[rcthompson]

I'm glad to see a write-up of this. I've been searching recently for a way to reasonably define probability without having to invoke either hypothetical infinitely repeated experiments or placing bets (since the latter is really just implicitly invoking the former). I'm looking forward to part 2!

[peterwoerner]

Check out the first chapter of Jayne's probability theory. It's the clearest take down of the frequentist interpretations that you have and introduction to the Bayesian interpretation.

http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

[rcthompson]

Thanks, I had a quick skim through it and it seems really helpful. If I understand correctly, the claim is that the laws of probability as they are known comprise the only possible interpretation that satisfies the 3 desiderata set forth in chapter 1.

[peterwoerner]

I don't remember, the thing which really helped me click at least the bayesian interpretation was if we have A --> B and B, then A is more plausible and probability reasoning is a way to quantify how more plausible A is now that we know B is true.

Chapter 5 is also a doozy in terms of explaining some of the things going on currently.