Equality gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begriffsschrift, I assumed the latter. The reasons which seem to favour this are the following: a = a and a = b are obviously statements of differing cognitive value.…Now if we were to regard equality as a relation between that which the names ‘a’ and ‘b’ designate [bedeuten], it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself but to no other thing. What is intended to be said by a = b seems to be that the signs or names ‘a’ and ‘b’ designate [bedeuten] the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something.