Essays: Scientific, Political, and Speculative, Volume II

THE CLASSIFICATION OF THE SCIENCES

[ First published as a brochure in April 1864. The preface to the second edition, published in April 1869, I reproduce because of certain facts contained in it which are not without interest.]

The first edition of this Essay is not yet out of print. But a proposal to translate it into French having been made by Professor Réthoré, I have decided to prepare a new edition free from the imperfections which criticism and further thought have disclosed, rather than allow these imperfections to be reproduced.

The occasion has almost tempted me into some amplification. Further arguments against the classification of M. Comte, and further arguments in support of the classification here set forth, have pleaded for utterance. But reconsideration has convinced me that it is both needless and useless to say more – needless because those who are not committed will think the case sufficiently strong as it stands; and useless because to those who are committed, additional reasons will seem as inadequate as the original ones. [In the preface to the third edition, however, a reason is given for a change of decision on this point at that time made (February 1871): the reason being “the publication of several objections by Prof. Bain in his Logic.”]

This last conclusion is thrust on me by seeing how little M. Littré, the leading expositor of M. Comte, is influenced by fundamental objections the force of which he admits. After quoting one of these, he says, with a candour equally rare and admirable, that he has vainly searched M. Comte’s works and his own mind for an answer. Nevertheless, he adds – “j’ai réussi, je crois, à écarter l’attaque de M. Herbert Spencer, et à sauver le fond par des sacrifices indispensables mais accessoires.” The sacrifices are these. He abandons M. Comte’s division of Inorganic Science into Celestial Physics and Terrestrial Physics – a division which, in M. Comte’s scheme, takes precedence of all the rest; and he admits that neither logically nor historically does Astronomy come before Physics, as M. Comte alleges. After making these sacrifices, which most will think too lightly described as “sacrifices indispensables mais accessoires,” M. Littré proceeds to rehabilitate the Comtean classification in a way which he considers satisfactory, but which I do not understand. In short, the proof of these incongruities affects his faith in the Positivist theory of the sciences, no more than the faith of a Christian is affected by proof that the Gospels contradict one another.

Here in England I have seen no attempt to meet the criticisms with which M. Littré thus deals. There has been no reply to the allegation, based on examples, that the several sciences do not develop in the order of their decreasing generality; nor to the allegation, based on M. Comte’s own admissions, that within each science the progress is not, as he says it is, from the general to the special; nor to the allegation that the seeming historical precedence of Astronomy over Physics in M. Comte’s pages, is based on a verbal ambiguity – a mere sleight of words; nor to the allegation, abundantly illustrated, that a progression in an order the reverse of that asserted by M. Comte may be as well substantiated; nor to various minor allegations equally irreconcileable with his scheme. I have met with nothing more than iteration of the statement that the sciences do conform, logically and historically, to the order in which M. Comte places them; regardless of the assigned evidence that they do not.

Under these circumstances it is unnecessary for me to say more; and I think I am warranted in continuing to hold that the Comtean classification of the sciences is demonstrably untenable.

In an essay on “The Genesis of Science,” originally published in 1854, I endeavoured to show that the Sciences cannot be rationally arranged in serial order. Proof was given that neither the succession in which the Sciences are placed by M. Comte (to a criticism of whose scheme the essay was in part devoted), nor any other succession in which the Sciences can be placed, represents either their logical dependence or their historical dependence. To the question – How may their relations be rightly expressed? I did not then attempt any answer. This question I propose now to consider.

A true classification includes in each class, those objects which have more characteristics in common with one another, than any of them have in common with any objects excluded from the class. Further, the characteristics possessed in common by the colligated objects, and not possessed by other objects, involve more numerous dependent characteristics. These are two sides of the same definition. For things possessing the greatest number of attributes in common, are things that possess in common those essential attributes on which the rest depend; and, conversely, the possession in common of the essential attributes, implies the possession in common of the greatest number of attributes. Hence, either test may be used as convenience dictates.

If, then, the Sciences admit of classification at all, it must be by grouping together the like and separating the unlike, as thus defined. Let us proceed to do this.

