opposition to the absolute spirit of the old philosophy, is the distinctive mark of the positive philosophy;-now, this relative spirit is scarcely perceptible at all in mathematical conceptions, the extreme facility of mathematical deduction, often little other than technical mechanism, tending to deceive us as to the real scope of our knowledge. There is no lack of examples among geometers of inquisition into subjects wholly inaccessible to human reason; nor of obstinacy in substituting argument for observation. Sound biological speculation, on the contrary, perceives philosophy to rest on an historical basis; and this fulfilment of the first condition of positivism suffices to give sociology the supremacy. Again, the sense of the invariableness of natural laws cannot be much developed in mathematical researches, though it originated there; because the extreme simplicity of geometrical and mechanical phenomena hardly admits of a full and practical generalization of this great philosophical idea, notwithstanding the valuable confirmation arising from its extension to celestial phenomena. Hence it is that mathematicians drop the supposition of natural laws as soon as they encounter phenomena of any considerable degree of complexity, and especially when human action is in any way concerned; as we see by their pretended calculation of chances, through a special application of mathematical analysis, an extravagance which is wholly incompatible with true positivity, but from which the vulgar of our algebraists still expect, after a century of wasted labour, the perfecting of some of the most difficult of human studies. In the other sciences we find still increasing manifestations of the invariableness of natural laws; but in sociology alone we find the full illustration of it, because there it is extended to the most complex of all events, which were excluded even by the Cartesian philosophy. Whichever way we look at the positive method, we shall perceive the eminent logical superiority of the sociological over the mathematical point of view. All the logical resources that the human mind can employ are exemplified in mathematical practice; but, through the extreme simplicity of the subjects to which they are applied, the most important of the means cannot be defined; and their scope can be duly estimated only when their chief destination is found, amidst the difficulties of an increasing complexity of phenomena, in the series of departments of natural philosophy. A reaction ensues, which cannot but be highly favourable to mathematical science, while it exposes the precise value of its claims. The comparative method proper to biology, and the historical method proper to sociology, are the two greatest of logical creations, achieved in the face of extreme scientific difficulties but the disgraceful ignorance of almost all geometers of these two transcendent methods of logical investigation shows that it was not mathematics that furnished the conception, though some examples of them may be found in mathematical science, fruitless

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417 and unintelligible to all who have not derived them from their original source. So much for the logical estimate.

As for the scientific,-the superiority of the sociological spirit is no less evident, in regard to the universality required. Though the geometrical and mechanical point of view is universal, in as far as that the laws of extension and motion operate, in an elementary way, upon all phenomena whatever, yet, however valuable may be the special indications thence arising, they can never, even in the simplest cases, obviate the necessity of a direct study of the subject; and that direct study must always be the preponderant one. The mathematical conditions moreover become vague and imperfect in proportion to the complexity of the case, though they can never be absent, and must always be taken into the account, as I have shown by my estimate of astronomical conditions in sociology. In fact, though not in principle, mathematical science has restricted its claims to the field of inorganic philosophy, scarcely even contemplating the admission of chemistry in some remote future; a pretension very unlike that of the universality which was once proposed. Hence the necessity of other guidance in moral and social pursuit; and hence the confusion and barren social agitation of modern times. If restricted to the inorganic domain, the supremacy of mathematics becomes much less injurious: but even there it can last only till the physicists have learned to take the use and application of this powerful logical instrument into their own hands. As the most general laws of inert nature must remain for ever unknown to us, from our inevitable ignorance of cosmical facts, properly so called, the mathematical spirit can frequently handle physical questions only by such hypotheses about the mode of production of phenomena as I have before exposed. When the repugnance of physicists to admit geometers to solve physical problems shall have taken due effect, the supposed mathematical philosophy, which appeared, two centuries ago, to have taken possession of the whole field of human speculation, will be reduced to one province outside its own,-that of astronomy, which appears to belong properly to it, in virtue of the geometrical and mechanical nature of its corresponding problems. Even there, if we go to the extremity of the case, the mathematical interference in astronomy has a precarious and forced character, which will prove to be merely transitory. It is certain that astronomical, like physical, discovery has been much impeded by the intrusion of the geometers, who do not perceive, in the one case, any more than in the other, that the pursuit of any science is the work of students who understand the special destination of the instrument, logical or material, as well as its structure. The mathematicians would reduce the whole band of physical astronomers to the rank of mere settlers of certain coefficients, to the serious injury of astronomical discovery. In astronomy itself, then, it appears that the sway of the mathematical

VOL. II.

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spirit is likely, not to increase, but rapidly to decline, till it shall be at length restricted to its own province of abstract and concrete mathematics. It is only owing to the temporary needs of the human mind, during the preparation for discarding the old philosophy, that any other expectation was ever justifiable.

From these considerations I have been able to show, at least in the way of exclusion, that, on both logical and scientific grounds, the sociological spirit must be recognized as supreme, even without any elaborate contrast of its high aptitudes for universal direction with the impotence proper to the mathematical spirit. As the science is newly created, and now first proposed, this is not the place to exhibit at length its certain reactionary effects on the other sciences; nor would the few special examples which might already be cited meet with due appreciation till our mental habits are somewhat improved: so that it is chiefly à priori, under sound philosophical regulation, that the rational supremacy of the sociological spirit over every other kind, or rather degree, of the scientific spirit may be established: but the immediate grounds of this procedure are so unquestionable that they cannot but be assented to by all duly-prepared minds.

