Logical Nihilism and the Logic of ‘prem’

Logic and Logical Philosophy:1 (forthcoming)
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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.



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Andreas Fjellstad
University of Bergen

References found in this work

A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
Structural Reflexivity and the Paradoxes of Self-Reference.Rohan French - 2016 - Ergo: An Open Access Journal of Philosophy 3.
Logical Nihilism: Could There Be No Logic?Gillian Russell - 2018 - Philosophical Issues 28 (1):308-324.
Selected Works.Jan Łukasiewicz - 1970 - Amsterdam: North-Holland Pub. Co..

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