Do both systems satisfy the Kolmogorov axioms? One of them is countable additivity, right?
Of course, Kolmogorov's is hardly the only such development. My question is: Is there an isomorphism in reasoning that also serves as a proof of the equivalence?
Are you suggesting that Jaynes is only finitely additive? I have to admit that I don't know exactly how Jaynes's methodological preachments about taking the limit of finite set solutions translates into real math.
I'm not sure I understand your second paragraph either (I am only an amateur at math and less than amateur at analysis.) But my inclination is to say, "Yes, of course there is always a possible isomorphism in the reasonings upward from a shared collection of axioms. But no, there is not an isomorphism in the reasonings or justifications ad...
Previously: Book Club introductory post - Chapter 1 - Chapter 2
We will shortly move on to Chapter 3 (I have to post this today owing to vacation - see below). I have updated the previous post with a summary of chapter 2, with links to the discussion as appropriate. But first, a few announcements.
How to participate
This is both for people who have previously registered interest, as well as newcomers. This spreadsheet is our best attempt at coordinating 90+ Less Wrong readers interested in participating in "earnest study of the great literature in our area of interest".
If you are still participating, please let the group know - all you have to do is fill in the "Active (Chapter)" column. Write in an "X" if you are checked out, or the number of the chapter you are currently reading. This will let us measure attrition, as well as adapt the pace if necessary. If you would like to join, please add yourself to the spreadsheet. If you would like to participate in live chat about the material, please indicate your time zone and preferred meeting time. As always, your feedback on the process itself is more than welcome.
Refer to the Chapter 1 post for more details on how to participate and meeting schedules.
Facilitator wanted
I'm taking off on vacation today until the end of the month. I'd appreciate if someone wanted to step into the facilitator's shoes, as I will not be able to perform these duties in a timely manner for at least the next two weeks.
Chapter 3: Elementary Sampling Theory
Having derived the sum and product rules, Jaynes starts us in on a mainstay of probability theory, urn problems.
Readings for the week of 19/07: Sampling Without Replacement - Logic versus Propensity. Exercises: 3.1
Discussion starts here.