Limiting logical pluralism

Synthese 198 (Suppl 20):4905-4923 (2019)
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Abstract

In this paper I argue that pluralism at the level of logical systems requires a certain monism at the meta-logical level, and so, in a sense, there cannot be pluralism all the way down. The adequate alternative logical systems bottom out in a shared basic meta-logic, and as such, logical pluralism is limited. I argue that the content of this basic meta-logic must include the analogue of logical rules Modus Ponens and Universal Instantiation. I show this through a detailed analysis of the ‘adoption problem’, which manifests something special about MP and UI. It appears that MP and UI underwrite the very nature of a logical rule of inference, due to all rules of inference being conditional and universal in their structure. As such, all logical rules presuppose MP and UI, making MP and UI self-governing, basic, unadoptable, and required in the meta-logic for the adequacy of any logical system.

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Suki Finn
Royal Holloway University of London

References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge, Mass.: Harvard University Press.
The logical syntax of language.Rudolf Carnap - 1937 - London,: K. Paul, Trench, Trubner & co.. Edited by Amethe Smeaton.
Logical Pluralism.Jc Beall & Greg Restall - 2005 - Oxford, England: Oxford University Press. Edited by Greg Restall.
Wittgenstein on rules and private language.Saul A. Kripke - 1982 - Revue Philosophique de la France Et de l'Etranger 173 (4):496-499.

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