Mathematics can be taken in that way but there are important ways how it does’t work like that. Axioms are assumed, not believed and this can make a difference. There is also the whole business whether you are pro or anti axiom of choice. This divide is an example how the axioms are not evident and intuition conflicts genuinely happen. Then there are questions about what cardinalities exist or not which suffer from there not being a favorite axiom set or reason to prefer one ovedr the other.
Philosphy is more used to there being mutiple camps and some sorts of argumentation flying in some circles and not others. Adding axioms gives you fodder to consruct proofs but it also increases threshold to find the proof compelling. You could have dialogue like “I have a neat proof. Assume that A”, “I don’t believe A”, “Well you won’t believe my proof then”. You could think of mathematians starting their things with “To whomever shares these basic beliefs...”, they don’t argue or find commom ground but just list the prerequisite to find the material interesting. True it is more common to expect for simple explanastion to advance mathetmatical disagreements where phisophy expects for disagreements to stay lingering but the kind of moves happen on both ends.
“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.
Mathematics can be taken in that way but there are important ways how it does’t work like that. Axioms are assumed, not believed and this can make a difference. There is also the whole business whether you are pro or anti axiom of choice. This divide is an example how the axioms are not evident and intuition conflicts genuinely happen. Then there are questions about what cardinalities exist or not which suffer from there not being a favorite axiom set or reason to prefer one ovedr the other.
Philosphy is more used to there being mutiple camps and some sorts of argumentation flying in some circles and not others. Adding axioms gives you fodder to consruct proofs but it also increases threshold to find the proof compelling. You could have dialogue like “I have a neat proof. Assume that A”, “I don’t believe A”, “Well you won’t believe my proof then”. You could think of mathematians starting their things with “To whomever shares these basic beliefs...”, they don’t argue or find commom ground but just list the prerequisite to find the material interesting. True it is more common to expect for simple explanastion to advance mathetmatical disagreements where phisophy expects for disagreements to stay lingering but the kind of moves happen on both ends.
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.
I agree