A converse Barcan formula in Aristotle’s modal logic

Charles J Kelly


While critics correctly claim against Aristotle that universal affirmative and particular affirmative de re apodeictic propositions do not validly convert to a particular affirmative de re necessary counterpart, there is a type of valid convertibility for these propositions, a convertibility that at once reveals both an insight and a confusion on Aristotle’s part, the confusion amounting at times to a fallacy of amphiboly. Recognition of this convertibility through the introduction of a “relational necessity” which is neither de dicto nor de re will resolve a longstanding anomaly generated by Aristotle’s provocative claim that being white necessarily belongs to swans and to snow. By use of a modified Converse Barcan Formula, a distinctively Aristotelian ecthetic argument formally validating the apodeictic conversions is presented. Some implications of these results for the integrity and credibility of Aristotle’s modal syllogistic are briefly mentioned.

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