> Right, I agree, but that doesn't necessarily mean that we cannot prove any true claims. That's certainly true, but the fact that we can't locate a demarcatio

> Right, I agree, but that doesn't necessarily mean that we cannot prove any true claims. That's certainly true, but the fact that we can't locate a demarcation between provable and unprovable makes all analysis inside system X problematical as to the true nature of X, with an obvious connection to the present topic. > Unless I misunderstand, it just means that true claims whose proof we do not know cannot be distinguished from true claims whose proof does not exist. Not exactly. The demarcation is between theorems whose truth we can prove (and can prove that we can prove), and theorems we're not sure about but that may fall on the far side of the demarcation line. The second category is a problem that undermines any global analysis of logical systems. Remember that Russell and Whitehead's famous tome (http://en.wikipedia.org/wiki/Principia_Mathematica http://en.wikipedia.org/wiki/Principia_Mathematica) wasn't edited after Gödel's work, to simply remove those parts that were unsupportable, it was instead abandoned in its entirety. Gödel's work demonstrated that any such deterministic analysis of logical systems wasn't possible, in whole or in part. But again, this doesn't argue that a given logical system can't be used to prove theorems. It only argues against the claim that such a system can be proven to be both complete and internally consistent.