A modern formal logic primer: sentence logic by Paul Teller

A modern formal logic primer: sentence logic by Paul Teller

By Paul Teller

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55 Met. r 2 , 1003 a 358. - 56 cp. Muskens. 67 Soph. El. 4 , 1 6 5 b 30ff. - 58 De Int. 11, 20 b 138. - 5D Met. 4,1006 b l l f f . - * Bibliography of the subject in Philippe nos. 11. 6lff. - r SEMIOTICS 31 extensive knowledge of his ontologicaland epistemological doctrines : it must be omitted here. We shall, however, briefly deal with the Aristotelian theory of truth. 5 E. TRUTH Aristotle recognizes that “is” and “is not” are sometimes used as meaning “is true” resp. “is false”61 but he emphatically distinguishes both 62.

Sa(Pn -P) 31 Similar instances are explicitly adduced in the An. Post. in order to show that our principle is not needed in any demonstration. The evolution of Aristotle in that regard is easy to understand: the principle of contradiction must have appeared as the foundation of deduction where the reductio ad absurdum was the main instrument of thought - as it was in dialectics. But when Aristotle discovered his non-dialectical, but positively logical doctrine, the logical importance of the principle must have been considerably diminished by it.

A 22, 84 a 7f. and b 2. Cp. Scholz, Geschichte 6f. - 8 A n . Pr. B 16, 65 a 36; A 30, 46 a 9 ; B 23, 68 b 1 0 ; T o p , A 1, 100 a 22, 29; 0 11, 161 a 36 cp. Bonitz 183. - T o p . ; Met. E 1,1025 b 25; Met. K 7,1064 b 1. The Aoytxai in T o p . A 14, 105 b 19#. means clearly “epistemological”. - Met. r 3, 1005 b 2-5. 6 Top. A 1,100 a 25. - 7 A n . Pr. A 1, 24 b 18f. 26 ARISTOTLE it is that it does not attribute to the syllogism any definite status: for “Adyo$’ may mean equally well a verbal discourse, a train of thought, or an objective structure (of the kind of the Stoic ilextdv), while exactly the same is true of the xeot&oesc and 8~0sof which the syllogism is said to be composed.

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