Our business, it is clear, is with theoretical researches, letting alone their practical application altogether. Though we may conceive of a course of study which should unite the generalities of speculation and application, the time is not come for it. To say nothing of its vast extent, it would require preliminary achievements which have not yet been attempted. We must first be in possession of appropriate Special concejjtions, formed according to scientific theories; and for these we have yet to wait. Meantime, an intermediate class is rising up, whose particular destination is to organize the relations of theory and practice; such as the engineers, who do not labour in the advancement of science, but who study it in its existing state, to apply it to practical purposes. Such classes are furnishing us with the elements of a future body of doctrine on the theories of the different arts. Already, Monge, in his view of descriptive geometry, has given us a general theory of the arts of construction. But we have as yet only a few scattered instances of this nature. The time will come when out of such results, a dejjartment of Positive philosophy may arise: but it will be in a distant future.
If we remember that several sciences are implicated in every important art, — that, for instance, a true theory of Agriculture requires a combination of physiological, chemical, mechanical, and even astronomical and mathematical science, — it will be evident that true theories of the arts must wait for a large and equable develo])ment of these constituent sciences.
One more preliminary remark occurs, before we finish the THE PRIMARY AND SECONDARY SCIENCES. 23 prescription of our limits, — the ascertainment of our field of inquiry. We must distinguish between the two classes of Natural science; — the abstract or general, Abstract which have for their object the discovery of science, the laws which regulate phenomena in all conceivable cases: and the concrete, particu- Concrete lar, or descriptive, which are sometimes called science.
Natural sciences in a restricted sense, whose function it is to apply these laws to the actual history of existing beings. The first are fundamental; and oiir business is with them alone, as the second are derived, and however important, not rising into the rank of our subjects of contemplation. We shall treat of physiology, but not of botany and zoology, which are derived from it. We shall treat of chemisti-y, but not of mineralogy, which is secondary to it. We may say of Concrete Physics, as these secondary sciences are called, the same thing that we said of theories of the arts, — that they require a preliminai'y knowledge of several sciences, and an advance of those sciences not yet achieved; so that, if there were no other reason, we must leave these secondary classes alone. At a future time Concrete Physics will have made progress, according to the development of Abstract Physics, and will afford a mass of less incoherent materials than those which it now presents. At present, too few of the students of these secondary sciences appear to be even aware that a due acquaintance with the primary sciences is requisite to all successful prosecution of their own.
We have now considered.
First, that science being composed of speculative knowledge and of practical knowledge, we have to deal only with the first; and Second, that theoretical knowledge, or science properly so called, being divided into general and particular, or abstract and concrete science, we have again to deal only with the first.
Being thus in possession of our proper subject, duly prescribed, we may proceed to the ascertainment of the true order of the fundamental sciences.
The classification of the sciences is not so easy a matter as it may appear. However elLificSion. natural it may be, it will always involve something, if not arbitrary, at least artificial; and in so far, it will always involve imperfection. It is impossible to fulfil, quite rigorously, the object of presenting the sciences iu their natural connection, and according to their mutual dependence, so as to avoid the smallest danger of being involved in a vicious circle. It is easy to show why. Historical and Every science may be exhibited under two dogmatic methods or procedures, the Historical and methods. ^i^q Dogmatic. These are wholly distinct from each other, and any other method can be nothing but some combination of these two. By the first method knowledge is presented in the same order in which it was actually obtained by the human mind, together with the way iu which it was obtained. By the second, the system of ideas is presented as it might be conceived of at this day, by a mind which, duly prepared and placed at the right l>oint of view, should begin to reconstitute the science as a whole. A new science must be pursued historically, the only thing to be done being to study in chronological order the different works which have contributed to the progress of the science. But when such materials have become recast to form a general system, to meet the demand for a moi*e natural logical order, it is because the science is too far advanced for the historical order to be practicable or suitable. The more discoveries are made, the greater becomes the labour of the historical method of study, and the more effectual the dogmatic, because the new conceptions bring forward the earlier ones in a fresh light. Thus, the education of an ancient geometer consisted simply in the study, in their due order, of the very small number of original treatises then existing on the dilferent parts of geometry.
