SYLLOGISM, a name expressing a principal branch or department of logic. When i we reason, or get at truth by means of inference, we are said to proceed either inductively (see INDUCTION) or deductively. Deductive reasoning, when fully and methodically expressed, takes the form called the syllogism. "This thing will sink in water, for it is a stone," is a deductive argument, but not fully stated; the complete form is: "Stones sink in water; this is a stone; therefore, this will sink in water"—which form is called a syllogism.
To a perfect syllogism it is necessary that there should be three, and no more than three, propositions (see PROPOSITION); these are the conclusion, or the matter to be proved, and two others that are the means of proving it, called the premises. It is also neces sary that there should be three, and no more than three, terms, namely, the subject and the predicate of the conclusion, and one, called the middle term, which must occur in both premises, being the connecting link for bringing the two other terms together in the conclusion. The predicate of the conclusion is called the major term, because it is in its scope the largest of the three; the subject of the conclusion is the minor term, as being the smallest in scope. The three terms enter into the premises in this manner: the major term and middle term make one premise, called the major premise; the middle term and the minor term make the minor premise. In the syllogism above stated, the terms are, "a thing that will sink in water" (major), "this thing" (minor), "stone" (middle); the premises are, "stones sink in water" (major), "this thing is a stone" (minor); the conclusion is, " this thing will sink in water." The form now given, although the regular and fundamental form to prove any affirm ative conclusion, is not the only form that an argument may assume. The totality of syllogistic forms is divided into figures, and each figure into moods, which are the dis tinct syllogistic forms, the principle of division being as follows: the figure is deter mined by the position of the middle term, which may be the subject of the major premise, and the predicate of the minor (1st figure), the predicate in both (2d figure), the subject in both (3d figure), the predicate of the major and the subject of the minor (4th figure).
The word "figure" is borrowed from rhetoric, where it means a departure from plain and ordinary speaking, as metaphor, hyperbole, etc. But, as remarked by Hamilton, _ only the last three of the foregoing enumeration should be called " figures. ' The first should be considered as embracing the regular forms of reasoning, and the others as properly figures—that is, forms more or less inverted, irregular, or unnatural, although still correctly representing reasonings that actually occur. These forms may be all reduced to forms in the 1st figure; their inversions or distortions being, as Hamilton would say, redressed, or restored to the primitive or fundamental type, namely, the syllo gisms of the 1st figure.
The 4th figure did not belong to the original scheme of Aristotle, and it is usually considered as both unnatural and unnecessary, being only an awkward inversion of the first. There would then be the natural or standard syllogisms (the 1st fig.), and two sets of figurative departures from them (2d and 3d figs.): The syllogisms of each figure are said to differ in mood, or according to the quality and the quantity of the propositions—that is, according as these are affirmative or nega tive (quality), universal or particular (quantity).
The entire scheme may be presented as follows: The symbols used are P (predicate of conclusion), major term; S (subject of conclusion), minor term; M, middle term. The general type of the first figure or standard is: 31 is P. S is M. S is P.
When the quality and the quantity of the propositions are expressed, there arise four syllogisms of.this form—two affirmative, and two negative: All 31 are P.