The broadest natural division among the Sciences, is the division between those which deal with the abstract relations under which phenomena are presented to us, and those which deal with the phenomena themselves. Relations of whatever orders, are nearer akin to one another than they are to any objects. Objects of whatever orders, are nearer akin to one another than they are to any relations. Whether, as some hold, Space and Time are nothing but forms of Thought [2 - I have been charged with misrepresenting Kant and misunderstanding him, because I have used the expression “forms of Thought” instead of “forms of Intuition.” Elsewhere I have shown that my argument against him remains equally valid when the phrase “forms of Intuition” is used. Here I may in the first place add that I did but follow some Kantists in saying “forms of Thought,” and I may add in the second place that the objection is superficial and quite irrelevant to the issue. Thought when broadly used as antithetical to Things includes Intuition: it comprehends in this sense all that is subjective as distinguished from all that is objective, and in so doing comprehends Intuition. Nor is this all. There cannot be Intuition without Thought: every act of intuition implies an act of classing without which the thing intuited is not known as such or such; and every act of classing is an act of thought.]; or whether, as I hold myself, they are forms of Things, that have generated forms of Thought through organized and inherited experience of Things; it is equally true that Space and Time are contrasted absolutely with the existences disclosed to us in Space and Time; and hence the Sciences which deal exclusively with Space and Time, are separated by the profoundest of all distinctions from the Sciences which deal with the existences contained in Space and Time. Space is the abstract of all relations of co-existence. Time is the abstract of all relations of sequence. And dealing as they do entirely with relations of co-existence and sequence, in their general or special forms, Logic and Mathematics form a class of the Sciences more widely unlike the rest, than any of the rest are from one another.

The Sciences which deal with existences themselves, instead of the blank forms in which existences are presented to us, admit of a sub-division less profound than the division above made, but more profound than any of the divisions among the Sciences individually considered. They fall into two classes, having quite different aspects, aims, and methods. Every phenomenon is more or less composite – is a manifestation of force under several distinct modes. Hence result two objects of inquiry. We may study the component modes of force separately; or we may study them as co-operating to generate in this composite phenomenon. On the one hand, neglecting all the incidents of particular cases, we may aim to educe the laws of each mode of force, when it is uninterfered with. On the other hand, the incidents of the particular case being given, we may seek to interpret the entire phenomenon, as a product of the several forces simultaneously in action. The truths reached through the first kind of inquiry, though concrete inasmuch as they have actual existences for their subject-matters, are abstract inasmuch as they refer to the modes of existence apart from one another; while the truths reached by the second kind of inquiry are properly concrete, inasmuch as they formulate the facts in their combined order, as they occur in Nature.

The Sciences, then, in their main divisions, stand thus: —

• SCIENCE is

• that which treats of the forms in which phenomona are known to us: ABSTRACT SCIENCE (Logic and Mathematics)

• that which treats of the phenomena themselves:

• in their elements: ABSTRACT-CONCRETE SCIENCE (Mechanics, Physics, Chemistry, etc.)

• in their totalities: CONCRETE SCIENCE (Astronomy, Geology, Biology, Psychology, Sociology, etc.)