The writings of Archimedes and Apollonius were, in fact, about all. On the contrary, a modern geometer comnronly finishes his education without having read a single original work dating further back than the most recent discoveries, which cannot be known by any other means. Thus the Dogmatic Method is for ever superseding the Historical, as we advance to a higher j^osition in science. If every mind had to pass through all the stages that every predecessor iu the study had gone through, it is clear that, however easy it is to learn rather than invent, it would be impossible HISTORICAL AND DOGMA'lIC METHODS OF STUDY. 25 to effect the purpose of education, — to place the student on the vantage-ground gained by the labours of all the men who have gone before. By the dogmatic method this is done, even though the living student may have only an ordinary intellect, and the dead may have been men of lofty genius. By the dogmatic method, therefore, must every advanced science be attained, with so much of the historical combined with it as is rendered necessary by discoveries too recent to be studied elsewhere than in their own records.
The only objection to the preference of the Dogmatic method is that it does not show how the science was attained; but a moment's reflection will show that this is the case also with the Historical method. To pursue a science historically is quite a different thing from learning the history of its progress. This last pertains to the study of human history, as we shall see when we reach the final division of this work. It is true that a science cannot l)e completely understood without a knowledge of how it arose; and again, a dogmatic knowledge of any science is necessary to an understanding of its history; and therefore we shall notice, in treating of the fundamental sciences, the incidents of their origin, when distinct and illustrative; and we shall use their history, in a scientific sense, in our treatment of Social Physics; but the historical study, important, even essential, as it is, remains entirely distinct from the 2)roper dogmatic study of science. These considerations, in this place, tend to define more precisely the spirit of our course of inquiry, while they more exactly determine the conditions imder which we may hope to succeed in the construction of a true scale of the aggregate fundamental sciences. Great confusion would arise from any attempt to adhere strictly to historical order in our exposition of the sciences, for they have not all advanced at the same rate; and we must be for ever borrowing from each some fact to illustrate another, without regard to priority of origin. Thus, it is clear that, in the system of the sciences, astronomy must come before physics, properly so called: and yet, several branches of physics, above all, optics, are indispensable to the complete exposition of astronomy. Minor defects, if inevitable, cannot invalidate a classification which, on the whole, fulfils the principal conditions of the case. They belong to what is essentially artificial in our division of intellectual labour. In the main, however, our classification agrees with the history of science; the more general and simple sciences actually occurrring first and advancing best in human history, and being followed by the more complex and restricted, though all wei'e, since the earliest times, enlarging simultaneously.
A simple mathematical illustration will precisely represent the difficulty of the question we have to resolve, while it will sum up the preliminary considerations we have just concluded.
We propose to classify the fundamental sciences. They are six, as we shall soon see. We cannot make them less; and most scientific men would reckon them as more. Six objects admit of 720 different dispositions, or, in populai" language, changes. Thus we have to choose the one right order (and there can be but one right) out of 720 possible ones. Very few of these have ever been proposed; yet we might venture to say that there is probably not one in favour of which some plausible reason might not be assigned; for Ave see the wildest divergences among the schemes which have been proposed, — the sciences which are placed by some at the head of the scale being sent by others to the further extremity. Our problem is, then, to find the one rational order, among a host of possible systems. True principle Now we must remember that we have to of classifica- look for the principle of classification in the t'ion. comparison of the different orders of phenomena, through which science discovers the laws which are her object. What we have to determine is the real dependence of scientific studies. Now, this dependence can result only from that of the corresponding phenomena. All observable ]>henomena may be included within a very few natural categories, so arranged as that the study of each category may be grounded on the principal laws of the preceding, and serve as the basis of the next ensuing.
This order is determined by the degree of simplicity, GeneraUty. <^>r. what comes to the same thing, of generality of their phenomena. Hence results Dependence. their successive dependence, and the greater or lesser facility for being studied.
