method. All the others, even that of Man, are preparatory to it. Here alone can the general sense of natural law be decisively developed, by eliminating for ever arbitrary wills and chimerical entities, in the most difficult case of all. The old philosophy must be doomed to extinction, when a regular study is able to disclose the laws of the continuous variation of human opinions. I have repeatedly said that this science permits, above any other, the prominent use of à priori considerations, both from its position in the hierarchy, by which it depends on all the rest, and in virtue of the perfect unity which is given to it by its plenitude of logical resources. It will soon be admitted to be the most logical of all the sciences, considering the degree of precision compatible with the nature of the phenomena, since the most difficult and varied speculations are naturally connected with one single fundamental theory. But the most striking feature to us is the extension of the means of investigation required by, and involved in, this most complex subject of human study. It enjoys all the resources of the anterior sciences; but they would be almost useless, and even deceptive, without the addition of the historical method, properly so called, which investigates, not by comparison, but by gradual filiation. We have reviewed this method in its dogmatic form, and in its application, and we have seen how it must preponderate over all other resources, so as to bring out and utilize the properties of positive investigation, by which the regular action of human faculties is to be perfected. Thus a universal logical method corresponds in this case to a universal scientific view; and the result is that the human mind here finds its natural position. It would occupy too much space to exhibit the reaction of this science upon those that precede it; and it would be as yet premature. I have done what I proposed, in constituting the true system of positive philosophy, as a result of the preparation instituted by Bacon and Descartes; and its practical construction is a work for a future time,— probably near at hand.

These are the five phases of the positive method, through whose succession the scientific spirit rises gradually to the dignity of the philosophical spirit, effacing at length the

provisional distinction between them which had been necessary during the earlier part of the human evolution. If we consider the miserable theoretical state from which human reason set out, we shall not wonder that so long a tutelage was required to enable Man to extend to his abstract and general speculations the same mental training that popular wisdom spontaneously employs in its partial and practical acts. Though there can be no exemption from the necessity of reproducing this natural succession for ever, the systematic education now prepared for, in place of the instinctive, will render the process much more rapid and easy; and I rejoice in the privilege of having prepared it for my successors, by the elaboration of this my original scheme.

In this chapter, I have wrought out the most difficult and important part of my work, in as far as it relates to our general conclusions, according to the constant preponderance of our logical over our scientific needs; and especially at a time when, the doctrine being in a backward state, the philosophical procedure must consist in instituting the Method completely. What I have done in this direction must be considered as a natural equivalent of the discourse of Descartes on method, allowing for the diversities resulting from the new situation of modern mind, and the new corresponding wants. Descartes had for his subject the introductory evolution which had been for two centuries preparing for the ascendancy of rational positivism; while I have had to examine the fulfilment of that preparation, in order to determine the final constitution of a sound philosophy in connection with social objects,—a view which Descartes avoided, but which Bacon already anticipated. This most difficult part of my task being achieved, I have only to complete my object by making a rapid scientific survey, to answer to the logical, and to venture upon an anticipation of the action of the positive philosophy, when it shall have attained its full maturity.

t

CHAPTER XIV.

ESTIMATE OF THE RESULTS OF POSITIVE DOCTRINE IN ITS PREPARATORY STAGE.

AS I have intimated, our scientific conclusions cannot be so important or so extensive as our logical conclusions, because they relate to a system of knowledge scarcely yet instituted: yet it is necessary to follow up the logical summary with a sketch of the proper nature and connection of the abstract studies that we have examined in succession; our present view regarding them as so many necessary elements of a single body of doctrine, according to our principle.

