My solution to Frege's identity statement puzzle-

Gotlob Frege asked "how do we account for the difference in cognitive significance between "a=b" and "a=a" when they are true?".
And to answer the question he came up with the ideas of sense and reference.
But my answer to his question is:
Because a = a is an identity statement but a=b is actually a property statement not an identity statement.
Saying a = a is like saying an aubergine is an aubergine. Saying a = b could be like saying an aubergine is an eggplant but it could equally be like saying an aubergine is purple because 'eggplant' is not the identity of 'aubergine' it is a synonym possessed by aubergine; it is a property of an aubergine.
In the same way a = b means a possesses the property of also being b.
Also Frege says a=a is self evident but a=b is not self evident which, I think, makes a=b more like a property statement than an identity statement. Property statements aren't self evident; the properties of things have to be discovered, for example, the weight or height of something has to be measured.