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.

Highlights

  • According to a metaphysical reading of logical pluralism, there is a plurality of correct logics

  • In order to see what I see is special about Modus Ponens (MP) and Universal Instantiation (UI), we must take atour via Kripke and Padró’s adoption problem, which can be outlined as such: Certain basic logical principles cannot be adopted, because, if a subject already infers in accordance with them, no adoption is needed, and if the subject does not infer in accordance with them, no adoption is possible

  • The morals that one can draw from this paper are: Logical novices cannot adopt basic logical rules

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Summary

Introduction

According to a metaphysical reading of logical pluralism, there is a plurality of correct logics (as opposed to only one, as the logical monist says). — relates to mathematics, but to all questions of logic.2 In order for this Principle to make sense, there must be a plurality of logics for us to be tolerant towards that are worthy of being chosen. I show that pluralism at the level of logical systems requires a certain monism at the level of meta-logic, and so, in a sense, there cannot be pluralism all the way down This is not just the claim that there must be some unifying feature to all of the logics that qualifies them as being pluralistic tokens of a monistic type. S4907 requirements at the level of meta-logic, and the plurality of adequate alternative logical systems is limited to those that share a certain meta-logic. For the same reason that UI and MP are unadoptable, they are basic and required at the meta-level M

The adoption problem
The adopter
The adoption
The adopted
General structure of rules
Modus Ponens and Universal Instantiation
Adjunction and the law of non‐contradiction
Justification and basicness
Implications for logical pluralism
Conclusion
Compliance with ethical standards
Full Text
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