Revisiting McKinsey's 'Syntactical' Construction of Modality

Australasian Journal of Logic 17 (2):123-140 (2020)
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In 1945 J.C.C. McKinsey produced a ‘semantics’ for modal logic based on necessity defined in terms of validity. The present papers looks at how to update F.R. Drake’s completeness proof for McKinsey’s semantics by comparing McKinsey ‘models’ with the now standard Kripke models. It also looks at the motivation behind the system McKinsey called S4.1, but which we now call S4M; and use this motivation to produce a McKinsey semantics for that system. One lesson which emerges from this work is an appreciation of the superiority of the current possible worlds semantics based on frames and models, both in terms of an intuitive understanding of modality, and also in terms of the ease of working with particular systems.



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Max Cresswell
Victoria University of Wellington

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Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
Modalities and Quantification.Rudolf Carnap - 1946 - Journal of Symbolic Logic 13 (4):218-219.

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