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Varieties of logical consequence by their resistance to logical nihilism
Russell, Gillian
Russell, Gillian
Author
Abstract
Some recent work on logical pluralism has suggested that the view might be in danger of collapsing into logical nihilism, the view on which there are no valid arguments. The goal of this chapter is to argue that the prospects for preventing such a collapse vary with one’s account of logical consequence. Section 1 lays out four central approaches to consequence, beginning with the approaches Etchemendy (On the Concept of Logical Consequence. CSLI: Stanford, 1999) called interpretational and representational, and then adding a Quinean substitutional approach as well as the more recent universalist account given in Williamson (Modal Logic as Metaphysics. Oxford: Oxford University Press, 2013; Semantic Paradoxes and Abductive Methodology. In Reflections on the Liar, ed. B. Armour-Garb, 325–346. Oxford: Oxford University Press, 2017). Section 2 recounts how the threat of logical nihilism arises in the debate over logical pluralism. Section 3 then looks at the ways the rival accounts of logical consequence are better or worse placed to resist the threat.
Keywords
logical nihilism, logical minimalism, logical pluralism, interpretational logical consequence, representationalist logical consequence, substitutional logical consequence, universalist logical consequence, Timothy Williamson, empty names, vagueness, incomplete predicates, self-reference, overdetermination, inconsistency
Date
2019
Type
Book chapter
Journal
Book
Pluralisms in truth and logic
Volume
Issue
Page Range
331-361
Article Number
ACU Department
Dianoia Institute of Philosophy
Faculty of Theology and Philosophy
Faculty of Theology and Philosophy
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Open Access Status
License
All rights reserved
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Controlled