NDLI: Duality and Inferential Semantics

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Duality and Inferential Semantics

Content Provider	Springer Nature Link
Author	Trafford, James
Copyright Year	2015
Abstract	It is well known that classical inferentialist semantics runs into problems regarding abnormal valuations (Carnap in Formalization of logic. Harvard University Press, Cambridge, 1943; Hjortland in Notre Dame J Formal Logic 55(4):445–467, 2014; Peregrin in J Philos Logic 39(3):255–274, 2010). It is equally well known that the issues can be resolved if we construct the inference relation in a multiple-conclusion sequent calculus. The latter has been prominently developed in recent work by Restall (Logic, methodology and philosophy of science: proceedings of the twelfth international congress. Kings College Publications, pp 189–205, 2005), with the guiding interpretation that the valid sequent says that the simultaneous assertion of all of Γ with the denial of all of Δ is incoherent. However, such structures face significant interpretive challenges (Rumfitt in Grazer Philos Stud 77(1):61–84, 2008; Steinberger in J Philos Logic 40(3):333–355, 2011; Tennant in The taming of the true. Oxford University Press, Oxford, 1997), and they do not provide an adequate grasp on the machinery of the duality of assertions and denials that could (a) provide an abstract account of inferential semantics; (b) show why the dual treatment is semantically superior. This paper explores a slightly different tack by considering a dual-calculus framework consisting of two, single-conclusion, inference relations dealing with the preservation of assertion and the preservation of denial, respectively. In this context, I develop an abstract inferentialist semantics, before going on to show that the framework is equivalent to Restall’s, whilst providing a better grasp on the underlying proof-structure.
Starting Page	495
Ending Page	513
Page Count	19
File Format	PDF
ISSN	11221151
Journal	Axiomathes
Volume Number	25
Issue Number	4
e-ISSN	15728390
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-01-09
Publisher Place	Dordrecht
Access Restriction	Subscribed
Subject Keyword	Inferentialism Proof Refutation Multiple-conclusion Semantics Sequent Philosophy Ontology Linguistics Cognitive Psychology Logic
Content Type	Text
Resource Type	Article
Subject	Philosophy Mathematics

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