NATURAL LAW IN SCIENCE AND PHILOSOPHY NATURAL LAW IN SCIENCE AND PHILOSOPHY B 7 EMILE BOUTROUX (Member of the Academy) Authorized Translation by FRED ROTH WELL NEW YORK THE MACMILLAN COMPANY 1914 "B PREFACE BY THE AUTHOR MORE than twenty years have elapsed since these lessons were delivered at the Sorbonne. In the interval, science has advanced with giant strides ; and there can be no doubt but that I should have to examine many a scientifico-philosophical theory of which this work makes no mention, were I now to recommence the course I then gave. All the same, I do not think that the problem raised in my classes during the session 1892-3 has been solved or that it has ceased to elicit the keenest interest. Our object is to discover whether the idea of natural law is the same for the scientist as it is for the philosopher. Science proposes to explain things scien- tifically. And, in these days more espe- cially, the concept of scientific explanation has received precise definition. It comprises \ neither the knowledge of the intrinsic nature of things, nor that of their origin or value. 5 NATURAL LAW IN SCIENCE AND PHILOSOPHY It implies the possibility of extracting, from the given reality, sensibly constant rapports, and it declares that such a rap- port is explained, when it has been possible to reduce it to some other rapport already known and recognized as permanent and general. Science is reduction. Mathematics is its ideal, its form par excellence, for it is in mathematics that assimilation, identifica- tion, is most perfectly realized. The uni- verse, scientifically explained, would be a certain formula, one and eternal, regarded as the equivalent of the entire diversity and movement of things. The philosopher asks himself whether natural law as assumed by science, wholly coincides with law as really existing in nature ; whether science and reality are so alike that science may be regarded as exhaust- ing everything intelligible and true that the real contains. The theory upheld in the present work is that no absolute coincidence exists be- tween the laws of nature as science assumes them to be, and the laws of nature as they really are. The former may be compared to laws proclaimed by a legislator and im- 6 PREFACE BY THE AUTHOR posed a priori upon reality. The latter are harmonies towards which we ascertain that the actions of different beings really tend. The former are abstract rapports, the elements of which are themselves rapports; the latter are concrete rapports, the terms of which are real subjects, true beings. Now, the doctrine here set forth consists in regarding scientific intelligibility as the most objective form, but not as the sole type, of intelligibility. Science acquires that perfection which characterizes it, by setting aside, sending about their business, as Plato would say ( e ' x a ' L P eLV }> indivi- duals, natural beings. The philosophy with which our doctrine is connected admits that between individuals themselves, be- tween concrete realities as such, there may be found relations which, though they can- not be reduced to mathematical relations, nevertheless exhibit a certain order which satisfies the intelligence. There exist in- telligible relations other than those of re- ducibility and identity : it is the purpose of philosophy to reveal and define such relations. In Plato, for instance, we have the commonalty, or mutual participation 7 NATURAL LAW IN SCIENCE AND PHILOSOPHY LO) in Aristotle, finality ; in Des- V cartes, evident connexion ; in Leibnitz, har- mony ; and in Hegel, rational synthesis. Thus, philosophy both widens and renders flexible without destroying the concept of intelligibility. The present doctrine regards as both con- tingent and intelligible those relations be- tween beings that it discovers in the relations between relations ; it sees in the mechanically necessary rapports implied by science, an abstraction, that consists in isolating the relations from their living sub- jects, and looking upon them as self -sufficient. In the reality of things, the rigid, eternal, - mathematical order, which science considers from its own point of view, serves to obscure an order that is invisible, supple and un- trammelled, and therefore all the more beautiful : ap/u.ovirj dcpavfo (paveprjs Kpeirrcov (Heraclitus). EMILE BOUTROUX. Contents i PAGE PREFACE BY THE AUTHOR. . ..*'.< 5 I THE PROBLEM OF THE MEANING OF NATURAL LAWS . . ... ii II THE LOGICAL LAWS . , . . .21 III A THE MATHEMATICAL LAWS . . ... 35 IV ,-THE MECHANICAL LAWS . . . .46 sf THE MECHANICAL LAWS (continued] . 61 VI THE PHYSICAL LAWS . . . . 79 VII THE CHEMICAL LAWS . . .- '.. . 94 VIII THE BIOLOGICAL LAWS . . . .109 9 CONTENTS PAGE IX THE BIOLOGICAL LAWS (continued) . . . 127 X THE BIOLOGICAL LAWS (continuation and end) . 143 XI THE PSYCHOLOGICAL LAWS . .. . | I5 s XII THE PSYCHOLOGICAL LAWS (continuation and end) 175 XIII THE SOCIOLOGICAL LAWS . .'...' . 188 XIV CONCLUSION . . , , , , 204 10 NATURAL LAW IN SCIENCE AND PHILOSOPHY THE PROBLEM OF THE MEAN- ING OF NATURAL LAWS IT is our purpose to study the idea of natural law as presented in modern times, to interpret it philosophically and determine its metaphysical and moral signi- fication. In order to state the problem with the" requisite precision, we shall rely on the results of the speculations of the seventeenth and eighteenth centuries, specu- lations closely connected with the develop- ment of modern science. Bacon and Descartes, the founders of modern philosophy, regarded science as having, for its object, to arrive at laws which should possess the dual characteristic of ii NATURAL LAW IN SCIENCE AND PHILOSOPHY universality and reality. It was the ambi- tion of both, in spite of appearances which are often wrongly interpreted, to supersede the ancient point of view, in accordance with which, laws were only general and ideal, to rise beyond the probable and the possible, and to obtain a sure knowledge of the real. But though their object is identical, their methods of attaining it are different : Bacon takes the path of empiri- cism ; Descartes that of rationalism. The