(Also note that it’s a red flag to call this kind of informal argument a “proof,” not for fundamental reasons but because that’s the kind of thing cranks always do.)
I somewhat recently updated away from this stance. The rate is not anomalous so it can’t work as evidence. It is not a thing that cranks do, its a thing that people talking about a subject do.
I agree that people often use “proof” to mean “an argument which I expect could be turned into a proof.” There is a spectrum from “I’m quite confident” to “I think there’s a reasonable chance it will work” (where the latter would usually be called a “proof sketch.”)
But this argument is not on that spectrum, it’s not even the same kind of object. If you talk to a mathematician or computer scientist you shouldn’t call something like this a proof.
(I have much more sympathy for someone saying “Yes this isn’t what a mathematician or computer scientist would call a proof, I’m just using language differently from them” than someone saying “Actually this is the same kind of thing that people usually call a proof.” Though you lose a lot of credibility if you do that while peppering your writing with references to other theorems and implying a similarity.)
I does feel like isolated demand of rigour. Mathematicians writing to other mathematicians about new results seems like a fair comparison of speech activity and this expresses a similar level of confidence (carefully combed analysis willing to defend but open to being wrong and open to details on questioning).
I don’t understand what the two types that would make a type error would be. Both are the one shared by “It can be shown that an angle can not be trisected with compass and ruler”. People that are far in inferential distance have some license to remain a bit clouded and not reach full clarity in short sentences. And I think it is perfectly fair to classify someone that you can’t make sense of to be a nutjob while that distance remains.
I somewhat recently updated away from this stance. The rate is not anomalous so it can’t work as evidence. It is not a thing that cranks do, its a thing that people talking about a subject do.
https://www.lesswrong.com/posts/NqEmPZDSBgEpF8oHG/proof-as-mere-strong-evidence?commentId=cSRrFM9TDHKLwkXkJ
I agree that people often use “proof” to mean “an argument which I expect could be turned into a proof.” There is a spectrum from “I’m quite confident” to “I think there’s a reasonable chance it will work” (where the latter would usually be called a “proof sketch.”)
But this argument is not on that spectrum, it’s not even the same kind of object. If you talk to a mathematician or computer scientist you shouldn’t call something like this a proof.
(I have much more sympathy for someone saying “Yes this isn’t what a mathematician or computer scientist would call a proof, I’m just using language differently from them” than someone saying “Actually this is the same kind of thing that people usually call a proof.” Though you lose a lot of credibility if you do that while peppering your writing with references to other theorems and implying a similarity.)
I does feel like isolated demand of rigour. Mathematicians writing to other mathematicians about new results seems like a fair comparison of speech activity and this expresses a similar level of confidence (carefully combed analysis willing to defend but open to being wrong and open to details on questioning).
I don’t understand what the two types that would make a type error would be. Both are the one shared by “It can be shown that an angle can not be trisected with compass and ruler”. People that are far in inferential distance have some license to remain a bit clouded and not reach full clarity in short sentences. And I think it is perfectly fair to classify someone that you can’t make sense of to be a nutjob while that distance remains.