FU>DAMENTAL PRINCIPLES OF CLASSIFICATION. 2^ It is clear, a priori, that the most simple phenomena must be the most general; for whatever is observed in the greatest number of cases is of course the most disengaged from the incidents of particular cases. We must begin then with the study of the most general or simple phenomena, going on successively to the more particular or complex. This must be the most methodical way, for this order of generality or simplicity fixes the degree of facility in the study of phenomena, while it detennines the necessary connection of the sciences by the successive dependence of their phenomena. It is worthy of remark in this j^lace that the most general and simple phenomena are the furthest removed from Man's ordinary sphere, and must thereby be studied in a calmer and more rational frame of mind than those in which he is more nearly implicated; and this constitutes a new ground for the corresponding sciences being developed more rapidly.
We have now obtained our rule. Next we j^roceed to our classification.
We ai'e first struck by the clear division of Inor<jcanic ami all natural phenomena into two classes — of Organic pheinorganic and of organic bodies. The orga- n"i»ena. nized are evidently, in fact, more complex and less general than the inorganic, and depend upon them, instead of being depended on by them. Therefore it is that physiological study should begin with inorganic phenomena; since the organic include all the qualities belonging to them, with a special order added, viz. the vital phenomena, which belong to organization. We have not to investigate the nature of either; for the positive philosophy does not inquire into natures. Whether their nature be supposed different or the same, it is evidently necessary to separate the two studies of inorganic matter and of living bodies. Our classification will stand through any future decision as to the way in which living bodies are to be regarded; for, on any supposition, the general laws of inorganic physics must be established before we can proceed with success to the examination of a dependent class of phenomena.
Each of these great halves of natural t t philosophy has subdivisions, inorganic physics must, in accordance with our rule of generality and the order of dependence of phenomena, be divided into two,., ^ sections — of celestial and terrestrial phenomena. Thus we have Astronomy, geometrical and mechanical, and Terrestrial Physics. The necessity of this division is exactly the same as in the former case.
Astronomical phenomena are the most general, simple, aud abstract of all; and therefore the study of natural philosoj^hy must clearly begin with them. They are themselves independent, while the laws to which they are subject influence all others whatsoever. The general eifects of gravitation preponderate, in all terrestrial phenomena, over all effects which may be peculiar to them, and modify the original ones. It follows that the analysis of the simplest terrestrial phenomenon, not only chemical, but even purely mechanical, presents a greater complication than the most compound astronomical phenomeuon. The most difficult astronomical question involves less intricacy than the sinaple movement of even a solid body, when the determiniug circumstances are to be computed. Thus we see that we must separate these two studies and proceed to the second only through the first, from which it is derived.
In the same manner, we find a natural division of Terrestrial Physics into two, according as we regard bodies in their mechanical or their chemical character. 2. 1 hysics. Hence we have Physics, properly so called, 3 Chemistrv. ''^^^ Chemistry. Again, the second class must be studied through the first. Chemical phenomena are more complicated than mechanical, and depend upon them, without influencing them in return. Every one knows that all chemical action is first submitted to the influence of weight, heat, electricity, etc., and presents moreover something which modifies all these. Thus, while it follows Physics, it presents itself as a distinct science.
Such are the divisions of the sciences relating to in-TT Orpa-vto organic matter. An analogous division arises in the other half of Natural Philosophy — the science of organized bodies.
Here we find ourselves j^resented with two orders of phenomena; those which relate to the individual, and ORGANIC PHYSICS. 29 those which relate to the species, especially when it is gregarious. With regard to Man, especially, this distinction is fundamental. The last order of phenomena is evidently dependent on the first, and is more complex. Hence we have two great sections in organic physics — Physiology, properly so called, and Social Physics, which is dependent on it. In all ^' P'lysiology. Social phenomena we perceive the working 2 Sociolof-v of the physiological laws of the individual; and moreover something which modifies their effects, and which belongs to the influence of individuals over each other — singularly complicated in the case of the human race by the influence of generations on their successors. Thus it is clear that our social science must issue from that which relates to the life of the individual. On the other hand, there is no occasion to suppose, as some eminent physiologists have done, that Social Physics is only an appendage to physiology. The phenomena of the two are not identical, though they are homogeneous; and it is of high importance to hold the two sciences separate. As social conditions modify the operation of physiological laws, Social Physics must have a set of observations of its own.
