A study in Burleigh: Tractatus de regulis generalibus consequentiarum.

Abstract

There is perhaps no other prominent logician in the late Middle Ages who would realize the nature, the scope, and the importance of propositional logic better than Walter Burleigh (1275-1345).Not only the content, but the very arrangement of his tracts shows that his conception of logic is entirely different from that of the commentators on Aristotle's Organon.He placed the tract on consequences at the beginning of his logical treatise, and his tract contains the syllogistic rules as a very minor part.This is significant, for many of Burleigh's contemporaries, such as Ralph Strodus, William of Ockham, John Buridan, William of Shyreswood, and Albert of Saxony, may have written lengthier tracts on consequences, but placed them after the tract on categorical syllogistic or even appended them toward the end of their Summae.Burleigh seems to have realized that we may and indeed must consider the relations among unanalyzed propositions prior to considering the relations among analyzed propositions constituting a syllogism.By consequentia a conditional proposition is meant, the antecedent and the consequent of which may themselves be complex.Like most logicians of his time, Burleigh distinguished several types of them: those that hold in virtue of an extrinsic means or logical rules and those that hold in virtue of an intrinsic means; formal and material; and absolute and factual.These divisions are not mutually exclusive.This paper is concerned only with the last mentioned division of consequences.An attempt is made to present Burleigh's views in the language of contemporary logic.Wherever modalities are not in question, I propose to utilize the notation of the system of material implication.This procedure may have its objections, since the examples illustrating several of the rules given by Burleigh seem to indicate that he had in mind formal connections between propositions such as found between a premiss-set and the conclusion of a categorical syllogism; yet, unless words such as 'cannot', 'must', 'may', etc., cannot be shown to have a modal function, non-modal symbolism will be employed, with the following proviso: that, depending

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