Harmony and the Context of Deducibility

Hjortland, Ole T. (Oktober 2012): Harmony and the Context of Deducibility. In: Hjortland, Ole T. und Novaes, Catarina D. (Hrsg.): Insolubles and Consequences: Essays in honour of Stephen Read. Tributes, Bd. 18. College Publications.

Abstract

The philosophical discussion about logical constants has only recently moved into the substructural era. While philosophers have spent a lot of time discussing the meaning of logical constants in the context of classical versus intuitionistic logic, very little has been said about the introduction of substruc-tural connectives. Linear logic, affine logic and other substructural logics offer a more fine-grained perspective on basic connectives such as conjunction and disjunction, a perspective which I believe will also shed light on debates in the philosophy of logic. In what follows I will look at one particularly interesting instance of this: The development of the position known as logical inferentialism in view of substructural connectives. I claim that sensitivity to structural properties is an interesting challenge to logical inferentialism, and that it ultimately requires revision of core notions in the inferentialist litera-ture. Specifically, I want to argue that current definitions of proof theoretic harmony give rise to problematic nonconservativeness as a result of their insensitivity to substructurality. These nonconservativeness results are undesirable because they make it impossible to consistently add logical constants that are of independent philosophical interest.

• Dokumententyp: Buchbeitrag
• Fakultät: Philosophie, Wissenschaftstheorie und Religionswissenschaft > Munich Center for Mathematical Philosophy (MCMP) ; Philosophie, Wissenschaftstheorie und Religionswissenschaft > Munich Center for Mathematical Philosophy (MCMP) > Logic
• Themengebiete: 100 Philosophie und Psychologie > 100 Philosophie ; 100 Philosophie und Psychologie > 160 Logik
• ISBN: 978-1-84890-086-8
• Sprache: Englisch