= 27d567bc2d48d9f40e9ccc20ea370b15)
Nisan comments on Reflection in Probabilistic Logic - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (171)
Annoying pedantic foundational issues: The collection of models is a proper class, but we can instead consider probability measures over the set of consistent valuations
, which is a set. And it suffices to consider the product σ-algebra.
I assumed that this meant "there is some probability space whose set of outcomes is some set of models", rather than "there is a measure over 'the canonical' probability space of all models", whatever that could mean.
This is the smallest σ-algebra such that for every sentence phi of L, {A : phi in A} is measurable, right? If so, it is pleasingly also the Borel-σ-algebra on the Stone space of consistent valuations (aka complete theories) of L. (Assuming L is countable, but I believe the paper does that anyway.)
Yes, I asked Paul about this and this is the interpretation he gave.