Cartesians consider that it is possible to find the principles of universal and real 1 laws in certain mental operations, which have not yet been sufficiently investigated. Descartes analyses the matter immediately given, i.e. ideas, and in them finds elements the specific characteristic of which is that they are obvious when compared with intellectual intuition. These elements, according to him, are the principles sought after. And, indeed, they seem calculated to supply universal laws ; but as it is from the mind that they have been drawn, will they allow of real laws being discovered ? This is the pro- blem with which Descartes is immediately confronted. In his Cogito, ergo sum, what 12 PROBLEM OF THE MEANING OF NATURAL LAWS is the meaning of ergo ? Even now it is no easy matter to connect personal exis- tence with the Cogito ? But the existence of God, and in particular of things corporeal, will call for a real deduction, one of ever increasing complexity. After Descartes, Male- branche considers it necessary to distin- guish the laws of action or of existence from those of essence ; and so he con- ceives his theory of occasional causes. Spinoza proves that a similar distinction may be drawn between internal and exter- nal causality ; he endeavours to connect the laws of existence with those of essence. According to Leibnitz, these various systems cannot supersede possibility. It is indis- pensable that a new principle, equally abso- lute, the principle of sufficient reason, be added to that of contradiction, the only one with which they are acquainted. This will be the distinctive principle of the real. Again, deep within existing things, separa- tions befcome marked. Everything is not reducible to mathematical order ; substances govern it; and in this higher order, we must consider, on the one hand, physics, the domain of efficient causes, and on the 13 NATURAL LAW IN SCIENCE AND PHILOSOPHY other hand, ethics, the domain of final causes. In the case of Kant, these distinctions be- come separations, which, to us, are radical and absolute. Again deep within the real world and coming between the physical and the moral laws, he sets up the biological laws, which, to our mind, at all events, are incapable of being reduced to the former, and presuppose finality. And lastly, Schelling and Hegel regard -the laws of essence and of existence as inadequate : to account for the real, we must. .posit laws of development, deter- mine a process which precedes all essence and all existence alike, and is the repro- duction, in thought, of the very creation of things. Thus, rationalistic philosophy, starting with unity, has found itself compelled to recog- nize different types of laws. It has been confronted with experience, and, when its principles have been compared with facts, has been forced to enlarge its scope. Truth to tell, rationalistic philosophy ex- pected to reduce this diversity and make it intelligible. Only apparently, however, and by continually modifying the con- cept of intelligibility, did it effect this. 14 PROBLEM OF THE MEANING OF NATURAL LAWS Descartes, by his intuition, actually modifies the idea of intellectualism which the ancients had set up. Spinoza places in the fore- ground a new notion, that of the infinite, which the ancients regarded as the very essence of unintelligibility. Leibnitz boldly affirms the actual realization of this infinite. Kant effects a revolution in the doctrine of intelligibility by recognizing two kinds of logic : the old logic of Aristotle, which is purely formal and incapable of establishing anything ; and transcendental logic, which proceeds by synthetic judgments d priori. Finally, Schelling and Hegel, who even affirm the identity of contradictories, openly reject the standpoint of the old logic. The latter, then, has been regarded as inade- quate to explain existence, and intellectualism has almost been compelled to abrogate it entirely, in attaining to a comprehension of the real. But, say the empiricists, what is the use of troubling about the d priori principles of intellectualism ? There is no need to de- part from nature in order to understand her. Observation and induction, if properly ap- plied, are sufficient to realize the modern 15 NATURAL LAW IN SCIENCE AND PHILOSOPHY idea of science. Still, a difficulty here arises, the very opposite of that which the rational- ists encountered. In the case of Descartes, the problem was to link on the real to the universal ; the problem for Bacon is to link on the universal to the real. The latter philosopher, indeed, looks upon the mind as absolutely passive ; or rather, in order to establish science, the mind must make itself truly passive, a veritable tabula rasa on which the events of the outer world are impressed. Bacon, however, be- sides being still embarrassed by the scholastic conception of quality, rather expresses a desideratum than demonstrates the possi- bility of realizing valid inductions. Locke clearly sees that the thing which needs explanation is the connexion of ideas ; he maintains that we connect our ideas by means of faculties innate within ourselves. Mere passiveness is inadequate as an ex- planation : experience traces innumerable characters on a tabula rasa ; but the soul, of itself, unites together the simple ideas with which this external influence supplies it. Still, of what worth are laws thus created by human faculties ? What sort of universality 16 PROBLEM OF THE MEANING OF NATURAL LAWS can they claim ? Hume comes along and explains that we have, deep within our- selves, the power to join together the ideas of phenomena in relations of resemblance, contiguity and causality. As regards causa- lity, which, of itself, would never obtrude upon us, habit replaces the intuition lacking, makes association practically indissoluble, and so inclines us to look upon the laws of nature as really universal and necessary. Therefore, just as intellectualism, in order to comprehend reality, has had to extend and perhaps to violate its principle, so also em- piricism, to attain to universality, has found itself compelled to deviate from