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Carinthium comments on Skepticism about Probability - Less Wrong Discussion
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This is the problem which must be dealt with. Rather than assume an assumption must be correct, you must somehow show it will work even if you start from no assumptions.
Your universal propositional calculus might not be able to generate that proposition, but my calculus can easily prove: Yours won't generate any propositions if it has no axioms.
This is precisely the problem. I was posting in the hopes of finding some clever solution to this problem- a self-proving axiom, as it were.