Figure 3. In this figure, only particulars can be proved. It is frequently useful when we wish to take objection to a universal proposition laid down by an opponent by establishing an instance in which such universal proposition does not hold good.
It is the natural figure when the middle term is a singular term, especially if the other terms are general. It has been already shewn that if one and only one term of an affirmative proposition is singular, that term is almost necessarily the subject. For example, such a reasoning as Socrates is wise, Socrates is a philosopher, therefore, Some philosophers are wise, can only with great awkwardness be expressed in any figure other than figure 3.
Figure 4. This figure is seldom used, and some logicians have altogether refused to recognise it. We shall return to a discussion of it subsequently. See section [262].
Lambert in his Neues Organon expresses the uses of the different syllogistic figures as follows: “The first figure is suited to the discovery or proof of the properties of a thing; 317 the second to the discovery or proof of the distinctions between things; the third to the discovery or proof of instances and exceptions; the fourth to the discovery or exclusion of the different species of a genus.”
EXERCISES.
248. Why is IE an inadmissible, while EI is an admissible, mood in every figure of the syllogism? [L.]
249. What moods are good in the first figure and faulty in the second, and vice versâ? Why are they excluded in one figure and not in the other? [O.]
250. (i) Shew that O cannot stand as premiss in figure 1, as major in figure 2, as minor in figure 3, as premiss in figure 4.
(ii) Shew that it is impossible to have the conclusion in A in any figure but the first. What fallacies would be committed if there were such a conclusion to a reasoning in any other figure? [C.]
251. Two valid syllogisms in the same figure have the same major, middle, and minor terms, and their major premisses are subcontraries; determine—without reference to the mnemonic verses—what the syllogisms must be. [K.]
252. Prove, by general reasoning, that any mood valid both in figure 2 and in figure 3 is valid also in figure 1 and in figure 4. [C.]