this being the only medium through which the conclusions of the Positive mode of thought and the premises of the Theological could be temporarily made compatible. At a later period, when the real character of the positive laws of nature had come to be in a certain degree understood, and the theological idea had assumed, in scientific minds, its final character, that of a God governing by general laws, the positive spirit, having now no longer need of the fictitious medium of imaginary entities, set itself to the easy task of demolishing the instrument by which it had risen. But though it destroyed the actual belief in the objective reality of these abstractions, that belief has left behind it vicious tendencies of the human mind, which are still far enough from being extinguished, and which we shall presently have occasion to characterize.
The next point on which we have to touch is one of greater importance than it seems. If all human speculation had to pass through the three stages, we may presume that its different branches, having always been very unequally advanced, could not pass from one stage to another at the same time. There must have been a certain order of succession in which the different sciences would enter, first into the metaphysical, and afterwards into the purely positive stage; and this order M. Comte proceeds to investigate. The result is his remarkable conception of a scale of subordination of the sciences, being the order of the logical dependence of those which follow on those which precede. It is not at first obvious how a mere classification of the sciences can be not merely a help to their study, but itself an important part of a body of doctrine; the classification, however, is a very important part of M. Comte's philosophy.
He first distinguishes between the abstract and the concrete sciences. The abstract sciences have to do with the laws which govern the elementary facts of Nature; laws on which all phaenomena actually realized must of course depend, but which would have been equally compatible with many other combinations than those which actually come to pass. The concrete sciences, on the contrary, concern themselves only with the particular combinations of phaenomena which are found in existence. For example; the minerals which compose our planet, or are found in it, have been produced and are held together by the laws of mechanical aggregation and by those of chemical union. It is the business of the abstract sciences, Physics and Chemistry, to ascertain these laws: to discover how and under what conditions bodies may become aggregated, and what are the possible modes and results of chemical combination. The great majority of these aggregations and combinations take place, so far as we are aware, only in our laboratories; with these the concrete science, Mineralogy, has nothing to do. Its business is with those aggregates, and those chemical compounds, which form themselves, or have at some period been formed, in the natural world. Again, Physiology, the abstract science, investigates, by such means as are available to it, the general laws of organization and life. Those laws determine what living beings are possible, and maintain the existence and determine the phaenomena of those which actually exist: but they would be equally capable of maintaining in existence plants and animals very different from these. The concrete sciences, Zoology and Botany, confine themselves to species which really exist, or can be shown to have really existed: and do not concern themselves with the mode in which even these would comport themselves under all circumstances, but only under those which really take place. They set forth the actual mode of existence of plants and animals, the phaenomena which they in fact present: but they set forth all of these, and take into simultaneous consideration the whole real existence of each species, however various the ultimate laws on which it depends, and to whatever number of different abstract sciences these laws may belong. The existence of a date tree, or of a lion, is a joint result of many natural laws, physical, chemical, biological, and even astronomical. Abstract science deals with these laws separately, but considers each of them in all its aspects, all its possibilities of operation: concrete science considers them only in combination, and so far as they exist and manifest themselves in the animals or plants of which we have experience. The distinctive attributes of the two are summed up by M. Comte in the expression, that concrete science relates to Beings, or Objects, abstract science to Events.2
The concrete sciences are inevitably later in their development than the abstract sciences on which they depend. Not that they begin later to be studied; on the contrary, they are the earliest cultivated, since in our abstract investigations we necessarily set out from spontaneous facts. But though we may make empirical generalizations, we can form no scientific theory of concrete phaenomena until the laws which govern and explain them are first known; and those laws are the subject of the abstract sciences. In consequence, there is not one of the concrete studies (unless we count astronomy among them) which has received, up to the present time, its final scientific constitution, or can be accounted a science, except in a very loose sense, but only materials for science: partly from insufficiency of facts, but more, because the abstract sciences, except those at the very beginning of the scale, have not attained the degree of perfection necessary to render real concrete sciences possible.
