Ancient Formal Logic by Innocentius Marie Bochenski

By Innocentius Marie Bochenski

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42 Still later he found that we may take the laws of whatever figure as axioms. 43 We shall not describe those various axiomatic systems in detail; the important thing which they show is that Aristotle seemed to have considered in a later stage all syllogistic laws as being on the same level and was only interested in their logical relations and deducibility. I n An. Pr. B he proceeds quite as a contemporary logician would proceed. 42 An. Pr. A 7, 29 b 18. - 43 An. Pr. A 45, 50 b 5fl. 10. Modal Logic The theory of modal sentences and syllogisms is the most developed and at the same time the most refined logical doctrine of Aristotle.

Logic seems to have no place in Aristotle’s system of sciences 4, and was perhaps considered by him rather as an “instrument” which must be learned before those sciences. 6 This does not mean, however, that Aristotle would not consider logic as a theoretical discipline - the very fact that he devoted so much effort and space to apparently useless logical problems shows that this was not the case. We find no definition of logic in the preserved Aristotelian works; but its subject is clearly the syllogism and this is twice defined as a “ildyos in which some things being laid down, something different from them necessarily follows because of those laid down things” 6 (or: “because they are such” 7).

FORMAL LAWS OF ASSERTORIC SYLLOQISTICS 61 9 B. CONVERSION Aristotle says that a sentence of the form rSxP1 (where the “x” stands for one of the functors “a” “d’ “i” or “ 0 ” ) converts (&vaat&m) if, when this sentence be assumed, another sentence of the form ‘ P x S (with a functor of the same or of a different form) must also be admitted. There are three laws of conversion of assertoric sentences : * 9. 41. SeP 3 PeS. 19 This is proved as follows: suppose that 9. 41 is false. We then have rSeP1 and ‘Pis’.

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