I would love to have a clear sense of exactly what it is E. T. Jaynes argues and where I disagree with it but that would take some real effort and I have other more things I’m more interested in doing with that effort, at least right now
From an “external view” it looks to me like Jaynes can’t possibly have resolved these issues in the clear-cut way people claim, because people who are clearly good at this kind of stuff don’t write as though he did. There would almost have to be this conspiracy of ignorance going on where a bunch of philosophy-of-math people just decided to ignore a completely perfect argument and spend all their time talking about Dutch Books and “Teller’s P” and all this other stuff. I don’t know where the flaw in Jaynes is, but if there is not one then something … unlikely is going on here
And that doesn’t make me want to put in the effort, but I’m pretty sure what I’d get out is “Jaynes doesn’t resolve the interpretation of probability once and for all” and that’s what all the experts on this stuff already seem to think, so for now I can just believe them because they’re experts
Well, Jaynes’ work is definitely mentioned a little, but not very much, among the phil. of math and sci folks I’ve frequented. Most of the ones that don’t have never put in the effort to understand him (My philsci lecturer heard I was using him in my essay and asked me to help him clear some thing up about his work). I’m not sure exactly what you hear people saying, but he himself admitted that his project was incomplete. Theres an odd disconnect regarding objective and subjective bayesianism in some philosophical circles, but Jaynes slots right in as a card carrying-objective bayesian (depending on which set of definitions you use, he may *also* be a subjective bayesian).
The thing is, Jaynes was primarily concerned with a very different debate - the semi-practical one of statistics, ‘frequentism’ vs bayesianism, not the related-but-distinct debates in philosophy, so his remarks tend to be a little tricky to slot neatly into the debate. Occasionally, he took purported problems for bayesianism, like the parameter invariance problems, and basically sad ‘yes, this is troubling, but [detailed examination of frequentist approach and why it has the same problem or worse]’.
Most of the substantive things Jaynes said just weren’t as directly related to the philosophical debates as they seem. I’m not saying they’re not relevant, but it’s work to repackage them as responses to the right questions when you can, and to be frank there just isn’t that many people doing work on objective bayesianism (at least in philsci, which is the field I’m passingly familiar with).
Having said all that… Look, I went through the relevant about 10% of PT:LOS and half a dozen other little papers of Jaynes’ for a paper in a philsci course. I’m not an expert in any of this yet, my math isn’t up to properly understand it at anywhere near the speed and depth other people (like, say scientiststhesis), but if you’ve got specific questions, I can *try* to help?
This is very interesting.
I guess I’m confused and a bit unnerved by the distinction you make between
“the semi-practical one of statistics, ‘frequentism’ vs bayesianism”
and
“the related-but-distinct debates in philosophy”
since I’ve been treating these as nearly indistinct and assuming others will do the same. Of course in actual applications one runs often into the question of whether a “Bayesian” or “non-Bayesian” method will work better in a particular case, and this is distinct from the big philosophical debate about whether perfect Bayesianism (to which most methods are approximations) is a good ideal or not.
But positions on these questions seem highly related; people who are “philosophical Bayesians” usually seem to be highly in favor of approximate-Bayes methods in real problems, in my experience, and likewise the typical self-identified “Bayesian” seems to really believe in “philosophical” Bayesianism – that Bayes is the best ideal – not just that approximate-Bayes methods are neat and useful. (As far as I can tell, self-describing as “a Bayesian” implies that one takes both of these positions)
The problem I’m running into here is that all the self-identified Bayesians in this conversation are directing me to Jaynes, and, as you say, it can be hard to translate Jaynes’ arguments into the philosophical terms I want to use.
For example, Jaynes is not very clear on synchronic vs. diachronic, and when reading him I have to constantly figure out whether I think what he’s saying is true diachronically, as a principle about response to new information, or only synchronically, as a principle about self-consistently tracing out the implications of your current beliefs.
OK, here’s where I ask a question. In this post I talk about how it’s not very clear to me when, in Chs. 2-4 of PT:LOS, Jaynes is talking synchronically and when he’s talking diachronically. Both of the Bayesians who have argued against me here claim that Jaynes’ presentation of Cox’s theorem in Ch. 2 is convincing if you interpret it as diachronic rather than synchronic, so that e.g. P(B|A) is not just a term in your current belief system, but what you should update if you observe A. This would require all of the postulates behind the theorem to be consistent with the diachronic interpretation, and intuitive given that interpretation.
I thought about this idea – “diachronic Cox” as a justification for conditionalization – for maybe 30-60 minutes when it was first mentioned to me and I couldn’t find anything wrong with it. However, this feels very strange to me because Cox’s theorem is usually cited as a purely synchronic result; if just making it diachronic gets us conditionalization, many people should have noticed that, when instead no one in the philosophy/statistics community seems to have done so. (In fact, close reading of Jaynes suggests to me that he thinks of his result in Ch. 2 as a synchronic result, which would make “diachronic Cox” a simple and extremely effective argument that has gone unnoticed by everyone including the author of the only text that even looks like it might be supporting it.)
So my question is: is there a flaw in “diachronic Cox” as a justification for conditionalization, and if not, why is it not usually listed as one of the justifications for conditionalization? (I haven’t been able to figure this out yet and am wary of putting more effort into it; please only put effort into it yourself if you actually want to, and don’t treat this as a responsibility to me.)
(P.S.: there are people, like Earman, who dislike Cox even synchronically because they don’t find the postulates intuitive even synchronically, but let’s bracket that for now)
(P.P.S. Just to make this explicit, there do exist writers who defend something like “frequentism” as an actual ideal that they claim is superior to Bayesianism, like Deborah Mayo in the book reviewed here. I’m sure you know that already, but I just want to make sure it gets mentioned in this post for completeness)
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