These he attempts to arrange on the same principle of increasing speciality and complexity, but they hardly admit of such a scale, and M. Comte's mode of placing them varied at different periods. All the five being essentially independent of one another, he attached little importance to their order, except that barology ought to come first, as the connecting link with astronomy, and electrology last, as the transition to chemistry.
If the best classification is that which is grounded on the properties most important for our purposes, this classification will stand the test. By placing the sciences in the order of the complexity of their subject matter, it presents them in the order of their difficulty. Each science proposes to itself a more arduous inquiry than those which precede it in the series; it is therefore likely to be susceptible, even finally, of a less degree of perfection, and will certainly arrive later at the degree attainable by it. In addition to this, each science, to establish its own truths, needs those of all the sciences anterior to it. The only means, for example, by which the physiological laws of life could have been ascertained, was by distinguishing, among the multifarious and complicated facts of life, the portion which physical and chemical laws cannot account for. Only by thus isolating the effects of the peculiar organic laws, did it become possible to discover what these are. It follows that the order in which the sciences succeed one another in the series, cannot but be, in the main, the historical order of their development; and is the only order in which they can rationally be studied. For this last there is an additional reason: since the more special and complete sciences require not only the truths of the simpler and more general ones, but still more their methods. The scientific intellect, both in the individual and in the race, must learn in the move elementary studies that art of investigation and those canons of proof which are to be put in practice in the more elevated. No intellect is properly qualified for the higher part of the scale, without due practice in the lower.
Mr Herbert Spencer, in his essay entitled "The Genesis of Science," and more recently in a pamphlet on "the Classification of the Sciences," has criticised and condemned M. Comte's classification, and proposed a more elaborate one of his own: and M. Littré, in his valuable biographical and philosophical work on M. Comte ("Auguste Comte et la Philosophie Positive"), has at some length criticised the criticism. Mr Spencer is one of the small number of persons who by the solidity and encyclopedical character of their knowledge, and their power of co-ordination and concatenation, may claim to be the peers of M. Comte, and entitled to a vote in the estimation of him. But after giving to his animadversions the respectful attention due to all that comes from Mr Spencer, we cannot find that he has made out any case. It is always easy to find fault with a classification. There are a hundred possible ways of arranging any set of objects, and something may almost always be said against the best, and in favour of the worst of them. But the merits of a classification depend on the purposes to which it is instrumental. We have shown the purposes for which M. Comte's classification is intended. Mr Spencer has not shown that it is ill adapted to those purposes: and we cannot perceive that his own answers any ends equally important. His chief objection is that if the more special sciences need the truths of the more general ones, the latter also need some of those of the former, and have at times been stopped in their progress by the imperfect state of sciences which follow long after them in M. Comte's scale; so that, the dependence being mutual, there is a consensus, but not an ascending scale or hierarchy of the sciences. That the earlier sciences derive help from the later is undoubtedly true; it is part of M. Comte's theory, and amply exemplified in the details of his work. When he affirms that one science historically precedes another, he does not mean that the perfection of the first precedes the humblest commencement of those which follow. Mr Spencer does not distinguish between the empirical stage of the cultivation of a branch of knowledge, and the scientific stage. The commencement of every study consists in gathering together unanalyzed facts, and treasuring up such spontaneous generalizations as present themselves to natural sagacity. In this stage any branch of inquiry can be carried on independently of every other; and it is one of M. Comte's own remarks that the most complex, in a scientific point of view, of all studies, the latest in his series, the study of man as a moral and social being, since from its absorbing interest it is cultivated more or less by every one, and pre-eminently by the great practical minds, acquired at an early period a greater stock of just though unscientific observations than the more elementary sciences. It is these empirical truths that the later and more special sciences lend to the earlier; or, at most, some extremely elementary scientific truth, which happening to be easily ascertainable by direct experiment, could be made available for carrying a previous science already founded, to a higher stage of development; a re-action of the later sciences on the earlier which M. Comte not only fully recognized, but attached great importance to systematizing.4
But though detached truths relating to the more complex order of phaenomena may be empirically observed, and a few of them even scientifically established, contemporaneously with an early stage of some of the sciences anterior in the scale, such detached truths, as M. Littré justly remarks, do not constitute a science. What is known of a subject, only becomes a science when it is made a connected body of truth; in which the relation between the general principles and the details is definitely made out, and each particular truth can be recognized as a case of the operation of wider laws. This point of progress, at which the study passes from the preliminary state of mere preparation, into a science, cannot be reached by the more complex studies until it has been attained by the simpler ones. A certain regularity of recurrence in the celestial appearances was ascertained empirically before much progress had been made in geometry; but astronomy could no more be a science until geometry was a highly advanced one, than the rule of three could have been practised before addition and subtraction. The truths of the simpler sciences are a part of the laws to which the phaenomena of the more complex sciences conform: and are not only a necessary element in their explanation, but must be so well understood as to be traceable through complex combinations, before the special laws which co-exist and co-operate with them can be brought to light. This is all that M. Comte affirms, and enough for his purpose.5 He no doubt occasionally indulges in more unqualified expressions than can be completely justified, regarding the logical perfection of the construction of his series, and its exact correspondence with the historical evolution of the sciences; exaggerations confined to language, and which the details of his exposition often correct. But he is sufficiently near the truth, in both respects, for every practical purpose.6 Minor inaccuracies must often be forgiven even to great thinkers. Mr Spencer, in the very-writings in which he criticises M. Comte, affords signal instances of them.7
Combining the doctrines, that every science is in a less advanced state as it occupies a higher place in the ascending scale, and that all the sciences pass through the three stages, theological, metaphysical, and positive, it follows that the more special a science is, the tardier is it in effecting each transition, so that a completely positive state of an earlier science has often coincided with the metaphysical state of the one next to it, and a purely theological state of those further on. This statement correctly represents the general course of the facts, though requiring allowances in the detail. Mathematics, for example, from the very beginning of its cultivation, can hardly at any time have been in the theological state, though exhibiting many traces of the metaphysical. No one, probably, ever believed that the will of a god kept parallel lines from meeting, or made two and two equal to four; or ever prayed to the gods to make the square of the hypothenuse equal to more or less than the sum of the squares of the sides. The most devout believers have recognized in propositions of this description a class of truths independent of the devine omnipotence. Even among the truths which popular philosophy calls by the misleading name of Contingent the few which are at once exact and obvious were probably, from the very first, excepted from the theological explanation. M. Comte observes, after Adam Smith, that we are not told in any age or country of a god of Weight. It was otherwise with Astronomy: the heavenly bodies were believed not merely to be moved by gods, but to be gods themselves: and when this theory was exploded, there movements were explained by metaphysical conceptions; such as a tendency of Nature to perfection, in virtue of which these sublime bodies, being left to themselves, move in the most perfect orbit, the circle. Even Kepler was full of fancies of this description, which only terminated when Newton, by unveiling