By Innocentius Marie Bochenski
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Extra resources for Ancient Formal Logic
THE PRINCIPLE OF CONTRADICTION While we find no principle of identity in the preserved writings of Aristotle, 17 a whole book of Metaphysics (r) is devoted to the principle of contradiction (which is, however, not called so by Aristotle himself) and there are numerous formulations of it in his other works. Those formulations may be divided into logical and metalogical. The former are: “the same cannot belong and not belong together to the same under the same respect”1B and “Let __ DeInt. 10, 20 a 20-26.
Thus the relation of essentiality appeared as formally irrelevant ; in fact, at the beginning of the An. Pr. Aristotle states this explicitly 6. It does not mean that he repudiated later on all considerations about essential predication 7 ; but there is no doubt that by classifying predicables he discovered and clearly conceived formal logic. 6 C. THE CATEGORIES The second classification of the meanings of the copula rises out of an attempt to give a most general classification of all objects 8.
A 46, 51 b 40. - la ib. 4-52 a 4. - 14 An. Pr. A 46, 52 n 41. - 16 ib. 9. le De Int. 10, 20 a 20f. - l7 De Int. 10, 20 a 22f. De Int. 10, 20 a 251. 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.
Ancient Formal Logic by Innocentius Marie Bochenski