QUOTATIONS ON DEDUCTION.

APPENDIX K.

235. 1. From Fleming's Vocabulary of Philosophy, Ed. 1858, pp. 126-7.

Deduction (from deduco, to draw from, to cause to come out of,) is the mental operation which consists in drawing a particular truth from a general principle antecedently known. It is opposed to induction, which consists in rising from particular truths to the determination of a general principle. Let it be proposed to prove that Peter is mortal; I know that Peter is a man, and this enables me to say that all men are mortal, from which affirmation I deduce that Peter is mortal.

The syllogism is the form of deduction. Aristotle (Prior. Analyt., lib. 1, cap. 1) has defined it to be 66 an enunciation in which certain assertions being made, by their being true, it follows necessarily, that another assertion different from the first is true also."

Before we can deduce a particular truth, we must be in possession of the general truth. This may be acquired intuitively, as every change implies a cause; or inductively, as the volume of gas is in the inverse ratio of the pressure.

Deduction, when it uses the former kind of

truths, is demonstration or science. Truths drawn from the latter kind are contingent and relative, and admit of correction by increasing knowledge. The principle of deduction is, that things that agree with the same things agree with one another. The principle of induction is, that in the same circumstances, and in the same substances, from the same causes the same effects will follow.

The mathematical and metaphysical sciences are founded on deduction, the physical sciences rest on induction.

2. From Day's Elements of Logic, Ed. 1868, p. 105.

A Deductive Syllogism is a Mediate Reasoning in which the movement of Thought is from a Whole to a Part, mediated through a middle term, which is, respectively, a part of that whole and a whole of that part; as, Man is mortal; Caius is a man; therefore, Caius is mortal.

As the Deductive Syllogism is a Mediate Reasoning, its datum must consist of two Judgments, which, as given to Thought, are not of course at all validated by the Reasoning.

They must be regarded consequently as only assumed for the Reasoning, or must rest on evidence foreign to it. But the movement of Thought in itself may be valid, although the given Judgments are false; just as an arithmetical process may be correct, although applied to unreal objects.

3. From Bowen's Logic, Ed. 1874, pp. 261,

262.

Reasoning, however, proceeds not only in different wholes, but in different aspects of the same whole. We may, it is evident, regard any whole, considered as the complement of its parts, in either of two ways; for we may, on the one hand, look from the whole to the parts, and reason accordingly downwards; or, on the other hand, look from the parts to the whole they constitute, and reason accordingly upwards. The former of these reasonings is called Deductive, the latter Inductive. Deductive reasoning is founded on the maxim, 'What belongs to the containing whole belongs also to the contained parts;' Induction, on the contrary maxim,' What belongs to the constituent parts belongs also to the constituted whole.' Thus, in Deductive reasoning, the whole is stated first, and what is affirmed of it is affirmed of the parts it contains; in other words, a general law is laid down, and predicated of the particular instances to which it applies.

In Inductive reasoning, the parts are first stated, and what is predicated of them is also predicated of the whole they constitute; in other words, the particular instances are first 'stated as facts, and then the law they constitute is evolved.

4. From Hedge's Elements of Logick, Ed. 1854, pp. 118, 119.

Syllogism (=Deduction) and induction proceed in opposite directions. Induction. . begins with individual objects, as they exist in nature, and ascends by successive steps to the most general truths. Syllogism (=Deduction) begins where inductions terminates. It commences with

some universal proposition, and follows back the footsteps of the former process, transferring at each stage the predicate of the more general to the less general rank of beings; or, in other words, predicating the genus of the species, and the species of the individual.

Syllogism (=Deduction) is employed with advantage in communicating to others, in an exact and perspicuous manner, the general principles of science. It may also be used with success in exposing the weakness of arguments, stated in loose or figurative language. But it is of no service in helping us to the discovery of new truths. "We must know a thing first," Mr. Locke observes," and then we can prove it syllogistically"