  The argument we have presented above presupposes that Sally and Sally* and Bill and Bill* are numerically distinct but qualitatively indiscernible pairs of objects. Although many find this to be a genuine possibility, thanks in large part to Max Black (1952) and Robert Adams (1979), there is a long tradition that subscribes to the Identity of Indiscernibles (PII), according to which, for any objects x and y, if, for every quality F, x is F if and only if y is F (i.e., if x and y are qualitatively indiscernible), then x=y. But the argument can be developed in such a way that it does not presuppose the falsity of PII. Let there be a quality that Bill and Bill* lacks. Then the distinctness of Bill from Bill* is consistent with PII. But now let Sally (and thus Sally*) be unaware of Bill's (and Bill*'s) instantiating that quality. As long as Bill and Bill* are qualitatively indiscernible as far as Sally is concerned and yet intuitively Sally is thinking of Bill and not Bill*, the above argument for the irreducibility of demonstrative identification to descriptive identification goes through, even if it is not possible for there to be distinct objects with all the same qualities.