'But to assign some probability to the wrong answer is logically equivalent to assigning probability to 0=1.'
Huh? This doesn't make sense to me. First of all, it seems like a basic category-mistake: acts of assigning probabilities don't seem to be the sorts of things that can bear logical relations like equivalence to each other.
Perhaps that's just pedantry and there's a simple rephrasing that says what you really want to say, but I have a feeling I would take issue with the rephrased version too. Does it trade on the idea that all false mathematical propositions are logically equivalent to each other? (If so, I'd say that's a problem, because that idea is very controversial, and hardly intuitive.)
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d)
Pardon a second comment (I hope that's not bad etiquette), but here are a couple of further qualms/criticisms attending to which could improve the post:
Regarding your use of the phrase 'foundations of probability' to refer to arguments for why a certain kind of robot should use probabilities: this seems like a rather odd use for a phrase that already has at least two well established uses. (Roughly (i) basic probability theory, i.e. that which gives a grounding or foundation in learning the subject, and (ii) the philosophical or metaphysical underpinnings of probability discourse: what's it about, what kinds are there, what makes true probability claims true etc.?) Is it really helpful to be different on this point, when there is already considerable ambiguity?
Furthermore, and perhaps more substantively, your bit on Dutch Books doesn't seem to give any foundations in your sense: Dutch Book arguments aren't arguments for using probability (i.e. at all, i.e. instead of not using it), but rather for conforming, when already using probability, to the standard probability calculus. So there seems to be a confusion in your post here.