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

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

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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!