QUOTATIONS ON INDUCTION.

APPENDIX I.

233. 1. From Smith-Synonyms Discriminated-" Inference"-ed. 1878.

Inference (Lat. in, and ferre, to bring) is the broadest of these terms (see below), denoting any process by which from one truth or fact laid down or known we draw another. Inference may be either by induction or deduction, and hence may be probable or certain. Inference by induction is more or less probable, except where all cases of the kind have been collated, when it ceases, strictly speaking, to be inference, and is only the assigning of a common name, or stating an universal proposition. From having seen twenty swans all white, one might infer that all swans are so. This would be only a probability in itself, and, as a fact, not true. In induction we observe a sufficient number of individual facts or cases, and extending by analogy what is true of them to others of the same class, establish a general principle or law. This is the method of physical science. The process of deduction is the converse of this. We lay down a general truth, and connect a particular case with it by means of a middle term. When inference is

conducted by the syllogistic process, it is Deduction (Lat. deducere, to draw from), which, if rightly conducted, must be logically sound, though not necessarily true in fact. In a chain of reasoning the minor, subordinate, or less fully-expressed conclusions are called inferences, as distinguished from the great common inference or Conclusion, which terminates and establishes, or, as it were, shuts up (Concludere, to shut) the argument. A conclusion is a proposition viewed relatively to others from which it has been deduced. A Consequence (Lat. consequi, to follow) is a conclusion regarded as admitting of degrees of closeness or directness. Between the first stage of any argument and any particular consequence several links of reasoning may intervene. Hence the common phrase, 66 remote consequences, as meaning results which will follow sooner or later from what has been stated or conceded.

2. From Day's Elements of Logic, ed. 1868, p. 226.

The accepted characteristics of Induction

are:

(a) It is a process of Thought that is identical in essential character in all those movements of Intelligence which induce, which infer mediately otherwise than by deduction. There is but one Induction, as there is but one Deduction in all Thought.

(b) It is a reasoning, being a derivative Judgment, not a Concept; an inference from datum, implying a new proper Judgment-Cog

a

nition, not a mere synthesis of subjects or of predicates—that is, not a Concept.

(c) It is a mediate reasoning, being derived not from a single Judgment, but from a plurality of Judgments, related to each other under the relationship of part to complementary part in two of their terms which are alike related to the third or middle term as parts to a whole.

3. From Fleming's Vocabulary of Philosophy, ed. 1858, pp. 252-254.

Method or Process of Induction.—“ It has been said that Aristotle attributed the discovery of induction to Socrates, deriving the word from the Socratic accumulation of instances, serving as antecedents to establish the requisite conclusion."-Devey, Log., p. 151, note.

Induction is a kind of argument which infers, respecting a whole class, what has been ascertained respecting one or more individuals of that class.-Whately, Log., book ii., chap. 5, § 5.

"Induction is that operation of mind by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, induction is the process by which we conclude that what is true of certain individuals of a class, is true of the whole class, or that what is true at certain times will be true under similar circumstances at all times. Mill, Log., b. iii., ch. 2, § 1.

"Induction is usually defined to be the process of drawing a general rule from a sufficient number of particular cases; deduction is the

converse process of proving that some property belongs to the particular case from the consideration that it belongs to the whole class in which the case is found. That all bodies tend to fall towards the earth is a truth which we have ob tained from examining a number of bodies coming under our notice, by induction; if from this general principle we argue that the stone we throw from our hand will show the same tendency, we adopt the deductive method.

More exactly, we may define the inductive method as the process of discovering laws and rules from facts, and causes from effects; and the deductive, as the method of deriving facts from laws and effects from their causes. (Thomson, Outline of the Laws of Thought, 2d edit., pp. 321, 323.)

According to Sir William Hamilton (Discussions, p. 156), "Induction has been employed to designate three very different operations-1. The objective process of investigating particular facts, as preparatory to induction, which is not a process of reasoning of any kind. 2. A material illation of the universal from the singular, as warranted either by the general analogy of nature, or the special presumptions afforded by the object-matter of any real science. 3. A for

mal illation of the universal from the individual, as legitimated solely by the laws of thought, and abstract from the conditions of this or that particular matter.' The second of these is the inductive method of Bacon, which proceeds by way of rejections and conclusions, so as to arrive at

those axioms or general laws from which we infer by way of synthesis other particulars unknown to us, and perhaps placed beyond reach of direct examination. Aristotle's definition coincides with the third, and induction is an inference drawn from all the particulars' (Prior Analyt., ii., c. 23). The second and third have been confounded. But the second is not a logical process at all, since the conclusion is not necessarily inferrible from the premiss, for the some of the antecedent does not necessarily legitimate the all of the conclusion, notwithstanding that the procedure may be warranted by the material problem of the science or the fundamental principles of the human understanding. The third alone is properly an induction of Logic; for Logic does not consider things, but the general forms of thought under which the mind conceives them; and the logical inference is not determined by any relation of casuality between the premiss and the conclusion, but by the subjective relation of reason and consequence as involved in the thought."

"The Baconian or Material Induction proceeds on the assumption of general laws in the relations of physical phenomena, and endeavours, by select observations and experiments, to detect the law in any particular case. This, whatever be its value as a general method of physical investigation, has no place in Formal Logic. The Aristotelian or Formal Induction proceeds on the assumption of general laws of thought, and inquires into the instances in which, by such