CO-ORDINATION OF PHASES OF POSITIVE SCIENCE. 379 combination of which determines the gradual institution of the positive method, in a spontaneous manner at first, and afterwards systematically. As the method is neither more nor less than a philosophical extension of popular wisdom to abstract speculation, it is clear that its basis, corresponding with that of common sense, admits of no useful dogmatic explanation. If on this ground we decline looking for such dogmatic explanation of the lowest subjects of speculation,—of which all we can say is that our ideas are spontaneous and universal,—much more must we abstain from such barren and vicious systematizing in logical researches, properly so called. Thus are the logical and scientific points of view to be finally regarded as correlative and indivisible aspects of each positive theory, neither being in reality more susceptible than the other of an abstract and general appreciation, independent of any determinate manifestation. Thus they have been treated throughout this work, in which the logical training has always coexisted with the scientific, and their connection being such that the scientific results of one science have often been found to be the logical resources of another; a fact which shows the impossibility of separating them. Relations of Thus have we ascertained the composition of the positive' method: and we have only further to mark out the systematic co-ordination of the chief. successive phases which it has naturally presented. phases. Mathematics. No irrational exaggeration of the claims of Mathematics can ever deprive that part of philosophy of the property of being the natural basis of all logical education, through its simplicity, abstractness, generality, and freedom from disturbance by human passion. There, and there alone, we find in full development the art of reasoning, all the resources of which, from the most spontaneous to the most sublime, are continually applied with far more variety and fruitfulness than elsewhere; whereas, the art of observation, though there receiving its first scientific application, is scarcely traceable, even in mechanics. The more abstract portion of mathematics may in fact be regarded as an immense repository of logical resources, ready for use in scientific deduction and co-ordination: yet, as the human mind is indisposed to the most abstract speculation, it is geometry, rather than analysis, that will always be, in a logical view, the chief of the three branches of mathematics, and the fittest for the first elaboration of the positive method. When Descartes chose geometry for the ground of his organization of the relation of the abstract to the concrete, he made it the centre of mathematical conceptions, as analysis found there vast material and a noble application, in return for the generality which it imparted. Mechanics, on the contrary, though yet more important than geometry, in a scientific view, has by no means the same logical value, on account of its greater complexity; and the obligations of analysis to it are but secondary and indirect. In passing from geometrical to dynamical speculations, we feel how near we are to the limits of the mathematical province, from the extreme difficulty of treating the simplest questions in a thoroughly satisfactory manner. We have seen abundant reasons, in the course of our survey, why the mind that confines itself within the mathematical province is subject to a variety of fatal snares, and very ill prepared for the loftiest aims of human reason. Without recapitulating the faults and errors arising from the misuse of the mathematical spirit, it is enough to say that when a sound philosophy prevails, it will be felt that the first phase of positive logic not only cannot dispense with those which follow, but must look to them for much reactive assistance from their combination, without which mathematical logic itself cannot be completely understood and valued. Astronomy. These considerations show us the value of the next phase, the astronomical, in which the positive method obtains a second degree of development, in the closest connection with the first. It is overlaid, as we have seen, with mathematical ideas and procedures; but, discarding these as far as possible, we shall find that the distinction, logical and scientific, between this phase and the last is much greater than is commonly supposed. In geometry, the disproportion between the observation employed and the consequences obtained is so great as to render the function of observation almost in appreciable: whereas, in astronomy it is distinct and direct. Here, as the simplest and most general of the four resources for obtaining knowledge, it shows what may be done, in the most unfavourable situation, by a single sense in ascertaining the most intellectual kind of truth. Not less striking is the intervention of the logical processes which here guide an investigation singularly indirect and thus if, in a scientific view, astronomy is fairly regarded as the most fundamental part of the system of inorganic knowledge, it is no less, in a logical view, the most perfect type of the general study of nature. Here men learned to modify the earliest philosophy by conceptions derived from the study of the external world; and here we find the fittest dogmatic exposition of rational positivity. Here, throughout all time, will be found the first philosophical sense of natural law; and here may be learned what is meant by the explanation of any phenomenon, by means of resemblance or connection. The whole of its historical and dogmatic course discloses the agreement between our conceptions and our observations which is the essential character of real