@article {Tennant:2014:0144-5340:120,
title = "Aristotle's Syllogistic and Core Logic",
journal = "History and Philosophy of Logic",
parent_itemid = "infobike://tandf/thpl",
publishercode ="tandf",
year = "2014",
volume = "35",
number = "2",
publication date ="2014-04-03T00:00:00",
pages = "120-147",
itemtype = "ARTICLE",
issn = "0144-5340",
eissn = "1464-5149",
url = "https://www.ingentaconnect.com/content/tandf/thpl/2014/00000035/00000002/art00002",
doi = "doi:10.1080/01445340.2013.867144",
author = "Tennant, Neil",
abstract = "I use the CorcoranSmiley 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 GentzenPrawitz 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.",
}