its original direction, either by recognizing, with Locke, mental faculties that cannot be reduced to experience, or, as \jlume__ does, r egard- ing external jaws^as^the result of internal ljw^j:>|^ Thus it would appear very difficult for the human mind to conceive the laws of nature as being both universal and real at the same time. When we explain to ourselves univer- sality, reality slips out of our grasp, and vice versa. Must we then conjoin rationalism and empiricism, purely and simply ? The 17 B NATURAL LAW IN SCIENCE AND PHILOSOPHY conjunction of these two opposite points of view will give only a juxtaposition, not a synthesis. Now, what to philosophy was only an ideal and a problem, has been realized by science, which has succeeded in effecting a union between mathematics and experience, and supplying laws that are both concrete and intelligible. Its method has been to try to discover an appropriate positive principle for each order of realities. Newton supplied the type of scientific ex- planation by basing celestial mechanics on the law of gravitation, which is radically distinct from purely geometrical laws. The sciences have thus been emancipated, one after the other ; they have been set up as auto- nomous, with the aid of special principles regarded as irreducible ; for instance, a distinction has been made between physi- cal principles and those that are purely mechanical, between chemistry and physics, between vital properties and physical and chemical properties. No doubt attempts are made to liken every science, mutatis mutandis, to the mathematical sciences ; but certain sciences are no longer looked upon as a mere extension of the rest ; the 18 PROBLEM OF THE MEANING OF NATURAL LAWS special sciences are allowed to have their own specific principles. Therefore, in order to study the idea of natural law, we must start with the various sciences, at the same time appealing to philosophy for hints as to the manner of interpreting their principles and results. Wei will take the laws just as the sciences offer j them, divided into distinct groups, study; each group separately and ask ourselves/ questions regarding each of them : 1. Their nature. How far and in what sense are these laws intelligible ? Are there not differences in generality and complexity, or does the appearance of a new group really m mark the introduction of a new principle which is philosophically irreducible ? 2. Their objectivity. Do we regard these laws as forming the substance of things, or do they govern only the mode in which phenomena appear ? Are they true abso- lutely or only relatively ? Are they elements or merely symbols of reality ? 3. Their meaning. Does determination really exist in nature, or does it simply represent the way in which we must connect things in order to make of them objects of thought ? 19 NATURAL LAW IN SCIENCE AND PHILOSOPHY In this way, we shall attempt to answer, from the present-day standpoint, the old question as to whether there are things that depend on ourselves, whether we are really capable of acting, or whether action is pure illusion. 20 II THE LOGICAL LAWS THE logical laws are those that govern all scientific research. By logical laws we usually mean those of syllogistic logic as formulated by Aristotle ; but there are logical laws of a still more general nature to wit, the three principles of identity, con- tradiction and excluded middle. The principle of identity may be expressed thus : A is A . I do not say Being, but simply A, i.e. anything whatsoever that is capable of being conceived ; nor do I say A = A, for the sign = is a mathematical sign, actually limiting the very relation which has to be established. The prin- ciple of identity, thus defined, represents the type of possibility. The principle of contra- diction, on the other hand, represents the type of the false, of logical impossibility : its expression is A is not- A. This affirma- 21 NATURAL LAW IN SCIENCE AND PHILOSOPHY tion is impossible, i.e. A and not- A cannot be presented or posited together. The prin- ciple of excluded middle means that there is no middle term between A and not- A. It may be called the principle of indirect possi- bility, for the new element in what it enun- ciates is that if not-A is excluded, A is posited. Two negatives make an affirmative : such is the essence of this latter principle. Suppose there is a middle term between A and not-A, this middle term will be both not-A and not-not-A. Now, if not-not-A A, the middle term will be both not-A and A, which lands us in a contradiction. Just as the second principle prevents two contra- dictories from being posited together, so the third prevents them from being abolished together. These strictly logical laws are intelligi- bility itself, they appear as the type of evi- dence ; but, of themselves alone, they do not constitute the whole of logic. Ordinary, so-called syllogistic, logic, is not content with these three principles. Consider the principle of contradiction as formulated by Aristotle ; it contains elements which, mani- festly, are not included in the strictly logi- 22 THE LOGICAL LAWS cal laws. "It is impossible for one and the same thing to belong and not to belong to one and the same subject at the same time and in the same connexion/' Pure logic does not say of what nature A must be ; whereas in the case of Aristotelian logic, A is not anything whatsoever : it is concept, i.e. a determinate thing. Besides, the ex- pressions : ' ' at the same time and in the same connexion/' are not found in the formulae of pure logic, From this standpoint, let us examine concept, the arrangement of con- cepts into propositions and the arrangement of propositions into syllogisms. What is concept ? It is not absolute unity, for, in order to explain things, it must involve multiplicity. Nor is it absolute mul- tiplicity, for it reduces diversity to unity. It thus represents a certain conjunction of elements of a certain nature, a relation not merely of homogeneity but of heterogene- ity, at least relative, between modes of being. Nor can proposition, any more than con- cept, be strictly