= 27d567bc2d48d9f40e9ccc20ea370b15)
hairyfigment comments on 5 Axioms of Decision Making - 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 (60)
Subjective probabilities are inconsistent in any model which includes Peano arithmetic by straightforward application of Gödel's incompleteness theorems, which is essentially any non-finite model.
Most people here seem to be extremely unwilling to admit that probabilities and uncertainty are not the same thing.
People tell me otherwise.
I don't know if that actually solves the problem. Nor do I know if it makes sense to claim that understanding the two meanings of a Gödel statement, and the link between them, puts you in a different formal system which can therefore 'prove' the statement without contradiction. But it seems to me this accounts for what we humans actually do when we endorse the consistency of arithmetic and the linked mathematical statements. We don't actually have the brains to write a full Gödel statement for our own brains and thereby produce a contradiction.
In your example below, X(Y is consistent) might in fact be 0.5 because understanding what both systems say might put us in Z. Again, this may or may not solve the underlying problem. But it shouldn't destroy Bayesianism to admit that we learn from experience.