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?
Anime Explains the Epimenides Paradox
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?