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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:

http://www.mit.edu/~yablo/pwsr.pdf

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:

http://www.accionfilosofica.com/misc/1183297103crs.pdf

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.)


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