The only really universal point of view is the human, or, speakThe Sociologi- ing more exactly, the social. This is the only one cal element. which recurs and is perpetually renewed, in every department of thought; in regard to the external world as well as to Man. Thus, if we want to conceive of the rights of the sociological spirit to supremacy, we have only to regard all our conceptions, as I have explained before, as so many necessary results of a series of determinate phases, proper to our mental evolution, personal and collective, taking place according to invariable laws, statical and dynamical, which rational observation is competent to disclose. Since philosophers have begun to meditate deeply on intellectual phenomena, they have always been more or less convinced, in spite of all prepossession, of the inevitable reality of these fundamental laws; for their existence is always supposed in every study, in which any conclusion whatever would be impossible if the formation and variation of our opinions were not subject to a regular order, independent of our will, and the pathological change of which is known to be in no way arbitrary. But, besides the extreme difficulty of the subject, and its vicious management hitherto, human reason being capable of growth only in social circumstances, it is clear that no decisive discovery could be made in this way till society should have attained a generality of view which was not possible till our day. Imperfect as sociological study may yet be, it furnishes us with a principle which justifies and guides its intervention, scientific and logical, in all the essential parts of the speculative system, which can thus alone be brought into unity. It appears to me that the mere existence of this book is a sufficient testimony to

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the reality and fertility of the new general philosophy; for it presents the spectacle of the whole range of sciences subjected to one point of view, without interference with the independence of any, and with a confirmation instead of a weakening of their respective characters, by the power of a single thought-by the application of a single general law. Brief as my expositions have necessarily been, thoughtful readers cannot but be aware of the new light, generated by the creation of Sociology, cast upon all the foregoing sciences. Considering the inorganic sciences alone, in which such philosophical intervention is most questioned, we shall find the following results:

1. In Chemistry, the conception of facultative dualism, by which difficulties in high chemical speculation may be dealt with which had hitherto appeared insurmountable:

2. In Physics, the foundation of a sound theory of scientific hypotheses, for want of which the positivity of the leading conceptions was seriously impaired :

3. In Astronomy, the just estimate of sidereal astronomy,* aud the reduction of our researches to our own system:

4. In Mathematics, the rectification of the bases of Rational Mechanics, of the whole system of geometrical conceptions, and of the first procedures of analysis, ordinary and transcendental.

All these improvements, tending alike to consolidation and advancement, are due, more or less directly, to the supremacy of the historical view proper to sociology; the only view which permits our first and constant attention to be given to the statical and dynamical working out of questions relating to the respective constitution of the various parts of natural philosophy.

We may thus fairly decide that the philosophical principle of unity is afforded by Sociology, and not by Mathematics. As the varying constitution of the speculative class necessarily represents the corresponding situation of the human mind in general, the nascent positivism of the last three centuries has given to the mathematicians more and more of that authority which, till the end of the medieval period, had belonged to moral and social researches. This provisional anomaly will now come to an end; for, when sociological theory has once reached the positive state, there is nothing except the opposition of the ignorant and the interested, to prevent the human view from resuming its natural place at the head of all human speculation. I have said that this conclusion was not only the first but the greatest: and in fact, the question of supremacy is the only one important to decide, at the point that we have now reached. The only possible alternative is now decided, by considerations drawn from abstract science alone, according to the original conditions of this Work ;-that abstract science which, after Bacon, I have called the First Philosophy, Compare vol. i. p. 153, note.

*

because it is the basis of all speculation whatever; but the same decision may be reached by considerations of concrete science, and even by æsthetic contemplation: for the sociological organization of positive philosophy favours their expansion; whereas the mathematical mode, if fully carried out, would be fatal to it.

In regard to the first order of evidence,-if abstract science must be the main subject of speculative study, it must serve as the basis of concrete science, which can acquire rationality only by the ascertainment and due description of the philosophical elements concerned; and the mathematical spirit, urged too far, and countenancing the use of analysis alone, is incompatible with the reality and concentration necessary to the study of the existence of actual beings. The sociological spirit, on the contrary, while duly preserving its abstract character, is highly favourable, by both complexity of subject and generality of view, to the mental dispositions requisite for the rational cultivation of natural history, which indeed is, from its human and synthetic character, much more congenial with sociology than with any other fundamental science,— not excepting even biology. The general interests of concrete study require therefore that the direction of abstract philosophy should reside in the science in which the inconveniences of abstractness are reduced to the utmost, in virtue of the most complete reality of the habitual point of view. The same considerations apply to the æsthetic case. The sociological mode must be fittest to regulate the subordination of the sense of the beautiful to the knowledge of the true and the scientific spirit most disposed to unity must be most suitable to the synthetic character of æsthetic contemplation, which always, perceptibly or not, relates to the emotions of the human being. If the positive philosophy has been often reproached with its anti-æsthetic character, it is owing to the sway of the mathematical spirit for three centuries,-the dispersive and mechanical tendency of which affords fair ground for the reproach. By its contrasting character of true and fertile unity, the sociological philosophy will prove itself more favourable to Art than the theological, even in the polytheistic period. The positive spirit, in its sociological form, undertakes to disclose the general laws of the human evolution, of which the æsthetic evolution is one of the chief elements; and the requisite historical process is eminently adapted to exhibit the relation which must ever subordinate the sentiment of ideal perfection to the idea of real existence and by discarding henceforth all superhuman intervention, sociological philosophy will establish an irreversible agreement between the æsthetic and scientific points of view.

There may be somewhat more doubt in regard to the remaining case, that of Industry; because, depending as it does on the knowledge of the inorganic world, geometrical and mechanical first, and then physical and chemical,-it may appear to be in danger of