We say that a sentence A is a permissive consequence of a set of premises ! whenever, if all the premises of ! 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.
|Title of host publication||Unifying the Philosophy of Truth|
|Editors||Theodora Achourioti, Henri Galinon, José Martínez Fernández, Kentaro Fujimoto|
|Place of Publication||Dordrecht Germany|
|Number of pages||22|
|Publication status||Published - 2015|
|Name||Logic, Epistemology, and the Unity of Science|
Egré, P., Cobreros, P., Ripley, D., & van Rooij, R. (2015). Vagueness, Truth and Permissive Consequence. In T. Achourioti, H. Galinon, J. Martínez Fernández, & K. Fujimoto (Eds.), Unifying the Philosophy of Truth (1 ed., Vol. 36, pp. 409-430). (Logic, Epistemology, and the Unity of Science; Vol. 36). Springer.