Aristotle's Many-sorted Logic

Bulletin of Symbolic Logic 14 (1):155-156 (2008)
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As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 proof of the completeness of Aristotle’s syllogistic.

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John Corcoran
PhD: Johns Hopkins University; Last affiliation: University at Buffalo


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