The Positive Philosophy opens with the statement of a certain law of which Comte was the discoverer, and which has always been treated both by disciples and dissidents as the key to his system. This is the Law of the Three States. It is as follows. Each of our leading conceptions, each branch of our knowledge, passes successively through three different phases; there are three different ways in which the human mind explains phenomena, each way following the other in order. These three stages are the Theological, the Metaphysical, and the Positive. Knowledge, or a branch of knowledge, is in the Theological state, when it supposes the phenomena under consideration to be due to immediate volition, either in the object or in some supernatural being. In the Metaphysical state, for volition is substituted abstract force residing in the object, yet existing independently of the object; the phenomena are viewed as if apart from the bodies manifesting them; and the properties of each substance have attributed to them an existence distinct from that substance. In the Positive state inherent volition or external volition and inherent force or abstraction personified have both disappeared from men's minds, and the explanation of a phenomenon means a reference of it, by way of succession or resemblance, to some other phenomenon,—means the establishment of a relation between the given fact and some more general fact. In the Theological and Metaphysical state men seek a cause or an essence; in the Positive they are content with a law. To borrow an illustration from an able English disciple of Comte:—'Take the phenomenon of the sleep produced by opium. The Arabs are content to attribute it to the "will of God." Molière's medical student accounts for it by a soporific principle contained in the opium. The modern physiologist knows that he cannot account for it at all. He can simply observe, analyse, and experiment upon the phenomena attending the action of the drug, and classify it with other agents analogous in character' (Dr. Bridges).

The first and greatest aim of the Positive Philosophy is to advance the study of society into the third of the three stages,—to remove social phenomena from the sphere of theological and metaphysical conceptions, and to introduce among them the same scientific observation of their laws which has given us physics, chemistry, physiology. Social physics will consist of the conditions and relations of the facts of society, and will have two departments,—one statical, containing the laws of order; the other dynamical, containing the laws of progress. While men's minds were in the theological state, political events, for example, were explained by the will of the gods, and political authority based on divine right. In the metaphysical state of mind, then, to retain our instance, political authority was based on the sovereignty of the people, and social facts were explained by the figment of a falling away from a state of nature. When the positive method has been finally extended to society, as it has been to chemistry and physiology, these social facts will be resolved, as their ultimate analysis, into relations with one another, and instead of seeking causes in the old sense of the word, men will only examine the conditions of social existence. When that stage has been reached not merely the greater part, but the whole, of our knowledge will be impressed with one character—the character, namely, of positivity or scientificalness; and all our conceptions in every part of knowledge will be thoroughly homogeneous. The gains of such a change are enormous. The new philosophical unity will now in its turn regenerate all the elements that went to its own formation. The mind will pursue knowledge without the wasteful jar and friction of conflicting methods and mutually hostile conceptions; education will be regenerated; and society will reorganise itself on the only possible solid base—a homogeneous philosophy.

The Positive Philosophy has another object besides the demonstration of the necessity and propriety of a science of society. This object is to show the sciences as branches from a single trunk,—is to give to science the ensemble or spirit of generality hitherto confined to philosophy, and to give to philosophy the rigour and solidity of science. Comte's special object is a study of social physics, a science that before his advent was still to be formed; his second object is a review of the methods and leading generalities of all the positive sciences already formed, so that we may know both what system of inquiry to follow in our new science, and also where the new science will stand in relation to other knowledge.

The first step in this direction is to arrange scientific method and positive knowledge in order, and this brings us to another cardinal element in the Comtist system, the classification of the sciences. In the front of the inquiry lies one main division, that, namely, between speculative and practical knowledge. With the latter we have no concern. Speculative or theoretic knowledge is divided into abstract and concrete. The former is concerned with the laws that regulate phenomena in all conceivable cases; the latter is concerned with the application of these laws. Concrete science relates to objects or beings; abstract science to events. The former is particular or descriptive; the latter is general. Thus, physiology is an abstract science; but zoology is concrete. Chemistry is abstract; mineralogy is concrete. It is the method and knowledge of the abstract sciences that the Positive Philosophy has to reorganise in a great whole.

Comte's principle of classification is that the dependence and order of scientific study follows the dependence of the phenomena. Thus, as has been said, it represents both the objective dependence of the phenomena and the subjective dependence of our means of knowing them. The more particular and complex phenomena depend upon the simpler and more general. The latter are the more easy to study. Therefore science will begin with those attributes of objects which are most general, and pass on gradually to other attributes that are combined in greater complexity. Thus, too, each science rests on the truths of the sciences that precede it, while it adds to them the truths by which it is itself constituted. Comte's series or hierarchy is arranged as follows:—(1) Mathematics (that is, number, geometry, and mechanics), (2) Astronomy, (3) Physics, (4) Chemistry, (5) Biology, (6) Sociology. Each of the members of this series is one degree more special than the member before it, and depends upon the facts of all the members preceding it, and cannot be fully understood without them. It follows that the crowning science of the hierarchy, dealing with the phenomena of human society, will remain longest under the influence of theological dogmas and abstract figments, and will be the last to pass into the positive stage. You cannot discover the relations of the facts of human society without reference to the conditions of animal life; you cannot understand the conditions of animal life without the laws of chemistry; and so with the rest.

