SYLLOGISM, in logic, an argument or term of reasoning, consisting of three pro positions ; the two first of which are called premises, and the last the conclusion. Syl logisms are nothing but the expressions of our reasonings, reduced to form and me thod : and hence, as every act of reasoning implies three several judgments, so every syllogism must include three distinct pro positions. Thus, in the following syllo. gism : Every creature possessed of reason and liberty is accountable for his action. Man is a creature possessed of reason and liberty : Therefore man is accountable for his ac tions.
We may observe that there are three several propositions, expressing the three judgments implied in the act of reasoning? the two first propositions answer the two previous judgments in reasoning, and are hence called premises ; as being placed be fbre the other, which is termed the con clusion. We are also to remember, that the terms expressing the two ideas whose relation we inquire after, as here, " man" and " accountahleness," are in general called the extremes ; and that the inter mediate idea, by means of which the agreement or disagreement of the two ex tremities is traced, viz. " a creature pos sessed of reason and liberty," takes the name of the middle term. Hence, by the premises of a syllogism, we are always to understand the two propositions, where the middle term is severally compared to the two extremes ; for these constitute the the previous judgments, whence the truth we are in quest of, is by reasoning dedu ced. The conclusion is, that other propo sition, in which the extremes themselves are joined or separated, agreeably to what appears upon the above comparison. As, therefore, the conclusion is made up of the extreme terms of the syllogism ; so that extreme, which serves as the predicate of the conclusion, goes by the name of the major term ; and the other term, or sub ject of the conclusion, is called the minor term. From this distinction of the ex tremes arises also a distinction between the premises ; that proposition, which compares the greater extreme with the middle term being called the major propo sition; and the other, where the lesser ex treme is compared with the middle term, being called the minor proposition. In a
single act of reasoning, the premises of the syllogism must be self-evident truths, otherwise the conclusion could not follow. For instance, in the major of the above mentioned syllogism, viz. "every creature possessed of reason and liberty is accoun table for his actions," if the connection between the subject and predicate could not be perceived by a bare attention to the ideas themselves, the proposition would require a proof itself ; in which case, a new middle term must be sought for, and a new syllogism formed to prove the said gra*: and should it so happen, that in this second essay there was still some proposition, whose truth did not appear at first sight, recourse must be had to a third syllogism to prove it. And when, by con ducting our thoughts in this manner, we at last arrive at some syllogism, where the premises or previous propositions are in tuitive, or self-evident truths, the mind then rests in full security, as perceiving that the several conclusions it has passed through, stand upon the immoveable foun dation of self-evidence, and when traced to their source, terminate in it. The great art lies, in so adjusting our syllogisms to one another, that the propositions seve rally made use of as premises, may be manifest consequences of what goes be fore, so as to form one connected demon stration.
With respect to the different forms or figures of syllogisms, it frequently hap pens that the middle term is the subject of the major term, and the predicate of the minor ; but though this disposition of the middle term be the most natural and obvious, it is not, however, necessary ; since the middle term is often the subject of both the premises, or the predicate in both ; and sometimes it is the predicate in the major, and the subject in the minor proposition. Now this variety in the or der and disposition of the middle term, constitutes what logicians call the forms or figures of syllogism.
But besides this distinction of syllo gisms into different figures, there is also a further subdivision of them in every figure, called modes, or moods. See