It was fully explained by Aristotle, that the simplest case of Ratiocination consists of three propositions, which he called a syllogism. A piece of ratiocination may consist of one, or more syllogisms, to any extent; but every single step is a syllogism.
A ratiocination, then, or syllogism, is first resolved into three propositions. The following may be taken as one of the simplest of all examples. “All men are animals: kings are men: therefore kings are animals.”
Next, the Proposition is resolved into its proximate elements. These are three; two Terms, one called the Subject, the other the Predicate, and the Copula. 425 What is the particular nature of each of these elements we have already seen, and here, therefore, need not stay to inquire.
The ancient writers on Logic proceeded in their analysis, no farther than Terms. After this, they only endeavoured to enumerate and classify terms; to enumerate and classify propositions; to enumerate and classify syllogisms; and to give the rules for making correct syllogisms, and detecting incorrect ones. And this, as taught by them, constituted the whole science and art of Logic.
What, under this head, we propose to explain, is—the process of association involved in the syllogism, and in the belief which is part of it.
That part of the process which is involved in the two antecedent propositions, called the premises, has been already explained. It is only, therefore, the third proposition, called the conclusion, which further requires exposition.
We have seen, that in the proposition, “All men are animals,” Belief is merely the recognition that the meaning of the term, “all men,” is included in that of the term “animals,” and that the recognition is a case of association. In the proposition also, “kings are men,” the belief is merely the recognition, that the individuals named “kings,” are part of the many, of whom “men,” is the common name. This has already been more than once explained. And now, therefore, remains only to be shewn what further is involved in the third proposition, or conclusion, “kings are animals.”
In each of the two preceding propositions, two terms or names are compared. In the last 426 proposition, a third name is compared with both the other two; immediately with the one, and, through that, with the other; the whole, obviously, a complicated case of association.
In the first proposition, “all men are animals,” the term, “all men,” is compared with the term animals; in other words, a certain association, already expounded, takes place. In the second proposition, “kings are men,” the term “kings,” is compared with the term “all men;” comparison here, again, being only a name for a particular case of association. In the third proposition, “kings are animals,” the name “kings,” is compared with the name “animals,” but mediately through the name, “all men.” Thus, “kings,” is associated with “all men,” “all men,” with “animals;” “kings,” therefore, with “animals,” by a complicated, and, at the same time, a rapid, and almost imperceptible process. It would be easy to mark the steps of the association. But this would be tedious, and after so much practice, the reader will be at no loss to set them down for himself.[109]
[109] This chapter, which is of a very summary character, is a prolongation of the portion of the chapter on Belief, which examines the case of belief in the truth of a proposition; and must stand or fall with it. The question considered is, how, from belief in the truth of the two premises of a syllogism, we pass into belief in the conclusion. The exposition proceeds on the untenable theory of the import of propositions, on which I have so often had occasion to comment. That theory, however, was not necessary to the author for shewing how two ideas may become inseparably associated through the inseparable association of each of them with a third idea: and inasmuch as an inseparable association between the subject and 427 predicate, in the author’s opinion, constitutes belief, an explanation of ratiocination conformable to that given of belief follows as a matter of course.