for this affirmed addition must be sought out of the proposition.

Analytic proofs correspond very nearly, but not exactly, to those denominated by Aristotle and Cicero intrinsic. They include, thus, the species of arguments enumerated by them from definition; from the relation of species and genus; from partition or enumeration of parts. They do not embrace, however, all those which are derived from things bearing some affinity to the matter of the proposition. Indeed, they take in but a part of one variety of this species, namely, that from conjugates or words derived from the same root.*

§ 131. Analytic proofs, being derived from the very terms of the proposition, need not, for any practical purpose of invention be further subdivided; the search being at once definitely directed and the weight and relation of all arguments of this class being indicated in the very nature of analytic proofs as such.

The terms of the proposition may be analyzed by partition or by division, and the character of the proof will vary in a certain respect with the nature of the proposition. But it is obviously of no importance how the analysis is made or what is the form of the proof thus obtained so far as it respects any purpose of invention.

§ 132. Analytic proofs carry with them the highest validity and force in all confirmation.

There can clearly be no higher or stronger proof than that which is contained in the very statement of the proposition. In this case, the proposition is only to be placed before the mind and assent is necessary. There may be need of proof of other kinds to show that the terms of the proposition actually contain the conceptions or truths on which the truth of the proposition depends. But these con

* See Cic. Top. 2-4.

ceptions being admitted to be there, the exhibition of them compels assent. In proving that the malicious setting fire to an outhouse whereby a dwelling is accidentally consumed is arson, it may be necessary to prove, by testimony or otherwise, that arson necessarily includes the idea of malice, the overt act of setting fire, the endangering of human life. But if these are admitted to be constituent ideas of the complex notion arson, the proof is conclusive.

§ 133. The principle of this most generic division of proofs into analytic and synthetic indicates the first step to be taken in the invention of arguments. It is, study carefully the terms of the proposition itself.

This is a fundamental and all-important rule in all confirmation. Many questions, not to say most that are controverted, are resolved at once by the explication of the meaning of the terms employed to express them. They are controverted only because the parties see them in different aspects. But even where the question is viewed in the same light, the explication of the meaning of the terms is often the effectual method of deciding the controversy. And where not, where synthetic proofs are requisite, the mind is, by the thorough examination of the question in all possible lights, furnished with the best helps and guides to invention.

§ 134. Synthetic proofs, being derived from without the proposition, are either such as are given by the mind itself acting under the necessary laws of its being, or such as are derived from without the mind.

The former species may be denominated INTUITIVE; the latter, EMPIRICAL proofs.

In demonstrating the truth of a mathematical proposition we can trace out the steps from the premise to the conclusion without aid from external proof. The diagrams

and numerical figures or alphabetical symbols which we often or generally make use of in mathematical reasoning, merely facilitate our mental operations. A Newton or a Pascal could reason out the theorem independently of such aids. In other words, the mind in this case intuitively perceives the connection between the subject and the predicate. And it matters not whether the reasoning be more or less simple or brief. No mere analysis of the terms of the proposition, however, can give the proof. The mind intuitively, necessarily, adds the predicate to the subject. The quotient of a b divided by a is seen unavoidably by every one so soon as he understands what is meant by the statement. Yet no mere analysis could give the proof. While they are therefore in their very nature distinguishable from analytic proofs, being apprehended at once by the mind, they may be denominated intuitive.

Empirical proofs, being derived from without the mind, come to it only through experience, and hence obtain their

name.

Intuitive, like analytic proofs, need no subdivision. They include among others all those proofs which constitute what are called in logic immediate reasonings, such as logical conversion of terms, restriction, transference of quality, hypothetical and disjunctive syllogisms.

§ 135. Intuitive, like analytic proofs, possess apodictic or demonstrative certainty.

Unless there be inaccuracy in the application of them, they must always compel assent. Hence, it would be entirely unnecessary for conviction to advance any other arguments, were it not that, in the first place, there may be suspicion of inaccuracy in the application of the proof; and, secondly, that the human mind has passions as well as intellectual powers, and in respect to both is subject to the laws of habit, and hence

"convinced against its will

Is of the same opinion still."

Hence the necessity of superadding other proofs; mainly that the native love of truth may have opportunity of rising by the contemplation of proof and triumphing over prejudice and aversion.

§ 136. Empirical proofs are divided into three general classes: I. ANTECEDENT PROBABILITY; II. SIGNS, III. EXAMPLES.

The grounds of this classification may be thus exhibited. The empirical is either substance or cause. Empirical proofs, consequently, are those which lie in those relations of thought which are proper to an object viewed as substance or those proper to an object viewed as cause. The essential relations proper to a substance are those of substance and attribute; those proper to a cause are cause and effect; attributes being logical parts of a substance-whole, and effects logical parts of a causal whole. Now as all the movements of thought are in the relations of wholes and parts, and as these movements lie in one or the other of the two coördinate relations, either between whole and part, or between part and complementary part, we have two general movements of thought, - the one between the whole and the part, called the deductive; the other between the part and complementary part, called the inductive. But under the general deductive movement we have two specific forms of thought, as we may think in either direction from the whole to the part or from the part to the whole. It is plain that if there is a whole there are parts, and if there is a part there is a whole of which it is a part. If, for instance, we can exhibit a whole - man as rational, we can exhibit it as proof that a part of that whole, say Hottentot, is rational. Or in the causal relation, if we can exhibit the sun as earth-illuminating, we can use that as proof that the sun must illuminate any part of the earth, as New Holland, that is turned towards the sun. We may likewise reason

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from a part to the whole; we may infer a substance, an aggregate of attributes from a single attribute recognized but as a part; or infer a cause from an effect, The existence of an attribute proves a substance; the existence of an effect proves a cause, We have thus under the general movement of thought between whole and part, a class of proofs which Aristotle denominated generally Signs. Further, we may infer from one part to another part, For example, if this magnet, being a part of a whole class of bodies called magnets, attract, this other magnet, which is also a part of the class, likewise attracts. This last class of proofs, from part to complementary part, Aristotle called Examples,

Inasmuch as there are but the two general forms of mediate reasonings mentioned, the deductive and the inductive, we can recognize but these two general classes of empirical proofs, each however admitting divers subdivisions.

Mediate reasonings are in Logic termed syllogisms. When fully expressed, they necessarily require two propositions called premises, which together constitute what is called the antecedent of the reasoning, and a third proposition, which is the consequent or conclusion; and there can be but these three propositions in any simple syllogism. The reason of this is, that in every mediate reasoning, in every syllogism, we attain the conclusion which asserts a relation between its terms its subject and predicate-only as we see a like relation between each of these terms and a third term. This relation between each of these terms and the third term respectively, is expressed in the two premises. But in discourse it is seldom necessary to set forth in form both of the premises, the other being readily supplied in thought. Thus in the syllogism or mediate reasoning, All magnets attract iron; this body is a magnet; therefore, this body attracts iron, either premise may remain unexpressed, as it would be sufficient to argue, This is a magnet; therefore, it attracts iron; or, All magnets attract iron; therefore, this body attracts iron. Every one would readily supply the suppressed