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Publication Details

The Transposition of the Aristotelian Sylogistics by Menas of Boole’s Algebra

(Original title: Převod Aristotelovy sylogistiky prostředky Booleovy algebry)
Filozofia, 50 (1995), 11, 604-609.
Type of work: Papers
Publication language: Czech

Aristotel’s sylogisms (BARBARA, CESARE, CELARENT) are transitive ones. Their transitivity is to be understood either as the transitivity of inclusive groups, or as the transitivity of implication. They can as well be represented by specific symbols corresponding to his conception of logic. Aristotel’s sylogistics can also be seen as an inclusion of groups in the conclusion, an inclusion following from true inclusions of premises. The premise "C c C", which is always true, is not explicit in the premises, yet its presence is involved. There are then two types ofjudgements which the author takes into account. The author aims at their interpetation by means of Boole’s algebra and symbolics, by which the basic Aristotel’s formulas can be reduced to two: А с В and C c C, with the exception of those expressing transitivity. The ananlysis wants also to show, that Aristotel did not connect the functor of negation with the one-place predicate, but with broader units (judgements, sentences). Thus he has closed for himself the way to modern conception of logic, which he was very close to.

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