Natural Semantics: Why Natural Deduction is Intuitionistic

Theoria 67 (2):114-139 (2001)
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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DOI 10.1111/j.1755-2567.2001.tb00200.x
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References found in this work BETA
What is Logic?Ian Hacking - 1979 - Journal of Philosophy 76 (6):285-319.
Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
Investigations Into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
The Adequacy Problem for Inferential Logic.J. I. Zucker & R. S. Tragesser - 1978 - Journal of Philosophical Logic 7 (1):501 - 516.

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Citations of this work BETA
Expressive Power and Incompleteness of Propositional Logics.James W. Garson - 2010 - Journal of Philosophical Logic 39 (2):159-171.

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