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(This does not mean that the language cannot contain a detachable conditional; just that this conditional is not used for the Schema.) This has some plausibility.The -schema can be thought of as expressing no more than the claim that its two sides have the same truth value (both true or both false).What I will show is that MT-revenge arguments do not fail I discuss a possible rejoinder, namely the idea that the MT-semantics is a mere tool to prove non-triviality results and, as such, it does not characterize genuine semantic notions; I argue that this reply also fails to neutralize MT-revenge arguments.
Most theories of truth come with an MT-semantics, which is used to provide an interpretation for them, or to prove them non-trivial.
However, MT-revenge paradoxes are often considered to be as easy to construct as they are to defuse, and ultimately unproblematic., §§21–23).
(Contraction holds.) A natural objection to the proposal is that it renders the -schema impotent, since we can never get from one side of it to the other.
In particular, the truth predicate cannot be used to make blind endorsements.
More generally, I argue that the difference between ‘standard’ and ‘revenge’ paradoxes is ill-conceived and should be abandoned.
This will contribute to show that the theories that provide a uniform account of truth and other semantic notions are the ones best equipped to avoid the paradoxes altogether—‘standard’ and ‘revenge’ alike., revenge paradoxes can be characterized as arguments to the effect that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate.
The objection may not be as telling as it appears, however, since material detachment is still a valid default inference (see IC 8.5, and ch. (The liar paradox, etc., are still forthcoming unconditionally.) This essay is based on a series of seminars given at the University of St Andrews in December 2008.
Thanks go to the participants of the seminar for their thoughtful comments and criticisms, and especially to Ole Hjortland, Stephen Read, Stewart Shapiro, Crispin Wright, and Elia Zardini.
And this is exactly what the material biconditional expresses.
One of the virtues of this approach is that it provides a very simple solution to the Curry paradox, since MP fails for ⊃.