It is needful to define the words abstract and concrete as thus used; since they are sometimes used with other meanings. M. Comte divides Science into abstract and concrete; but the divisions which he distinguishes by these names are quite unlike those above made. Instead of regarding some Sciences as wholly abstract, and others as wholly concrete, he regards each Science as having an abstract part, and a concrete part. There is, according to him, an abstract mathematics and a concrete mathematics – an abstract biology and concrete biology. He says: – “Il faut distinguer, par rapport à tous les ordres de phénomènes, deux genres de sciences naturelles: les unes abstraites, générales, ont pour objet la découverte des lois qui régissent les diverses classes de phénomènes, en considérant tous les cas qu’on peut concevoir; les autres concrètes, particulières, descriptives, et qu’on désigne quelquefois sous le nom de sciences naturelles proprement dites, consistent dans l’application de ces lois a l’histoire effective des différens êtres existans.” And to illustrate the distinction, he names general physiology as abstract, and zoology and botany as concrete. Here it is manifest that the words abstract and general are used as synonymous. They have, however, different meanings; and confusion results from not distinguishing their meanings. Abstractness means detachment from the incidents of particular cases. Generality means manifestation in numerous cases. On the one hand, the essential nature of some phenomenon is considered, apart from disguising phenomena. On the other hand, the frequency of the phenomenon, with or without disguising phenomena, is the thing considered. Among the phenomena presented by numbers, which are purely ideal, the two coincide; but excluding these, an abstract truth is not realizable to perception in any case of which it is asserted, whereas a general truth is realizable to perception in every case of which it is asserted. Some illustrations will make the distinction clear. Thus it is an abstract truth that the angle contained in a semi-circle is a right angle – abstract in the sense that though it does not hold of actually-constructed semi-circles and angles, which are always inexact, it holds of the ideal semi-circles and angles abstracted from real ones; but this is not a general truth, either in the sense that it is commonly manifested in Nature, or in the sense that it is a space-relation that comprehends many minor space-relations: it is a quite special space-relation. Again, that the momentum of a body causes it to move in a straight line at a uniform velocity, is an abstract-concrete truth – a truth abstracted from certain experiences of concrete phenomena; but it is by no means a general truth: so little generality has it, that no one fact in Nature displays it. Conversely, surrounding things supply us with hosts of general truths that are not in the least abstract. It is a general truth that the planets go round the Sun from West to East – a truth which holds good in several hundred cases (including the cases of the planetoids); but this truth is not at all abstract, since it is perfectly realized as a concrete fact in every one of these cases. Every vertebrate animal whatever, has a double nervous system; all birds and all mammals are warm-blooded – these are general truths, but they are concrete truths: that is to say, every vertebrate animal individually presents an entire and unqualified manifestation of this duality of the nervous system; every living bird exemplifies absolutely or completely the warm-bloodedness of birds. What we here call, and rightly call, a general truth, is simply a proposition which sums up a number of our actual experiences; and not the expression of a truth drawn from our actual experiences, but never presented to us in any of them. In other words, a general truth colligates a number of particular truths; while an abstract truth colligates no particular truths, but formulates a truth which certain phenomena all involve, though it is actually seen in none of them.

