By Terence Parsons
Terence Parsons provides a brand new examine of the advance and logical complexity of medieval common sense. simple rules of common sense have been utilized by Aristotle to end up conversion rules and decrease syllogisms. Medieval logicians multiplied Aristotle's notation in different methods, reminiscent of quantifying predicate phrases, as in 'No donkey is each animal', and permitting singular phrases to seem in predicate place, as in 'Not each donkey is Brownie'; with the enlarged notation come extra logical rules. The ensuing approach of good judgment is ready to care for relational expressions, as in De Morgan's puzzles approximately heads of horses. a vital factor is a mechanism for facing anaphoric pronouns, as in 'Every girl loves her mother'. Parsons illuminates the ways that medieval common sense is as wealthy as modern first-order symbolic good judgment, although its complete capability was once now not envisaged on the time. alongside the way in which, he presents an in depth exposition and exam of the speculation of modes of universal own supposition, and the worthwhile rules of good judgment incorporated with it. An appendix discusses the substitute symptoms brought within the 15th century to change quantifier scope.
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Extra info for Articulating Medieval Logic
Since there are in fact two distinct things, it is vacuously true that no matter how the terms and verbs other than the copula are interpreted, one never gets a true premise and a false conclusion. But the conclusion—that there are at least two things—does not follow intuitively from the premise, since it could be that there are not two things. This is an awkwardness for symbolic logic. But it is not a problem for medieval logic. For from a medieval point of view the source of the awkwardness rests on a defect in the notation of symbolic logic.
6. N is S N is P N is R Some R is P 1 EX 1 EX 2 3 UA 4 5 ES Hereafter I will assume UA as an available rule. Something interesting happens in the proof of Bocardo. ” This alternative proof would have the form: 1. 2. Every S is R Some S isn’t P 3. 4. 5. 6. X is S X isn’t P X is R Some R isn’t P 2 EX 2 EX 1 3 UA 4 5 ES Now this is an interesting move, for it appears to apply exposition to a particular negative proposition. And this is not in general valid. Suppose, for example, that there are no reduction of all syllogisms to perfect ones 37 As.
One is an analogue of Exposition but applied to a universal affirmative proposition. This is clearly valid, since exposition is applicable to the corresponding particular affirmative, which can be derived from the universal affirmative by an application of conversion per accidens followed by an application of simple conversion: Every S is P Some P is S Some S is P from previous line by conversion per accidens from previous line by simple conversion I will thus assume that it is a legitimate shortcut to apply exposition directly to a universal proposition, as Aristotle does here.
Articulating Medieval Logic by Terence Parsons