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

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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.

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