“I have a neat proof. Assume that A”, “I don’t believe A”, “Well you won’t believe my proof then”
The proof won’t be a convincing argument for agreeing with its conclusion. But the proof itself can be checked without belief in A, and if it checks out, this state of affairs can be described as belief in the proof.
yes, althought most proofs use their axioms so one needs the ability to hold the axiom tentatively. if one is incapable of imagining what it would be to hold A then following the proof is going to be challenging.
But “Y proves X” has meanings of “makes X very firmly true” and “Y has X as theorem” which are not always the same thing.
The proof won’t be a convincing argument for agreeing with its conclusion. But the proof itself can be checked without belief in A, and if it checks out, this state of affairs can be described as belief in the proof.
yes, althought most proofs use their axioms so one needs the ability to hold the axiom tentatively. if one is incapable of imagining what it would be to hold A then following the proof is going to be challenging.
But “Y proves X” has meanings of “makes X very firmly true” and “Y has X as theorem” which are not always the same thing.