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INEFFABILITY AND REVENGE

  • CHRIS SCAMBLER (a1)

Abstract

In recent work Philip Welch has proven the existence of ‘ineffable liars’ for Hartry Field’s theory of truth. These are offered as liar-like sentences that escape classification in Field’s transfinite hierarchy of determinateness operators. In this article I present a slightly more general characterization of the ineffability phenomenon, and discuss its philosophical significance. I show the ineffable sentences to be less ‘liar-like’ than they appear in Welch’s presentation. I also point to some open technical problems whose resolution would greatly clarify the philosophical issues raised by the ineffability phenomenon.

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* DEPARTMENT OF PHILOSOPHY NEW YORK UNIVERSITY NEW YORK CITY, NY 10003, USA E-mail: cscambler@gmail.com

References

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[1]Barwise, J. (1975). Admissible Sets and Structures: An Approach to Definability Theory. Berlin: Springer-Verlag.
[2]Field, H. (2003). A revenge-immune solution to the semantic paradoxes. Journal of Philosophical Logic, 32(2), 139177.
[3]Field, H. (2007). Solving the paradoxes, escaping revenge. In Beall, J. C., editor. Revenge of the Liar: New Essays on the Paradox. Oxford: Oxford University Press, pp. 53144.
[4]Field, H. (2008). Saving Truth from Paradox. Oxford University Press.
[5]Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72(19), 690716.
[6]Moschovakis, Y. (1974). Elementary Induction on Abstract Structures. Dover Publications.
[7]Welch, P. (2008). Ultimate truth vis a vis stable truth. Review of Symbolic Logic, 1(1), 126142.
[8]Welch, P. (2011). Truth, logical validity and determinateness: A commentary on saving truth from paradox. Review of Symbolic Logic, 4(3), 348359.
[9]Welch, P. (2014). Some observations on truth hierarchies. Review of Symbolic Logic, 7(1), 130.
[10]Welch, P. (2019). Some observations on truth hierarchies: A correction. Review of Symbolic Logic, doi:10.1017/S1755020319000042.

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INEFFABILITY AND REVENGE

  • CHRIS SCAMBLER (a1)

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