Designing Paradoxes: A Revision-theoretic Approach

Journal of Philosophical Logic 51 (4):739-789 (2022)
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Abstract

According to the revision theory of truth, the binary sequences generated by the paradoxical sentences in revision sequence are always unstable. In this paper, we work backwards, trying to reconstruct the paradoxical sentences from some of their binary sequences. We give a general procedure of constructing paradoxes with specific binary sequences through some typical examples. Particularly, we construct what Herzberger called “unstable statements with unpredictably complicated variations in truth value.” Besides, we also construct those paradoxes with infinitely many finite primary periods but without any infinite primary period, those with an infinite critical point but without any finite primary period, and so on. This is the first formal appearance of these paradoxes. Our construction demonstrates that the binary sequences generated by a paradoxical sentence are something like genes from which we can even rebuild the original sentence itself.

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Ming Hsiung
Zhongshan University

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References found in this work

Saving Truth From Paradox.Hartry Field - 2008 - Oxford, England: Oxford University Press.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.

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