David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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History and Philosophy of Logic 29 (4):309-325 (2008)
This article studies the mathematical properties of two systems that model Aristotle's original syllogistic and the relationship obtaining between them. These systems are Corcoran's natural deduction syllogistic and ?ukasiewicz's axiomatization of the syllogistic. We show that by translating the former into a first-order theory, which we call T RD, we can establish a precise relationship between the two systems. We prove within the framework of first-order logic a number of logical properties about T RD that bear upon the same properties of the natural deduction counterpart ? that is, Corcoran's system. Moreover, the first-order logic framework that we work with allows us to understand how complicated the semantics of the syllogistic is in providing us with examples of bizarre, unexpected interpretations of the syllogistic rules. Finally, we provide a first attempt at finding the structure of that semantics, reducing the search to the characterization of the class of models of T RD
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References found in this work BETA
Patrick Blackburn, Maarten de Rijke & Yde Venema (2002). Modal Logic. Cambridge University Press.
Benson Mates (1972). Elementary Logic. New York,Oxford University Press.
Jan Łukasiewicz (1957/1987). Aristotle's Syllogistic From the Standpoint of Modern Formal Logic. Garland Pub..
John Corcoran (1972). Completeness of an Ancient Logic. Journal of Symbolic Logic 37 (4):696-702.
John Corcoran (1974). Aristotelian Syllogisms: Valid Arguments or True Universalized Conditionals? Mind 83 (330):278-281.
Citations of this work BETA
Edgar Andrade-Lotero & Catarina Dutilh Novaes (2012). Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW] Journal of Philosophical Logic 41 (2):387-418.
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