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The Expressive Power of Medieval Logic

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Chapter Summary

This chapter talks about the development of logic in the Aristotelian tradition, from Aristotle to the mid-fourteenth century. It compares four systems of logic with regard to their expressive power. Aristotle's logic is limited to the four forms of proposition in the traditional square of opposition plus some elementary principles about singular propositions. Aristotle used three principles to establish his principles of conversion and syllogisms. They are: reductio, exposition and expository syllogism. Aristotle uses the conversion principles plus the first figure universal syllogisms to prove all of the remaining forms of syllogism. Interestingly, he could also have proved the first figure universal syllogisms using only his principles of reduction, exposition, and expository syllogism. The chapter provides a modern symbolization of medieval logic. It addresses the question: What kind of logical structure do medieval logicians attribute to the propositions that they deal with?

Keywords: Aristotelian tradition; expository syllogism; medieval logic; reductio; singular Propositions



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