17(5

LOGIC.

ferent moods of syllogism ; and he who thinks it worth whileto construct so many in the first figure, always rememberingthat the middle term of each must be the predicate of themajor anti the subject of the minor proposition, will easilydiscern what number of these moods are legitimate, and givetrue conclusions.

Besides the rules which are proper to each figure,Aristotle has given some which are common to all, by whichthe legitimacy of syllogism may be tried. These are re-duced to five : 1st. There must be only three terms in a syllo-gism : as every r term occurs in two of the propositions, itmust he precisely the same in both, if not, the syllogism issaid to have four terms, which renders it vicious. 2d. Themiddle term must he taken universally in one of the pre-mises. 3d. Both premises must not be particular propositions,nor both negative. 4th. The conclusion must be particular,if either of the premises be particular; and negative, ifeither of the premises he negative. 5th. No term can betaken universally in the conclusion, if not taken universallyin the premises.

For understanding the 2d and 5th of these rules, it isnecessary to observe, that a term is said to be taken uni-versally, not only when it is the subject of an universalproposition, but also when it is the predicate of a negativeproposition. On the other hand, a term is said to be takenparticularly, when it is neither the subject of a particular,nor the predicate of an affirmative proposition.

There are also various other divisions of syllogism, regu-lated according to mood and figure; hut as the precedingrequire the most notice, they shall suffice; and we nowproceed to

Part V.— Induction, which is that portion of rationalphilosophy, of which the wonder and admiration of theancient and modern world, the divine Socrates , made soadmirable a use in the developement of moral truth, andthereby explained divine things. We commence by ob-serving, that all reasoning ultimately proceeds from firstTruths, either taken self-evidently, i.e. for granted; andthe first truths of all syllogistic reasonings are also generalpropositions. Except in mathematics and the sciencesconversant about mere ideas, which have no immediaterelation to things: without the mind, we cannot assumeas truths propositions which are general. A mathematician,indeed, may be considered as taking his ideas from thebeginning in their general form. Every proposition com-posed of such ideas is general; and those which are theo-