convertible terms) it is no matter which is
made the subject, and which the predicate,
e. g. "a good government is that which has
the happiness of the governed for its object;"
if this be a right definition, it will follow that
"a government which has the happiness of
the governed for its object is a good one."
Most propositions in mathematics are of this
description: e. g.

"All equilateral triangles are equiangular;" and
"All equiangular triangles are equilateral."

CHAP. III.-Of Arguments.

§ 1.

The third operation of the mind, viz. reasoning, (or discourse) expressed in words, is argument; and an argument stated at full length, and in its regular form, is called a syllogism: the third part of Logic therefore treats of the syllogism. Every Argument* Syllogism.

* I mean, in the strict technical sense; for in popular use the word Argument is often employed to denote the latter of these two parts alone: e.g. "This is an Argument to prove so and so;" "this conclusion is established by the Argument:" i. e. Premises.-See Appendix, No. I. art. Argument.

consists of two parts; that which is proved; and that by means of which it is proved: the former is called, before it is proved, the question; when proved, the conclusion (or inference ;) that which is used to prove it, if stated last (as is often done in common discourse,) is called the reason, and is introduced by "because," or some other causal conjunction; (e. g. Cæsar deserved death, because he was a tyrant, and all tyrants deserve death." If the conclusion be stated last (which is the strict logical form, to which all Reasoning may be reduced) then that which is employed to prove it is called the premises,* and the Conclusion is then introduced by some illative conjunction, as "therefore," e. g.

"All tyrants deserve death:

Cæsar was a tyrant;

therefore he deserved death."+

* Both the premises together are sometimes called the antecedent.

+ It may be observed that the definition here given of an argument is in the common treatises of logic laid down as the definition of a syllogism; a word which I have confined to a more restricted sense. There cannot evidently be any argument, whether regularly or irregularly expressed, to which the definition given by Aldrich, for instance, would not apply; so that he appears to employ "syllogism" as synonymous with "argument." But besides that it is clearer and more convenient, when we have these two words at hand, to employ them in the two senses respectively which we want to express, the truth

Argument.

Since, then, an argument is an expression Definition of in which " from something laid down and granted as true (i. e. the Premises) something else (i. e. the Conclusion) beyond this must be admitted to be true, as following necessarily (or resulting) from the other; and since Logic is wholly concerned in the use of language, it follows that a Syllogism (which is an argument stated in a regular logical form) must be "an argument so expressed, that the con- Definition of clusiveness of it is manifest from the mere force of the expression," i. e. without considering the meaning of the terms: e. g. in this syllogism," Y is X, Z is Y, therefore Z is X:" the conclusion is inevitable, whatever terms X, Y, and Z, respectively are understood to stand for. And to this form all legitimate arguments may ultimately be brought.

is, that in so doing I have actually conformed to Aldrich's practice for he generally, if not always, employs the term syllogism in the very sense to which I have confined it: viz. to denote an argument stated in regular logical form; as, e. g. in a part of his work (omitted in the late editions) in which he is objecting to a certain pretended syllogism in the work of another writer, he says, " valet certe argumentum; syllogismus tamen est falsissimus," &c. Now (waiving the exception that might be taken at this use of "falsissimus," nothing being, strictly, true or false, but a proposition) it is plain that he limits the word ["syllogism" to the sense in which it is here defined, and is consequently inconsistent with his own definition of it.

Syllogism.

Aristotle's dictum.

§ 2.

The rule or axiom (commonly called “dictum de omni et nullo") by which Aristotle explains the validity of this argument, is this: "whatever is predicated of a term distributed, whether affirmatively or negatively, may be predicated in like manner of every thing contained under it." Thus, in the examples above, X is predicated of Y distributed, and Z is contained under Y (i. e. is its subject;) therefore X is predicated of Z: so "all tyrants," &c. (p. 74.) This rule may be ultimately applied to all arguments; (and their validity ultimately rests on their conformity thereto) but it cannot be directly and immediately applied to all even of pure categorical syllogisms; for the sake of brevity, therefore, some other axioms are commonly applied in practice, to avoid the occasional tediousness of reducing all syllogisms to that form in which Aristotle's dictum is applicable.*

Instead of following Aldrich's arrangement, in laying down first the canons which apply to all the figures of categorical syllogisms, and then going back to the "dictum of Aristotle" which applies to only one of them, I have pursued what appears a simpler and more philosophical arrangement, and more likely to impress on the learner's mind a just view of the science; viz. 1st. to give the rule (Aristotle's dictum) which applies to the

We will speak first of pure categorical syllogisms; and the axioms or canons by which their validity is to be explained: viz. first, if two terms agree with one and the same third, they agree with each other: secondly, if one term agrees and another disagrees with one and the same third, these two disagree with each other. On the former of these canons rests the validity of affirmative conclusions; on the latter, of negative: for no categorical syllogism can be faulty which does not violate these canons; none correct which does: hence on these two canons are built the rules or cautions which are to be observed with respect to syllogisms, for the purpose of ascertaining whether those canons have been strictly observed or not.

1st. Every syllogism has three, and only three terms: viz. the middle term, and the two terms (or extremes, as they are commonly called) of the Conclusion or Question. Of

most clearly and regularly-constructed argument, the Syllogism in the first figure, to which all reasoning may be reduced; then the canons applicable to all categoricals; then, those belonging to the hypotheticals; and lastly, to treat of the Sorites; which is improperly placed by Aldrich before the hypotheticals. By this plan the province of strict Logic is extended as far it can be; every kind of argument which is of a syllogistic character, and accordingly directly cognizable by the rules of logic, being enumerated in natural order.