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CHAPTER I: Preliminary Observations on Induction in General - John Stuart Mill, The Collected Works of John Stuart Mill, Volume VII - A System of Logic Ratiocinative and Inductive 
The Collected Works of John Stuart Mill, Volume VII - A System of Logic Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation (Books I-III), ed. John M. Robson, Introduction by R.F. McRae (Toronto: University of Toronto Press, London: Routledge and Kegan Paul, 1974).
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Preliminary Observations on Induction in General
§ 1. [Importance of an inductive logic] The portion of athe presenta inquiry upon which we are now about to enter, may be considered as the principal, both from its surpassing in intricacy all the other branches, and because it relates to a process which has been shown in the preceding Book to be that in which the investigation of nature essentially consists. We have found that all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions, and the interpretation of inductions: that all our knowledge, not intuitive, comes to us exclusively from that source. What Induction is, therefore, and what conditions render it legitimate, cannot but be deemed the main question of the science of logic—the question which includes all others. It is, however, one which professed writers on logic have almost entirely passed over. The generalities of the subject have not been altogether neglected by metaphysicians; but, for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths, their analysis of the inductive operation, even when unexceptionable as to correctness, has not been specific enough to be made the foundation of practical rules, which might be for induction itself what the rules of the syllogism are for the interpretation of induction: while those by whom physical science has been carried to its present b state of improvement—and who, to arrive at a complete theory of the process, needed only to generalize, and adapt to all varieties of problems, the methods which they themselves employed in their habitual pursuits—never until very lately made any serious attempt to philosophize on the subject, nor regarded the mode in which they arrived at their conclusions as deserving of study, independently of the conclusions themselves.c
§ 2. [The logic of science is also that of business and life] For the purposes of the present inquiry, Induction may be defined, the operation of discovering and proving general propositions. It is true that (as already shown) the process of indirectly ascertaining individual facts, is as truly inductive as that by which we establish general truths. But it is not a different kind of induction; it is aaa form of the bveryb same process: since, on the one hand, generals are but collections of particulars, definite in kind but indefinite in number; and on the other hand, whenever the evidence cwhich we derivec from observation of known cases justifies us in drawing an inference respecting even one unknown case, we should on the same evidence be justified in drawing a similar inference with respect to a whole class of cases. The inference either does not hold at all, or it holds in all cases of a certain description; in all cases which, in certain definable respects, resemble those we have observed.
If these remarks are just; if the principles and rules of inference are the same whether we infer general propositions or individual facts; it follows that a complete logic of the sciences would be also a complete logic of practical business and common life. Since there is no case of legitimate inference from experience, in which the conclusion may not legitimately be a general proposition; an analysis of the process by which general truths are arrived at, is virtually an analysis of all induction whatever. Whether we are inquiring into a scientific principle or into an individual fact, and whether we proceed by experiment or by ratiocination, every step in the train of inferences is essentially inductive, and the legitimacy of the induction depends in both cases on the same conditions.
True it is that in the case of the practical inquirer, who is endeavouring to ascertain facts not for the purposes of science but for those of business, such for instance as the advocate or the judge, the chief difficulty is one in which the principles of induction will afford him no assistance. It lies not in making his inductions, but in the selection of them; in choosing from among all general propositions ascertained to be true, those which furnish d marks by which he may trace whether the given subject possesses or not the predicate in question. In arguing a doubtful question of fact before a jury, the general propositions or principles to which the advocate appeals are mostly, in themselves, sufficiently trite, and assented to as soon as stated: his skill lies in bringing his case under those propositions or principles; in calling to mind such of the known or ereceivede maxims of probability as admit of application to the case in hand, and selecting from among them those best adapted to his object. Success is here dependent on natural or acquired sagacity, aided by knowledge of the particular subject, and of subjects allied with it. Invention, though it can be cultivated, cannot be reduced to rule; there is no science which will enable a man to bethink himself of that which will suit his purpose.
But when he has thought of something, science can tell him whether that which he has thought of will suit his purpose or not. The inquirer or arguer must be guided by his own knowledge and sagacity in fthef choice of the inductions out of which he will construct his argument. But the validity of the argument when constructed, depends on principles and must be tried by tests which are the same for all descriptions of inquiries, whether the result be to give A an estate, or to enrich science with a new general truth. In the one case and in the other, the senses, or testimony, must decide on the individual facts; the rules of the syllogism will determine whether, those facts being supposed correct, the case really falls within the formulæ of the different inductions under which it has been successively brought; and finally, the legitimacy of the inductions themselves must be decided by other rules, and these it is now our purpose to investigate. If this third part of the operation be, in many of the questions of practical life, not the most, but the least arduous portion of it, we have seen that this is also the case in some great departments of the field of science; in all those which are principally deductive, and most of all in mathematics; where the inductions themselves are few in number, and so obvious and elementary that they seem to stand in no need of the evidence of experienceg, whileg to combine them so as to prove a given theorem or solve a problem, may call for the hutmosth powers of invention and contrivance with which our species is gifted.
