Download PDF by Joseph M. Bocheński: Ancient Formal Logic

By Joseph M. Bocheński

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10. 221. 10. 222. 10. 223. N ( S z )3 N ( P z ) N(SeP) = ( z ) . N(P2)5 N ( S O P )= (32). N ( - P) Similar laws may be obtained from the above by substituting “E” for “N” (these will be referred to henceforth by the above number followed by “E”). Indeed, one of the most striking aspects of the Aristotelian modal syllogistic is that the principle “peiorem semper sequitur conclusio partem” which applies to assertoric syllogisms does not apply here. g. (10. N ( S a P ) (1) and also (10. SeP. Most of these laws become valid, indeed, if we assume 10.

His reasoning is briefly this: if 7. 23, then 7. 21, but if so, one of the two, ryx1 or r- yx1 must be always true; and this implies that one of them is necessary; while it is evident, he says, that there are contingent events. Thus the application of 7. 21 to future contingent events is rejected. In the body of the Organon we find no trace of any consequence of those doubts, however. The tertium non datur is always supposed to be universally valid. 34 An. Pr. A 46, 51 b 368. 18a 37f. - 36 Met.

SeP 3 () (SeP)l7 SOP 3 () (SOP)18 Another law which results from the above definition is 3 0( A 4 [lo. 1 while As 3 E ( A s ) is invalid on the Aristotelian assumptions; but this is not stated by Aristotle himself. 10 B. THE STRUCTURE OF MODAL SENTENCES I n one - but in only one - text of the An. Pr. A l9 Aristotle describes a two-fold structure of the contingent sentences. He says that “ B may belong to A” may mean either (1) B may belong to that to which A belongs or (2) B may belong to that to which A may belong.

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Ancient Formal Logic by Joseph M. Bocheński

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