Thus[5] in each inference made by Induction, there is introduced some General Conception, which is given, not by the phenomena, but by the mind. The conclusion is not contained in the premises, but includes them by the introduction of a New Generality. In order to obtain our inference, we travel beyond the cases which we have before us; we consider them as mere exemplifications of some Ideal Case in which the relations are complete and intelligible. We take a Standard, and measure the facts by it; and this Standard is constructed by us, not offered by Nature. We assert, for example, that a body left to itself will move on with unaltered velocity; not because our senses ever disclosed to us a body doing this, but because (taking this as our Ideal Case) we find that all 74 actual cases are intelligible and explicable by means of the Conception of Forces, causing change and motion, and exerted by surrounding bodies. In like manner, we see bodies striking each other, and thus moving and stopping, accelerating and retarding each other: but in all this, we do not perceive by our senses that abstract quantity, Momentum, which is always lost by one body as it is gained by another. This Momentum is a creation of the mind, brought in among the facts, in order to convert their apparent confusion into order, their seeming chance into certainty, their perplexing variety into simplicity. This the Conception of Momentum gained and lost does: and in like manner, in any other case in which a truth is established by Induction, some Conception is introduced, some Idea is applied, as the means of binding together the facts, and thus producing the truth.
[5] I repeat here remarks made at the end of the Mechanical Euclid, p. 178.
3. Hence in every inference by Induction, there is some Conception superinduced upon the Facts: and we may henceforth conceive this to be the peculiar import of the term Induction. I am not to be understood as asserting that the term was originally or anciently employed with this notion of its meaning; for the peculiar feature just pointed out in Induction has generally been overlooked. This appears by the accounts generally given of Induction. ‘Induction,’ says Aristotle[6], ‘is when by means of one extreme term[7] we infer the other extreme term to be true of the middle term.’ Thus, (to take such exemplifications as belong to our subject,) from knowing that Mercury, Venus, Mars, describe ellipses about the Sun, we infer that all Planets describe ellipses about the Sun. In making this inference syllogistically, we assume that the evident proposition, ‘Mercury, Venus, Mars, do what all Planets do,’ may be taken conversely, ‘All 75 Planets do what Mercury, Venus, Mars, do.’ But we may remark that, in this passage, Aristotle (as was natural in his line of discussion) turns his attention entirely to the evidence of the inference; and overlooks a step which is of far more importance to our knowledge, namely, the invention of the second extreme term. In the above instance, the particular luminaries, Mercury, Venus, Mars, are one logical Extreme; the general designation Planets is the Middle Term; but having these before us, how do we come to think of description of ellipses, which is the other Extreme of the syllogism? When we have once invented this ‘second Extreme Term,’ we may, or may not, be satisfied with the evidence of the syllogism; we may, or may not, be convinced that, so far as this property goes, the extremes are co-extensive with the middle term[8]; but the statement of the syllogism is the important step in science. We know how long Kepler laboured, how hard he fought, how many devices he tried, before he hit upon this Term, the Elliptical Motion. He rejected, as we know, many other ‘second extreme Terms,’ for example, various combinations of epicyclical constructions, because they did not represent with sufficient accuracy the special facts of observation. When he had established his premiss, that ‘Mars does describe an Ellipse about the Sun,’ he does not hesitate to guess at least that, in this respect, he might convert the other premiss, and assert that ‘All the Planets do what Mars does.’ But the main business was, the inventing and verifying the proposition respecting the Ellipse. The Invention of the Conception was the great step in the discovery; the Verification of the Proposition was the great step in the proof of the discovery. If Logic consists in pointing out the conditions of proof, the Logic of Induction must consist in showing what are the conditions of proof, in such inferences as this: but this subject must be pursued in the next chapter; I now speak principally of the act of 76 Invention, which is requisite in every inductive inference.
[6] Analyt. Prior. lib. ii. c. xxiii. Περὶ τῆς ἐπαγωγῆς.