It would be easy to make the divisions of the Organic half of Science correspond with those of the Inorganic, by dividing j^hysiology into vegetable and animal, according to popular custom. But this distinction, however important in Concrete Physics (in that secondary and special class of studies before declared to be inappropriate to this wox'k), hardly extends into those Abstract Physics with which we have to do. Vegetables and animals come alike under our notice, when our object is to learn the general laws of life — that is, to study physiology. To say nothing of the fact that the distinction grows ever fainter and more dubious with new discoveries, it bears no relation to our plan of research; and we shall therefore consider that there is only one division in the science of organized bodies.
Thus we have before us Five fundamental Sciences in successive dependence, — Astro- gcien^*^^^''^.nomy, Physics, Chemistry, Physiology, and 30 POSniVli PHILOSOPHY.
finally Social Physics. The first considers the most general, simple, abstract, and remote phenomena known to ns, and those which affect all others without being affected by them. The last considers the most particular, compound, concrete phenomena, and those which are the most interesting to Man. Between these two, the degrees of speciality, of complexity, and individuality are in regular proportion to the place of the respective sciences in the scale exhibited. Ti --n- f This — casting out everything arbitrary — we must regard as the true fihation ot the sciences; and in it we find the plan of this work.
. As we proceed, we shall find that the same their parts principle which gives this order to the whole body of science arranges the parts of each science; and its soundness will therefore be freshly attested us often as it presents itself afresh. There is no refusing a principle which distributes the interior of each science after the same method with the aggregate sciences. But this is not the place in which to do more than indicate what we shall contemplate more closely hereafter. We must now rapidly review some of the leading properties of the hierarchy of science that has been disclosed. Corroborations. This gradation is in essential conformity. with the order which has spontaneously lication follows taken place among the branches of natural the order of philosophy, when pursued separately, and disclosure of without any purposeof establishing such order, sciences. Such an accordance is a strong presumption that the arrangement is natural. Again, it coincides with the actual development of natural philosophy. If no leading science can be effectually pursued otherwise than through those which precede it in the scale, it is evident that no vast development of any science could take place prior to the great astronomical discoveries to which we owe the impulse given to the whole. The progression may since have been simultaneous; but it has taken place in the order we have recognized.
This consideration is so important that it ro-eneousnS." i^ difiicult to understand without it the law which governs this history, as we have already seen, CLASSIFICATION CORROBORATED. 31 cannot be verified, unless we combine it with the scientific gradation just laid down: for it is according to this gradation that the different human theories have attained in succession the theological state, the metaphysical, and finally the positive. If we do not bear in mind the law which governs progression, we shall encounter insurmountable difiiculties: for it is clear that the theological or metaphysical state of some fundamental theories must have temporarily coincided with the positive state of others which precede them in our established gradation, and actually have at times coincided with them; and this must involve the law itself in an obscurity which can be cleared up only by the classification we have proposed.
Again, this classification marks, with pre- 3. Marks relacision, the relative perfection of the different tive perfection sciences, which consists in the degree of pre- ^^ sciences, cision of knowledge, and in the relation of its different branches. It is easy to see that the more general, simple, and abstract any phenomena are, the less they depend on others, and the more jjrecise they are in themselves, and the more clear in their relations with each other. Thus, organic phenomena are less exact and systematic than inorganic; and of these again terrestrial are less exact and systematic than those of astronomy. This fact is completely accounted for by the gradation we have laid down; and we shall see as we proceed, that the possibility of applying mathematical analysis to the study of phenomena is exactly in proportion to the rank which they hold in the scale of the whole.
