Theoria 67 (2):114-139 (2001)
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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References found in this work BETA
The Runabout Inference Ticket.Arthur Prior - 1967 - In Peter Strawson (ed.), Analysis. Oxford University Press. pp. 38-9.
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Investigations Into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
Citations of this work BETA
Failures of Categoricity and Compositionality for Intuitionistic Disjunction.Jack Woods - 2012 - Thought: A Journal of Philosophy 1 (4):281-291.
Expressive Power and Incompleteness of Propositional Logics.James W. Garson - 2010 - Journal of Philosophical Logic 39 (2):159-171.
A New Semantics for Vagueness.Joshua D. K. Brown & James W. Garson - 2017 - Erkenntnis 82 (1):65-85.
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