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Stephen Yablo#Yablo's paradox

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+#REDIRECT [[Stephen Yablo#Yablo's paradox]]
-'''Yablo's paradox''' is a [[logical paradox]] similar to the [[liar paradox]] published by [[Stephen Yablo]] in 1993.<ref>{{cite journal |url=http://www.mit.edu/~yablo/pwsr.pdf |title=Paradox Without Self-Reference |journal=[[Analysis (journal)|Analysis]] |volume=53 |issue=4 |year=1993 |pages=251–252 |doi=10.1093/analys/53.4.251 }}</ref> Unlike the liar paradox, which uses a single sentence, this paradox uses an infinite sequence of statements, each of which refers to the truth values of the later statements in the sequence. Analysis of the statements shows there is no consistent way to assign truth values to all the statements, although no statement directly refers to itself.
+{{Rcat shell|
-== Paradox and analysis ==
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+{{R from merge|Stephen Yablo}}
-Yablo's paradox arises from considering the following [[infinite set]] of sentences:
+{{R with possibilities}}
+{{R to section}}
-* (S<sub>1</sub>): for all k > 1, S<sub>k</sub> is false
+{{R printworthy}}
-* (S<sub>2</sub>): for all k > 2, S<sub>k</sub> is false
+}}
-* (S<sub>3</sub>): for all k > 3, S<sub>k</sub> is false
+[[Category:Eponymous paradoxes]]
-* ...
+[[Category:Logical paradoxes]]
-* ...
-The paradox can be analyzed as follows. First, suppose that some statement S<sub>i</sub> is true. Then it [[Logical consequence|follows from]] the statement of  S<sub>i</sub> that every statement later in the sequence is false, and in particular that S<sub>''i''+1</sub> is false.  Hence, since S<sub>''i''+1</sub> is false, there is some ''j''>''i''+1 such that S<sub>''j''</sub> is true. But, because ''j'' is also greater than ''i'', this means that S<sub>''i''</sub> must have been false. This is a contradiction, so the original assumption that S<sub>''i''</sub> is true must be wrong. Thus S<sub>''i''</sub> must be false for every ''i''. But this means, in particular, that S<sub>''i''</sub> is false for every ''i''>1, and thus S<sub>''1''</sub> is true. This is paradoxical, because the analysis has already shown that S<sub>''1''</sub> cannot be true.
-The analysis shows that there is no consistent way to assign truth values to the statements in the paradox.  Moreover, none of the sentences refers to itself, but only to the subsequent sentences; this leads Yablo to claim that his paradox does not rely on self-reference. However, this claim is disputed.<ref>{{cite journal |url=http://ferenc.andrasek.hu/papersybprx/jcbeal_is_yablo_non_circular.pdf |title=Is Yablo’s paradox non-circular? |journal=[[Analysis (journal)|Analysis]] |volume=61 |issue=3 |year=2001 |pages=176-187 |doi=10.1093/analys/61.3.176 }}</ref><ref>{{cite journal |url=http://www.accionfilosofica.com/misc/1183297103crs.pdf |title=Yablo’s paradox |journal=[[Analysis (journal)|Analysis]] |volume=57 |issue=4 |year=1997 |pages=236-242 |doi=10.1093/analys/57.4.236 }}</ref>
-==References==
-{{reflist}}
-[[Category:Paradoxes]]
-[[es:Paradoja de Yablo]]