Deduction Volume 1 (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. 1870 Excerpt: ...be negative) that, in this Figure, it is possible to prove negative conclusions only. In the Third Figure, the canons are, (1) The minor premise is affirmative. (2) The conclusion is particular. If the minor premise were negative, the conclusion must be negative, and the major term affirmative, which would involve an illicit process of the major. Again, the conclusion must be particular, whether the syllogisms be affirmative or negative. The minor premise being affirmative, there cannot be a uniSPECIAL CANONS OF THE FIGURES. 153 versal affirmative conclusion without illicit minor. In a universal negative conclusion both terms are distributed: and they cannot both be distributed in the premises, unless both premises were negative, which could not be. In the fourth Figure, (1) In the negative moods, the major is universal. Some Z is not Y, Some Z is Y All Y is X, No Y is X could not yield even particular conclusions, without illicit process of the major. We should have to infer--Some X is not Z: and Z is undistributed in the premises in consequence of the particularity of the major. (2) If the major is affirmative, the minor is universal. A particular minor to an affirmative major would give All Z is Y, All Z is Y Some Y is X, Some Y is not X both forms containing undistributed middle. (3) If the minor is negative, both premises are universal. Try All Z is Y, Some Z is Y, Some Y is not X, No Y is X. There is, in the first form, undistributed middle; and in the second, the weakest conclusion, Some X is not Z, contains illicit process of the major. This rule is implied in the two preceding. By the First rule, the Major is universal, because the mood is negative. By the Second rule, the Minor is universal, because the major is affirmative. (4) If the minor is af...