conformable to the formula A is A. A is A teaches us nothing. Now, a proposition must always teach some- 23 NATURAL LAW IN SCIENCE AND PHILOSOPHY thing, and thus admit of the formula A is B. And, lastly, the reasoning which links propositions to one another is not an exact identity, either ; it is to propositions what propositions are to concept. Thus, we have not simply deduced, from the laws of pure logic, matter appropriate to the application of these laws ; we have composed the syllo- gism with the aid of the laws of pure logic and of a super added matter. Does this matter, at all events, exactly harmonize with the logical form supplied by the three fundamental principles ? Can the pure logical form be applied to it with- out being weakened. The history of philo- sophy teaches us that Aristotelian logic has had many adversaries. The English school, for instance, regards it as a vain sport of the mind, and intellectualist philo- sophers, such as Herbart, make ineffectual attempts to establish logically the legitimacy of the idea of connexion. In syllogistic logic, there is something not only new, but also strange, when compared with pure logic. Concept, in fact, must express a unity in- volving a multiplicity. But then, what idea are we to form of this conjunction ? If we 24 THE LOGICAL LAWS say that multiplicity is potentially in con- cept, we introduce an element of obscurity. If we say that concept contains its parts as a vase contains whatever is put into it, we are the victims of a physical conception, we pre-suppose the confused idea of space. Frequently we think we form a clear idea of space because we reduce it to a collection of elements. But, when unity has vanished, concept is non-existent, and to bring reason- ing to bear on facts themselves, as immediate matter, would imply the suppression of logic altogether. And so judgment contains something obscure. What is the connexion it sets up between subject and predicate ? Is it a relation of determination ? For instance, does the judgment : Paul is a man mean that mankind is matter of which Paul is a specification ? To understand judgment in this fashion is to relapse into the obscure metaphysical notions of potency and act, form and matter. Will it be urged that the predicate is analytically drawn out of the subject ? But that is only a sensible image, obscure to the understanding. Finally, syllogism also lends itself to objec- 25 NATURAL LAW IN SCIENCE AND PHILOSOPHY tions that have never been clearly refuted : either tautology or the vicious circle is the danger it has to face. All men are mortal: this major premise implies the conclusion. Every man is mortal : this expression, indeed, does away with the vicious circle ; but the word Every (Tout), whether expressing a metaphysical essence or indicating the exist- ence of a genus, raises insoluble difficulties. Speaking generally, syllogistic logic pre- supposes the distinction between the implicit and the explicit, a distinction which cannot be cleared up. \ Not only, then, do the laws of syllogistic logic contain something more than do the flaws of pure logic, they also deviate from 'them, to some extent. What, now, is the origin of Aristotelian logic? This origin is not wholly d priori, since it cannot be resolved exactly into pure logic. Must we say, along with the empiricists, that it is wholly d posteriori ? To maintain this doctrine is to affirm that, strictly speaking, there are no syllogistic laws, but only special laws applicable to future events, in so far as they are demonstrated by experience and induction. Such was the opinion of Stuart 26 THE LOGICAL LAWS Mill. Quite logically Herbert Spencer main- tained that in reality there were only reasonings by analogy, and no syllogisms at all. And yet, the answer might be urged, this syllogistic ex- actly represents the reasoning process of reflec- tive consciousness. Indeed, we cannot do with- out it ; whatever we do, it is implied in every demonstration which carries conviction with it. It has not the full evidence of pure logic, though it shares therein ; consequently, it is not wholly d posteriori but seems rather a blend of d priori and d posteriori. The human mind, we may say, bears within itself the principles of pure logic ; but since the matter offered to it does not seem to conform ex- actly with these principles, it endeavours to adapt logic to things so as to interpret the latter in a way that approaches perfect intelli- gibility as nearly as possible. Syllogistic logic may therefore be regarded as a method, an ensemble of symbols by which the mind is rendered capable of thinking things, a mould into which it will introduce reality to make it intelligible. It is in this way that we would answer the question of the nature and degree of intelligibility of the logical laws. 27 NATURAL LAW IN SCIENCE AND PHILOSOPHY At first sight, it may appear useless to question the objectivity of these laws, for there is nothing that seems more certain, more beyond all dispute, than this objectivity. And yet logic has been attacked quite as frequently as it has been extolled. No doubt it is a grave reproach against a person to say that he is not logical ; as a rule, we admire those who are capable of organizing a vast mass of material after the type of the principles of identity and contradiction. But then, at times, we blame those who are looked upon as stubbornly logical and systematical : every system, it is alleged, is artificial ; to try to find some shade of difference even at the risk of encountering contradiction, is the way to grasp reality. This diver- gence of opinions seems as though it might be explained by the distinction established above. Pure logical laws are indisputable, but they concern not at all or but very slightly the inner nature of things ; the laws of syllogistic go deeper into the nature of things, but a certain amount of discretion must be used in applying them. The former we regard as absolutely neces- sary : it does not lie within our power to 28 THE LOGICAL LAWS conceive of them as aught but purely sub- jective and unrealized by nature ; we