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What does it mean when a certain axiom is neither provable nor deniable?
Does it imply that such axiom is self-evident and can't be doubted?
I don't think that "real skeptics"(a skeptic who is so deep in doubt that he doubts his own existence and even his own doubt) like Pyrrho would be happy with that.

Let's consider, for example, what philosopher Hilary Putnam has called "the minimal principle of contradiction": (MPC) Not every contradiction is true. Arguably, MPC is unprovable because whichever premises and inference rules we might use to try to prove MPC are no better-known by us, and no more securely correct, than MPC itself is. But MPC would also appear to be undeniable, since in standard logic to deny MPC is to imply that every contradiction is true, and it's hard (for me, anyway) to make any sense of the notion of denying something in circumstances in which every contradiction is true. So, arguably, MPC is self-evident and can't be doubted: that is, the notion of MPC' s being doubted makes no sense. You suggest that this result would bother...

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