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ChristianKl comments on Rationality Quotes March 2012 - Less Wrong
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Yes, non-empirical is the wrong word. I mean to assert that mathematics is independent of empirical fact (and therefore non-social. A sufficiently intelligent Cartesian skeptic could derive all of mathematics in solitude).
Didn't Gödel show that nobody can derive all of mathematics in solitude because you can't have a complete and consistented mathamatical framework?
Goedel showed that no one can derive all of mathematics at all, whether in solitude or in a group, because any consistent system of axioms can't lead to all the true statements from their domain.
Anyone know whether it's proven that there are guaranteed to be non-self-referential truths which can't be derived from a given axiom system? (I'm not sure whether "self-referential" can be well-defined.)
It is. At least, it's possible to express Goedel statements in the form "there exist integers that satisfy this equation".
It can't.