I’m sorry, but I don’t think there was anything remotely “rude” or “terribly dishonest” about my previous comment. If you think I am mistaken about anything I said, just explain why. Criticizing my rhetorical style and accusing me of violating social norms is not something I find helpful.
Quite frankly, I also find criticisms of the form “you sound more confident than you should be” rather annoying. E.g:
it creates the impression that the subjective reasons you give for dismissing point 3 have weight equal to the objective reasons history has given for dismissing points 1 and 2.
That’s because for me, the reasons I gave in point 3 do indeed have similar weight to the reasons I gave in points 1 and 2. If you disagree, by all means say so. But to rise up in indignation over the very listing of my reasons—is that really necessary? Would you seriously have preferred that I just list the bullet points without explaining what I thought?
So what’s wrong with reasoning like this:
Nothing at all, except for the false claim that nobody likes the consequences of the Axiom of Choice. (Some people do like them, and why shouldn’t they?)
The target of my critique—and I thought I made this clear in my response to cousin_it—is the critique of mainstream mathematical reasoning, not the research program of exploring different axiomatic set theories. The latter could easily be done by someone fully on board with the soundness of traditional mathematics. Just as it is unnecessary to doubt the correctness of Euclid’s arguments in order to be interested in non-Euclidean geometry.
Criticizing my rhetorical style and accusing me of violating social norms is not something I find helpful.
Until very recently, I held a similar attitude. I think it’s common to be annoyed by this sort of criticism… it’s distracting and rarely relevant.
That said, it seems to me that the above “rarely” isn’t rare enough. If you’re inadvertently violating a social norm, wouldn’t you like to know? If you already know, what does it matter to have it pointed out to you? Just ignore the redundant information.
I think this principle extends to a lot of speculative or subjective criticism. The potential value of just one accurate critique taken to heart seems quite high. Does such criticism have a positive expected value? That depends on the overall cost of the associated inaccurate or redundant statements (i.e., the vast majority of them). It seems this cost can be made to approach zero by just not taking them personally and ignoring them when they’re misguided, so long as they’re sufficiently disentangled from “object-level” statements.
I’m sorry, but I don’t think there was anything remotely “rude” or “terribly dishonest” about my previous comment. If you think I am mistaken about anything I said, just explain why. Criticizing my rhetorical style and accusing me of violating social norms is not something I find helpful.
Quite frankly, I also find criticisms of the form “you sound more confident than you should be” rather annoying. E.g:
That’s because for me, the reasons I gave in point 3 do indeed have similar weight to the reasons I gave in points 1 and 2. If you disagree, by all means say so. But to rise up in indignation over the very listing of my reasons—is that really necessary? Would you seriously have preferred that I just list the bullet points without explaining what I thought?
Nothing at all, except for the false claim that nobody likes the consequences of the Axiom of Choice. (Some people do like them, and why shouldn’t they?)
The target of my critique—and I thought I made this clear in my response to cousin_it—is the critique of mainstream mathematical reasoning, not the research program of exploring different axiomatic set theories. The latter could easily be done by someone fully on board with the soundness of traditional mathematics. Just as it is unnecessary to doubt the correctness of Euclid’s arguments in order to be interested in non-Euclidean geometry.
Until very recently, I held a similar attitude. I think it’s common to be annoyed by this sort of criticism… it’s distracting and rarely relevant.
That said, it seems to me that the above “rarely” isn’t rare enough. If you’re inadvertently violating a social norm, wouldn’t you like to know? If you already know, what does it matter to have it pointed out to you? Just ignore the redundant information.
I think this principle extends to a lot of speculative or subjective criticism. The potential value of just one accurate critique taken to heart seems quite high. Does such criticism have a positive expected value? That depends on the overall cost of the associated inaccurate or redundant statements (i.e., the vast majority of them). It seems this cost can be made to approach zero by just not taking them personally and ignoring them when they’re misguided, so long as they’re sufficiently disentangled from “object-level” statements.