Postponing, therefore, the concrete sciences, as not yet formed, but only tending towards formation, the abstract sciences remain to be classed. These, as marked out by M. Comte, are six in number; and the principle which he proposes for their classification is admirably in accordance with the conditions of our study of Nature. It might have happened that the different classes of phaenomena had depended on laws altogether distinct; that in changing from one to another subject of scientific study, the student left behind all the laws he previously knew, and passed under the dominion of a totally new set of uniformities. The sciences would then have been wholly independent of one another; each would have rested entirely on its own inductions, and if deductive at all, would have drawn its deductions from premises exclusively furnished by itself. The fact, however, is otherwise. The relation which really subsists between different kinds of phaenomena, enables the sciences to be arranged in such an order, that in travelling through them we do not pass out of the sphere of any laws, but merely take up additional ones at each step. In this order M. Comte proposes to arrange them. He classes the sciences in an ascending series, according to the degree of complexity of their phaenomena; so that each science depends on the truths of all those which precede it, with the addition of peculiar truths of its own.
Thus, the truths of number are true of all things, and depend only on their own laws; the science, therefore, of Number, consisting of Arithmetic and Algebra, may be studied without reference to any other science. The truths of Geometry presuppose the laws of Number, and a more special class of laws peculiar to extended bodies, but require no others: Geometry, therefore, can be studied independently of all sciences except that of Number.
Rational Mechanics presupposes, and depends on, the laws of number and those of extension, and along with them another set of laws, those of Equilibrium and Motion. The truths of Algebra and Geometry nowise depend on these last, and would have been true if these had happened to be the reverse of what we find them: but the phaenomena of equilibrium and motion cannot be understood, nor even stated, without assuming the laws of number and extension, such as they actually are. The phaenomena of Astronomy depend on these three classes of laws, and on the law of gravitation besides; which last has no influence on the truths of number, geometry, or mechanics. Physics (badly named in common English parlance Natural Philosophy) presupposes the three mathematical sciences, and also astronomy; since all terrestrial phaenomena are affected by influences derived from the motions of the earth and of the heavenly bodies. Chemical phaenomena depend (besides their own laws) on all the preceding, those of physics among the rest, especially on the laws of heat and electricity; physiological phaenomena, on the laws of physics and chemistry, and their own laws in addition. The phaenomena of human society obey laws of their own, but do not depend solely upon these: they depend upon all the laws of organic and animal life, together with those of inorganic nature, these last influencing society not only through their influence on life, but by determining the physical conditions under which society has to be carried on. "Chacun de ces degré's successifs exige des inductions qui lui sont propres; mais elles ne peuvent jamais devenir systématiques que sous l'impulsion déductive resultée de tous les ordres moins compliqués."3
Thus arranged by M. Comte in a series, of which each term represents an advance in speciality beyond the term preceding it, and (what necessarily
Mr Herbert Spencer, who also distinguishes between abstract and concrete sciences, employs the terms in a different sense from that explained above. He calls a science abstract when its truths are merely ideal; when, like the truths of geometry, they are not exactly true of real things – or, like the so-called law of inertia (the persistence in direction and velocity of a motion once impressed) are "involved" in experience but never actually seen in it, being always more or less completely frustrated. Chemistry and biology he includes, on the contrary, among concrete sciences, because chemical combinations and decompositions, and the physiological action of tissues, do actually take place (as our senses testify) in the manner in which the scientific propositions state them to take place. We will not discuss the logical or philological propriety of either use of the terms abstract and concrete, in which twofold point of view very few of the numerous acceptations of these words are entirely defensible: but of the two distinctions M. Comte's answers to by far the deepest and most vital difference. Mr Spencer's is open to the radical objection, that it classifies truths not according to their subject-matter or their mutual relations, but according to an unimportant difference in the manner in which we come to know them. Of what consequence is it that the law of inertia (considered as an exact truth) is not generalized from our direct perceptions, but inferred by combining with the movements which we see, those which we should see if it were not for the disturbing causes? In either case we are equally certain that it
Système de Politique Positive, ii. 36.
