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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]] published by [[Stephen Yablo]] in 1985.<ref>{{cite journal | author=S. Yablo |url=https://www.researchgate.net/profile/Stephen_Yablo/publication/226983444_Truth_and_reflection/links/0046352a7540525226000000/Truth-and-reflection.pdf |title=Truth and reflection|journal=[[Journal of Philosophical Logic (journal)|Journal of Philosophical Logic]] |volume=14 |issue=2 |year=1985 |pages=297-348 |doi=10.1007/BF00249368 }}</ref> <ref>{{cite journal|author=S. Yablo|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>  It is similar to the [[liar paradox]]. Unlike the liar paradox, which uses a single sentence, this paradox uses an infinite sequence of statements, each referring 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. Since each sentence does not refer to itself, Yablo claims his paradox is "not in ''any'' way circular." However, [[Graham Priest]] disputes this.<ref>{{cite journal | author=G. Priest |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><ref>{{cite journal | author=J. Beall |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>
+{{Rcat shell|
-== Statement ==
+{{R with Wikidata item}}
+{{R from merge|Stephen Yablo}}
-Consider the following [[infinite set]] of sentences:
+{{R with possibilities}}
+{{R to section}}
-* (''S''<sub>1</sub>) For each ''i'' > 1, ''S<sub>i</sub>'' is not true.
+{{R printworthy}}
-* (''S''<sub>2</sub>) For each ''i'' > 2, ''S<sub>i</sub>'' is not true.
+}}
-* (''S''<sub>3</sub>) For each ''i'' > 3, ''S<sub>i</sub>'' is not true.
+[[Category:Eponymous paradoxes]]
-* ...
+[[Category:Logical paradoxes]]
-== Analysis ==
-Assume there is an ''n'' such that ''S''<sub>''n''</sub> is true. Then ''S''<sub>''n'' + 1</sub> is not true, so there is some ''k'' > ''n'' + 1 such that ''S''<sub>''k''</sub> is true. But ''S''<sub>''k''</sub> is not true because ''S''<sub>''n''</sub> is true and ''k'' > ''n''. Assuming ''S<sub>n</sub>'' is true implies a contradiction, ''S<sub>k</sub>'' is true and not true, so our assumption is absurd. We must conclude for each ''i'', the sentence ''S''<sub>''i''</sub> is not true. But if ''S<sub>i</sub>'' is not true, it is also true, so we have the paradox that each sentence in Yablo's list is true and not true.
-==References==
-{{reflist}}
-==External links==
-*{{cite IEP |url-id=par-liar |title="Liar Paradox"}}
-*{{cite IEP |url-id=yablo-pa |title="Yablo's Paradox"}}
-{{Logical paradoxes}}
-[[Category:Self-referential paradoxes]]