Open Mathematics

But suppose there in fact existed a wonderful correspondence between our concepts and the world... whereby it was in fact metaphysically impossible for certain claims constitutive of those concepts not to be true. This is, of course, not implausible in the case of logic and arithmetic... where what’s important is not a believer’s ability to justify his claims, but merely the reliability of the processes by which he arrived at them. Indeed... the beliefs might be arrived at by steps that were not only necessarily reliable, but might also be taken to be so by the believer in ways that might in fact depend in no way upon experience, but only on his competence with the relevant concepts. - The Stanford Encyclopedia of Philosophy


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