Equality challenges our capacity to think, because it gives rise to questions that
are not quite easy to answer. Is it a relation? a relation
between objects? or between names or signs for objects?
I had assumed the latter in my Begriffsschrift. The reasons that seem to favour it are the following:
a=a and a=b are obviously sentences of different cognitive value: a=a holds a priori, and, following Kant, should be called analytic, while sentences of the form a=b often contain valuable extensions of our knowledge and cannot always be justified a priori. The discovery that a new sun does not rise every morning but always the same one has probably been one of the most consequential discoveries in astronomy. Even now we cannot always take for granted that we will recognize a small planet or comet. Now, if we wanted to view equality as a relation between that which the names “a” and “b” mean, 3 then it would seem that a=b could not be different from a=a, in case
a=b is true. It would express a relation of a thing to itself, namely such a relation in which each thing stands to itself, but none stands to another. What one wants to say by a=b seems to be that the signs or…