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Logic and Logical Philosophy

Logical Nihilism and the Logic of ‘prem’
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Logical Nihilism and the Logic of ‘prem’

Authors

  • Andreas Fjellstad Department of Philosophy, University of Bergen https://orcid.org/0000-0002-3239-4484

DOI:

https://doi.org/10.12775/LLP.2020.023

Keywords

nihilism, non-reflexive logic, non-transitive logic, dual valuations, modus ponens

Abstract

As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one can obtain non-reflexive logics in which ‘prem’ behaves as stipulated by Russell (2018) but which nonetheless has valid inferences supporting uniform substitution of any formula for propositional variables such as modus tollens and modus ponens.

References

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Logic and Logical Philosophy

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Published

2020-11-10

How to Cite

1.
FJELLSTAD, Andreas. Logical Nihilism and the Logic of ‘prem’. Logic and Logical Philosophy. Online. 10 November 2020. Vol. 30, no. 2, pp. 311-325. [Accessed 4 July 2025]. DOI 10.12775/LLP.2020.023.
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