= 27d567bc2d48d9f40e9ccc20ea370b15)
gRR comments on Logical Uncertainty as Probability - Less Wrong Discussion
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 (22)
That was my goal - to come up with a minimum necessary for consistency, but still sufficient to prove the 1/2 probability for digits of PI :) If you wish to make OLC stronger, you're free to do so, as long as it remains decidable. For example, you can define OLC(X) to be {everything provable from X by at most 10 steps of PA-power reasoning, followed by propositional calculus closure}.
In your scheme you have P=1/2 for anything nontrivial and its negation that's not already in X. It just so happens that this looks reasonable in case of the oddity of a digit of pi, but that's merely a coincidence (e.g. take A="a millionth digit of pi is 3" rather than "...odd").
No, a statement and its negation are distinguishable, unless indeed you maliciously hide them under quantifiers and throw away the intermediate proof steps.