We have perceived throughout that, in the case of the human evolution at least, there exists a natural agreement between our knowledge and our needs. The knowledge which is inaccessible to us is precisely that which could answer no purpose but gratifying a vain curiosity. We have no concern with anything but the laws of phenomena which affect human beings; such action, however indirect, constituting a basis of positive estimate, the full realization of which can follow only very remotely the manifestation of the corresponding needs, at any rate till we can institute a better research. This scheme must comprehend, on the one hand, Humanity itself, in its existence and action; and, on the other hand, the general medium, whose permanent influence is an essential element in the whole movement. Every scientific, as well as logical consideration, shows the necessity of the study of the medium; and thus naturally divides science into two departments,-inorganic and organic science; the first being the indispensable preparation for the second: and the second simply modifying the phenomena of the first by a nobler action. The three essential modes of the first order--the mathematical, physical and chemical, and the two which are proper to organic existence -the individual and the social, thus present a scientific

THE MATHEMATICAL ELEMENT.

387

The Mathema

tical element.

series precisely correspondent to the logical that we have just reviewed; and its five stages will, in like manner, lead us up to the normal state of true philosophy. Mathematical existence is the simplest and most universal of all; and, in a geometrical form first, and then a mechanical, is the only kind of existence cognizable by us in the many and important cases in which our investigation can proceed only on visual evidence. This is the scientific ground of the priority of the mathematical element in positive philosophy; and, scientifically speaking, the only great result derivable from it is a systematic development of the sense of logical laws, without which physical laws could not be conceived of. Thus, numerical speculations, the source of the logical instrument of analysis, have historically furnished the earliest manifestation of ideas of order and harmony, gradually extended afterwards to the most complex subjects.. Apart from that, mathematical science evidently consists especially in geometry and mechanics, answering to our primitive notions of existence and action; for, in the statical case, all phenomena are reducible to relations of magnitude, form, or position; and, in the dynamical case, to mere movement, partial or general. Such a simplification is practically inconvenient, and may be misleading, as the encroachments of geometers plainly show: but it is true in an abstract sense; and therefore universally true, whatever other conditions may be added in cases of growing complexity. Geometry, too, is more general than mechanics; for we can conceive of existence without motion; as in the case of stationary stars, which come under only geometrical conditions; and to geometry we owe the earliest conception of laws of agreement, which may be regarded quite apart from those of succession. Yet, in a scientific sense, Mechanics is the more important branch of mathematics, on account of its more direct and complete relations with the rest of natural philosophy; and on account also of the implication of mechanical speculations with geometrical considerations; a drawback upon their logical perfection, but a source of marked reality, enabling them to represent the whole of mathematical existence. This introduction to natural philosophy, with its astronomical manifestation, is,

x

we know, the only portion of inorganic science which has attained its full normal constitution; and for this reason I hold it extremely important to show the coincidence between the primary laws on which this constitution depends, and the laws which seem to be proper to organic existence; that we may perceive by the direct correlativeness of the two extreme cases, the tendency of all our knowledge to scientific unity, corresponding to the logical unity already recognized. The intermediate ideas,-those of the physicochemical order,—will no doubt add their confirmation when they shall have become rationally established.

I have shown that the physical laws which Application to Sociology. are the basis of the theory of motion and equilibrium, and therefore all their consequences, are as applicable to the mechanical phenomena of living bodies as to any others (allowing for the difficulties arising from a complication of details); and we have seen, in a more special manner, that the study of animal mechanics, in the province of biology, must begin with such an application, and would be wholly unintelligible without it; but we have now to go much further, showing that the application must extend even to the social form of existence. As to the first of these laws, Kepler's law of inertia, improperly so called,-seen in its true light as the law of mechanical persistence, is merely a particular case of the tendency of all natural phenomena to persevere in their state, unless disturbed; a tendency specially established with regard to the most simple and general phenomena. I have traced back the biological case of Habit to this principle, modified only by the characteristic intermittence of the corresponding phenomena. In social life, less rapid and more durable than individual life, we see an analogous .exemplification in the obstinate tendency of every political system to perpetuate itself. In physics, again, we have noticed, in acoustics, phenomena which prove that, in the smallest molecular changes, there is a disposition to the reproduction of acts which were before supposed proper to living beings, and which evidently come under the law of mechanical persistence. It is impossible to deny here the subordination of all natural effects to some universal laws, modified according to the conditions of each case. It is