I think this may be based on a casual use of the word “proof”. A formal proof is … proof. You have to keep in mind that the axioms used may not correlate to the real world in any specific instance, and to that extent, a proof isn’t evidence at all—there’s no tie to the universe, it’s all map.
In colloquial and legal use, “proof” is used differently—it really does just mean “strong evidence”. I think almost everyone knows this, but maybe I’m wrong.
I think “proof” as used in the post was meant to refer to neither the colloquial use nor fully-formalized statements, but proofs as they are actually used by human mathematicians: written arguments which the community of mathematicians believe could be formalized if necessary. Then the question is how much confidence we should have in a statement given that such a “proof” exists. Mathematicians are quite good at determining which proofs are valid, but as the post points out, they are not infallible.
You seem to be getting at the validity/soundness distinction. Formal arguments rely on premises; a formal argument can rigourously show that its conclusions follow from its premises, IE that it’s valid; but the conclusion can still be doubtful if the premises are,.IE it’s not sound.
wow, strong downvote with no explanation? still doesn’t seem wrong to me—if you won’t explain, just consider this just another chance to dock my karma.
Edit: comment karma positive now, unsure if the strong-down was removed or someone else used a strong-up to counter it. NBD, karma is meaningless and this wasn’t a particularly important comment (since many others said similar things).
Also confused at it seems very similar to a point I made with sligthly different turns of phrase and I have trouble imagining how those rephrasing would change the meaning significantly.
If an assumption is violated then the whole rest of the system is inapplicable in that context ie weight 0.
I think this may be based on a casual use of the word “proof”. A formal proof is … proof. You have to keep in mind that the axioms used may not correlate to the real world in any specific instance, and to that extent, a proof isn’t evidence at all—there’s no tie to the universe, it’s all map.
In colloquial and legal use, “proof” is used differently—it really does just mean “strong evidence”. I think almost everyone knows this, but maybe I’m wrong.
I think “proof” as used in the post was meant to refer to neither the colloquial use nor fully-formalized statements, but proofs as they are actually used by human mathematicians: written arguments which the community of mathematicians believe could be formalized if necessary. Then the question is how much confidence we should have in a statement given that such a “proof” exists. Mathematicians are quite good at determining which proofs are valid, but as the post points out, they are not infallible.
You seem to be getting at the validity/soundness distinction. Formal arguments rely on premises; a formal argument can rigourously show that its conclusions follow from its premises, IE that it’s valid; but the conclusion can still be doubtful if the premises are,.IE it’s not sound.
PS. Not the downvoter.
wow, strong downvote with no explanation? still doesn’t seem wrong to me—if you won’t explain, just consider this just another chance to dock my karma.
Edit: comment karma positive now, unsure if the strong-down was removed or someone else used a strong-up to counter it. NBD, karma is meaningless and this wasn’t a particularly important comment (since many others said similar things).
Also confused at it seems very similar to a point I made with sligthly different turns of phrase and I have trouble imagining how those rephrasing would change the meaning significantly.
If an assumption is violated then the whole rest of the system is inapplicable in that context ie weight 0.