If the identity of the logical processes which prove particular facts and those which establish general scientific truths, required any additional confirmation, it would be sufficient to consider that in many branches of science, single facts have to be proved, as well as principles; facts as completely individual as any that are debated in a court of justice; but which are proved in the same manner as the other truths of the science, and without disturbing in any degree the homogeneity of its method. A remarkable example of this is afforded by astronomy. The individual facts on which that science grounds its imost important deductionsi , such facts as the magnitudes of the bodies of the solar system, their distances from one another, the figure of the earth, and its rotation, are scarcely any of them accessible to our means of direct observation: they are proved indirectly, by the aid of inductions founded on other facts which we can more easily reach. For example, the distance of the moon from the earth was determined by a very circuitous process. The share which direct observation had in the work consisted in ascertaining, at one and the same instant, the zenith distances of the moon, as seen from two points very remote from one another on the earth’s surface. The ascertainment of these angular distances ascertained their supplements; and since the angle at the earth’s centre subtended by the distance between the two places of observation was deducible by spherical trigonometry from the latitude and longitude of those places, the angle at the moon subtended by the same line became the fourth angle of a quadrilateral of which the other three angles were known. The four angles being thus ascertained, and two sides of the quadrilateral being radii of the earth; the two remaining sides and the diagonal, or in other words, the moon’s distance from the two places of observation and from the centre of the earth, could be ascertained, at least in terms of the earth’s radius, from elementary theorems of geometry. At each step in this demonstration ja new induction is taken inj , represented in the aggregate of its results by a general proposition.
Not only is the process by which an individual astronomical fact was thus ascertained, exactly similar to those by which the same science establishes its general truths, but kalsok (as we have shown to be the case in all legitimate reasoning) a general proposition might have been concluded instead of a single fact. In strictness, indeed, the result of the reasoning is a general proposition; a theorem respecting the distance, not of the moon in particular, but of any inaccessible object; showing in what relation that distance stands to certain other quantities. And although the moon is almost the only heavenly body the distance of which from the earth can really be thus ascertained, this is merely owing to the accidental circumstances of the other heavenly bodies, which render them incapable of affording such data as the application of the theorem requires; for the theorem itself is as true of them as it is of the moon.*
We shall fall into no error, then, if in treating of Induction, we limit our attention to the establishment of general propositions. The principles and rules of Induction as directed to this end, are the principles and rules of all Induction; and the logic of Science is the universal Logic, applicable to all inquiries in which man can engagel .
[b]MS, 43, 46 high
[c]MS Although, for these reasons, there is not yet extant a body of Inductive Logic, scientifically constructed; the materials for its construction exist, widely scattered, but abundant: and the selection and arrangement of those materials is a task with which intellects of the highest order, possessed of the necessary acquirements, have at length consented to occupy themselves. Within a few years three writers, profoundly versed in every branch of physical science, and not unaccustomed to carry their speculations into still higher regions of knowledge, have made attempts, of unequal but all of very great merit, towards the creation of a Philosophy of Induction: Sir John Herschel, in his Discourse of the Study of Natural Philosophy; Mr. Whewell, in his History and Philosophy of the Inductive Sciences; and, greatest of all, M. Auguste Comte, in his Cours de Philosophie Positive [6 vols. Paris: Bachelier, 1830-42], a work which only requires to be better known, to place its author in the very highest class of European thinkers. That the present writer does not consider any of these philosophers, or even all of them together, to have entirely accomplished this important work, is implied in his attempting to supply the deficiency; but with his comparatively imperfect knowledge of the various physical sciences, the attempt would have been desperate unless the materials had been brought together, and had undergone a partial elaboration, by their more competent hands; even if he could have dispensed with the many important logical ideas and principles, for the first suggestion of which he has been indebted to one or other of those writers.] 43 as MS . . . attempting to contribute something farther towards its achievement; but . . . as MS] 46 as MS . . . intellects of a high order, possessed . . . as MS . . . M. Auguste Comte, in his Cours de Philosophie Positive. That . . . as 43
[a-a]MS, 43, 46, 51 another
[b-b]+43, 46, 51, 56, 62, 65, 68, 72
[c-c]MS we possess, derived
[d]MS, 43, 46 him with
[e-e]MS, 43, 46 recognised
[f-f]MS, 43, 46 his
[g-g]MS ; but
[h-h]MS, 43 highest
[i-i]MS highest inductions
[j-j]MS, 43, 46, 51, 56, 62, 65, 68 we take in a new induction
[k-k]MS, 43, 46 moreover
[* ] Dr. Whewell thinks it improper to apply the term Induction to any operation not terminating in the establishment of a general truth. Induction, he says (Philosophy of Discovery, p. 245), “is not the same thing as experience and observation. Induction is experience or observation consciously looked at in a general form. This consciousness and generality are necessary parts of that knowledge which is science.” And he objects (p. 241) to the mode in which the word Induction is employed in this work, as an undue extension of that term “not only to the cases in which the general induction is consciously applied to a particular instance, but to the cases in which the particular instance is dealt with by means of experience in that rude sense in which experience can be asserted of brutes, and in which of course we can in no way imagine that the law is possessed or understood as a general proposition.” This use of the term he deems a “confusion of knowledge with practical tendencies.”
[l]MS , and the test of all the conclusions at which he can arrive] 43, 46 as MS . . . arrive by inference