We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisit of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference.
CITATION STYLE
Cobreros, P., Egré, P., Ripley, D., & Rooij, R. van. (2015). Vagueness, Truth and Permissive Consequence. In Logic, Epistemology, and the Unity of Science (Vol. 36, pp. 409–430). Springer Science and Business Media B.V. https://doi.org/10.1007/978-94-017-9673-6_21
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