Limiting the words to their proper meanings as thus defined, it becomes manifest that the three classes of Sciences above separated, are not distinguishable at all by differences in their degrees of generality. They are all equally general; or rather they are all, considered as groups, universal. Every object whatever presents at once the subject-matter for each of them. In every fragment of substance we have simultaneously illustrated the abstract truths of relation in Time and Space; the abstract-concrete truths in conformity with which the fragment manifests its several modes of force; and the concrete truths resulting from the joint manifestation of these modes of force, and which give to the fragment the characters by which it is known as such or such. Thus these three classes of Sciences severally formulate different, but co-extensive, classes of facts. Within each group there are truths of greater and less generality: there are general abstract truths, and special abstract truths; general abstract-concrete truths, and special abstract-concrete truths; general concrete truths, and special concrete truths. But while within each class there are groups and sub-groups and sub-sub-groups which differ in their degrees of generality, the classes themselves differ only in their degrees of abstractness. [3 - Some propositions laid down by M. Littré, in his book – Auguste Comte et la Philosophie Positive (published in 1863), may fitly be dealt with here. In the candid and courteous reply he makes to my strictures on the Comtean classification in “The Genesis of Science,” he endeavours to clear up some of the inconsistencies I pointed out; and he does this by drawing a distinction between objective generality and subjective generality. He says – “qu’il existe deux ordres de généralité, l’une objective et dans les choses, l’autre subjective, abstraite et dans l’esprit.” This sentence, in which M. Littré makes subjective generality synonymous with abstractness, led me at first to conclude that he had in view the same distinction as that which I have above explained between generality and abstractness. On re-reading the paragraph, however, I found this was not the case. In a previous sentence he says – “La biologie a passé de la considération des organes à celles des tissus, plus généraux que les organes, et de la considération des tissus à celle des éléments anatomiques, plus généraux que les tissus. Mais cette généralité croissante est subjective non objective, abstraite non concrète.” Here it is manifest that abstract and concrete, are used in senses analogous to those in which they are used by M. Comte; who, as we have seen, regards general physiology as abstract and zoology and botany as concrete. And it is further manifest that the word abstract, as thus used, is not used in its proper sense. For, as above shown, no such facts as those of anatomical structure can be abstract facts; but can only be more or less general facts. Nor do I understand M. Littré’s point of view when he regards these more general facts of anatomical structure, as subjectively general and not objectively general. The structural phenomena presented by any tissue, such as mucous membrane, are more general than the phenomena presented by any of the organs which mucous membrane goes to form, simply in the sense that the phenomena peculiar to the membrane are repeated in a greater number of instances than the phenomena peculiar to any organ into the composition of which the membrane enters. And, similarly, such facts as have been established respecting the anatomical elements of tissues, are more general than the facts established respecting any particular tissue, in the sense that they are facts which the various parts of organized bodies exhibit in a greater number of cases – they are objectively more general; and they can be called subjectively more general only in the sense that the conception corresponds with the phenomena.Let me endeavour to clear up this point: – There is, as M. Littré truly says, a decreasing generality that is objective. If we omit the phenomena of Dissolution, which are changes from the special to the general, all changes which matter undergoes are from the general to the special – are changes involving a decreasing generality in the united groups of attributes. This is the progress of things. The progress of thought , is not only in the same direction, but also in the opposite direction. The investigation of Nature discloses an increasing number of specialities; but it simultaneously discloses more and more the generalities within which these specialities fall. Take a case. Zoology, while it goes on multiplying the number of its species, and getting a more complete knowledge of each species (decreasing generality); also goes on discovering the common characters by which species are united into larger groups (increasing generality). Both these are subjective processes; and in this case, both orders of truth reached are concrete – formulate the phenomena as actually manifested. The truth that mammals of all kinds have seven cervical vertebræ (I believe there is one exception) is a generalization – a general relation in thought answering to a general relation in things. As the existence of seven cervical vertebræ in each mammal is a concrete fact, the statement of it is a concrete truth, and the statement colligating such truths is not made other than concrete by holding of case after case.M. Littré, recognizing the necessity for some modification of the hierarchy of the Sciences, as enunciated by M. Comte, still regards it as substantially true; and for proof of its validity, he appeals mainly to the essential constitutions of the Sciences. It is unnecessary for me here to meet, in detail, the arguments by which he supports the proposition, that the essential constitutions of the Sciences, justify the order in which M. Comte places them. It will suffice to refer to the foregoing pages, and to the pages which are to follow, as containing the definitions of those fundamental characteristics which demand the grouping of the Sciences in the way I have pointed out. As already shown, and as will be shown still more clearly by and bye, the radical differences of constitution among the Sciences, necessitate the colligation of them into the three classes – Abstract, Abstract-Concrete, and Concrete. How irreconcilable is M. Comte’s classification with these groups, will be at once apparent on inspection. It stands thus: —• Mathematics (including rational Mechanics)… partly Abstract, partly Abstract-Concrete.• Astronomy.. Concrete.• Physics.. Abstract-Concrete.• Chemistry.. Abstract-Concrete.• Biology.. Concrete.• Sociology.. Concrete.]

Let us pass to the sub-divisions of these classes. The first class is separable into two parts – the one containing universal truths, the other non-universal truths. Dealing wholly with relations apart from related things, Abstract Science considers first, that which is common to all relations whatever; and, second, that which is common to each order of relations. Besides the indefinite and variable connexions which exist among phenomena, as occurring together in Space and Time, we find that there are also definite and invariable connexions – that between each kind of phenomenon and certain other kinds of phenomena, there exist uniform relations. This is a universal abstract truth – that there is an unchanging order, or fixity of law, in Space and Time. We come next to the several kinds of unchanging order, which, taken together, form the subjects of the second division of Abstract Science. Of this second division, the most general sub-division is that which deals with the natures of the connexions in Space and Time, irrespective of the terms connected. The conditions under which we may predicate a relation of coincidence or proximity in Space and Time (or of non-coincidence or non-proximity) from the subject-matter of Logic. Here the natures and amounts of the terms between which the relations are asserted (or denied) are of no moment: the propositions of Logic are independent of any qualitative or quantitative specification of the related things. The other sub-division has for its subject-matter, the relations between terms which are specified quantitatively but not qualitatively. The amounts of the related terms, irrespective of their natures, are here dealt with; and Mathematics is a statement of the laws of quantity considered apart from reality. Quantity considered apart from reality, is occupancy of Space or Time; and occupancy of Space or Time is measured by units of one or other order, but of which the ultimate ones are simply separate places in consciousness, either coexistent or sequent. Among units that are unspecified in their natures (extensive, protensive, or intensive), but are ideally endowed with existence considered apart from attributes, the quantitative relations that arise, are those most general relations expressed by numbers. Such relations fall into either of two orders, according as the units are considered simply as capable of filling separate places in consciousness, or according as they are considered as filling places that are not only separate, but equal. In the one case, we have that indefinite calculus by which numbers of abstract existences, but not sums of abstract existence, are predicable. In the other case, we have that definite calculus by which both numbers of abstract existences and sums of abstract existence are predicable. Next comes that division of Mathematics which deals with the quantitative relations of magnitudes (or aggregates of units) considered as coexistent, or as occupying Space – the division called Geometry. And then we arrive at relations, the terms of which include both quantities of Time and quantities of Space – those in which times are estimated by the units of space traversed at a uniform velocity, and those in which equal units of time being given, the spaces traversed with uniform or variable velocities are estimated. These Abstract Sciences, which are concerned exclusively with relations and with the relations of relations, may be grouped as shown in Table I.

