366. “All scientific persons are willing to learn; all unscientific persons are credulous; therefore, some who are credulous are not willing to learn, and some who are willing to learn are not credulous.”
Shew that the ordinary rules of immediate and mediate inference justify this reasoning; but that a certain assumption is involved in thus avoiding the apparent illicit process. Shew also that, accepting the validity of obversion and simple conversion, we have an analogous case in any inference of a particular from a universal, [J.]
367. An invalid syllogism of the second figure with a particular premiss is found to break the general rules of the syllogism in this respect only, that the middle term is undistributed. If the particular premiss is false and the other true, what do we know about the truth or falsity of the conclusion? [K.]
368. A syllogism is found to offend against none of the syllogistic rules except that with two affirmative premisses it has a negative conclusion. Determine the mood and figure of the syllogism. [K.]
412 369. Given two valid syllogisms in the same figure in which the major, middle, and minor terms are respectively the same, shew, without reference to the mnemonic verses, that if the minor premisses are contradictories, the conclusions will not be contradictories. [K.]
370. Find two syllogisms, having neither strengthened premisses nor weakened conclusions, and having M and N respectively as their middle terms, which satisfy the following conditions: (a) their conclusions are to be subcontraries; (b) their premisses are to prove that Some M is N, and to be consistent with the fact that Some M is not N. [J.]
371. Is it possible that there should be two syllogisms having a common premiss such that their conclusions, being combined as premisses in a new syllogism, may give a universal conclusion? If so, determine what the two syllogisms must be. [N.]
372. Three given propositions form the premisses and conclusion of a valid syllogism which is neither strengthened nor weakened. Shew that if two of the propositions are replaced by their contra-complementaries, the argument will still be valid, provided that the proposition remaining unaltered is either a universal premiss or a particular conclusion. [J.]
373. A certain proposition stands as minor premiss of a syllogism in the second figure whose major term is X. The same proposition stands also as major premiss of a syllogism in the third figure whose minor term is Y. If the given syllogisms are both formally and materially correct, shew how in every case we may conclude syllogistically that “some Y is not X” [J.]
374. Find out the valid syllogisms that may be constructed without using a universal premiss of the same quality as the conclusion.
Shew how these syllogisms may be directly reduced to one another; and represent diagrammatically the combined information that they yield, on the supposition that they have the same minor, middle, and major terms respectively. [J.]
375. Express the exact information contained in the two propositions, All S is M, All M is P, by means of (1) two propositions having S and not-S respectively as subjects; (2) two propositions having M and not-M respectively as subjects; (3) two propositions having P and not-P respectively as subjects. [K.]