Kilwardby's 55th Lesson

Autor(en): Lenzen, Wolfgang
Stichwörter: Aristotle's Thesis; connexive logic; Kilwardby; Logic; Philosophy; Science & Technology - Other Topics
Erscheinungsdatum: 2020
Volumen: 29
Ausgabe: 4
Startseite: 485
Seitenende: 504
In ``Lectio 55'' of his Notule libri Priorurn, Robert Kilwardby discussed various objections that had been raised against Aristotle's Theses. The first thesis, AT1, says that no proposition q is implied both by a proposition p and by its negation, similar to p. AT2 says that no proposition p is implied by its own negation. In Prior Analytics, Aristotle had shown that AT2 entails AT1, and he argued that the assumption of a proposition p such that (similar to p -> p) would be ``absurd''. The unrestricted validity of AT1, AT2, however, is at odds with other principles which were widely accepted by medieval logicians, namely the law Ex Impossibili Quodlibet, EIQ, and the rules of disjunction introduction. Since, according to EIQ, the impossible proposition (p boolean AND similar to p) implies every proposition, it also implies similar to(p boolean AND similar to p), in contradiction to AT2. Furthermore, by way of disjunction introduction, the proposition ( boolean OR similar to p) is implied both by p and by similar to p, in contradiction to AT1. Kilwardby tried to defend AT1, AT2 against these objections by claiming that EIQ holds only for accidental but riot for natural implications. The second argument, however, cannot be refuted in this way because Kilwardby had to admit that every disjunction (p boolean OR q) is naturally implied by its disjuncts. He therefore introduced the further requirement that, in order to constitute a genuine counterexample to AT1, (p -> q) and (similar to p -> q) have to hold ``by virtue of the same thing''. In a recently published paper, Spencer Johnston accepted this futile defence of AT1 and developed a formal semantics that would fit Kilwardby's presumably connexive implication. This procedure, however, is misguided because the remaining considerations of Lesson 55 - which were entirely ignored by Johnston show that Kilwardby eventually recognized that AT2 is bound to fail. After all he concluded: ``So it should be granted that from the impossible its opposite follows, and that the necessary follows from its opposite''.
ISSN: 14253305
DOI: 10.12775/LLP.2020.013

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