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By Innocentius Marie Bochenski

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Yet this might have been a beginning of a logic of probability. The relations between the above modalities may be stated in the following laws: 10. 13. 10. 14. 10. 15. N ( A 2 )3 A z 13 As 3 () ( A z )14 N ( A z )3 () ( A z )l5 A n . , A 15, 34 b 7-18. - 7 De Int. - A n . Pr. ; 17, 37 a 271. - 9 A n . Pr. A 13, 32 a 18-20; cp. ; De Int. ; and Met. 0 3. 1047 a 240. - loDe Int. 13. l1 cp. 10. 31 below. - la A n . Pr. A 3, 25 b 140. - l3 cp. De Int. 13, 23 a 21f. - l4 cp. A n . Pi-. A 16, 36 a 15-17; 22, 40 a 25-32.

That equivalence is meant here is clear from the use of these laws in the proofs of syllogistic modes. All of these laws are correct on Aristotelian assumptions, if we also presuppose the structure of modal sentences as explained above. As a matter of fact we have: &(Ax) 3 " ( A Z ) . N N ( N A X ) -NN(N - Az). #. Ss. E( E(#oP) N [lo. 111 Px) [lo. 11 - A A [lo. 21 El [lo. 371 [lo. 211 El [lo. 212 El [lo. 371 [lo. 213 El. 10 D. CONVERSION The laws of conversion of necessary and possible are analogous to 9.

SeM. SeM. PoS (Fapesmo) 38 (Frisesomorum) 38 and more siniilar laws by use of 9. 41-43. This last rule is not applied in detail by Aristotle, who states only three laws: 23 We give also the usual scholastic names (due t o Peter of Spain). An. Pr. A 4, 25 b 378. - 25 ib. 408. - 28 An. Pr. 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 .

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Ancient Formal Logic by Innocentius Marie Bochenski

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