Arithmetizations of Syllogistic à la Leibniz

à Lukasiewicz had every reason to suppose that Leibniz’s winged Calculemus! had been connected with the Aristotelian syllogistic [4, § 34]. Indeed, after Louis Couturat’s pioneer efforts in commenting and publishing Leibniz’s logical opuscula ([1], [2]). The basic idea of the arithmetization of syllogistic was to establish a correspondence between terms and suitable integers (the characteristic numbers of notions), so that the logical truth of a proposition would turn into an arithmetical truth of unsuccessful. The second one used a translation of terms into pairs of co-prime numbers and was successful, as SÃlupecki proved ([8]; see also [4, § 34]). This second translation obviously was more soffisticated but the bigger trouble was in the paper we justify the viability of the earlier (and less complicated) Leibniz idea. Moreover, we propose two translations into arithmetic which are appropriate for syllogistic with all Boolean term operations.