I defended my negative thesis about the explanation of identity statements against some possible objections in the paper, but one unaddressed challenge I have been thinking about in the years since writing the bulk of the paper (it took a long time to get it published, and I stopped trying for a while) is Kripke's celebrated 'schmidentity' argument. Here it is:
Suppose identity were a relation in English between the names. I shall introduce an artificial relation called 'schmidentity’ (not a word of English) which I now stipulate to hold only between an object and itself. Now then the question whether Cicero is schmidentical with Tully can arise, and if it does arise the same problems will hold for this statement as were thought in the case of our original identity statement to give the belief that this was a relation between the names. If anyone thinks about this seriously, I think he will see that therefore probably his original account of identity was not necessary, and probably not possible, for the problems it was originally meant to solve, that therefore it should be dropped, and identity should just be taken to the relation between a thing and itself. This sort of device can be used for a number of philosophical problems. (Kripke (1980), p. 108.)As you can see, the schmidentity argument is framed primarily as an argument against the name-relation view of identity statements, which I also argued against. But this argument also threatens my position. As I see it, the challenge is as follows. Kripke's schmidentity predicate is a term which is explicitly introduced - explained, it is natural to say - as ascribing a relation which holds between all objects and themselves and in no other case. So, whatever is true of identity statements, schmidentity statements can be - indeed have been - explained by means of the object-relation stuff which I wanted to say fails to explain the meaning of identity statements. But schmidentity statements could be used to do what we do with identity statements. So then what grounds have we for supposing that identity statements differ semantically from schmidentity statements? Perhaps none. But then if identity statements and schmidentity statements are semantically on a par, and the latter can (are) explained by the object-relation stuff, then so can the former. So now it looks like my position is wrong.
I think this is a serious challenge to my position (about the object-relation claim not being explanatory of identity statements), but I can't help feeling that it misses something and that my position is right in some way. I will try to respond to the challenge in my next post here.
Haze, Tristan (2016). On Identity Statements: In Defense of a Sui Generis View. Disputatio 8 (43):269-293.Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.