Journal of Philosophical Logic 36 (3):251-307 (2007)

Philippe Schlenker
Institut Jean Nicod
Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo's paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). We generalize Yablo's results along two dimensions. First, we study the behavior of generalized Yablo-series in which each sentence s(i) has the form: For Q k > i, s(k) is true, where Q is a generalized quantifier (e.g., no, every, infinitely many, etc). We show that under broad conditions all the sentences in the series must have the same truth value, and we derive a characterization of those values of Q for which the series is paradoxical. Second, we show that in the Strong Kleene trivalent logic Yablo's results are a special case of a more general fact: under certain conditions, any semantic phenomenon that involves self-reference can be emulated without self-reference. Various translation procedures that eliminate self-reference from a non-quantificational language are defined and characterized. An Appendix sketches an extension to quantificational languages, as well as a new argument that Yablo's paradox and the translations we offer do not involve self-reference
Keywords Kripke’s theory of truth  paradox  self-reference  strong Kleene logic  truth  Yablo’s paradox
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DOI 10.1007/s10992-006-9035-x
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References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The Semantic Conception of Truth and the Foundations of Semantics.Alfred Tarski - 1943 - Philosophy and Phenomenological Research 4 (3):341-376.
Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
What Truth Depends On.Hannes Leitgeb - 2005 - Journal of Philosophical Logic 34 (2):155-192.

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Citations of this work BETA

What Paradoxes Depend On.Ming Hsiung - 2018 - Synthese:1-27.
Dangerous Reference Graphs and Semantic Paradoxes.Landon Rabern, Brian Rabern & Matthew Macauley - 2013 - Journal of Philosophical Logic 42 (5):727-765.
Boolean Paradoxes and Revision Periods.Ming Hsiung - 2017 - Studia Logica 105 (5):881-914.

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