SYLLOGISM (ervSsleryfonor). Tho object and character of logic are explained tinder the word OM:AXON; the position of this article in the pravent work is explained in Loons Every sentence in which different assertions are combined to produce another and a final assertion, is either a syllogism, a collection of syllogisms, or a mass of words with-1 out mauling ; and when we separate the constituent assertions, and write the whole under the forms of logic, we are not thereby ceasing to consider the sentenco which contains those assertions, or, as many fancy, dealing with a new species of ratiocination. All that is called reasoning, and which cannot be made syllogistic, is not reasoning at all ; and all which cannot easily be made syllogistic, is obscure ; for the syllogism is the simple form in which the act of reasoning is an act of intuition.
Aristotle defines syllogism thus : "Syllogism is speech' or language in which certain things being assumed, something different from what is assumed results by virtue of the assumption; and, by virtue of the assumption, I mean it results through the assumption ; and, by ' through the assumption' I mean that no external term is required in order to there being a necessary result." (' Analyt. Prior.' i. 1.) So easy indeed is the deduction, when the premises are properly dis posed as preparatory to a syllogism, that many persons doubt the utility of the syllogism altogether. With these we are not now arguing ; we shall only observe that he must be fortunate in the clearness of his mind, who, knowing the logical mode, is never obliged to have recourse to it to destroy ambiguity or heighten evidence ; and particularly so in his opponents, who, in verbal or written controversy, never finds it necessary to employ it in trying their arguments. The syllogism is the instrument of self-examination, and the weapon of last resort in dis pute; and a bad syllogism, with one of the premises implied only, and not expressed, is the first resource of fallacy ; which last is sometimes even allowed to remain unrefuted, by neglect of placing it in a logical form. To bring forward the suppressed premiss is the visible destruc tion of every such argument which is logically bad. As an instance, take the following in a letter from Cardan to Tartalea : " Neither am I moved with envy, for if you are either equal to, or less thou myself, I have no cause for it ; and, if you be greater in this art, I ought to endeavour to equal you, and not to speak evil of you." This is meant for reasoning, and there are two syllogisms with suppressed premises, or rather two sorites (a term presently explained), with a suppressed premiss in each. In one case Cardan assumes that be does not envy
Tartalea because be need not ; in the other, that he does not because he ought to do otherwise : if he meant to assume and assert that he never did anything which he had no need to do, and always did every thing which he ought to do, his reasoning is logical ; but if he would have hesitated to make these assertions, he was then writing fallacy. In justice to Cordon's logic, however, it is but fair to say, that he was not the man to hesitate at either assertion. [CARDAN, in BIOG. Div.] Every sentence in which the conclusion is a necessary consequence of previous assertions contained in that same sentence, is a syllogism, provided that the conclusion be obtained from two distinct assertions, and two only. Thus, " Some As are Ds, for every 13 is A,' is not a syl logism, though logically true. [CONVERSE.) Every assertion may be reduced to one of four forms, the universal affirmative, the universal negative, the particular affirmative, and the particular negative. From these, by combination, all syllosisms are derived ; and the laws of combination, and the manner expressing them, constituted that branch of science which is now often turned into ridicule, particularly as to its notation, and the strange and uncouth words by which the species of syllogisms were denoted. The following letters always signify the several species of propositions :— A, the universal affirmative ; every x is Y. E, the universal negative ; uo x is Y.
1, the particular affirmative ; some Ns are Ys. 0, the particular negative ; some x s are not Y s.
Since every conclusion must be drawn from the comparison of two things with a third, a syllogism cousiste of two propositions, in each of which the same term occurs compared with another : this term is called the middle term. Thus, in Every v is x, Every z is Y, • Therefore Every z is x, Y, the subject of the first assertion, and the predicate of the second, is the middle term. The two first assertions are the premises, the third is the conclusion. The predicate of the conclusion is called the major term; the subject of the conclusion the minor term : and the major or minor premiss is that which contains the major or minor term of the conclusion. The major premiss is always written first.
The order of the terms in the premises and conclusiou must be either /V.