From Wittgenstein’s N-operator to a New Notation for Some Decidable Modal Logics

History and Philosophy of Logic 40 (1):63-80 (2018)

Abstract
Wittgenstein’s N-operator is a ‘primitive sign’ which shows every complex proposition is the result of the truth-functional combination of a finite number of component propositions, and thus provides a mechanical method to determine logical truth. The N-operator can be interpreted as a generalized Sheffer stroke. In this paper, I introduce a new ‘primitive sign’ that is a hybrid of generalized Sheffer stroke and modality, and give a uniform expression for modal formulas. The general form of modal formula in the new notation is [A0···An−1; B0···Bm−1], which is semantically equivalent to ¬A0∨···∨¬ An−1∨◊. Based on this new notation, I propose several analytic axiomatic systems for some decidable modal logics. Every axiom of these analytic systems is an ‘Atomic-Sheffer’, which is the result of the combination of a finite number of component propositions. The inferential rules are analytic in that the set of elementary propositions that are combined in the premiss overlaps the set of elementar...
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DOI 10.1080/01445340.2018.1437519
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References found in this work BETA

Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
A Simple Treatment of Truth Functions.Alan Ross Anderson & Nuel D. Belnap - 1959 - Journal of Symbolic Logic 24 (4):301-302.
Wittgenstein's Operator N.P. T. Geach - 1981 - Analysis 41 (4):168--171.

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On the Curious Calculi of Wittgenstein and Spencer Brown.Gregory Landini - 2018 - Journal for the History of Analytical Philosophy 6 (10).

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