do not even see how experience could contradict them, since all they do is to declare that if something is, it is. But that which constitutes their strength also constitutes their weakness : they leave indeterminate the very things to which they apply. When I say, A is A, I lay no prohibition upon myself from implying that A, in itself, is devoid of identity. We have therefore to discover whether the very nature of things also is in conformity with these principles. The Eleatics maintained that being, in effect, expresses identity, and is exempt from contradiction, but over against such a system the history of philo- sophy sets that of Hegel, who, on the other , hand, regards contradiction and necessary^ strife as in the inmost nature of things. There is no difference between these two systems, as regards the laws of pure logic. They both conform to these laws. For Hegel did not say that, in stating a proposi- tion, you could also state the contradictory proposition. He thought that if, in the formula A is A, we replace A by its real value, we have, from the very outset, being 29 NATURAL LAW IN SCIENCE AND PHILOSOPHY identical with non-being. Which is the true doctrine, the Eleatic or that of Hegel ? Neither of them, probably. At all events, it is not the consideration of logical laws in themselves, but only the consideration of the concrete laws of nature, that can teach us to what extent real beings essentially partici- pate in identity and contradiction. It is less hazardous and more customary to regard the laws of syllogistic as the expres- sion of the universal conditions to which the laws of nature are subject. According to this view, dogmatists are inclined to assimilate logic to reality. They base their opinion on what they call the natural harmony between thought and things, a principle they look upon as necessary and innate. This principle, however, is nothing but a wish, a desire, a mere postulate. Moreover, even if it were certain, it would not guarantee the objectivity of syllogistic logic, if this latter, as we have endeavoured to show, is not thought itself but rather a misrepresenta- tion of the principles of thought resulting precisely from the opposition between thought and things. Must we then altogether renounce the 30 THE LOGICAL LAWS objectivity of this logic, and, with the empiri- cists, maintain that there are only facts, and that these facts create within us habits, imperious enough, no doubt, but purely subjective ? It would appear that the logical v / laws cannot be regarded as derived exclusively from experience : this latter presents no groupings analogous to concepts, and concept is not a tardy acquisition of the mind. In spite of a prejudice handed down to us from Locke, it is with general concepts that the child begins, and it is precisely the function of experience to contradict and break them up. Concept, then, originates in the mind. No doubt it is formed on the occasion of experience and with materials borrowed from experience, but it is the mind that forms it. Now, it is beyond dispute that our reasonings are sus- ceptible of being in harmony with facts ; when they are out of harmony, we do not consider that reasoning is a vicious instru- ment, but rather that we have insufficient data, that our field of operations is too limited. Consequently, things possess relations which, in a measure, correspond to syllogistic con- catenation. In nature, there is something resembling classes of beings or species, and NATURAL LAW IN SCIENCE AND PHILOSOPHY something resembling classes of facts or laws. Still, we cannot know, d priori, how far this condition is realized ; nothing but the develop- ment of science can tell us that. Perhaps the following is all we can conjecture d priori. Man, to all appearance, is not a monster in nature ; the intelligence that characterizes him must bear some relation to the nature of beings in general. Therefore, at the root of things, there must be, if not an intelligence similar to the human, at all events properties and dispositions that bear some analogy with this intelligence. It is reasonable to admit in nature a sort of tendency towards intelligi- bility. If this be the case, reasoning repre- sents a mode of interpretation, of interroga- tion which may legitimately be employed in dealing with nature. What, now, is the signification of the logical laws ? Logic, certainly, is the most perfect type of absolute necessity, but it offers a^ minimum of objectivity/ It governs the / surface of things but does not determine their nature ; it remains true, whatever be that nature. The necessity it implies will be safeguarded, even if beings are to be considered as endowed with spontaneity, even if beings 32 THE LOGICAL LAWS are free. It is an absolute master, though infinitely remote from ourselves; an insur- mountable barrier, though between it and ourselves there is more space than we shall ever be able to compass. If syllogism is, in reality, but a symbol invented by the human mind, it cannot be regarded as self-evident that the necessity, proper to it, is, in effect, found realized in things. This necessity is the relationship implied in the notions of species and genus. The special sciences alone will inform us if there are genera and species in nature. How- ever, as man is not an empire within an empire, as not only are our reasonings successful, but it is natural that they should be successful, we have reason to infer that in things there! is a tendency to order and classification, toj the realization of species and laws. And so already we dimly foresee that in the being all around us there might exist a duality analogous to that which we acknowledge within ourselves. Besides intelligence, we possess a mass of faculties grouped under the heading of activity. Intelligence is the rule of activity ; but we cannot say d priori how far activity realizes intelligence. Per- 33 c NATURAL LAW IN SCIENCE AND PHILOSOPHY haps the same thing happens in nature. There is a principle of necessity, but this principle is only the rule, not the basis of things. The knowledge of particular laws alone will give us some idea as to how far necessity is realized. 