ISBN: 9781154991840

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not … More...

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1900 edition. Excerpt: ...is false, and if one be false, the other is true,--that is, they are the two members of the disjunctive proposition ''Either A is B or A is C,'' or ''A is either B or C,'' in Ueberweg''s sense. (b) And from the two hypothetical may also be inferred the original disjunctive in Mill''s sense. The two hypothetical from the disjunctive, according to Mill, are--(1) If A is not C, A is B. (2) If A is not B, A is C. It has been already shown above that of the two propositions ''A is B'' and ''A is C,'' the falsity of the one implies the truth of the other--i.e., they are the two members of the disjunctive proposition ''A is either B or C'' in Mill''s sense. (c) Is it possible to infer immediately a disjunctive proposition from a single hypothetical 1 This is not possible in Ueberwegfs sense of a disjunctive. But this is possible of a disjunctive in Mill''s sense. From the hypothetical ''If A is B, A is C follows the disjunctive ''Either A is not B or A is C The proof is as follows:--(1) If A is B, A is C. By contraposing this we get, (2) If A is not C, A is not B. If ''A is C'' be false, ''A is not C is true by the Law of Excluded Middle; and.. from (2) ''A is not B'' is true. Again, if''A is not B'' be false, ''A is B'' is true by the same law; and.. from (1) ''A is C is true. Hence, of the two propositions ''A is C'' and ''A is not B,'' the falsity of the one implies the truth of the other. They are, therefore, the two members of the disjunctive proposition ''Either A is not B or A is C'' in Mill''s sense. Thus, a disjunctive in Mill''s sense can be inferred from a single hypothetical proposition; but this is not possible in Ueberweg''s sense of a disjunctive. Exercises. I. Distinguish the following disjunctive propositions from each other, and note the ambiguity, if any, in... P. K. Ray, Books, History, A Text-Book of Deductive Logic for the Use of Students Books>History <

ISBN: 9781154991840

P.K. Ray, Paperback, English-language edition, Pub by General Books LLC Books History~~General A-Text-Book-Of-Deductive-Logic-For-The-Use-Of-Students~~P-K-Ray General Books LLC