Yablo's paradox

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Yablos paradox is the liar paradox related paradox that in 1993 by Stephen Yablo was published, it had mentioned in an article already 1985th It consists of an infinite sequence of statements , each of which relates to all subsequent statements in the sequence. It is impossible to assign a clear truth value to all statements . Since - in contrast to the liar's paradox, which consists of a single self-referential statement - the statements do not refer to themselves, the paradox, according to Yablo, is "in no way circular ". However, this has been questioned by Graham Priest , among others , as has the question of whether it is even a paradox.

Consider the infinite sequence of statements S i :

  • S 1 : For all i> 1, S i is not true.
  • S 2 : For all i> 2, S i is not true.
  • ...
  • S n : For all i> n, S i is not true.

Suppose there was an n such that S n is a true statement. Then S n + 1 would not be a true statement, from which it follows that there must be some k > n + 1 for which S k is true. Since S n is true and k > n , from which it follows that S k is not true, a contradiction arises with regard to the truth value of S k . From this it follows that for all i the statement S i cannot be true. But then again S i is a true statement. So the paradox arises that every statement in the sequence is both true and not true.

Web links

Individual evidence

  1. ↑ a b Stephen Yablo: Paradox without Self-Reference . In: Analysis . tape 53 , no. 4 , October 1, 1993, ISSN  0003-2638 , pp. 251-252 , doi : 10.1093 / analys / 53.4.251 ( oup.com [accessed February 22, 2018]).
  2. ^ A b c Roy Cook: Yablo Paradox. In: Internet Encyclopedia of Philosophy. Retrieved February 22, 2018 (American English).
  3. ↑ Graham Priest: Yablo's Paradox . In: Analysis . tape 57 , no. 4 , October 1, 1997, ISSN  0003-2638 , pp. 236–242 , doi : 10.1093 / analys / 57.4.236 ( oup.com [accessed February 22, 2018]).
  4. ↑ Jc Beall: Is Yablo's paradoxical non-circular? In: Analysis . tape 61 , no. 3 , July 1, 2001, ISSN  0003-2638 , p. 176–187 , doi : 10.1093 / analys / 61.3.176 ( oup.com [accessed February 22, 2018]).