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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Acknowledgements
The paradox CP2 was discovered by Landini while reflecting on Orilia’s CP1. The pars destruens of the paper, in which these paradoxes are discussed and type theory is criticized, thus results from the cooperation of the two authors. The pars construens in which a type-free revision-theoretic approach to property theory is put forward is due to Orilia. Landini plans to make an alternative proposal in a future work. We wish to thank Riccardo Bruni and two anonymous referees for their useful comments.
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Orilia, F., Landini, G. Truth, Predication and a Family of Contingent Paradoxes. J Philos Logic 48, 113–136 (2019). https://doi.org/10.1007/s10992-018-9480-3
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DOI: https://doi.org/10.1007/s10992-018-9480-3