TY - CHAP
T1 - Vagueness, Truth and Permissive Consequence
AU - Egré, Paul
AU - Cobreros, Pablo
AU - Ripley, David
AU - van Rooij, Robert
N1 - Funding Information:
We are grateful to two anonymous referees for detailed comments, and to the editors for their assistance in the preparation of this paper. We also thank audiences in Amsterdam, Barcelona and Paris. We thank the European Research Council under the European Community?s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n 229 441-CCC, the ANR project BTAFDOC (?Beyond Truth and Falsity: Degrees of Confidence?), and the program ?Non-Transitive Logics? (Ministerio de Econom?a y Competitividad, Government of Spain, FFI2013-46451-P). We also thank grants ANR-10-LABX-0087 IEC and ANR-10-IDEX-0001-02 PSL*.
Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Nontransitive consequence
KW - Paradox
KW - Permissive consequence
KW - Principle of tolerance
KW - Three-valued logic
KW - Transparent truth
KW - Vagueness
UR - http://www.scopus.com/inward/record.url?scp=85096407464&partnerID=8YFLogxK
U2 - 10.1007/978-94-017-9673-6_21
DO - 10.1007/978-94-017-9673-6_21
M3 - Chapter (Book)
AN - SCOPUS:85096407464
SN - 9789401796729
VL - 36
T3 - Logic, Epistemology, and the Unity of Science
SP - 409
EP - 430
BT - Unifying the Philosophy of Truth
A2 - Achourioti, Theodora
A2 - Galinon, Henri
A2 - Martínez Fernández, José
A2 - Fujimoto, Kentaro
PB - Springer
CY - Dordrecht Germany
ER -