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The latter would be an axiom. A disproof would be a proof that there is no proof, so if you’d proven that no proof exists one way or the other then you’ve prove
by Filligree 2y ago
The latter would be an axiom. A disproof would be a proof that there is no proof, so if you’d proven that no proof exists one way or the other then you’ve proven it can’t be disproven _or_ proven.
Which means you’ve hit a branch in mathematics. You can assume it to be either true or false, and you’ll get new results based on that; both branches are equally valid.
- LegionMammal978 2y agoConstructively speaking, a disproof is a "proof that a statement leads to a contradiction". A "proof that there is no proof (assuming consistency)" can exist just fine, and that's exactly what the incompleteness theorem is, alongside a "proof that there is no disproof, i.e., that a contradiction cannot be derived from the statement (assuming consistency)".