An Introductory Text-Book of Logic

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. 1905 Excerpt: ...This is in fig. ii.: --All P is M, No S is M: .'. No S is P. The first J in the name indicates that the original minor premise is to be converted simply; the m indicates that the original premises are to be transposed. The C indicates that from the new pair of premises, thus obtained, we are to draw the conclusion in Celarent, fig. i.; and the second N s indicates that if we convert this conclusion in Celarent simply, we shall get our original conclusion. Convert the original minor, and transpose: --No M is S, All P is M, from which in Celarent the conclusion is, No P is S, from which again by simple conversion, No S is P, which is the original conclusion. The process of Reduction in the case of the fourth figure has already been illustrated ( 9). This operation, of direct application of Immediate Inference and transposition, is called direct reduction. By this means we are also said to reduce ostensively (SeiKriK&s). Aristotle did not admit any Immediate Inference except conversion; and under this limitation we cannot reduce Baroco and Bocardo directly. Accordingly they are reduced by a distinct process known as reduction per impossibile (Sta Tov aBvvdrov) or indirect reduction: assume the falsity of the conclusion (/.-., the truth of its contradictory); take this contradictory with one of the original premises, as the two premises of a new syllogism in Barbara,1 the conclusion of which will be incompatible with the other premise of the original syllogism. Hence either the original conclusion is true or one of the original premises false; and, since in Deductive Logic the premises are always assumed to be true, we can only accept the former alternative. Barbara, being in the first figure, is known to be valid. Examples: (a) Reduce Baroco per im...