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Anomylous 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.
Outside of mathematics, a statement that is provable is also disprovable. Then it's called a hypothesis.
I'm reminded of the joke where an engineer, a physicist, and a mathematician are going to a job interview. The interviewer has rigged a fire to start in the wastepaper basket, to see how they react in a crisis situation. The engineer sees the fire, sees the water cooler, grabs the water cooler and dumps it on the fire. The physicist sees the fire, sees the water cooler, grabs pencil and paper, calculates the exact amount of water needed to extinguish the fire, then pours that amount of water into the basket, exactly extinguishing the fire. The mathematician sees the fire, sees the water cooler, and says, "Ah! A solution exists!".