4 ms·
> We seem to think that once a proof is published in a reputable journal then it is definitely true, but really we should only think "a small number of qualifie
by doitLP 8y ago
> We seem to think that once a proof is published in a reputable journal then it is definitely true, but really we should only think "a small number of qualified people have read it and think it is fine"
This same could be said of many other professions, medicine and psychology to start. It seems a related manifestation of the Gells-Mann Amnesia.
- Moodles 8y agoYup, not picking on mathematics at all :-)
- ericsoderstrom 8y agoMath is different in that one feels there should be something close to "absolute truth." That is, given a set of axioms, it is possible to verify with complete certainty whether a proof follows from those axioms or not. Though when proofs become so long and abstruse that only a handful of people can even read them, perhaps that's no longer true. In other fields, it's more clear that nothing is known with 100% certainty. That differences of opinion or experimental error could always lead to uncertainty.
- atmanthedog 8y agoUnfortunately, math doesn't really permit this type of truth: if your axioms are strong enough to prove general statements about arithmetic, there is no effective procedure to determine whether an arbitrary proof follows from those axioms.
- rocqua 8y agoStill, given a set of axioms, statements will fall into one of three categories. 1) Provably True, 2) Provably False, 3) Undecideable Claims that a statement is in category 1 are fully verifiable (by providing the proof). The same goes with claims that a statement is in category 2.
- smadge 8y agoDid you mean to write “there is no effective procedure to determine whether an arbitrary formula follows from those axioms?” A proof is exactly how we demonstrate that a formula follows from the axioms.