Content Implication and Yablo's Sequence of Sentences
DOI:
https://doi.org/10.12775/LLP.2019.012Keywords
Yablo’s paradox, paradox, self-reference, circularity, content implicationAbstract
This paper is a continuation of [Łukowski, 2019], where it is shown that just like sets, sentences can also be understood in two ways: distributively or collectively. A distributive understanding of sets leads to the Russell antinomy, and a distributive understanding of sentences to liar antinomy. A collective understanding of sets frees up the set theory from Russell’s antinomy. Taking a similar approach to sentences no liar like paradoxes appear. The aim of the paper is to examine Yablo’s problem from this collective perspective. Given its nature, by using the content implication connective it becomes possible to assign logical values to all Yablo’s sentences. Moreover, it seems that Yablo’s problem is not a case of circularity.
References
Beall, J.C., 1999, “Completing Sorensen’s menu: A non-modal Yabloesque curry”, Mind 108 (432): 737–739. DOI: http://dx.doi.org/10.1093/mind/108.432.737
Beall, J.C., 2001, “Is Yablo’s paradox non-circular?”, Analysis 61 (3): 176–187. DOI: http://dx.doi.org/10.1093/analys/61.3.176
Bloom, S.L., and R. Suszko, 1972, “Investigations into the sentential calculus with identity”, Notre Dame Journal of Formal Logic 13 (3): 289–308. DOI: http://dx.doi.org/10.1305/ndjfl/1093890617
Bolander, T., 2008, “Self-reference”, Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/self-reference
Bringsjord, S., and B. van Heuveln, 2003, “The ‘mental-eye’ defence of an infinitized version of Yablo’s paradox”, Analysis 63 (1): 61–70. DOI: http://dx.doi.org/10.1093/analys/63.1.61
Bueno, O., and M. Colyvan, 2003a, “Yablo’s paradox and referring to infinite objects”, Australasian Journal of Philosophy 81 (3): 402–412. DOI: http://dx.doi.org/10.1080/713659707
Bueno, O., and M. Colyvan, 2003b, “Paradox without satisfaction”, Analysis 63 (2): 152–156. DOI: http://dx.doi.org/10.1093/analys/63.2.152
Cieślinski C., and R. Urbaniak, 2013, “Gödelizing the Yablo sequence”, Journal of Philosophical Logic 42 (5): 679–695. DOI: http://dx.doi.org/10.1007/s10992-012-9244-4
Colyvan, M., 2009, “Vagueness and truth”, pages 29-40 in H. Dyke (ed.), From Truth to Reality: New Essays in Logic and Metaphysics, London: Routledge.
Cook, R.T., 2006, “There are non-circular paradoxes (but Yablo’s isn’t one them!)”, The Monist 89 (1): 118–149. DOI: http://dx.doi.org/10.5840/monist200689137
Hardy, J., 1995, “Is Yablo’s paradox liar-like?”, Analysis 55 (3): 197–198. DOI: http://dx.doi.org/10.1093/analys/55.3.197
Hsiung, M., 2013, “Equiparadoxicalityof Yablo’s paradox and the liar”, Journal of Logic, Language and Information 22 (1): 23–31. DOI: http://dx.doi.org/10.1007/s10849-012-9166-0
Goldstein, L., 1994, “A Yabloesque paradox in set theory”, Analysis 54 (4): 223–227. DOI: http://dx.doi.org/10.1093/analys/54.4.223
Goldstein, L., 2013, “Paradoxical partners: semantical brides and set-theoretical grooms”, Analysis 73 (1): 33–37. DOI: http://dx.doi.org/10.1093/analys/ans130
Ketland, J., 2004, “Bueno and Colyvan on Yablo’s paradox”, Analysis 64 (2): 165–172. DOI: http://dx.doi.org/10.1093/analys/64.2.165
Leitgeb, H., 2002, “What is a self-referential sentence? Critical remarks on the alleged (non-) circularity of Yablo’s paradox”, Logique et Analyse 177–178: 3–14.
Luna, L., 2009a, “Yablo’s paradox and beginningless time”, Disputatio 3 (26): 89–96. DOI: http://dx.doi.org/10.2478/disp-2009-0002
Luna, L., 2009b, “Ungrounded causal chains and beginningless time”, Logic and Logical Philosophy 18 (3–4): 297–307. DOI: http://dx.doi.org/10.12775/LLP.2009.014
Łukowski, P., 1997, “An approach to the liar paradox”, pages 68–80 in New Aspects in Non-Classical Logics and Their Kripke Semantics, RIMS: Kyoto University.
Łukowski, P., 2006, Paradoksy, Łódź: Wydawnictwo Uniwersytetu Łódzkiego.
Łukowski, P., 2011, Paradoxes, Dordrecht-Heidelberg-London-New York: Springer. DOI: http://dx.doi.org/10.1007/978-94-007-1476-2
Łukowski, P., 2019, ““Distributive” or “collective” approach to sentences”, Logic and Logical Philosophy. DOI: http://dx.doi.org/10.12775/LLP.2019.011
Priest, G., 1997, “Yablo’s paradox”, Analysis 57 (4): 236–242. DOI: http://dx.doi.org/10.1093/analys/57.4.236
Schlenker, P., 2007a, “How to eliminate self-reference: A précis”, Synthese 158 (1): 127–138. DOI: http://dx.doi.org/10.1007/s11229-006-9054-8
Schlenker, P., 2007b, “The elimination of self-reference: Generalized Yablo-series and the theory of truth”, Journal of Philosophical Logic 36 (3): 251–307. DOI: http://dx.doi.org/10.1007/s10992-006-9035-x
Simons, P., 2015, “Stanisław Leśniewski”, The Stanford Encyclopedia of Philosophy, Winter 2015 Edition, E. N. Zalta (ed.), https://plato.stanford.edu/archives/win2015/entries/lesniewski/.
Sorensen, R., 1998, “Yablo’s paradox and kindred infinite liars”, Mind 107 (425): 137–155. DOI: http://dx.doi.org/10.1093/mind/107.425.137
Suszko, R., 1975, “Abolition of the Fregean axiom”, Lecture Notes in Mathematics 453: 169–239.
Uzquiano, G., 2004, “An infinitary paradox of denotation”, Analysis 64 (2): 128–131. DOI: http://dx.doi.org/10.1093/analys/64.2.128
Yablo, S., 1985, “Truth and reflection”, Journal of Philosophical Logic 14: 297–349. DOI: http://dx.doi.org/10.1007/BF00249368
Yablo, S., 1993, “Paradox without self-reference”, Analysis 53: 251–252. DOI: http://dx.doi.org/10.1093/analys/53.4.251
Yablo, S., 2004, “Circularity and paradox”, pages 139–157 in T. Bolander, V.F. Hendricks and S.A. Pedersen (eds.), Self-Reference, Stanford: CSLI Publications. http://www.mit.edu/~yablo/circularity¶dox.pdf
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 456
Number of citations: 0