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Whewell's mind is better fitted, as it seems to us, for an inductive philosopher, than for a philosopher of induction; he examines mental processes as he would physical facts, and seems to aim only at giving an account which would describe them, not putting his mind into them to tell how they do really arise within; he regards them like an observer, ab extra, as needing classification and explanation, but does not take his own consciousness through the actual history of their formation, and so has no sensitiveness as to the different relations of kind, and internal authority, in which they stand to his own judgment. Mr. Mill's intellect, on the other hand, is one subtle enough in analysis, and that delights in deductive inference, but which can yield no belief to anything that is not capable either of direct perception, or of stringent deduction from facts of direct perception. He is inclined, therefore, to attribute any degree of influence to known causes, i. e. to facts capable of direct observation, rather than to assume any, even the slightest, cause, not capable of such perception, however perfectly it may account for the facts, and however disproportionate those facts may be to the hitherto observed results of any observed antecedents; in short, his tendency is rather to ascribe the very greatest degrees of influence to perceived causes, than the very smallest to those which are only assumed. Of this characteristic tendency in Mr. Mill's mind, his rejection of all a priori truth, his utilitarian creed in morals, his strong leaning to the doctrine that men's minds differ, not from different original constitution, but from the various influences to which they are subjected, and his remarks on Hypotheses, are perhaps sufficient indications. These remarks will make it clear why we cannot concur
Whewell's expectation that the Philosophy of Induction will become at all more lucid “in a controversial than in a didactic form," at least while the controversy is one between two minds so little able to catch each other's point of view; and while one of them monopolises nearly all the analytic power, so that he is confirmed rather than shaken in his own views by the learned, but ill-conceived, and ill-arranged objections of his opponent. In reviewing this controversy, therefore, we shall find it convenient to give first the theory of Mr. Mill, and in our review of that
theory to interweave the conflicting views (so far as they are systematic at all) maintained by Dr. Whewell.
At the very outset we are met with the question (so uniformly debated till a science has reached a very perfect state), what exactly are we to understand by the mental operation that is called Induction ?-assuming meanwhile as a practical rule to guide us in seeking the answer to the question, that it is that operation (performed in all practical reasoning) by which we infer from particular data what is not contained either implicitly or explicitly therein, and what we cannot therefore arrive at by either deduction or analysis alone. Mr. Mill very properly therefore excludes from his definition of Induction, the formal syllogistic Induction, the èraywyn of Aristotle, which gives no new inference, but only predicates in a fresh proposition of a whole class, what has been predicated severally of each individual contained in that class, and also the deductive mathematical processes (as the formation of new terms in a series according to the analogy of the old) which only assume the appearance of Induction from the omission of a demonstration which might be supplied (viz., that successive terms must follow each other, according to the same law). Mr. Mill then goes on to exclude a process from Induction proper, which he afterwards places amongst the operations subsidiary to Induction, the process of combining, through some essential property common to them all, the particular facts or data from which the inference is to be drawn. Thus, for example, that all the observed points in a planet's motion are points in an ellipse of which one focus would represent the position of the sun, is only a description of observed facts, obtained by comparing them with the relative calculated positions of points in an ellipse; and as there is no new inference made here, but only a comparison between facts deduced from the laws of a mathematical curve, with facts noted by observation, Mr. Mill rightly denies to such a process the name of Induction.* This is however violently contested
* We may note that there is no dispute between Mr. Mill and Dr. Whewell as to the conclusions that the remaining unobserved points of the planet's orbit would also coincide with the ellipse, and that the planet would continue to move in the same ellipse. These are of course strictly inductive inferences, but so obvious, that Kepler's discovery is scarcely thought of as including them. CHRISTIAN TEACHER.No. 47.
