ P red icates have a ttr ib u te s as th e ir ‘in tensions' o r m eanings (or would if there were a ttr ib u te s) and they have sets as the ir ex tensions; b u t th ey are nam es of neither. V ariables eligible for quan tifica tion therefore do no t belong in pred ica te positions. T hey belong in nam e positions" (67). L e t us g ran t th a t p red icates are no t names. W hy m ust we then
suppose, as the “ therefo re" in Q uine’s sentence would ind icate we m ust, th a t variab les eligible for quan tifica tion do no t belong in p red ica te positions? Quine earlier (66/7) gives th is a rgum en t:
Consider first some ordinary quantifications: ‘(3*)(x walks)', ‘(jc) (jc walks)’, 4(3 x)(x is prime)’. The open sentence after the quanti fier shows V in a position where a name could stand; a name of a walker, for instance, or of a prime number. The quantifications do not mean tha t names walk or are prime; what are said to walk or to be prime are things tha t could be named by names in those positions. To put the predicate letter 4/^’ in a quantifier, then, is to treat predi cate positions suddenly as name positions, and hence to treat predi cates as names of entities of some sort. The quantifier ‘(3 F)' or ‘(F )’ says not tha t some or all predicates are thus and so, but th a t some or all entities of the sort named by predicates are thus and so.
