and private. At a time when practical considerations are excessively preponderant, I have restored the dignity of philosophy, and established the social reality of sound. theoretical speculations by instituting a systematic subordination of the one to the other, such as is essential to social stability and greatness. At a time when human reason is liable to be frittered away under an empirical system of dispersive speciality, I have announced, and even introduced the reign of the spirit of generality, under which alone a universal sentiment of duty can prevail. These three objects have been attained by the institution of a new science, the last and most important of all, which is as positive and logical as any of the other sciences I have treated of, and without which the system of true philosophy can have neither unity nor substance. The future progress of Sociology can never offer so many difficulties as this original formation of it; for it furnishes both the method by which the details of the past may serve as indications of the future, and the general conclusions which afford universal guidance in special researches. This scientific foundation completes the elementary system of natural philosophy prepared by Aristotle, announced by the scholastics of the Middle Ages, and directly proposed, in regard to its general spirit, by Bacon and Descartes. All that remains for me to do is to co-ordinate the elements which I have passed under review, in the form of six fundamental sciences, under the heads of Method, Doctrine, and the general unity of the positive philosophy.

CHAPTER XIII.

FINAL ESTIMATE OF THE POSITIVE METHOD.

Now

OW that we have completed our review of the six great sciences, it is evident that the hierarchical succession from Mathematics to Sociology is the means by which our understanding is gradually borne up to the definitive point of view of the positive philosophy, the true general spirit of which could not otherwise be disclosed. We have traced an individual evolution corresponding to the aggregate one, that we may, in a general way, consider to have set out from the conjoint philosophical and scientific action of Bacon and Descartes, in alliance with Kepler and Galileo. The entire survey was necessary to the estimate, methodical and doctrinal, of each principal phase of rational positivism; and the homogeneousness of the partial disclosures has prepared us for their convergence towards an identical final philosophy, never till now ascertained. All that remains for me to do is to exhibit the co-ordination of the different conceptions, logical and scientific, under a genuine principle of unity; by which we may discern what will be the intellectual and social action of the system which will henceforth guide the conduct of human life. That such a philosophical unity is the first condition of social reorganization the preceding chapter has shown us; and those who do not feel the social want are becoming more and more aware of the speculative necessity. The ancient system being worn out and discarded, and new materials and instrumentalities being obtained, the time has fully arrived for consolidating the great speculative evolution of the last two centuries, under penalty of sinking into the mental degradation which disgraced the old Greek and Medieval populations on the expiration of an old régime, and before the institution of

a new.

Principle of
Unity.

ever.

Which element shall

The necessary co-ordination is an easy task, because positivity has been presented to us in a series of states, more and more complete, each of which includes all that went before; so that the last, the most complex that human reason can ever be employed upon,-is the universal bond of connection among all positive speculations whatLaborious as has been our examination of the whole series, our conclusions may, by such preparation, be drawn briefly, and without any difficulty. The chief question is as to which of the speculative elements must finally prevail over the rest,— philosophical unity requiring the preponderprevail. ance of one, for the practical development of the positive principle. The constitution of the scientific hierarchy shows that the intellectual pre-eminence must belong either to the first or the last degree of the scale; either to mathematics or sociology; for they alone can evidently be universal, the one from its origin, and the other from its destination. Mathematical science (in which we may here include astronomy, as the embodiment of mathematics) claims a logical supremacy, in virtue of the indisputable extension of geometrical and mechanical laws to all possible orders of phenomena. In the other view, Sociological philosophy (in which we may include biology, as its basis) may establish its claim, now that the condition of genuine positivity is fulfilled, since all speculations of every kind may be regarded as necessary results of the speculative evolution of the human race. It will be undisputed that the two intermediate sciences, physics and chemistry, have no pretension, on account of either origin or destination, to be more than powerful auxiliaries of the rival impulsions. The question lies between mathematics and sociology.

According to my theory, Mathematics necessarily prevailed during the long training of the human mind to positivism; and Sociology alone can guide genuine speculation when its basis is once fully ascertained. This distinction, which is the first and greatest of First general Conclusion. our general conclusions, involves at once the explanation and the solution of the lamentable antagonism which has been growing up for three

WHICH ELEMENT SHALL PREVAIL.

347

centuries between the scientific genius and the philosophical, the one having claimed a positivity, and the other a generality, which are now for the first time reconciled. Before the progression of the human race was referred to natural laws, men neglected the consideration of generality for that of positivity, because the generality remained connected with a worn-out system which had to be discarded before progress could be made: but now that the positive character is extended to all orders of speculation, sociological conceptions may resume the supremacy which belongs to their nature, and of which they were only provisionally deprived during the last medieval period, by the temporary exigencies occasioned by the positive evolution.

We have seen, throughout this Work, that Mathematical science is the source of positivity: but we have also seen that mathematical conceptions are by their nature incapable of forming a genuine, complete, and universal philosophy. Yet all the attempts for three centuries past to constitute a philosophy that should replace that which was worn out have proceeded on the mathematical principle. The only one of all these premature attempts which deserves eternal remembrance on account of its services is the Cartesian philosophy, which furnished the type of those that followed, while very superior to them all. This great scheme, which laid down geometry and mechanics as the basis of universal science, happily fostered for a century, in spite of its enormous inconveniences, the rise of positivity in all the chief departments of inorganic philosophy: but it not only failed to include moral and social researches, and was therefore imperfect, but it introduced disturbance into the simplest biological speculations, which has not even yet entirely subsided. However vast might be the progress of mathematical theories, they could never get over this imperfection, which became the more manifest, the stronger were the efforts to apply them; and by degrees their application was left to inferior workers, through a confused, but increasing sense in superior minds of their inaptitude. The attempts to find a starting-point in the physico-chemical sciences, unjustifiable as they were, afford evidence of the need that was felt of a universal connection, and explain why even philosophers, properly so called, have deserted

the moral and social point of view for what they took to be a surer basis. The fruitlessness of the notion is no evidence that it was given up by scientific men, who have still hoped, with every accession of discovery, to find their mathematical principle universally applicable at last; and the practical effect of their persuasion was simply to prejudice them against any other systematic conception, and even against any portion of natural philosophy which was too complex to be brought under mathematical management. This is, even now, the great obstacle in the way of philosophical advancement; and in order to see how alone positive speculations may be brought into universal connection, the best way evidently is to compare the opposite courses of proceeding, the mathematical and the sociological.

The Mathe

ment.

The claims of the mathematical spirit relate matical ele- chiefly to Method; yet, as scientific logic there first arose, it could develop all its characteristics only by being extended to more and more complex subjects, till, through greater and greater modification, it finally entered into the most difficult speculations of all, and those which required a combination of all anterior means of investigation, as well as those which were proper to themselves. If, then, scientific men should stand forward to represent the positive attainments made in their respective sciences, the sociologists would be the only ones who could be regarded as having a complete knowledge of the positive method, while the geometers would have a more imperfect conception of it than any others, precisely because they know it only in its rudimentary state, while the sociologists alone would have carried it out completely. I have shown how the relative point of view, in 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