There is one liability to be guarded against, Defects are in which we may mention here. We must beware iis, not in of confounding the degree of precision which science. we are able to attain in regard to any science, with the certainty of the science itself. The certainty of science, and our precision in the knowledge of it, are two very different things, which have been too often confounded; and are so still, though less than formerly. A very absurd proposition may be very precise; as if we should say, for instance, that the sum of the angles of a triangle is equal to three right angles; and a very certain proposition may be wanting in precision in our statement of it; as, for instance, when we assert that every man will die. If the different sciences offer to us a varying degree of precision, it is frona no want of certainty in themselves, but of our mastery of their phenomena.
The most interesting property of our Education formula of gradation is its effect on education, both general and scientific. This is its direct and unquestionable result. It will be more and more evident as we proceed, that no science can be effectually pursued without the preparation of a competent knowledge of the anterior sciences on which it depends. Physical ])hiloso])hers cannot understand Physics without at least a general knowledge of Astronomy; nor Chemists, without Physics and Astronomy; nor Physiologists, without Chemistry, Physics, and Astronomy; nor, above all, the students of Social philosophy, without a general knowledge of all the anterior sciences. As such conditions are, as yet, rarely fulfilled, and as no organization exists for their fulfilment, there is amongst us, in fact, no rational scientific education. To this may be attributed, in great part, the imperfection of even the most important sciences at this day. If the fact is so in regard to scientific education, it is no less striking in regard to general education. Our intellectual system cannot be renovated till the natural sciences are studied in their proper order. Even the highest understandings are apt to associate their ideas according to the order in which they were received: and it is only an intellect here and there, in any age, which in its utmost vigour can, like Bacon, Descartes, and Leibnitz, make a clearance in their field of knowledge, so as to reconstruct from the foundation their system of ideas.
Such is the operation of our great law Method upon scientific education through its effect on Doctrine. We cannot appreciate it duly without seeing how it affects Method.
As the phenomena which are homogeneous have been classed under one science, while those which belong to other sciences are heterogeneous, it follows that the Positive Method must be constantly modified in an uniform manner in the T-ange of the same fundamental science, and will luidergo modifications, different and more and more com- EFFECT ON METHOD. 33 pound, in passing from one science to another. Thus, under the scale laid down, we shall meet with it in all its varieties; which could not happen if we were to adopt a scale which should not fulfil the conditions we have admitted. This is an all-important consideration; for if, as we have already seen, we cannot understand the positive method in the abstract, but only by its application, it is clear that we can have no adequate conception of it but by studying it in its varieties of application. Wo one science, however well chosen, could exhibit it. Though the Method is always the same, its j^rocedure is varied. For instance, it should be Observation with regard to one kind of phenomena, and Experiment with regard to another; and different kinds of experiment, according to the case. In the same way, a general precept, derived from one fundamental science, however applicable to another, must have its spirit preserved by a reference to its origin; as in the case of the theory of Classifications. The best idea of the Positive Method would, of course, be obtained by the study of the most primitive and exalted of the sciences, if we were confined to one; but this isolated view would give no idea of its capacity of application to others in a modified form. Each science has its own proper advantages; and without some knowledge of them all, no conception can be formed of the power of the Method.
One more consideration must be briefly adverted to. It is necessary, not only to have o/sciences"*^ ^ a general knowledge of all the sciences, but to study them in their order. What can come of a study of complicated phenomena, if the student have not learned, by the contemplation of the simpler, what a Law is, what it is to Observe; what a Positive conception is; and even what a chain of 2*easoning is? Yet this is the way our young physiologists proceed every day, — plunging into the study of living bodies, without any other preparation than a knowledge of a dead language or two, or at most a superficial acquaintance with Physics and Chemistry, acquired without any philosophical method, or reference to any true point of departure in Natural philosophy. In the same way, with x'egard to Social phenomena, which are yet more complicated, what can be effected but by the rectification I. D of tlie intellectnal iustrument, through an adequate study of the range of anterior phenomena? There are many who admit this: but they do not see how to set about the work, nor understand the Method itself, for want of the preparatory study; and thus, the admission remains barren, and social theories abide in the theological or metaphysical state, in spite of the efforts of those who believe themselves positive reformers.
These, then, are the four points of view under which Ave have recognized the importance of a Rational and Positive Classification.