The elimination of self-reference: Generalized Yablo-series and the theory of truth [Book Review]

Journal of Philosophical Logic 36 (3):251 - 307 (2007)
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
Categories (categorize this paper)
DOI 10.2307/30226891
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,667
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Hannes Leitgeb (2005). What Truth Depends On. Journal of Philosophical Logic 34 (2):155-192.
Roy T. Cook (2004). Patterns of Paradox. Journal of Symbolic Logic 69 (3):767-774.

View all 16 references / Add more references

Citations of this work BETA
Ming Hsiung (2013). Equiparadoxicality of Yablo's Paradox and the Liar. Journal of Logic, Language and Information 22 (1):23-31.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

31 ( #102,719 of 1,726,249 )

Recent downloads (6 months)

5 ( #147,227 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.