The Accident of Logical Constants

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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.
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First archival date: 2020-01-11
Latest version: 2 (2020-01-17)
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References found in this work BETA
Truth and Truthmakers.Armstrong, D. M.
Philosophy of Logic.Quine, W. V. O.
Notebooks, 1914-1916.Wittgenstein, Ludwig

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