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The development of modus ponens in antiquity: from Aristotle to the 2nd century AD. (Philosophical Abstracts).

"Aristotelian logic," as it was taught from late antiquity until the twentieth century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as "hypothetical syllogisms." However, Aristotle did not discuss such arguments, nor did he call any arguments hypothetical syllogisms. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them hypothetical syllogisms; nor did they describe them as ponendo ponens, and so forth. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, the author offers some explanations by tracing the development of certain elements of Aristotle's logic via the early Peripatetics to the logic of later antiquity. The author considers the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called "hypothetical syllogisms"? On what grounds were they considered valid? She argues that such arguments were neither part of Aristotle's dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle's logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some twentieth-century theories.
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Author:Bobzien, Susanne
Publication:The Review of Metaphysics
Date:Jun 1, 2003
Words:263
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