34 Ill THE MATHEMATICAL LAWS AFTER the logical laws, the mathema-\ tical laws are those that appear most I general. It would seem, at the outset, as if they, too, were perfectly clear, and that it was superfluous to question their intelligibi- lity. Was it not to these laws that Descartes appealed, when seeking after the type of evidence ? And yet, in order to establish the effective value of mathematics, this same Descartes regarded it as necessary to fall back upon divine immutability and * truth. On the other hand, the entire em- piric school calls in question the certainty proper to mathematics. It may also be said that the distinction between logic and mathe- matics is a fact of ordinary life ; judging by the mathematical inaptitude of certain dialecticians who, in other matters, are exceedingly subtle, and vice versa, there 35 NATURAL LAW IN SCIENCE AND PHILOSOPHY would appear to be two ways of reasoning, quite distinct from each other. These con- siderations call upon us to examine the nature of mathematical certainty. For one school of philosophers, mathematics is a mere application, a special development of general logic. So thought Leibnitz. If this be the case, the difference between the mathematical and the logical laws is not an essential one : the latter are simply more general than the former ; there is nothing in mathematics that cannot be reduced to logic. For other schools, on the contrary, in conformity with the doctrine of Kant, these two kinds of law are irreducible to each other ; in the mathematical there is some- thing more than in the logical relationship. Now, speaking generally, the speculations of mathematicians seem more favourable to the second theory than to the first. What is there new in mathematics, when compared with logic ? In a general way : intuition. Then what is it that character- izes mathematical intuition ? Logic, if we consider the matter closely, (presupposes a given whole, a concept which it purposes to analyse; in this 36 THE MATHEMATICAL LAWS concept, it admits elements set alongside of each other, and does not determine the bond that unites them. Mathematics, on the other hand, does an essentially synthetic work ; it posits the relations which logic supposits, creates a link between the various parts of a multiplicity, proceeds from the simple to the compound, itself generates the compound instead of taking it as given. Thus, mathe- matical intuition is really something new, though in what way ? In conceptual logic, in so far as it is dis- tinguished from really pure logic, the notion of the general actually embarrasses the under- standing which is trying to arrive at perfect intelligibility. In mathematics, there is more than this. Fundamental definitions are not mere propositions. An infinite number of definitions are frequently condensed in a mathematical definition. For instance, in numeration, the unit is taken as the starting- point, and the following definitions are formed : 2 = i+i;3==2+i;4 = 3+ I * etc -' or > in a general way, 0+2 = (0+i)+i; a + 3 = (a + 2) + i ; a + 4 = (a + 3) + i. After thus forming the definitions of the first few numbers, we add : etc. What is 37 NATURAL LAW IN SCIENCE AND PHILOSOPHY this etc. but the idea of an endless number of definitions, analogous to those we have created ? Now, the arithmetician reduces this infinity to the following formula : a + b a + (b ~ J ) + J > a definition which in itself con- tains an infinite number of definitions. Such a concept is more than a novelty, in relation to the purely logical concept : it is already a deviation from perfect intelligibility. It is the same with demonstrations. Mathe- matics frequently calls for a mode of reasoning different from logical deduction, and which consists in generalizing, with demonstrative force, the result of a particular demonstration. This we see in the theory of addition, on which the whole of mathematics is based. Suppose we have to demonstrate that a + i = i + #. First we make a = i, then we have 1 + 1 = 1+1, by identity. Then we adopt a roundabout method, and say : suppose (a i) + i = i + (a i). If this supposition is granted, adding i to each of the two members, we have (a i) + i + i i + (a i) + i, which, on crossing out the terms that cancel each other, gives 0+1 = i + a. We have supposed that (a i) + i = i + (#i). But if we call (a, i) : a, 38 THE MATHEMATICAL LAWS we are brought back to the preceding prob- lem. We may continue in this way until we come to the case in which a = i. This mode of demonstration is called reasoning by re- currence. As we see, it is a demonstration that contains as large a number of demon- strations as we please, since a may be sup- posed as large as we please. The same kind of reasoning takes place in a great number of cases, for instance, in demonstrating that the sum of several consecutive odd numbers from i upwards is equal to the square of their number. This reasoning is a kind of apodeictic induction. There is induction, for in this case demonstration deals first with the particular, and generalization comes only afterwards. And the induction is apodeic- tic, since it extends to all possible cases. Now, from the logical point of view : it is strange that a generalization can thus be conceived as necessary ; and the reason we are here compelled to bring together these two words, which might almost be said to repel each other, lies not only in the fact that mathematics is not a simple development of logic, but that it does not even simply differ from it, as synthesis differs from analysis. 