Authors
Tristan Grøtvedt Haze
University of Melbourne
Abstract
Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free language with the full expressive power of first-order logic with identity, I show that this is true of logic more generally. Furthermore, having, in a logical theory, non-trivial valid forms that do not involve logical terms is not merely a technical possibility. As the case of adverbs shows, issues about the range of argument forms logic should countenance can quite naturally arise in such a way that they do not turn on whether we countenance certain terms as logical.
Keywords formal validity  logical constants  logical terms  nature of logic
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DOI 10.1002/tht3.440
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References found in this work BETA

Philosophy of Logic.W. V. O. Quine - 1970 - Harvard University Press.
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Invariance Criteria as Meta-Constraints.Gil Sagi - 2022 - Bulletin of Symbolic Logic 28 (1):104-132.

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