Integument

“ In Deductive proof, this is done by the major premise of every syllogism: if the major says that 'All fat men are humorists,' and we can establish the minor, 'X is a fat man,' we have secured the essential [Pg 308] resemblance that carries the conclusion. In induction, the Law of Causation and its representatives, the Canons, serve the same purpose, specifying the essential marks of a cause. But, in Analogy, the resemblance relied on cannot be stated categorically. ”

“ There remains a third improper use of the term Induction, which it is of real importance to clear up, because the theory of Induction has been, in no ordinary degree, confused by it, and because the confusion is exemplified in the most recent and elaborate treatise on the inductive philosophy which exists in our language. The error in question is that of confounding a mere description, by general terms, of a set of observed phenomena, with an induction from them. ”

“ In various languages, too, we find relics of ancient modes of thought in the simplest words and expressions used for arithmetical calculations. Words and phrases for this purpose are frequently found to be derived from the words for hands, feet, fingers, and toes, just as clearly as in our own language some of our simplest measures of length are shown by their names to have been measures of parts of the human body, as the cubit, the foot, and the like, and therefore to date from a time when exactness was not required. ”

“ Now, Induction is mainly a process for finding the causes of effects: and in attempting to fathom the mode of tracing causes and effects in physical science, I soon saw that in the more perfect of the sciences, we ascend, by generalization from particulars, to the tendencies of causes considered singly, and then reason downward from those separate tendencies, to the effect of the same causes when combined. I then asked myself, what is the ultimate analysis of this deductive process; the common theory of the syllogism evidently throwing no light upon it. ”

“ But is there any thing of the nature of an induction in this process? Did he infer any thing that had not been observed, from something else which had? Certainly not. He had observed the whole of what the proposition asserts. That the land in question is an island, is not an inference from the partial facts which the navigator saw in the course of his circumnavigation; it is the facts themselves; it is a summary of those facts; the description of a complex fact, to which those simpler ones are as the parts of a whole. ”

“ Again, each body, and each point of a body, must occupy some place or position among other bodies; and the position of two bodies relatively to each other, of whatever nature the bodies be, may be unerringly inferred from the position of each of them relatively to any third body.
In the laws of number, then, and in those of space, we recognise, in the most unqualified manner, the rigorous universality of which we are in quest. Those laws have been in all ages the type of certainty, the standard of comparison for all inferior degrees of evidence. ”

“ The word Analogy, as the name of a mode of reasoning, is generally taken for some kind of argument supposed to be of an inductive nature, but not amounting to a complete induction. There is no word, however, which is used more loosely, or in a greater variety of senses, than Analogy. It sometimes stands for arguments which may be examples of the most rigorous induction. Archbishop Whately, for instance, following Ferguson and other writers, defines Analogy conformably to its primitive acceptation, that which was given to it by mathematicians: Resemblance of Relations. ”

“ Observation and Abstraction, the operations which formed the subject of the two foregoing chapters, are conditions indispensable to induction; there can be no induction where they are not. It has been imagined that Naming is also a condition equally indispensable. There are thinkers who have held that language is not solely, according to a phrase generally current, an instrument of thought, but the instrument; that names, or something equivalent to them, some species of artificial signs, are necessary to reasoning; that there could be no inference, and consequently no induction, without them. ”

“ Induction infers a rule. Now, the belief of a rule is a habit. That a habit is a rule active in us, is evident. That every belief is of the nature of a habit, in so far as it is of a general character, has been shown in the earlier papers of this series. Induction, therefore, is the logical formula which expresses the physiological process of formation of a habit. Hypothesis substitutes, for a complicated tangle of predicates attached to one subject, a single conception. ”

“ The induction which proceeds by simple enumeration is puerile, leads to uncertain conclusions, and is exposed to danger from one contradictory instance, deciding generally from too small a number of facts, and those only the most obvious. But a really useful induction for the discovery and demonstration of the arts and sciences, should separate nature by proper rejections and exclusions, and then conclude for the affirmative, after collecting a sufficient number of negatives. ”

“ At any one of these steps of Induction in the Table, the inductive proposition is a Theory with regard to the Facts which it includes, while it is to be looked upon as a Fact with respect to the higher generalizations in which it is included. In any other sense, as was formerly shown, the opposition of Fact and Theory is untenable, and leads to endless perplexity and debate. ”

“ The geometer, with his one definite figure before him, knows perfectly that his thoughts apply to countless other figures as well, and that although he sees lines of a certain special bigness, direction, color, etc., he means not one of these details. When I use the word man in two different sentences, I may have both times exactly the same sound upon my lips and the same picture in my mental eye, but I may mean, and at the very moment of uttering the word and imagining the picture, know that I mean, two entirely different things. ”

“ The Methods of Induction which are treated of in this and the preceding chapter, and which are specially applicable to causes governed by relations of Quantity or of Resemblance, commonly lead us to Laws of Phenomena only. Inductions founded upon other ideas, those of Substance and Cause for example, appear to conduct us somewhat further into a knowledge of the essential nature and real connexions of things. ”

“ Induction, then, is that operation of the 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 in similar circumstances at all times. ”

