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.
Pardon a second comment (I hope that’s not bad etiquette)
Well, if they’re right after each other you can always use the “edit” button to add to your original comment.
I’m going to stick with this terminology just because I like it—it won’t be important later. Also, I blame Sniffoy, for calling his post “A Summary of Savage’s Foundations for Probability and Utility.” :P
I claim that I do cover why Dutch books do provide a foundation to some extent, but I agree that Savage’s theorem is a better way to base probability upon decision-making.
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.
Well, if they’re right after each other you can always use the “edit” button to add to your original comment.
I’m going to stick with this terminology just because I like it—it won’t be important later. Also, I blame Sniffoy, for calling his post “A Summary of Savage’s Foundations for Probability and Utility.” :P
I claim that I do cover why Dutch books do provide a foundation to some extent, but I agree that Savage’s theorem is a better way to base probability upon decision-making.