(24) Illustrate the three mathematical axioms which the canons suggest. =12. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.= (1) Give an illustration of a valid conclusion being drawn from four terms. (2) Explain by circles the foregoing. (3) From three different business transactions, select the middle term of comparison. (4) Why should not those who are given to much which is argumentative, speak in syllogistic terms? (5) “He is a man of high ideals, and you know him to be strictly honest, therefore you have no excuse for not voting for him.” Recast this quotation with a view of making a logical syllogism. (6) Show by circles that there may be a vital difference between a _syllogism_ of three terms and an _equation_ of three terms. (7) Indicate by illustration that in conversational argumentation the minor premise naturally comes first. (8) Show by circles the meaning of “indeterminate conclusion.” (9) Rule five states that no conclusion can be drawn from two negatives. Defend this rule in connection with the following syllogism, which seems to contain a valid conclusion: Any statement which is not true cannot be accepted, This statement is not true, ∴ It cannot be accepted. (10) If the conclusion is particular, must one premise be particular? Explain. CHAPTER 12. FIGURES AND MOODS OF THE SYLLOGISM. =1. THE FOUR FIGURES OF THE SYLLOGISM.= By a figure of a syllogism is meant some particular arrangement of the three terms in the two premises. The conclusion is eliminated from this discussion, because in it the arrangement of the terms is constant, the major term always being used as the predicate of the conclusion and the minor as the subject. Using the symbols M, G and S, we find that there are four possible arrangements and, therefore, but _four figures_. These may be represented as follows: First Second Third Fourth figure figure figure figure M ― G G ― M M ― G G ― M S ― M S ― M M ― S M ― S ――――― ――――― ――――― ――――― S ― G S ― G S ― G S ― G No matter what the syllogism, if it is to be proved “_logical_,” it should be made to fit one of the four figure-types. To be sure, it may fit the figure without being logical, but it cannot be strictly logical without fitting the figure. The following valid syllogisms conform to the four figures as will be seen by the symbolized terms: M G First figure: All men are mortal, S M Socrates is a man, S G ∴ Socrates is mortal. M ― G S ― M ――――― S ― G