Abstract
ABSTRACT Two models of the Aristotelian syllogistic in arithmetic of natural numbers are built as realizations of an old Leibniz idea. In the interpretation, called Scholastic, terms are replaced by integers greater than 1, and s.Ap (“Every s is a p”) is translated as “s is a divisor of p”, sIp (“Some s is a p”) as “g.c.d. (s, p) > 1” (the same letters are used for the replacing numbers as well as for the terms). In the interpretation, called Leibnizian, terms are replaced by proper divisors of a special “Universe number” u < 1 (i.e., s < u, p < u), and sAp is translated as “s is divisible by p”, sIp as ‘l.c.m. (s, p) < u”. Both interpretations are proved to be adequate to the Aristotelian syllogistic. They are extended to syllogistic including term negation and term conjunction as well (and, therefore, all Boolean operations with terms).
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