knowledge. It yields us the true theory of scientific hypotheses: and it proves that its rationality is not less satisfactory than its positivity, by offering the first and most perfect example, thus far indeed the only one, of that rigorous philosophical unity which must be kept in view in every order of speculation. No other science, again, has so familiarly manifested that rational prevision which is the most marked characteristic of positive theory. Its imperfections proceed from a want of definiteness in the circumscription of the objects and the subjects of its researches; an imperfection which time will cure. Meanwhile it appears that, contrary to popular notions, the astronomical phase is a stage in advance of the mathematical, in all essential logical respects, and much nearer the true philosophical condition. For logical purposes, we may combine physics and chemistry, though for scientific examination they must be separated. The Physics and only logical feature of chemistry is its art of systematic nomenclature: otherwise, it merely applies, in a less perfect way, the general method of investigation developed by physics. In combination, these two sciences form the bond between the two extremes, logically and scientifically: on the one hand completing the study of the universe, and preparing for that of Humanity, and, on the other, exhibiting an intermediate complexity of subject, and corresponding to a medium state of positive investigation. They require all foregoing resources for investigation, and present a new mode of observing. In physics, the experimental method takes its rise; and it is immediately attended by the logical resource of the corpuscular or atomic theory; both being limited to the same kind of investigations. When the logical and scientific conditions proper to the position in the scale are fulfilled, there can be no doubt that this third phase of rational positivity will be found to be as superior to the astronomical phase as that is to the mathematical, imperfect as it now is in its oscillation between a barren empiricism and an oppressive mysticism, metaphysical or algebraic. The varied and complex nature of such an order of investigations could not admit, even under a better intellectual system, of a precision and co-ordination comparable to those permitted by celestial theories; but these imperfections, transient or permanent, do not prevent the sense of natural law from receiving here a considerable extension, by being applied to the most complex phenomena of inorganic existence. The next step is from inert to living nature: Biology. and we see the positive method rising to a new application much more different from the three former than they are from each other, and which will make this new science as essentially superior to the preceding by its logical plenitude as by its scientific importance, when its conditions are thoroughly understood. Thus far, investigations have permitted and required an almost indefinite parcelling out; but the interconnection of biological phenomena is such that no analytical operation can be conceived of otherwise than as introductory to a synthetical determination, the division between the abstract and the concrete being all the while maintained, and the more carefully on account of the small interval that separates them. A radical change in the scientific system now there BIOLOGY. 383 fore enters in, making the spirit of generality overrule the spirit of detail, till then preponderant, and thus carrying forward our reason remarkably towards its true natural condition. The statical view now comes out clearly in connection with the dynamical, in a manner especially suitable to biological speculations, in which these two kinds of estimate appear more distinct and correlative than in any former application. But the grand feature of this fourth phase is the vast extension of the general art of observing, then augmented by the institution of the comparative method, hitherto very subordinate and obscure, but now proved to be the most powerful logical instrument applicable to such speculations. Corresponding with it, and summing up its results, we have, under the same phase, the theory of classification. The logical condition of the phase ought to be judged of by this double creation, and not by its existing imperfection, which is owing to its more recent formation, its higher complexity, and an inferior fulfilment of the preparatory conditions of its rational culture. The sense of natural law must arise out of inorganic research; but it could not acquire its full efficacy till it was extended to biological speculations, which are above all adapted to discredit absolute notions by exhibiting the immense variety of modes of existence. Great as is the advance attained in this phase, it remains no less merely introductory than the rest, though holding a higher place. Its insufficiency becomes broadly apparent when we advance from the study of the organic life, by which it is least separated from the foregoing sciences, to the study of animality; for then, in applying ourselves to the highest positive speculations, in contemplating the moral and intellectual functions of the brain, we become at once sensible of the irrationality of such a scientific constitution: for the most decisive case of all cannot be understood but by subordinating the study of it to the ulterior science of. social development, for the reasons already assigned to show the impossibility of understanding our mental nature from the individual point of view; a method which must be unproductive in whatever way it is instituted. In every view, social science offers the attributes of a completion of the positive Sociology. |