Limiting logical pluralism
Limiting logical pluralism
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 (MP) and Universal Instantiation (UI). 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 (most relevantly to logical pluralism) required in the meta-logic for the adequacy of any logical system.
Finn, Suki
d74d44c0-38f4-4cc7-8807-92ca56c88783
Finn, Suki
d74d44c0-38f4-4cc7-8807-92ca56c88783
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 (MP) and Universal Instantiation (UI). 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 (most relevantly to logical pluralism) required in the meta-logic for the adequacy of any logical system.
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Finn - Limiting Logical Pluralism
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Accepted/In Press date: 8 February 2019
e-pub ahead of print date: 19 February 2019
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Local EPrints ID: 428581
URI: http://eprints.soton.ac.uk/id/eprint/428581
ISSN: 0039-7857
PURE UUID: 504f874b-8d13-4cdd-9e66-3f7e61a6defa
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Date deposited: 01 Mar 2019 17:30
Last modified: 16 Mar 2024 00:19
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Author:
Suki Finn
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