But it seems that the following statement is a counterexample.

Ψ: It is impossible to know Ψ.

**Ψ is true (and, thus, it is impossible to know Ψ).**

Claim.

Claim.

*Proof. *Assume (to reach a contradiction) that Ψ is not true. Then it is possible to know Ψ. So, there is a world w such that Ψ is known at w. Since Ψ is known at w, Ψ is true at w. But then it is impossible to know Ψ at w. Hence, (assuming T or stronger) Ψ is not known at w. Contradiction.

[Does this work? It is just a "modalized" version of the Knower. Has this already been done?]

## 3 comments:

Well...I guess I just proved that \psi is true, so should know it! Is this a proof or a paradox? Now I'm confused...again.

Check out Peter Milne's "Omniscient Beings Are Dialetheists" in Analysis. There is a similar (though not the same) paradox.

Check out "an unsolved puzzle about knowledge" by Tymoczko, Phil Quarterly 1984. I think it's very similar. He claims its a paradox.

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