ryujin

• ryujin 12 Mar 2013 23:50 UTC

  1 point

  in reply to: Eliezer Yudkowsky’s comment on: You only need faith in two things

  So I gather we define a Goodstein relation G such that [xGy] in PA if [y = Goodstein(x)] in ZFC, then you’re saying PA plus the axiom [not(exists y, (256Gy and exists z, (yGz)))] is inconsistent but the proof of that is huge because it the proof basically has to write an execution trace of Goodstein(Goodstein(256)). That’s interesting!

• ryujin 12 Mar 2013 23:40 UTC

  0 points

  in reply to: Eliezer Yudkowsky’s comment on: You only need faith in two things

  Given that we can’t define that function in PA what do you mean by Goodstein(256)?