You've all seen it. Sentences like "this sentence is false": if they're false, they're true, and vice versa, so they can't be either true or false. Some people solve this problem by doing something really complicated: they introduce infinite type hierarchies wherein every sentence you can express is given a "type", which is an ordinal number, and every sentence can only refer to sentences of lower type. "This sentence is false" is not a valid sentence there, because it refers to itself, but no ordinal number is less than itself. Eliezer Yudkowsky mentions but says little about such things. What he does say, I agree with: ick!

In addition to the sheer icky factor involved in this complicated method of making sure sentences can't refer to themselves, we have deeper problems. In English, sentences can refer to themselves. Heck, this sentence refers to itself. And this is not a flaw in English, but something useful: sentences ought to be able to refer to themselves. I want to be able to write stuff like "All complete sentences written in English contain at least one vowel" without having to write it in Spanish or as an incomplete sentence.¹ How can we have self-referential sentences without having paradoxes that result in the universe doing what cheese does at the bottom of the oven? Easy: use fuzzy logic.

Follow up to  Efficient Cross-domain Optimization

When I am skeptical that we will ever understand intelligence, I am skeptical that we will ever be able to reliably map a systems description onto its optimization power. This has implications for how well we will create intelligences and how well intelligences will be at self-improving.

Obviously we can't predict the effectiveness of an arbitrary program, due to rice's theorem and intelligence being a non-trivial property. So the best we can hope for is predicting the effectiveness of a set of programs. Is such a function possible? This is my take on the subject.

The Epimenides Paradox or Liar Paradox is "This sentence is false."  Type hierarchies are supposed to resolve the Epimenides paradox... Using an indefinitely extensible, indescribably infinite, ordinal hierarchy of meta-languages. No meta-language can contain its own truth predicate - no meta-language can talk about the "truth" or "falsity" of its own sentences - and so for every meta-language we need a meta-meta-language.

I didn't create this video and I don't know who did - but it does a pretty good job of depicting how I feel about infinite type hierarchies: namely, pretty much the same way I feel about the original Epimenides Paradox.

Bonus problem: In what language did I write the description of this video?