Natural Semantics: Why Natural Deduction is Intuitionistic

Theoria 67 (2):114-139 (2001)
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Abstract

In this paper investigates how natural deduction rules define connective meaning by presenting a new method for reading semantical conditions from rules called natural semantics. Natural semantics explains why the natural deduction rules are profoundly intuitionistic. Rules for conjunction, implication, disjunction and equivalence all express intuitionistic rather than classical truth conditions. Furthermore, standard rules for negation violate essential conservation requirements for having a natural semantics. The standard rules simply do not assign a meaning to the negation sign. Intuitionistic negation fares much better. Not only do the intuitionistic rules have a natural semantics, that semantics amounts to familiar intuitionistic truth conditions. We will make use of these results to argue that intuitionistic connectives, rather than standard ones have a better claim to being the truly logical connectives

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James W. Garson
University of Houston

References found in this work

The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
The Philosophical Basis of Intuitionistic Logic.Michael Dummett - 1978 - In Truth and other enigmas. Cambridge: Harvard University Press. pp. 215--247.
The runabout inference ticket.Arthur Prior - 1967 - In P. F. Strawson (ed.), Philosophical logic. London,: Oxford University Press. pp. 38-9.
What is logic?Ian Hacking - 1979 - Journal of Philosophy 76 (6):285-319.

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