by Dr. Whewell, who does not distinguish in any way this preliminary process, viz., the happy guess (suggested, no doubt, generally to a mind full of guiding analogies) which picks out the essential property that unites the particular facts, from the inferences which may be drawn from those facts. Now here, as elsewhere, Dr. Whewell betrays an entire inability to seize and hold fast the thought which alone can determine such a dispute. Induction is an inferential process. Is the introduced conception of the ellipse an inference or only a guess ? Had Dr. Whewell seen the true point in debate, he might have maintained that the introduction of this new conception might at least have been an inference. Had Kepler, on examining the determined points in the orbit of Mars, reasoned with himself that he had formerly found similar relative distances in examining the relation of points known to belong to an ellipse, and so inferred that this curve might be itself an ellipse, the process would have been really inductive, an argument from that looser kind of induction that is called analogy, which, as Mr. Mill himself says, consists in the argument, “Two things resemble each other in one or more respects ; a certain proposition is true of the one, therefore it is true of the other."-(C. xx. & 2.) So the inference in this case would have been in the form, " These distances resemble the distances I obtained previously for points similarly situated on a known curve. That curve was an ellipse, therefore this curve also may perhaps be an ellipse.” Nor is there anything to prevent such an inferential process from being actually applied to obtain the true description of phenomena. When Snell was examining the relations of the angle of incidence to that of refraction, and endeavouring to determine their law of connection, he might very well have noticed that the variations in the angles of incidence and refraction resembled those in two angles of a triangle, whose opposite sides are varied so as to maintain a constant ratio to each other; and noting this resemblance, he might have been led to suggest as an hypothesis, that this would be the law describing the variations required ; and such a process would have been analogical and therefore strictly induc
these variations remind me of certain others : those others were reducible to a certain rule, hence these
may perhaps be reduced to the same or a similar rule.” * Mr. Mill would not, we are sure, deny to such a process as this, the name of Induction :-and this, or something of this sort, it is, which makes Dr. Whewell contend so strongly and strangely for the inductive nature of a mere guess; he feels that these tentative guesses might be suggested by analogical reasoning which would make the trial really an inductive inference; also that possibly this was really the case with Keplert and other such discoverers of the true description of related phenomena, resulting in their reduction to a single class; and hence he has concluded that
; in all such cases, even where the process is purely tentative, the true description, when gained, must have been gained by induction.
But, says Dr. Whewell, Kepler “ bound together particular observations of separate places of Mars by the notion, or, as I have called it, the conception, of an ellipse which was supplied by his own mind,” and this, others, who knew the facts, could not do; therefore it was an Induction. Now suppose the trying an ellipse to have been purely a speculation, and not inferred from any conscious analogy with Kepler's former experience; what is the real process ?-registered observations are compared with certain other known facts, and they are found to agree. The mental judgment that they do agree, is obviously deductive, not inductive. There is no inductive inference at all, unless the conjecture itself is no guess, but results from a real inference, which, though probable enough, Dr. Whewell nowhere asserts. He might say, indeed, none but a mathematician and an astronomer could have known what curves it would be useless to try, and what might be successful; therefore that it is not in any case a mere guess, but inferred from scientific experience; the determined points might have belonged (as far as Kepler knew) to any one of certain curves, but to no others : then in such a case it may be admitted, that there might have been an inductive inference, viz., that the points would be found to belong to one or other of these curves. This inference however was not peculiar to the discoverer of the ellipse, but common to all the astronomers of his day: if to try the ellipse was a mere consequence of Kepler's determination to try all possibilities, till he found the truth,—then there was absolutely no new inference from the particular data at all (no induction) in the introduction of the conception of the ellipse, and the discovery was due to persevering labour, not to the application of an inductive process.
* This may have been the real process followed by Snell. He did not give the law of the sines, but "expresses the law in a geometrical form more simply.”—Whewell's History of Philosophy, Vol. II. p. 503.
† That this might have been the case with Kepler, seems probable from what Dr. Whewell tells us in his History of the Inductive Sciences, Vol. I. p. 450 : “When Kepler's first hypothesis was enveloped in the complex construction requisite to apply it to each point of the orbit, it was far more difficult to see where the error lay, and Kepler hit upon it only by noticing the coincidence of certain numbers, which as he says raised him as if from sleep, and gave him a new light."
We may add that this mistake has no doubt been strengthened in Dr. Whewell's mind by neglecting to distinguish between the unconscious suggestions, and the conscious inferences that take place in every mind. The mere guess of Kepler, even though he could have assigned no analogy whatever for its probability, would be very different from the
unscientific man. Still it would not be an induction, for induction implies conscious inference. This discussion would be of little importance in itself, did it not take up so large a portion of Dr. Whewell's very short reply to Mr. Mill, and did it not introduce a discussion, in which Mr. Mill seems to us to have involved himself and his science in some confusion. In reasoning against Dr. Whewell's doctrine, that the mere introduction of the new conception which binds together the phenomena into a single class is an act of Induction (an operation termed by Dr. Whewell, and, after him, by Mr. Mill, the colligation of facts), he uses an argument which, we think, Dr. Whewell rightly rejects as erroneous. As this is almost the only theoretical point which Dr. Whewell seems to us to have made good against Mr. Mill, and as it is in itself a point of some interest, we shall extract the whole of Dr. Whewell's reply.
“There is another argument which Mr. Mill employs, in order to show that there is a difference between mere colligation, which is Description, and induction in the more proper sense of the term. He notices with commendation a remark which I had made (i. 364, Mill's Logic), that at different stages of the progress of science, the