253. Shew, without individual reference to the different figures, that EAO is a strengthened syllogism in every figure, and that AAI is a strengthened syllogism whenever it is valid. [K.]
254. Shew, by general reasoning, that every valid syllogism in which the middle term is twice distributed contains a strengthened premiss. Does it follow that it must have also a weakened conclusion? [K.]
255. Shew that the following two rules would suffice as the special rules for the fourth figure: (i) The conclusion and major cannot have the same form unless it be particular affirmative; (ii) The conclusion and minor cannot have the same form unless it be universal negative. [J.]
CHAPTER III.
THE REDUCTION OF SYLLOGISMS.
256. The Problem of Reduction.—By reduction is meant a process whereby the reasoning contained in a given syllogism is expressed in some other mood or figure. Unless an explicit statement is made to the contrary, reduction is supposed to be to figure 1.
The following syllogism in figure 3 may be taken as an example:
| All M is P, | |
| Some M is S, | |
| therefore, | Some S is P. |
It will be seen that by simply converting the minor premiss, we have precisely the same reasoning in figure 1.