“ Distinguish between induction as a mode of inference and induction as a method.
(7) State and explain the law of universal causation. Illustrate fully.
(8) Make evident that a cause may involve many antecedents.
(9) State and explain by illustration the law of uniformity of nature.
(10) Verify by illustration the notion that the “fact of causation” conditions all induction.
(11) Which of the two laws is empirical, “causation” or “uniformity”? Why?
(12) Show that induction is a form of thinking.
(13) Why should the law of uniformity of nature convince man that nature is honest? ”

“ The truths of geometry are summed up and embodied in its definitions and axioms.... Let us turn to the axioms, and what do we find? A string of propositions concerning magnitude in the abstract, which are equally true of space, time, force, number, and every other magnitude susceptible of aggregation and subdivision. Such propositions, where they are not mere definitions, as some of them are, carry their inductive origin on the face of their enunciation.... ”

“ No such assurance, however, can be had, on any of the ordinary subjects of scientific inquiry. Popular notions are usually founded on induction by simple enumeration; in science it carries us but a little way. ”

“ Nature of Induction.—Induction is described as a process of reasoning in which the mind arrives at a conclusion by an examination of particular cases, or judgments. A further distinguishing feature of the inductive process is that, while the known judgments are particular in character, the conclusion is accepted as a general law, or truth. As in deduction, the reasoning process arises on account of some difficulty, or problem, presented to the mind, as for example:
What is the effect of heat upon air? ”

“ To begin with the conditions of direct Induction.—An Induction is an universal real proposition, based on observation, in reliance on the uniformity of Nature: when well ascertained, it is called a Law. ”

“ The process of reasoning by which we discover such laws is called induction. As we can seldom be sure that we have apprehended all the related facts, it is clear that our inductions must generally be incomplete. ”

“ Now, when we study the structure of the human body, we look upon it first as a symmetrical whole, then we separate it into its largest, most distinct members,—the head, the trunk, the arms, the legs. After we have noted the relations of these parts, we take up each part as a whole and proceed again in the same way. In analyzing sentences we shall pursue the same method.
Every sentence is a unit just as the body is; like the body, too, it is made up of smaller units. In studying its structure we should first of all find the units which compose the sentence-unit. ”

“ When, from the observation of a number of individual instances, we ascend to a general proposition, or when, by combining a number of general propositions, we conclude from them another proposition still more general, the process, which is substantially the same in both instances, is called Induction. ”

“ But when I abstract from all determinateness of the angles and of their sides, no angles and sides of any kind remain as given objects, and hence nothing remains as object of my observation, or—if you denominate the observation of a given and actual exclusively perception, as I believe you do—no perception of any kind remains. ”

“ As has been already pointed out, this is all that art can do. To test a generalization, by showing that it either follows from, or conflicts with, some stronger induction, some generalization resting on a broader foundation of experience, is the beginning and end of the logic of Induction. ”

“ There are two general ways of obtaining our basis for the process of Inductive Reasoning. One of these is called Perfect Induction and the other Imperfect Induction. Perfect Induction is possible only when we have had the opportunity of examining every particular object or thing of which the general idea is expressed. For instance, if we could examine every fish in the universe we would have the basis of Perfect Induction for asserting the general truth that "all fishes are cold-blooded." ”

“ It needs scarcely be observed, that general propositions of which no one can tell exactly what they assert, can not possibly have been brought to the test of a correct induction. Whether a name is to be used as an instrument of thinking, or as a means of communicating the result of thought, it is imperative to determine exactly the attribute or attributes which it is to express; to give it, in short, a fixed and ascertained connotation. ”

“ In the common or Syllogistic Logic, a certain Formula of language is used in stating the reasoning, and is useful in enabling us more readily to apply the Criterion of Form to alleged demonstrations. This formula is the usual Syllogism; with its members, Major Premiss, Minor Premiss, and Conclusion. It may naturally be asked whether in Inductive Logic there is any such Formula? whether there is any standard form of words in which we may most properly express the inference of a general truth from particular facts? ”

“ Just as in a syllogism we show that a part is contained in the whole, so in induction we show that a part is illustrated by the whole. It seems that every single fact contains many truths, but induction establishes their universality. A single brain contains all the truths of phrenology, a single stone includes the phenomena of gravitation, the temperance of a single individual exhibits the whole law of moderation, but we learn the universality of these truths by induction. ”

“ The statement, that the uniformity of the course of nature is the ultimate major premiss in all cases of induction, may be thought to require some explanation. The immediate major premiss in every inductive argument, it certainly is not. ”

“ A topic is taken, and without reference to the order of time or the words of the text, is unfolded as a proposition in Geometry—each thought being preliminary to that which follows, and the whole ending in the demonstration of some great truth, and the deduction of its legitimate corollaries. ”

“ The parts of the rational explanation or notion, into which that notion is divided, are prior to the notion, at least in some instances. But the notion of a right angle is prior to that of an acute angle or is one of the elements into which the notion of an acute angle is divided; for you cannot define an acute angle without introducing the right angle into your definition, nor can you define the semicircle without introducing the circle, nor the finger without introducing the man — the finger being such and such a part of the man. ”