Truth, Predication and a Family of Contingent Paradoxes

Journal of Philosophical Logic 48 (1):113-136 (2019)

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Abstract
In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revision-theoretic approach provides various well-motivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as testified by recent work in formal metaphysics by Williamson and Hale. There is a contingent Liar that has been taken to be a problem for type theory. But this is because this Liar has been presented without an explicit recourse to a truth predicate. Thus, type theory could avoid this paradox by incorporating such a predicate and accepting an appropriate theory of truth. There is however a contingent paradox of predication that more clearly undermines the viability of type theory. It is then suggested that a type-free property theory is a better option. One can pursue it, by generalizing the revision-theoretic approach to predication, as it has been done by Orilia with his system P*, based on T*. Although Gupta and Belnap do not explicitly declare a preference for T# over T*, they show that the latter has some advantages, such as the recovery of intuitively acceptable principles concerning truth and a better reconstruction of informal arguments involving this notion. A type-free system based on T# rather than T* extends these advantages to predication and thus fares better than P* in the intended applications of property theory.
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DOI 10.1007/s10992-018-9480-3
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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.
Formal Philosophy. [REVIEW]Richard Montague - 1975 - Canadian Journal of Philosophy 4 (3):573-578.
The Revision Theory of Truth.Vann McGee - 1996 - Philosophy and Phenomenological Research 56 (3):727-730.
Conditionals in Theories of Truth.Anil Gupta & Shawn Standefer - 2017 - Journal of Philosophical Logic 46 (1):27-63.

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Property Theory and the Revision Theory of Definitions.Francesco Orilia - 2000 - Journal of Symbolic Logic 65 (1):212-246.
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Gupta's Rule of Revision Theory of Truth.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (1):103-116.

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