39 NATURAL LAW IN SCIENCE AND PHILOSOPHY Mathematical intelligibility actually implies some modification of logical intelligibility. If this is so, what is the origin of the mathe- matical laws ? If they were wholly known d priori, their intelligibility would be perfect. As it is, they imply elements that cannot be fathomed by thought. We are compelled to acknowledge them : we cannot say we find them clearly springing from the funda- mental nature of the intellect. Nor can they be connected with knowledge d posteriori, for they deal only with limits. A limit cannot be understood empirically, since it is the purely ideal term towards which tends a quantity supposed to increase or decrease indefinitely. The mathematical laws pre- suppose a very complex elaboration. They re not known exclusively either d priori or d posteriori, but are a creation of the mind ; and this creation is not an arbitrary one, but, owing to the mind's resources, takes place with reference to experience and in view of it. Sometimes the mind starts with intuitions which it freely creates ; sometimes, by a process of elimination, it gathers up the axioms it regards as most suitable for pro- ducing a harmonious development, one that 40 THE MATHEMATICAL LAWS is both simple and fertile. Thus, mathe- matics is a voluntary and intelligent adapta- tion of thought to things, it represents the forms that will allow of qualitative diversity being surmounted, the moulds into which reality must enter in order to become as - intelligible as possible. Such is the nature, such the degree of intelligibility of the mathematical laws. What follows, as regards their objectivity ? Accord- ing to Descartes, mathematics is realized such deep within the sensible world ; it constitutes the very substance of material things. After Descartes, this point of view became more and more limited and disputed, and the positivism of Auguste Comte summed/ up the results of criticism by declaring thai[ the higher is not reducible to the lower, and that, the more we would account for a loftier reality, the more we must introduce new laws which have a specificity of their own and cannot be reduced to the preceding ones. The mathematical laws, considered in themselves, appear inapt for realization, since they imply infinite number ; now, an actual infinite number is altogether incon- NATURAL LAW IN SCIENCE AND PHILOSOPHY ceivable. Every system of mathematical realism splits on this rock. But then, the idealist will say, what makes inconceivable the reality of infinite number, is that we insist on actualizing it as substance. If mind is the only reality and things but the projection and representations of its acts, the mathematical laws may be conceived as real, in so far as they form, within the mind itself, the groundwork of the world of repre- sentations. Our answer to the idealist will be that his system has no justification. In order that we may find, in mathematics, thought itself rendered objective, the laws of mathematics would have to be perfectly intelligible ; now, the mind cannot assimilate them without a certain effort. Moreover, our mathematics represents a particular form of mathematics ; others are possible, but the reason we keep to our own is solely because it is more simple or convenient for our com- prehension of external phenomena. How will the idealist distinguish what is absolutely necessary from what might be different in the development of mathematics ? There exists, it would appear, a means of maintaining the absolute objectivity of mathe- 42 THE MATHEMATICAL LAWS matics, in spite of the difficulties which the intellect experiences in realizing the infinite ; and that means consists in saying that the law of the real is actually the radical incon- sistency or illogism and even the identity of the contradictories. But what would then be conceived as realized would be something different from mathematics as such, since the latter was instituted for the very purpose of removing, as far as possible, the contradictions offered by phenomena, recording to others, the substance of things eludes us, but the mathematical laws represent their forms and relations ; these laws are the common element between ourselves and ex- ternal reality. Such, for instance, was the doctrine of Ampere. This is a simple and clear, though artificial, conception ; for the form and the substance of things cannot thus be radi- cally separated. When the form of a thing is perfectly known, it is no longer possible foi us to say that we are altogether ignorant oj its nature. The separation between matter and form is only a logical one, it cannot be a real separation. Not only, then, are the mathematical laws unreal, both in the sub- stantial and in the idealistic sense, but they do 43 , NATURAL LAW IN SCIENCE AND PHILOSOPHY not even express a form of things that is really separable from their matter. All the same, mathematics cannot be regarded as a mere convention, a simple sport of the mind. It is./ a fact that mathematics does apply to reality. How far and in what way cannot be deter- mined d priori. All we are permitted to say is that, since man, apparently, is no anomaly in nature, that which satisfies his intellect must not be unrelated to the rest of things. We may therefore conjecture that there exists a correspondence between the mathematical laws and the laws of things ; but it is the study of the particular concrete laws of nature that will teach us how far, in effect, the mathe- matical laws govern reality ."7 What, in short, is the meaning of mathe- matics as regards the necessity which may be ruling throughout the world ? These laws are still closely bordering on absolute necessity ; but they are also very far from things and from reality. And though they evi- dently have a closer connexion with being than v the logical laws have, still, we cannot say that they introduce absolute necessity into being, for they actually admit of a strict deduction only through imperfectly intelligible axioms 44 THE MATHEMATICAL LAWS which the mind has combined with a view to this very deduction. How far does the necessity peculiar to them rule in things ? This we shall learn by comparing the physical with the mathematical laws. We must now apply ourselves to investigating them. In the next chapter, we shall take up the mechani- cal laws and the idea of force. 