Intuitionistic Logic and Elementary Rules

Mind 120 (480):1035-1051 (2011)
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Abstract

The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the falsum as a primitive connective, classical and intuitionistic consequence satisfy exactly the same structural, introduction, and elimination (briefly, elementary) rules. Third, for falsum as primitive only, intuitionistic consequence is the least consequence relation that satisfies all classically correct elementary rules

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Author Profiles

David Makinson
London School of Economics
Lloyd Humberstone
Monash University

Citations of this work

Explicating Logical Independence.Lloyd Humberstone - 2020 - Journal of Philosophical Logic 49 (1):135-218.
Classical Harmony and Separability.Julien Murzi - 2020 - Erkenntnis 85 (2):391-415.

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References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge, Mass.: Harvard University Press.
Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
The taming of the true.Neil Tennant - 1997 - New York: Oxford University Press.
The Connectives.Lloyd Humberstone - 2011 - MIT Press. Edited by Lloyd Humberstone.
The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.

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