[7] The syllogism here alluded to would be this:—
Mercury, Venus, Mars, describe ellipses about the Sun;
All Planets do what Mercury, Venus, Mars, do;
Therefore all Planets describe ellipses about the Sun.
[8] Εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β καὶ μὴ ὑπερτείνει τὸ μέσον.—Aristot. Ibid.
4. Although in every inductive inference, an act of invention is requisite, the act soon slips out of notice. Although we bind together facts by superinducing upon them a new Conception, this Conception, once introduced and applied, is looked upon as inseparably connected with the facts, and necessarily implied in them. Having once had the phenomena bound together in their minds in virtue of the Conception, men can no longer easily restore them back to the detached and incoherent condition in which they were before they were thus combined. The pearls once strung, they seem to form a chain by their nature. Induction has given them a unity which it is so far from costing us an effort to preserve, that it requires an effort to imagine it dissolved. For instance, we usually represent to ourselves the Earth as round, the Earth and the Planets as revolving about the Sun, and as drawn to the Sun by a Central Force; we can hardly understand how it could cost the Greeks, and Copernicus, and Newton, so much pains and trouble to arrive at a view which to us is so familiar. These are no longer to us Conceptions caught hold of and kept hold of by a severe struggle; they are the simplest modes of conceiving the facts: they are really Facts. We are willing to own our obligation to those discoverers, but we hardly feel it: for in what other manner (we ask in our thoughts) could we represent the facts to ourselves?
Thus we see why it is that this step of which we now speak, the Invention of a new Conception in every inductive inference, is so generally overlooked that it has hardly been noticed by preceding philosophers. When once performed by the discoverer, it takes a fixed and permanent place in the understanding of every one. It is a thought which, once breathed forth, permeates all men’s minds. All fancy they nearly or quite knew it before. It oft was thought, or almost thought, though never till now expressed. Men accept it and retain it, and know it cannot be taken 77 from them, and look upon it as their own. They will not and cannot part with it, even though they may deem it trivial and obvious. It is a secret, which once uttered, cannot be recalled, even though it be despised by those to whom it is imparted. As soon as the leading term of a new theory has been pronounced and understood, all the phenomena change their aspect. There is a standard to which we cannot help referring them. We cannot fall back into the helpless and bewildered state in which we gazed at them when we possessed no principle which gave them unity. Eclipses arrive in mysterious confusion: the notion of a Cycle dispels the mystery. The Planets perform a tangled and mazy dance; but Epicycles reduce the maze to order. The Epicycles themselves run into confusion; the conception of an Ellipse makes all clear and simple. And thus from stage to stage, new elements of intelligible order are introduced. But this intelligible order is so completely adopted by the human understanding, as to seem part of its texture. Men ask Whether Eclipses follow a Cycle; Whether the Planets describe Ellipses; and they imagine that so long as they do not answer such questions rashly, they take nothing for granted. They do not recollect how much they assume in asking the question:—how far the conceptions of Cycles and of Ellipses are beyond the visible surface of the celestial phenomena:—how many ages elapsed, how much thought, how much observation, were needed, before men’s thoughts were fashioned into the words which they now so familiarly use. And thus they treat the subject, as we have seen Aristotle treating it; as if it were a question, not of invention, but of proof; not of substance, but of form: as if the main thing were not what we assert, but how we assert it. But for our purpose, it is requisite to bear in mind the feature which we have thus attempted to mark; and to recollect that, in every inference by induction, there is a Conception supplied by the mind and superinduced upon the Facts.
5. In collecting scientific truths by Induction, we often find (as has already been observed) a Definition 78 and a Proposition established at the same time,—introduced together, and mutually dependent on each other. The combination of the two constitutes the Inductive act; and we may consider the Definition as representing the superinduced Conception, and the Proposition as exhibiting the Colligation of Facts.
Sect. II.—Use of Hypotheses.