280. Prove, from the general rules of the syllogism, that the number of possible moods, irrespective of difference of figure, is 11.
In the 19 moods of the mnemonic verses, only 10 out of the possible 11 moods are represented. Find the missing mood, and account for its absence from the verses. [L.]
281. Given
(1) the conclusion of a syllogism in the first figure,
(2) the minor premiss of a syllogism in the second figure,
(3) the major premiss of a syllogism in the third figure,
340 examine in each case how far the quality and quantity of the two remaining propositions of the syllogism can be determined (it being given that the syllogism does not contain a strengthened premiss or a weakened conclusion).
Express the result, as far as possible, in general terms in each figure. [J.]
282. Find out in which of the valid syllogistic moods the combination of one premiss with the subcontrary of the conclusion would establish the subcontrary of the other premiss. [L.]
283. Construct a syllogism in accordance with each of the following two dicta:—
(1) Any object that is found to lack a property known to belong to all members of a class must be excluded from that class;
(2) If any objects that have been included in a class are found to lack a certain property, then that property cannot be predicated of all members of the class.
Assign the mood and figure of each argument, and shew the relations between the above dicta and the dictum de omni et nullo. [L.]
284. Shew that any given mood may be directly reduced to any other mood, provided (1) that the latter contains neither a strengthened premiss nor a weakened conclusion, and (2) that if the conclusion of the former is universal, the conclusion of the latter is also universal [K.]
285. Shew that any given mood may be directly or indirectly reduced to any other mood, provided that the latter has not either a strengthened premiss or a weakened conclusion, unless the same is true of the former also. [K.]
286. Examine the following statement of De Morgan’s:—“There are but six distinct syllogisms. All others are made from them by strengthening one of the premisses, or converting one or both of the premisses, where such conversion is allowable; or else by first making the conversion, and then strengthening one of the premisses.” [K.]
287. Shew, by the aid of the process of indirect reduction, that the special rules for Figure 4 given in section [244] are mutually deducible from one another. [RR.]