Is "true" hyper-intensional?
While I'm on the topic of repeating well-known mistakes, here's another idea I'm certainly not the first to come up with. Consider the liar paradox:
L := "L is not true" 1) Suppose L is true. 2) Then "L is not true" is true (by definition of L). 3) Then L is not true (by the Tarski Schema). etc.
The inference from (1) to (2) is only valid if "... is true" is an extensional or intensional context. So couldn't one block the paradox by declaring "true" hyper-intensional?
This suggestion isn't independent of the other obvious move, to reject the Tarski Schema: if "true" is not extensional, there are sentences P, Q such that P iff Q, and yet not: true(P) iff true(Q); hence not: (true(P) iff P) and (true(Q) iff Q). (The quantifiers here should be understood substitutionally; don't wanna quantify objectually into hyper-intensional contexts.) That is, if "true" is not extensional, the Tarski Schema is false.
In the other direction: if the Tarski Schema is false, there is a sentence P such that not: true(P) iff P. But presumably only some instances of the schema are false, say, those where P is self-referential or unfounded or where it contains semantic vocabulary. So there are other sentence Q, R such that ~(Q iff R) and (true(Q) iff Q) and (true(R) iff R). But then either ((P iff Q) and ~(true(P) iff true(Q))) or ((P iff R) and ~(true(P) iff true(R))). Either way, "true" is not extensional. (Update: Oops, use-mention mistake!)
It is somewhat odd for a predicate that applies to strings of symbols in the first place to be hyper-intensional. But there are cases like that: "... is here given in standard notation", "... is so-called because it was first proved by Kurt Gödel". And anyway, given that rejecting Tarski's schema also means rejecting the extensionality of "true" (and that intensionality, as opposed to hyper-intensionality, appears to be irrelevant here), we don't seem to have much of a choice.
So, has anyone tried to block the paradox by rejecting the move from (1) to (2)?