By Joseph M. Bocheński
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Extra info for Ancient Formal Logic
A 4, 26 a 23g. - 27 ib. 258. - 28 An. Pr. 5, 27 a 58. - 29 ib. 9-14. - 30 ib. 32f. - 31ib. 37f. - azAn. Pr. ; A 7, 2 9 a 37f. - 3 3 i i b . - 34 An. Pr. ; actually: ‘ M a s . SiPI. - 35 ib. 11; actually: ‘MiS. M a p . Sip’. - ib. 17g. ; actually : ‘Mas. SOP’. - 87 ib. 33f. - 38 An. Pr. A 7 , 29 a 238. 24 FORMAL LAWS O F ASSERTORIC SYLLOGISTICS * 9. 67. * 9. 68. * 9. 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.
E. by reduction to absurdity. We shall not reproduce his arguments which seem to be all fallacious and which simply could not have been stated in l9 A n . Pr. A 46, 51 b 36fl. - 2o Met. r 6, 1011 b l 5 f . - 21 Met. r3, 1005 b 238. - 22 Lukasiewicz, Der Satz, 17; Selamucha, 7 5 . - 23 T o p . B 7,113 a 22f. - 24 De Int. ; 10,20 a 168. - a5 Met. F 5, 1009 a 35f. 2o Met. r 4, 1005 b 19-23. 40 ARISTOTLE that form later on, as they contain the petitio principii and other errors. ;oEc cbxrj) 28. I n fact the opposite is thought in the An.
42. SaP 3 P i s 2o Proof: if not 9. 42, then we have ‘Sap1 and r- PiS1; this gives (by 9. 27) rPeS1; out of which we obtain by 9 . 4 1 rSeP1 and further on, (by 9. 0. the negation of the ‘Sap1 assumed. The law ( p3q) 3 p q1 is used here. s i p 3 P i s 21 * 9. 43. The proof is similar to the above, only 9. 24 is used instead of 9. 23. It has sometimes been said that the proof of 9. 41 supposes 9. 43, but this is not the case. The central step is based on laws concerning individual names: 8. 31, 8.