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general, either under the dominion of arbitrary agency, or abandoned to chance or blind destiny.
In proportion, however, as the mind is more cultivated, and man accustomed to reflect and reason on the objects continually presented to his senses, he is naturally, and even unconsciously, led to enlarge his persuasion of the general recurrence of natural phenomena, in the same order in which he has several times witnessed it. This persuasion easily extends itself to a great variety of particular instances, in which its correctness is soon verified by observation. The same habitual judgment thus gains strength by every hour's experience. The confidence with which the mind calculates, as it were, upon the permanence of a certain order in physical events, increases with rapidly-accumulating force; and the improvement of the faculties by study, and the enlargement of our stores of information from wider observation of physical facts, soon begins to induce the habit of extending our persuasion of the uniformity of natural causes, beyond the mere bounds of familiar phenomena, to those which are placed out of our immediate examination, but which we come naturally to imagine must be regulated by a like constancy.
Founded, then, on the natural constitution of the human mind, confirmed by daily experience, and verified by every advance in the accurate study both of mental and material phenomena, the belief in the existence of this uniformity becomes, in fact, the basis of all acquisition of knowledge, and enables us, without hesitation, to advance in our conclusions from the known to the unknown, from truths actually before us and within our reach, to those which may be hidden from us, or beyond the limits of sensible experience.
The belief in the uniformity and permanence of natural order, combined with, and perhaps dependent on, the tendency of the human mind to generalize its observations, unite to supply, as it were, at once the first impulse and primary elements of philosophic investigation. But it is further necessary that much care and skill be employed in the direction and use of them before they can produce any substantial results. We have then further to inquire how this is to be done; and we shall find that the models by which we must be guided, are to be found in the careful and extended study of already established natural relations.
Antecedent Probability in Induction.
The principles by which we are to be guided in advancing to sound generalizations of observed physical relations, must be those derived from the careful study and comparison of such generalizations previously confirmed in other corresponding instances, which will suggest probabilities antecedent to actual experience.
It will be to little purpose that we are persuaded of the existence of some uniformity in natural laws, unless we have this guide to assist in tracing what the principle of uniformity is in any particular case Without such assistance, we may go on collecting and observing a vast number of facts, and yet arrive at no conclusions, or only at such as are altogether empty and visionary.
As we have already remarked, that merely to affirm what we observe in common of a number of individuals, all of which are before us, is hardly worthy the name of an induction, so it is a violation of all just induction to infer a general property from too limited a number of instances. But what constitutes the sufficient number of instances must depend on the nature of the case, and the experience and power of judgment possessed by the inquirer.
And if we fall into the error of too small an induction, the usual cause of such error is rather that the induction is wanting in a just principle of probability in our first conjecture, or that we have proceeded on the supposition of a wrong sort of relation. It is this which has commonly much more to do with the justness of our conclusion than the mere number of instances collected. And, on the other hand, it often happens that a very few instances, or even almost a single instance, have been admitted without question as a sufficient verification: but this has depended entirely on the justness of the assumed relation.
We will illustrate these remarks by a few examples, both of successful and unsuccessful inductions, in different departments of science.
1. Newton, on passing a ray of light through a prism of glass, found it separated into coloured rays; and measuring the proportion in which it is thus spread out, or “ dispersed,” announced that proportion as the general law of prismatic dispersion.
Dr. Lucas repeated the experiment; but assigned a much less proportion as the law. Both parties positively maintained the correctness of their respective conclusions. But they had both argued on a faulty ground of induction: they had each taken for granted that their prisms ought to act equally on light. The fact was, they had used different sorts of glass, which vary considerably in dispersive power.
This is remarkable as one of the very few instances in which Newton failed in an induction; but such failures are instructive; for we learn to observe the reason of the error. It was manifestly from neglecting to consider, in this case, what probability there would be, previous to trial, that different sorts of glass should possess the same dispersive power.
On the other hand, Newton's capital result that “ to the same ray ever belongs the same refrangibility,” (the media being the same,) is a conclusion, indeed, of a most general nature, and which universal experience has amply confirmed, but it was founded on a very limited induction derived from prismatic experiments with, at most, three or four different media.
2. The early history of astronomy is full of examples of the compatibility of accumulated observation with the want of satisfactory induction. The ancient astronomers were indefatigable in the diligence with which they amassed observations. But they constructed out of them no theory which could attain a real permanence. The system of Ptolemy sufficed to a certain extent to represent the observed motions of the planets. The advance in accuracy of observations, however, soon required corresponding improvements in the system; which was obliged to be modified to accord with them : but, at length, the immense complexity introduced by the cycles and epicycles which were necessary to account for the apparent motions, began to induce a persuasion that such complication could not be the real law of nature: juster principles were therefore to be sought. No astronomer ever laboured more sedulously in making and recording observations, than Tycho Brahe. But though persuaded of the insufficiency of the Ptolemaic hypothesis, he did not succeed in constructing a better: not from deficiency of facts, but from his strangely-erroneous assumption of a guiding theoretical principle.
Kepler worked upon Tycho's materials. The labour which he bestowed on calculation was absolutely incredible.
But theory after theory was adopted and rejected, because he had not any other guide than random conjecture, and nothing but the accurate calculation of every detail could suffice to put those conjectures to the test. He had not