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as are now the subject of our consideration, and which may sometimes aid us in determining when the task has been rightly executed.

CHAPTER V.

OF CERTAIN CHARACTERISTICS OF SCIENTIFIC INDUCTION.

1. THE two operations spoken of in the preceding chapters, the Explication of the Conceptions of our own minds, and the Colligation of observed Facts by the aid of such Conceptions,-are, as we have just said, inseparably connected with each other. When united, and employed in collecting knowledge from the phenomena which the world presents to us, they constitute the mental process of Induction; which is usually and justly spoken of as the genuine source of all our real general knowledge respecting the external world. And we see, from the preceding analysis of this process into its two constituents, from what origin it derives each of its characters. It is real, because it arises from the combination of real facts, but it is general, because it implies the possession of general ideas. Without the former, it would not be knowledge of the external world; without the latter, it would not be knowledge at all. When Ideas and Facts are separated from each other, the neglect of facts gives rise to empty speculations, idle subtleties, visionary inventions, false opinions concerning the laws of phenomena, disregard of the true aspect of nature: while the want of ideas leaves the mind overwhelmed, bewildered, and stupified by particular sensations, with no means of connecting the past with the future, the absent with the present, the example with the rule; open to the impression of all

appearances, but capable of appropriating none. Ideas are the Form, facts the Material, of our structure. Knowledge does not consist in the empty mould, or in the brute mass of matter, but in the rightly-moulded substance. Induction gathers general truths from particular facts;and in her harvest, the corn and the reaper, the solid ears and the binding band, are alike requisite. All our knowledge of nature is obtained by Induction; the term being understood according to the explanation we have now given. And our knowledge is then most complete, then most truly deserves the name of Science, when both its elements are most perfect;-when the Ideas which have been concerned in its formation have, at every step, been clear and consistent;-and when they have, at every step also, been employed in binding together real and certain Facts. Of such Induction I have already given so many examples and illustrations in the two preceding chapters, that I need not now dwell further upon the subject.

2. Induction is familiarly spoken of as the process by which we collect a general proposition from a number of particular cases: and it appears to be frequently imagined that the general proposition results from a mere juxtaposition of the cases, or at most, from merely conjoining and extending them. But if we consider the process more closely, as exhibited in the cases lately spoken of, we shall perceive that this is an inadequate account of the matter. The particular facts are not merely brought together, but there is a new element added to the combination by the very act of thought by which they are combined. There is a conception of the mind introduced in the general proposition, which did not exist in any of the observed facts. When the Greeks, after long observing the motions of the planets, saw that these motions might be rightly considered as produced by the motion of one wheel revolving in the inside of another wheel, these

wheels were creations of their minds, added to the facts which they perceived by sense. And even if the wheels were no longer supposed to be material, but were reduced to mere geometrical spheres or circles, they were not the less products of the mind alone,-something additional to the facts observed. The same is the case in all other discoveries. The facts are known, but they are insulated and unconnected, till the discoverer supplies from his own stores a principle of connexion. The pearls are there, but they will not hang together till some one provides the string. The distances and periods of the planets were all so many separate facts; by Kepler's Third Law they are connected into a single truth: but the conceptions which this law involves were supplied by Kepler's mind, and without these, the facts were of no avail. The planets described ellipses round the sun, in the contemplation of others as well as of Newton; but Newton conceived the deflection from the tangent in these elliptical motions in a new light, as the effect of a central force following a certain law; and then it was that such a force was discovered truly to exist.

Thus 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;

* I repeat here remarks made at the end of the Mechanical Euclid,

p. 178.

not because our senses ever disclosed to us a body doing this, but because (taking this as our ideal case) we find that all 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.

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. 66 Induction," says Aristotle*, "is when by means of one extreme term† we infer the other extreme term to be true of the middle term." Thus, (to take such exemplifications as belong to our subject,) from * Analyt. Prior., lib. ii., c. 23. Пepì rŷs èπaywyŷs. + 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.

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 Planets do what Mercury, Venus, Mars, do." But we 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*; 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 respect

* Εἰ οὖν ἀντιστρέφει τὸ Γ' τῷ Β καὶ μὴ ὑπερτείνει τὸ μέσον.—ARISTOT. Ibid.

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