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.
...MoreSimilar Citations
Book
Harari, Orna;
(2004)
Knowledge and Demonstration: Aristotle's Posterior Analytics
(/isis/citation/CBB000500290/)
Article
Bellissima, Fabio;
(2002)
Il sistema assiomatico-deduttivo degli Elementi armonici di Aristosseno
(/isis/citation/CBB000411050/)
Article
Formarier, Marie;
(2013)
ρυθμος, rhythmos et numerus chez Cicéron et Quintilien. Perspectives esthétiques et génériques sur le rythme oratoire latin
(/isis/citation/CBB001200976/)
Article
Correia, Manuel;
(2004)
Philoponus on the Nature of Logic
(/isis/citation/CBB000502259/)
Article
Schiefsky, Mark;
(2009)
Structures of Argument and Concepts of Force in the Aristotelian Mechanical Problems
(/isis/citation/CBB000932571/)
Article
Adams, Marcus P.;
(2015)
Demarcating Aristotelian Rhetoric: Rhetoric, the Subalternate Sciences, and Boundary Crossing
(/isis/citation/CBB001202194/)
Article
Halonen, Ilpo;
Hintikka, Jaakko;
(2000)
Aristotelian explanations
(/isis/citation/CBB000111284/)
Article
Keeling, Evan;
(2012)
Unity in Aristotle's Metaphysics H6
(/isis/citation/CBB001251233/)
Book
Rijk, Lambertus Marie de;
(2002)
Aristotle: Semantics and Ontology
(/isis/citation/CBB000301545/)
Book
Pasquale, Gianluigi;
(2005)
Aristotle and the Principle of Non-Contradiction
(/isis/citation/CBB000741068/)
Article
Piero Tarantino;
(2011)
L'origine della nozione aristotelica di "scienza dimostrativa"
(/isis/citation/CBB689955339/)
Article
Theodor Ebert;
Ron Polansky;
(2015)
What is a Perfect Syllogism in Aristotelian Syllogistic?
(/isis/citation/CBB668871792/)
Article
Raymonda, Dwayne;
(2010)
Polarity and Inseparability: The Foundation of the Apodictic Portion of Aristotle's Modal Logic
(/isis/citation/CBB001210975/)
Book
Tipton, Jason A.;
(2014)
Philosophical Biology in Aristotle's Parts of Animals
(/isis/citation/CBB001500574/)
Thesis
Hussain, Hammad A.;
(2010)
Aristotle's “Genetic Account” and the Problem of Induction
(/isis/citation/CBB001562741/)
Chapter
Detel, Wolfgang;
(2007)
Logic and Experience in Aristotle
(/isis/citation/CBB001020201/)
Article
Correia, Manuel;
(2009)
The Syllogistic Theory of Boethius
(/isis/citation/CBB001211442/)
Article
Konstantinos Nikolantonakis;
(2016)
Le contenu mathématique et les structures déductives des trois livres du traité "Les Sphériques" de Théodose de Tripoli
(/isis/citation/CBB188489627/)
Book
Suto, Taki;
(2012)
Boethius on Mind, Grammar, and Logic: A Study of Boethius' Commentaries on Peri Hermeneias
(/isis/citation/CBB001213920/)
Article
Acerbi, Fabio;
(2011)
The Language of the “Givens”: Its Forms and Its Use as a Deductive Tool in Greek Mathematics
(/isis/citation/CBB001034293/)
Be the first to comment!