= 27d567bc2d48d9f40e9ccc20ea370b15)
thomblake comments on Controlling your inner control circuits - 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 (146)
I don't think that's as rigorous as you'd like it to be. I don't grant the "almost certainly false" step.
Take a predicate P which is false for Pab but true in all other cases. Then, you cannot perform the rest of the steps in your proof with P. Consider that there is also the predicate Q such that Qab is true about half the time for arbitrary a and b. How will you show that most situations are like your R?
I'm also not sure your proof really shows a difference in cardinality. Even if most predicates are like your R, there still might be infinitely many true sentences you can construct, even if they're more likely to be false.
It's definitely not rigorous, and I tried to highlight that by calling it a heuristic. Without omniscience, I can't prove that the relations hold, but the evidence is uniformly supportive.
Can you name such a predicate other than the trivial "is not" (which is guaranteed for be true for all but one entity, as in A is not A) which is true for even a majority of entities? The best I can do is "is not describable by a message of under N bits," but even then there are self-referential issues. If the majority of predicates were like your P and Q, then why would intelligence be interesting? "Correctness" would be the default state of a proposition and we'd only be eliminating a (relatively) small number of false hypotheses from our massive pool of true ones. Does that match either your experience or the more extensive treatment provided in Eliezer's writings on AI?
If you grant my assertion that Rab is almost certainly false if c is substituted for b, then I think the cardinality proof does follow. Since we cannot put the true sentences in one-to-one correspondence with the false sentences, and by the assertion there are more false sentences, the latter must have a greater (infinite?) cardinality than the former, no?
The cardinality of the sets of true and false statements is the same. The operation of negation is a bijection between them.
You're right. I was considering constructive statements, since the negation of an arbitrary false statement has infinitesimal informational value in search, but you're clearly right when considering all statements.
If by "almost certainly false" you mean that say, 1 out of every 10,000 such sentences will be true, then no, that does not entail a higher order of infinity.
I meant, as in the math case, that the probability of selecting a true statement by choosing one at random out of the space of all possible statements is 0 (there are true statements, but as a literal infinitesimal).
It's possible that both infinities are countable, as I am not sure how one would prove it either way, but that detail doesn't really matter for the broader argument.
See the note by JGWeissman--this is only true when considering constructively true statements (those that carry non-negligible informational content, i.e. not the negation of an arbitrary false statement).