(AMS Bumper Sticker)

Web math-frolic.blogspot.com

Thursday, April 24, 2014

Truthiness From Yablo

This isn't everyone's cup-o-tea, but I've mentioned Yablo's Paradox before, and, since I love it, will do so again! As Sam Alexander states, Yablo's Paradox is "a cute version of the Liar’s Paradox" that manages "to achieve paradox without any direct self-reference." The simply-stated paradox involves a countably infinite number of sentences, each of which refer only to sentences that come after it:
  • Sentence 1:  Sentence n is false for every n > 1
  • Sentence 2:  Sentence n is false for every n > 2
  • Sentence 3:  Sentence n is false for every n > 3
  • Etc....
Read Alexander's post here:  http://www.xamuel.com/dangerous-graphs/  (he discusses it in terms of "graphs").
And here is (Stephen) Yablo's amazingly short, original (1993) piece introducing the paradox:


Worth noting, that while Yablo claims his paradox involves neither self-reference nor circularity (because all steps along the way reference sentences that are yet to come), others disagree with this contention. If you're logically-inclined, see Graham Priest here:


and JC Beall here: http://ferenc.andrasek.hu/papersybprx/jcbeal_is_yablo_non_circular.pdf

(This is another good example of how things become muddled when infinity is involved; in the case of Yablo's Paradox, an infinite number of sentences.)

No comments: