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On Sense and Reference
Gottlob Frege

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 Begriffsschrift1 I assumed the latter. The reasons which seem to favour this are the following: a ˆ a and a ˆ b are obviously statements of differing cognitive value; a ˆ a holds a priori and, according to Kant, is to be labelled analytic, while statements of the form a ˆ b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names `a' and `b' designate, it would seem that a ˆ b could not differ from a ˆ a (i.e. provided a ˆ b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a ˆ b seems to be that the signs or names `a' and `b' designate 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. In that case the sentence a ˆ b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its
* I use this word in the sense of identity, and understand `a ˆ b' to have the sense of `a is the same as b' or `a and b coincide.'

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