This arrangement of the sciences and the Law of the Three States are together explanatory of the course of human thought and knowledge. They are thus the double key of Comte's systematisation of the philosophy of all the sciences from mathematics to physiology, and his analysis of social evolution, which is the basis of sociology. Each science contributes its philosophy. The co-ordination of all these partial philosophies produces the general Positive Philosophy. 'Thousands had cultivated science, and with splendid success; not one had conceived the philosophy which the sciences when organised would naturally evolve. A few had seen the necessity of extending the scientific method to all inquiries, but no one had seen how this was to be effected.... The Positive Philosophy is novel as a philosophy, not as a collection of truths never before suspected. Its novelty is the organisation of existing elements. Its very principle implies the absorption of all that great thinkers had achieved; while incorporating their results it extended their methods.... What tradition brought was the results; what Comte brought was the organisation of these results. He always claimed to be the founder of the Positive Philosophy. That he had every right to such a title is demonstrable to all who distinguish between the positive sciences and the philosophy which co-ordinated the truths and methods of these sciences into a doctrine' (G. H. Lewes).

We may interrupt our short exposition here to remark that Comte's classification of the sciences has been subjected to a vigorous criticism by Mr. Herbert Spencer. Mr. Spencer's two chief points are these:—(1) He denies that the principle of the development of the sciences is the principle of decreasing generality; he asserts that there are as many examples of the advent of a science being determined by increasing generality as by increasing speciality. (2) He holds that any grouping of the sciences in a succession gives a radically wrong idea of their genesis and their interdependence; no true filiation exists; no science develops itself in isolation; no one is independent, either logically or historically. M. Littré, by far the most eminent of the scientific followers of Comte, concedes a certain force to Mr. Spencer's objections, and makes certain secondary modifications in the hierarchy in consequence, while still cherishing his faith in the Comtist theory of the sciences. Mr. Mill, while admitting the objections as good, if Comte's arrangement pretended to be the only one possible, still holds that arrangement as tenable for the purpose with which it was devised. Mr. Lewes asserts against Mr. Spencer that the arrangement in a series is necessary, on grounds similar to those which require that the various truths constituting a science should be systematically co-ordinated, although in nature the phenomena are intermingled.

The first three volumes of the Positive Philosophy contain an exposition of the partial philosophies of the five sciences that precede sociology in the hierarchy. Their value has usually been placed very low by the special followers of the sciences concerned; they say that the knowledge is second-hand, is not coherent, and is too confidently taken for final. The Comtist replies that the task is philosophic, and is not to be judged by the minute accuracies of science. In these three volumes Comte took the sciences roughly as he found them. His eminence as a man of science must be measured by his only original work in that department,—the construction, namely, of the new science of society. This work is accomplished in the last three volumes of the Positive Philosophy and the second and third volumes of the Positive Polity. The Comtist maintains that even if these five volumes together fail in laying down correctly and finally the lines of the new science, still they are the first solution of a great problem hitherto unattempted. 'Modern biology has got beyond Aristotle's conception; but in the construction of the biological science, not even the most unphilosophical biologist would fail to recognise the value of Aristotle's attempt. So for sociology. Subsequent sociologists may have conceivably to remodel the whole science, yet not the less will they recognise the merit of the first work which has facilitated their labours' (Congreve).

We shall now briefly describe Comte's principal conceptions in sociology, his position in respect to which is held by himself, and by others, to raise him to the level of Descartes or Leibnitz. Of course the first step was to approach the phenomena of human character and social existence with the expectation of finding them as reducible to general laws as the other phenomena of the universe, and with the hope of exploring these laws by the same instruments of observation and verification as had done such triumphant work in the case of the latter. Comte separates the collective facts of society and history from the individual phenomena of biology; then he withdraws these collective facts from the region of external volition, and places them in the region of law. The facts of history must be explained, not by providential interventions, but by referring them to conditions inherent in the successive stages of social existence. This conception makes a science of society possible. What is the method? It comprises, besides observation and experiment (which is, in fact, only the observation of abnormal social states), a certain peculiarity of verification. We begin by deducing every well-known historical situation from the series of its antecedents. Thus we acquire a body of empirical generalisations as to social phenomena, and then we connect the generalisations with the positive theory of human nature. A sociological demonstration lies in the establishment of an accordance between the conclusions of historical analysis and the preparatory conceptions of biological theory. As Mr. Mill puts it:—'If a sociological theory, collected from historical evidence, contradicts the established general laws of human nature; if (to use M. Comte's instances) it implies, in the mass of mankind, any very decided natural bent, either in a good or in a bad direction; if it supposes that the reason, in average human beings, predominates over the desires or the disinterested desires over the personal,—we may know that history has been misinterpreted, and that the theory is false. On the other hand, if laws of social phenomena, empirically generalised from history, can, when once suggested, be affiliated to the known laws of human nature; if the direction actually taken by the developments and changes of human society can be seen to be such as the properties of man and of his dwelling-place made antecedently probable, the empirical generalisations are raised into positive laws, and sociology becomes a science.' The result of this method is an exhibition of the events of human experience in co-ordinated series that manifest their own graduated connection.

Next, as all investigation proceeds from that which is known best to that which is unknown or less well known, and as, in social states, it is the collective phenomenon that is more easy of access to the observer than its parts, therefore we must consider and pursue all the elements of a given social state together and in common. The social organisation must be viewed and explored as a whole. There is a nexus between each leading group of social phenomena and other leading groups; if there is a change in one of them, that change is accompanied by a corresponding modification of all the rest. 'Not only must political institutions and social manners on the one hand, and manners and ideas on the other, be always mutually connected; but further, this consolidated whole must be always connected by its nature with the corresponding state of the integral development of humanity, considered in all its aspects of intellectual, moral and physical activity' (Comte).