By Innocentius Marie Bochenski
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Additional info for Ancient Formal Logic
41-43). He proceeds as follows: given a mode of the form ‘pq 3 r 1 and a law of conversion rs 3 p’ he gets a mode of the form rsq 3 T I ; he actually says: as r s l converts into rp1, out of rsq 3 r1 we get ‘pq 3 T I . 1 which are stated explicitly in a generalized form (11. 63), and on the laws of the opposition (9. 20-31). e. the antecedent of a valid syllogism rpq 3 r 1 ; we get, consequently, rr1; now this entails - by a law of the theory of opposition (9. e. the negation of the assumed rs1.
69. 3. 3. PeS 53 (Baralipton) (Dabitis) (Celantes) 39 It is worth while to note, however, that assuming the Aristotelian theory of the major and minor term (ch. SC) it allows for the following laws : [9. 1 [9. 1 [9. 1 [9. 1 [9. 3. 3. PeX M a p . M a s . M a s . P i x M a p . 3. Pis (from (from (from (from (from Cesare) 40 Camestres) Darapti) Disamis) Datisi). I n the deduction of those laws the principle of syllogism rp3q : 3 : q 3 r . 3 . p 3 r l is used. The same principle with the laws of subalternation would allow deduction of the scholastic “subaltern” modes, five in number - Barbari, Celuront, Cesaro, Camestrop, and Celantop -, but there is no indication concerning them in the Organon.
9-12. - second: 5 , 2 6 b 34-39; third: 6, 28 a An. Pr. A 7, 29 a 19-27; B 1, 530 46 ARISTOTLE but to their extension; and this again becomes clear if we suppose, as in fact it is most probable, that his syllogism was developed out of the Platonic division (8LaIipucc) in such a way that the first figure was developed first of all and the two others formed by conversion of some of the functions in the modes of the first, at a later stage. The following scheme, in which the relative extension of the terms is indicated by lines, illustrates the point: Division 1st figure Major Middle Minor 8 D.
Ancient Formal Logic by Innocentius Marie Bochenski