• TABLE I.

• ABSTRACT SCIENCE.

• Universal law of relation – an expression of the truth that uniformities of connexion obtain among modes of Being, irrespective of any specification of the natures of the uniformities of connexion.

• Laws of relations

• that are qualitative; or that are specified in their natures as relations of coincidence or proximity in Time and Space, but not necessarily in their terms the natures and amount of which are indifferent. (LOGIC.)[4 - This definition includes the laws of relations called necessary, but not those of relations called contingent. These last, in which the probability of an inferred connexion varies with the number of times such connexion has occurred in experience, are rightly dealt with mathematically.]

• that are quantitative (MATHEMATICS)

• negatively: the terms of the relations being definitely-related sets of positions in space; and the facts predicated being the absences of certain quantities. (Geometry of Position.[5 - Here, by way of explanation of the term negatively-quantitative, it will suffice to instance the proposition that certain three lines will meet in a point, as a negatively-quantitative proposition; since it asserts the absence of any quantity of space between their intersections. Similarly, the assertion that certain three points will always fall in a straight line, is negatively-quantitative; since the conception of a straight line implies the negation of any lateral quantity, or deviation.])

• positively: the terms being magnitudes composed of

• units that are equal only as having independent existences. (Indefinite Calculus.[6 - Lest the meaning of this division should not be understood, it may be well to name, in illustration, the estimates of the statistician. Calculations respecting population, crime, disease, etc., have results which are correct only numerically, and not in respect of the totalities of being or action represented by the numbers.])

• equal units

• the equality of which is not defined as extensive, protensive, or intensive (Definite Calculus)

• when their numbers are completely specified (Arithmetic.)

• when their numbers are specified only

• in their relations (Algebra.)

• in the relations of their relations. (Calculus ofOperations.)

• the equality of which is that of extension

• considered in their relations of coexistence. (Geometry.)

• considered as traversed in Time

• that is wholly indefinite. (Kinematics.)

• that is divided into equal units (Geometry of Motion.[7 - Perhaps it will be asked – how can there be a Geometry of Motion into which the conception of Force does not enter? The reply is, that the time-relations and space-relations of Motion may be considered apart from those of Force, in the same way that the space-relations of Matter may be considered apart from Matter.])

