The Principles of Logic, for High Schools and Colleges (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1869 Excerpt: ... hypothesis;.. A is not D. If A D, B C E F, which is contrary to the hypothesis;.. A is not D. Hence, since neither A D nor A D, A = D. In a similar way it can be proved that B = E and C = F. 30. Hamilton's Notation, and Classification of Propositions. 1. Notation. f: = all in affirmative, and any in neg-ative propositions., --some. -H--= is not. (o-) S, -, P. If S and P intersect. (A) S: --, P. If S is subordinate to P. (Y) S, --: P. If P is subordinate to S. (I) S, --, P. If S and P intersect. (E) S: m+-: P. If Sis excluded from P. ( s )( p (r)) S: m---, P. If S is subordinate to P. (0) S, -: P. If P is subordinate to S. L(7) (3D 5. Opposition of Judgments. u E 1st. Contradictory opposition, existing between (E) and (I). a. Law.--Both can not be true nor both false. ' a. One must be true and the other false ft. The truth of either implies the falsity b. Corollaries. of the other. y. The falsity of either implies the truth of the other. c. Scholium.--In the classification of categorical propositions before given, it was stated that (A) and (0) are contradictories, as well as (E) and (I). In the present classification, the falsity of (0) does not necessarily imply the truth of (A), for (IT) may be true. The difference is owing to this, that in the former classification (A) includes both (IT) and (A) of the present classification; hence, the falsity of (0) implies the truth of either (U) or (A). 2d. Contrary opposition, existing between (U) and (E), (IT) and (?), (IT) and (0), (A) and (E), (A) and (0), (T) and (E), (Y) and (), one affirmative, the other negative. a. Law.--Both can not be true, but both may be false. a. The truth of either implies the falsity 1 of the other. /?. The falsity of neither implies the truth of the other. 3d. Inconsiste