You're looking at Less Wrong's discussion board. This includes all posts, including those that haven't been promoted to the front page yet. For more information, see About Less Wrong.

Benja comments on How to cheat Löb's Theorem: my second try - Less Wrong Discussion

14 Post author: Benja 22 August 2012 06:21PM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (25)

You are viewing a single comment's thread. Show more comments above.

Comment author: Benja 26 August 2012 05:42:29AM 0 points [-]

But "#[&7]" = "7", and if you replace the 7s with some other number, it's still true, right?

Ah! This is correct, but I would conceptualize it differently, as the combination of two distinct phenomena. First, #[...] is sort of the inverse of "...", which makes more sense to me because both of these are kinds of syntactic sugar -- we have both "#[e]" = e and "x + #['y']" = "x + y".

Second, "7" is the Gödel number of the unary numeral 7, and repr(7) also returns this Gödel number. In other words, "7" = &7. Putting the two together: "#[&7]" = &7 = "7".

Got it. [...] [G]ot it (I think).

:-) Thanks again for sticking with it!