David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of the History of Philosophy 48 (2):pp. 236-237 (2010)
The interpretation of Aristotle's syllogistic is a bellwether of the logical concerns of the interpreter's time. Aristotle's syllogistic is, in part, a two-tiered classification of syllogisms. Aristotle takes just a few syllogistic forms to be perfect or obviously acceptable and establishes the acceptability of the other imperfect syllogistic forms through a process of perfection—most often, by conversion of the premises of the imperfect syllogism into the premise-set of a perfect syllogism.The representation of the syllogistic as a modern logical system has, over the last fifty years, taken one of at least two approaches. Lukasiewicz in the 1950s interpreted the syllogistic as an axiomatic theory: the perfect syllogisms are axioms; the imperfect syllogisms are theorems, implications derived from the axioms by means of an underlying system of inferential reasoning; perfection establishes the truth of the imperfect syllogisms. By contrast, Corcoran and Smiley in the early 1970s independently represented the syllogistic as a Fitch-style natural deduction system: the perfect syllogisms and conversion rules are intuitively valid inference rules; the imperfect syllogisms are deductions with more than two premises providing step-wise derivation of a conclusion
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