Truth and Proof: Defending a Provability Account of Mathematical Truth in Light of Godel\u27s First Incompleteness Theorem

Godel\u27s First Incompleteness Theorem is frequently interpreted as having demonstrated that mathematical proof is necessarily divorced from mathematical truth, because, it is claimed, Godel demonstrated the existence of mathematical statements that, though true, are unprovable. I challenge this understanding, showing that Godel demonstrated that, if there is a divide, it is between formal and informal proof, and not between truth and proof. In fact, a provability account of mathematical truth--which maintains that all it means for a mathematical statement to be true is for it to be provable-- is defensible in light of Godel\u27s First Incompleteness Theorem. There is, however, more work to be done in understanding the nature of informal proof, as well as its relationship to formal proof