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LizzardWizzard comments on Belief in Belief - Less Wrong
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"Those who find this confusing may find it helpful to study mathematical logic, which trains one to make very sharp distinctions between the proposition P, a proof of P, and a proof that P is provable"
This is a bit of a side question, but wouldn't a proof that P is provable be a proof of P? In fact, it sounds like a particularly elegant form of proof.
Here's an example of what Doug Hofstadter writes in I Am A Strange Loop. Kurt Goedel discovered that Principia Mathematica by Bertrand Russell does provide reference to itself. So Russell in his book yields the propositions and their proofs, and then Goedel assigns specific numbers to proofs and therefore proves that there is a proof that they are in fact, provable