Intuitively substituting co-referential expressions—expressions that refer to the same thing—in a sentence shouldn’t make any difference to its character or truth value. “A rose by any other name…” But it does make a difference, which generates Frege’s Identity Puzzle and Frege’s Propositional Attitude Puzzle.
(1) The Morning Star = The Morning Star a priori
(2) The Morning Star = The Evening Star a posteriori
The identity in (1) is true: “The Morning Star” and “The Evening Star” are co-referential. But (1) and (2) have different “cognitive value”: (1) is a priori; (2) a posteriori. How can that be?
Frege’s Sense/Reference distinction provides an answer to this puzzle. The reference of “The Morning Star” and “The Evening Star” is the same: both refer to the planet Venus. But the sense of these phrases is different. So, whereas subbing one for the other doesn’t change the truth value of a sentence—its truth-or-falsity—it does change its “cognitive value,” in particular whether it’s a priori or a posteriori. However this doesn’t defang…
(I) Mark Twain = Samuel Clemens
(3) George believes that Mark Twain wrote Huckleberry Finn.
(4) George believes that Samuel Clemens wrote Huckleberry Finn.
Problem with this: substituting co-referential expressions changes truth value in (3) and (4) which isn’t supposed to happen because the truth value of the whole sentence, its reference, is supposed to be strictly determined by the reference of its parts.
Within the contexts of (3) and (4), “Mark Twain” and “Samuel Clemens” do not refer to the same thing so we have no reason to believe that the reference, i.e. the truth value of the whole sentences will be the same. Frege’s argument about the reference of subordinate clauses shifting to their customary senses is supposed to back this claim.