Passing from the Sciences concerned with the ideal or unoccupied forms of relations, and turning to the Sciences concerned with real relations, or the relations among realities, we come first to those Sciences which treat of realities, not as they are habitually manifested, but with realities as manifested in their different modes, when these are artificially separated from one another. While the Abstract Sciences are wholly ideal, relatively to the Abstract-Concrete and Concrete Sciences; the Abstract-Concrete Sciences are partially ideal, relatively to the Concrete Sciences. Just as Logic and Mathematics generalize the laws of relation, qualitative and quantitative, apart from related things; so, Mechanics, Physics, Chemistry generalize the laws of relation which different modes of Matter and Motion conform to, when severally disentangled from those actual phenomena in which they are mutually modified. Just as the geometrician formulates the properties of lines and surfaces, independently of the irregularities and thicknesses of lines and surfaces as they really exist; so the physicist and the chemist formulate the manifestations of each mode of force, independently of the disturbances in its manifestations which other modes of force cause in every actual case. In works on Mechanics, the laws of motion are expressed without reference to friction and resistance of the medium. Not what motion ever really is, but what it would be if retarding forces were absent, is asserted. If afterwards any retarding force is taken into account, then the effect of this retarding force is dealt with by itself: neglecting the other retarding forces. Consider, again, the generalizations of the physicist respecting molecular motion. The law that light varies inversely as the square of the distance, is absolutely true only when the radiation goes on from a point without dimensions, which it never does; and it also assumes that the rays are perfectly straight, which they cannot be unless the medium differs from all actual media in being perfectly homogeneous. If the disturbing effects of changes of media are investigated, the formulæ expressing the refractions take for granted that the new media entered are homogeneous; which they never really are. Even when a compound disturbance is allowed for, as when the refraction undergone by light in traversing a medium of increasing density, like the atmosphere, is calculated, the calculation still supposes conditions that are unnaturally simple – it supposes that the atmosphere is not pervaded by heterogeneous currents, which it always is. Similarly with the inquiries of the chemist. He does not take his substances as Nature supplies them. Before he proceeds to specify their respective properties, he purifies them – separates from each all trace of every other. Before ascertaining the specific gravity of a gas, he has to free this gas from the vapour of water, usually mixed with it. Before describing the properties of a salt, he guards against any error that may arise from the presence of an uncombined portion of the acid or base. And when he alleges of any element that it has a certain atomic weight, and unites with such and such equivalents of other elements, he does not mean that the results thus expressed are exactly the results of any one experiment; but that they are the results which, after averaging many trials, he concludes would be realized if absolute purity could be obtained, and if the experiments could be conducted without loss. His problem is to ascertain the laws of combination of molecules, not as they are actually displayed, but as they would be displayed in the absence of those minute interferences which cannot be altogether avoided. Thus all Abstract-Concrete Sciences have for their object, analytical interpretation. In every case it is the aim to decompose the phenomenon, and formulate its components apart from one another; or some two or three apart from the rest. Wherever, throughout these Sciences, synthesis is employed, it is for the verification of analysis. [8 - I am indebted to Prof. Frankland for reminding me of an objection that may be made to this statement. The production of new compounds by synthesis, has of late become an important branch of chemistry. According to certain known laws of composition, complex substances, which never before existed, are formed, and fulfil anticipations both as to their general properties and as to the proportions of their constituents – as proved by analysis. Here it may be said with truth, that analysis is used to verify synthesis. Nevertheless, the exception to the above statement is apparent only, – not real. In so far as the production of new compounds is carried on merely for the obtainment of such new compounds, it is not Science but Art – the application of pre-established knowledge to the achievement of ends. The proceeding is a part of Science, only in so far as it is a means to the better interpretation of the order of Nature. And how does it aid the interpretation? It does it only by verifying the pre-established conclusions respecting the laws of molecular combination; or by serving further to explain them. That is to say, these syntheses, considered on their scientific side, have simply the purpose of forwarding the analysis of the laws of chemical combination.] The truths elaborated are severally asserted, not as truths exhibited by this or that particular object; but as truths universally holding of Matter and Motion in their more general or more special forms, considered apart from particular objects, and particular places in space.

The sub-divisions of this group of Sciences, may be drawn on the same principle as that on which the sub-divisions of the preceding group were drawn. Phenomena, considered as more or less involved manifestations of force, yield on analysis, certain laws of manifestation which are universal, and other laws of manifestation, which, being dependent on conditions, are not universal. Hence the Abstract-Concrete Sciences are primarily divisible into – the laws of force considered apart from its separate modes, and laws of force considered under each of its separate modes. And this second division of the Abstract-Concrete group, is sub-divisible after a manner essentially analogous. It is needless to occupy space by defining these several orders and genera of Sciences. Table II. will sufficiently explain their relations.

• TABLE II.

• ABSTRACT-CONCRETE SCIENCE.

• Universal laws of forces (tensions and pressures), as deducible from the persistence of force: the theorems of resolution and composition of forces.

• Laws of forces as manifested by matter

• in masses (MECHANICS)

• that are in equilibrium relatively to other masses

• and are solid. (Statics.)