Making Sense of Aristotelian Demonstration. Mendell, H. Oxford Studies in Ancient Philosophy, 16:161–225, 1998. abstract bibtex Mendell's goal in this paper is to make Aristotle's Analytics plausible. My strategy has been twofold. I first loosened the reins of Aristotle's theory of the sylogism to make plausible the claim that ordinary mathematical reasoning about particulars really is universal reasoning and to show that Aristotle's notion of reasoning encompassed by the Prior Analytics is not restricted to canonical statements of the form 'All/some As are/are not B.' The result was a richer analysis of arguments, but also something less than a complete, formal logical theory. In this way, when we turned to the representation of demonstrations, we were freed to represent many sorts of arguments as being in Barbara. However, when we turned to demonstration, we saw that it also entailed that mathematics is encumbered by many more premisses than we expected. My excuse for this was that Aristotle allows two sorts of proving, by demonstrative deduction and by induction. I do not claim to have solved all problems in Aristotelian theory of demonstration: how to handle relations without ad hoc rules or how to handle auxiliary constructions or even how to handle all reductions. The result is not an elegant proof theory - it is barely a proof theory in any modern sense, but nor is it as implausible as the theory with which we began.
@article{mendell_making_1998,
title = {Making {Sense} of {Aristotelian} {Demonstration}},
volume = {16},
shorttitle = {Making {Sense} of {Aristotelian} {Demonstration}},
abstract = {Mendell's goal in this paper is to make Aristotle's Analytics plausible. My strategy has been twofold. I first loosened the reins of Aristotle's theory of the sylogism to make plausible the claim that ordinary mathematical reasoning about particulars really is universal reasoning and to show that Aristotle's notion of reasoning encompassed by the Prior Analytics is not restricted to canonical statements of the form 'All/some As are/are not B.' The result was a richer analysis of arguments, but also something less than a complete, formal logical theory. In this way, when we turned to the representation of demonstrations, we were freed to represent many sorts of arguments as being in Barbara. However, when we turned to demonstration, we saw that it also entailed that mathematics is encumbered by many more premisses than we expected. My excuse for this was that Aristotle allows two sorts of proving, by demonstrative deduction and by induction. I do not claim to have solved all problems in Aristotelian theory of demonstration: how to handle relations without ad hoc rules or how to handle auxiliary constructions or even how to handle all reductions. The result is not an elegant proof theory - it is barely a proof theory in any modern sense, but nor is it as implausible as the theory with which we began.},
journal = {Oxford Studies in Ancient Philosophy},
author = {Mendell, H.},
year = {1998},
keywords = {APo, APr, ARISTOTLE, DEMONSTRATION, SYLLOGISM},
pages = {161--225}
}
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