skeptical of the validity of the proofs and conclusions constructed in very abstracted, and not experimentally or formally verified math fields.
Can you give a few examples? I can’t tell if you’re skeptical that proofs are correct, or whether you think the QED is wrong in meaninful ways, or just unclearly proven from minimal axioms. Or whether you’re skeptical that a proof is “valid” in saying something about the real world (which isn’t necessarily the province of math, but often gets claimed).
I don’t think your claim is meaningful, and I wouldn’t care to argue on either side. Sure, be skeptical of everything. But you need to specify what you have lower credence in than your conversational partner does.
I can’t give a few examples, only a criteria under which I don’t trust mathematical reasoning: When there are few experiments you can do to verify claims, and when the proofs aren’t formally verified. Then I’m skeptical that the stated assumptions of the field truly prove the claimed results, and I’m very confident not all the proofs provided are correct.
For example, despite being very abstracted, I wouldn’t doubt the claimed proofs of cryptographers.
OK, I also don’t doubt the cryptographers (especially after some real-world time in ensuring implementations can’t be attacked, which validates both the math and the implementation.
I was thrown off by your specification of “in math fields”, which made me wonder if you meant you thought a lot of formal proofs were wrong. I think some probably are, but it’s not my default assumption.
If instead you meant “practical fields that use math, but don’t formally prove their assertions”, then I’m totally with you. And I’d still recommend being specific in debates—the default position of scepticism may be reasonable, but any given evaluation will be based on actual reasons for THAT claim, not just your prior.
No, I meant that most of non-practical mathematics have incorrect conclusions. (I have since changed my mind, but for reasons in an above comment thread).
Still a bit confused without examples about what is a “conclusion” of “non-practical mathematics”, if not the QED of a proof. But if that’s what you mean, you could just say “erroneous proof” rather than “invalid conclusion”.
The reason I don’t say erroneous proof is because I want to distinguish between the claim that most proofs are wrong, and most conclusions are wrong. I thought most conclusions would be wrong, but thought much more confidently most proofs would be wrong, because mathematicians often have extra reasons & intuition to believe their conclusions are correct. The claim that most proofs are wrong is far weaker than the claim most conclusions are wrong.
Hmm. I’m not sure which is stronger. For all proofs I know, the conclusion is part of it such that if the conclusion is wrong, the proof is wrong. The reverse isn’t true—if the proof is right, the conclusion is right. Unless you mean “the proof doesn’t apply in cases being claimed”, but I’d hesitate to call that a conclusion of the proof.
Again, a few examples would clarify what you (used to) claim.
I’ll bow out here—thanks for the discussion. I’ll read futher comments, but probably won’t participate in the thread.
Can you give a few examples? I can’t tell if you’re skeptical that proofs are correct, or whether you think the QED is wrong in meaninful ways, or just unclearly proven from minimal axioms. Or whether you’re skeptical that a proof is “valid” in saying something about the real world (which isn’t necessarily the province of math, but often gets claimed).
I don’t think your claim is meaningful, and I wouldn’t care to argue on either side. Sure, be skeptical of everything. But you need to specify what you have lower credence in than your conversational partner does.
I can’t give a few examples, only a criteria under which I don’t trust mathematical reasoning: When there are few experiments you can do to verify claims, and when the proofs aren’t formally verified. Then I’m skeptical that the stated assumptions of the field truly prove the claimed results, and I’m very confident not all the proofs provided are correct.
For example, despite being very abstracted, I wouldn’t doubt the claimed proofs of cryptographers.
OK, I also don’t doubt the cryptographers (especially after some real-world time in ensuring implementations can’t be attacked, which validates both the math and the implementation.
I was thrown off by your specification of “in math fields”, which made me wonder if you meant you thought a lot of formal proofs were wrong. I think some probably are, but it’s not my default assumption.
If instead you meant “practical fields that use math, but don’t formally prove their assertions”, then I’m totally with you. And I’d still recommend being specific in debates—the default position of scepticism may be reasonable, but any given evaluation will be based on actual reasons for THAT claim, not just your prior.
No, I meant that most of non-practical mathematics have incorrect conclusions. (I have since changed my mind, but for reasons in an above comment thread).
Still a bit confused without examples about what is a “conclusion” of “non-practical mathematics”, if not the QED of a proof. But if that’s what you mean, you could just say “erroneous proof” rather than “invalid conclusion”.
Anyway, interesting discussion.
The reason I don’t say erroneous proof is because I want to distinguish between the claim that most proofs are wrong, and most conclusions are wrong. I thought most conclusions would be wrong, but thought much more confidently most proofs would be wrong, because mathematicians often have extra reasons & intuition to believe their conclusions are correct. The claim that most proofs are wrong is far weaker than the claim most conclusions are wrong.
Hmm. I’m not sure which is stronger. For all proofs I know, the conclusion is part of it such that if the conclusion is wrong, the proof is wrong. The reverse isn’t true—if the proof is right, the conclusion is right. Unless you mean “the proof doesn’t apply in cases being claimed”, but I’d hesitate to call that a conclusion of the proof.
Again, a few examples would clarify what you (used to) claim.
I’ll bow out here—thanks for the discussion. I’ll read futher comments, but probably won’t participate in the thread.