  But Frege noticed (1892a) that this account of truth can’t be all there is to the meaning of identity statements. The statement ‘\(a=a\)’ has a cognitive significance (or meaning) that must be different from the cognitive significance of ‘\(a=b\)’. We can learn that ‘Mark Twain = Mark Twain’ is true simply by inspecting it; but we can’t learn the truth of ‘Mark Twain = Samuel Clemens’ simply by inspecting it — you have to examine the world to see whether the two persons are the same. Similarly, whereas you can learn that ‘\(117+136 = 117+136\)’ and ‘the morning star is identical to the morning star’ are true simply by inspection, you can’t learn the truth of ‘\(117+136 = 253\)’ and ‘the morning star is identical to the evening star’ simply by inspection. In the latter cases, you have to do some arithmetical work or astronomical investigation to learn the truth of these identity claims. Now the problem becomes clear: the meaning of ‘\(a=a\)’ clearly differs from the meaning of ‘\(a=b\)’, but given the account of the truth described in the previous paragraph, these two identity statements appear to have the same meaning whenever they are true! For example, ‘Mark Twain = Mark Twain’ is true just in case: the person Mark Twain is identical with the person Mark Twain. And ‘Mark Twain = Samuel Clemens’ is true just in case: the person Mark Twain is identical with the person Samuel Clemens. But given that Mark Twain just is Samuel Clemens, these two cases are the same case, and that doesn’t explain the difference in meaning between the two identity sentences. And something similar applies to all the other examples of identity statements having the forms ‘\(a=a\)’ and ‘\(a=b\)’.