Logical Nihilism and the Logic of ‘prem’

Logic and Logical Philosophy:1 (forthcoming)
  Copy   BIBTEX

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,174

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Logical Nihilism: Could There Be No Logic?Gillian Russell - 2018 - Philosophical Issues 28 (1):308-324.
Deleuze, Nietzsche, and the Overcoming of Nihilism.Ashley Woodward - 2013 - Continental Philosophy Review 46 (1):115-147.
Nihilism.Bülent Diken - 2008 - Routledge.
Logical Nihilism. [REVIEW]Curtis Franks - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 147-166.
Beyond Logical Pluralism and Logical Monism.Pavel Arazim - 2020 - Logica Universalis 14 (2):151-174.
The Accident of Logical Constants.Tristan Grøtvedt Haze - 2020 - Thought: A Journal of Philosophy 9 (1):34-42.
A Survey of Logical Realism.Tuomas E. Tahko - 2021 - Synthese 198 (5):4775-4790.
The Metaphysics of Logic.Penelope Rush (ed.) - 2014 - Cambridge University Press.
Mereological Nihilism and Theoretical Unification.Andrew Brenner - 2015 - Analytic Philosophy 56 (4):318-337.
The Theory of Form Logic.Wolfgang Freitag & Alexandra Zinke - 2012 - Logic and Logical Philosophy 21 (4):363-389.
A Conception of Tarskian Logic.Gila Sher - 1989 - Pacific Philosophical Quarterly 70 (4):341-368.

Analytics

Added to PP
2020-11-13

Downloads
55 (#211,780)

6 months
12 (#69,520)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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..

View all 15 references / Add more references