comte, auguste - the positive philosophy vol III

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either to mathematics or sociology; for they alone can evidently be uni- versal,—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 our general conclusions, involves at once the explanation and the solution of the lamentable antagonism which has been growing up for three 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 ail 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

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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 there; 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 claims of the mathematical spirit relate 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

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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 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

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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 then may be found in mathematical science, fruitless 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 was, 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

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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, Theo 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 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 a 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, speaking more exactly, the social. This is the only one 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

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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 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 hail 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, and 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

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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, because it is the basis of all speculation what ever; but the same decision may be reached by considerations of concrete science, and even be aesthetic 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 sci- ence,—not excepting even biology. The general interests of concrete study require therefore that the direction of abstract philosopher should

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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 aesthetic 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 aesthetic 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-aesthetic 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 aesthetic 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 aesthetic 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 abandonment if the mathematical spirit loses its rank in scientific speculation. I might allege in the first place, that there would be no great harm in retarding the progress of a kind of activity which, from its facility, and its adaptation to the commonest inclinations, threatens to absorb all others that are more noble. There can never be any serious apprehension that the growth of ideas and feelings suitable to a renovated social condition will proceed so fast and so far as to occasion any dangerous industrial negligence: and if such a thing could happen, the new philosophy, occupying the true point of view, would sufficiently rectify the fault. The mathematicians may be incapable of estimating social researches, but sociologists are free from their blindness, and can never possibly underrate mathematical labours. Again, we stand in much greater need, for industrial advancement, of a better use of means already acquired than of the unregulated accumulation of new ones: so that the restraint of synthetic

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tendencies is precisely the safeguard that we want against the desultory enterprises of wild analytical impulses: and thus again is the sociological requite more favourable than the mathematical to material improvement. Once more, when the action of man upon nature is duly systematized under the new body of doctrine, it must be done under the guidance of sociological philosophy, which alone is able to combine all the scientific aspects requisite for the great work,—the conditions and difficulties of which are yet scarcely suspected by our engineers, as I hinted in my former volume. Near the beginning of that volume I pointed out the true principle which must regulate the agreement between contemplation and action: and this reference must suffice, under my inability to go further into the subject here. Thus it appears that the supremacy of sociological philosophy over the mathematical is confirmed by all concrete, aesthetic, and technical considerations. The toilsome and protracted preparations by which this position must be attained is shown by the whole economy of this Work; and especially by the expositions of this volume. The vigour and patience requisite for the scientific and logical preparation, and for the ability to connect special progress with the general movement, form a striking contrast with the ease with which mathematicians qualify themselves for the authority which they claim. A few years spent in pursuing one kind of studies so simple as to be accessible to average ability, are the mathematical qualification; but the result has been, in the most triumphant days of mathematical ambition, a supremacy more apparent than real, and wholly destitute amidst all its pretensions to scientific universality, of the practical reality which belongs to sociological ascendancy.

This unity, thus established and regarded both historically and dogmatically, puts an end to the long and fatal antagonism between the conceptions which relate to Man, and those which concern the external world. Hitherto they have been concluded to be irreconcilable; but my philosophical solution combines them entirely and for ever. I need not repeat the history of this antagonism, from the first antipathy between the theological and positive spirit owing to their assumption of the opposite points of view through the Cartesian compromise, and the struggles of the mathematical philosophy with expiring theology and metaphysics, up to the present hour, when the solution is offered by the extension of the positive spirit to moral and social speculation, affording all the positivity of the one and all the generality of the other. With this antagonism disappears that other fatal one, closely implicated with it, by which

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intellectual progress appeared to be contradictory to moral progress. The state of things under which mental requirements gradually prevailed over moral needs, dates from the beginning of the modern transition,— and it was its most deplorable condition. The more deplorable that condition, the more regard is due to the philosophy which alone can resolve the antagonism. We have seen how this philosophy takes up the best work of Catholicism, where Catholicism let it drop, through its connection with a worn-out system. The natural preponderance of Morals which I have shown to be ascribable to the positive system, is quite as indispensable to the efficacy of the intellectual, as of the social evolution; for indifference to moral conditions, so far from corresponding with the exigencies of intellectual conditions, is a growing impediment to their fulfilment, inasmuch as it impairs the sincerity and dignity of speculative efforts, already too subservient to personal ambition, so as to destroy, in course of time, the very germ of genuine scientific progress. To make this connection perfectly clear, it is necessary to strip away the last metaphysical illusions, and show what is the true human point of view,—that it is not individual but social; for under either the statical or the dynamical aspect, Man is a mere abstraction, and there is nothing real but Humanity, regarded intellectually or, yet more, morally. It is only through its holding this view, that the theological philosophy has retained any of its influence to this day; and the fate of the metaphysical philosophy is decided by its inability to treat of Man otherwise than individually. The same vice marked the positive system, while it was directed by the mathematical spirit alone; and this compelled philosophers, as Cabanis and Gall, for instance, to fix on biology as the centre of scientific unity. This was so far a good as that it brought the modern centre of organization much nearer to its real seat; but it would not answer further than for a necessary transition; and it protracted the old intellectual system by impeding the development of sound social speculation, which it looked upon as merely a natural corollary of biological studies. Whether the science of the individual is instituted metaphysically or positively, it must be utterly ineffectual for the construction of any general philosophy, because it is excluded from the only universal point of view. The evolution of the individual mind can disclose no essential law: and it can afford neither indications nor verifications of any value unless brought under the methods of observation taught by the evolution of the human mind in general. Thus, the biological phase is only the last introductory stage, as each of the preceding sciences had