Some notes on the Aristotelian doctrine of opposition and the propositional calculus
Abstract
In this paper, we develop some of Williamson's ideas about the contribution of propositional calculus to a better understanding of Aristotelian logic. Specifically, the use he makes of truth tables in analyzing the structure of the traditional square of opposition is enhanced by a simple technique: The relations of dependence between different propositions allow us to construct “conditioned truth tables”. Taking advantage of this possibility, we propose a new interpretation of several passages of the Organon related to opposition.
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