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Chapter Summary

Robert Kilwardby distinguishes four senses in which the word "reduction" is used with reference to syllogisms which includes the reduction of a syllogism in one Figure to a syllogism. One syllogism may be reduced to another by a number of different methods. Direct Reduction is the method most widely used by Aristotle. This is a process in which a syllogistic premise is replaced by its converse or by another proposition that implies it, or else a syllogistic conclusion is replaced by its converse or by another proposition which it implies. Kilwardby devotes a great deal of effort to trying to understand the nature of the Conversions used in this process. He summarizes the Aristotelian laws of conversion for assertorics, necessity-proposition, possibility-propositions and contingency-propositions. Kilwardby concludes that Conversion is a consequence but not any sort of argument - recognizes that Conversion doesn't neatly fall under any of the concepts provided by Aristotelian logic.

Keywords: Aristotelian logic; assertorics; propositions; reduction; Robert Kilwardby; syllogism



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