Article ID: CBB001201198

Aristotle's Syllogistic and Core Logic (2014)

unapi

I use the Corcoran--Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen--Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic is a fragment of my (constructive and relevant) system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle.

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Authors & Contributors
Correia, Manuel
Hintikka, Jaakko
Halonen, Ilpo
Rijk, Lambertus Marie de
Bellissima, Fabio
Harari, Orna
Journals
Apeiron: Journal for Ancient Philosophy and Science
Ancient Philosophy
Studies in History and Philosophy of Science
Nuncius: Annali di Storia della Scienza
Early Science and Medicine: A Journal for the Study of Science, Technology and Medicine in the Pre-modern Period
Archive for History of Exact Sciences
Publishers
Brill
Kluwer Academic
Akademie-Verlag
University of Oklahoma
Concepts
Logic
Philosophy
Mathematics
Metaphysics
Deduction
Aristotelianism
People
Aristotle
Boethius, Anicius Manlius Severinus
Aristoxenus
Philoponos, Joannes Grammaticus
Plato
Time Periods
Ancient
6th century
Places
Greece
Rome
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