45 IV THE MECHANICAL LAWS OUR present object is to examine critically the idea we have of the laws of nature, in the hope of extracting information as to the relation these laws bear to reality, and the position of the human individual in nature herself. It is our ultimate end to know whether, in the present state of the sciences, we may yet regard ourselves as possessed of any power to act freely, any reality as persons. Along these lines, we have ex- amined the logical and mathematical laws, which, after all, are more than laws and express the most general relations, the con- ditions of all the rest. We have shown that the laws of real logic cannot actually be reduced exactly to the only principle most certainly known d priori, namely A is A, and that concept, judgment, syllogism, all imply a new element : the many as con- 46 THE MECHANICAL LAWS tained in the one, or again the relation of the explicit to the implicit. Mathematics also introduces new elements which the mind cannot thoroughly assimilate : it creates relations of adjustment ; it diversifies the identical with the aid of intuition ; more than that, in its generalizations, it cannot dispense with a mode of reasoning which may be called apodeictic induction. If both the mathe- i matical and the logical laws do not proceed I immediately from the nature of the mind, I neither are they deduced from experience.^ Indeed, were this the case, they would have to coincide with parts or aspects of reality : now, this is not so. Neither the universals of logic nor the infinite number of mathematics are given to us. We cannot even conceive how they could be. Thus, logic and mathe- 1 matics are solely derived neither from know- ledge d priori, nor from knowledge d posteriori : they represent the work of the mind which, incited by things to exert itself, creates a mass of symbols in order to subject these things to necessity and thus make them capable of be- ing assimilated by itself. The logical and the mathematical laws testify to the mind's need of conceiving things as being necessarily deter- 47 NATURAL LAW IN SCIENCE AND PHILOSOPHY mined ; Lbut it cannot be known d priori how far reality conforms with these mind-imagined symbols : we must appeal to observation and analysis of the real if we would know whether mathematics, in effect, rules through- out the universe. All that can be admitted, previous to this experimental study, is that there is probably a certain analogy between our intellectual nature and the nature of things. Were it not so, man would be isolated in the universe. This, however, is but conjecture.^ A consideration of the concrete sciences will alone enable us to say what degree of reality we must attribute to logic and to mathematics. The laws of reality given to us as approach- ing nearest to mathematical relations, are the mechanical laws. The essential and char- acteristic element of these laws is the notion of force. In order to understand the forma- tion and the present state of this notion, we will now study its historical evolution. In antiquity, and especially in the times of Plato and Aristotle, what seems, above all else, to strike the human mind, is the differ- ence between motion and rest. This opposi- tion is made the point of departure, and it is admitted that matter, in itself, is in a state 48 THE MECHANICAL LAWS of rest. What has then to be explained is the transition from rest to motion. To solve the question, the production of motion in man is considered. Now, motion appears, in man, as resulting from the action of the mind on the body. Thus, above matter, there is assumed a separate force, resembling a soul more or less, and as such, suited for acting upon bodies. This view may readily be connected with the teleological conception, in virtue of which God rules and moves the totality of things ; thus, it shows itself favourable to ethics and religion. On the other hand, it opposes the progress of science. How, in effect, are we to gauge and foresee the action of an immaterial force, called upon to exert itself from aesthetic and ethical reasons ? As a matter of fact, the science! of the real made little progress, so long as iti regarded things from this point of view. At the time of the Renaissance, a totally different conception grew up. Instead of con- trasting motion with rest, Galileo looked upon them as analogous : matter is self-sufficient, both in motion and in rest. Of itself and apart from supernatural intervention, it continues indefinitely in a uniform, rectilinear motion ; 49 D NATURAL LAW IN SCIENCE AND PHILOSOPHY of itself, it can pass neither from rest to motion nor from motion to rest : it is the principle of inertia. No doubt, if we wish to bring before the mind the first origin of motion, we must presuppose a first impulsion, a fillip, chiquenaude, as Pascal called it ; but as regards its present state, which alone is the object of science, matter contains within itself the explanation both of its motion and of its rest. From this idea of inertia, it was at first thought possible to infer the abolition of force as a separate idea. Thus, Descartes thought he could explain all physical pheno- mena by the one law of the conservation of the quantity of motion, a corollary of the prin- ciple of inertia. Force, as such, is banished from his system. This philosophy might have been developed deductively, like mathe- matics, of which it formed the continuation ; but there came a time when it was confronted with facts and then found to be inadequate. Newton, in order to account for the motions of the heavenly bodies, regarded it as necessary to re-establish the idea of force. He started with the principle of inertia, according to which a body retains its uniform, rectilinear motion for an indefinite period. The heavenly bodies, THE MECHANICAL LAWS however, moved in a curvilinear, non-uniform / fashion. To explain this modification of motion, we must admit that some external) force acts upon the moving body. This reappearance of the idea of force, moreover, is not the restoration of the ancient con- ception. The ancients regarded force as dwelling in a higher, metaphysical form ; it acts from above, after the fashion of a soul ; it is God Himself, who, by His perfection, produces the motions of the heavenly bodies. Newton, on the other hand, attributed force to matter ; an atom has not the power to modify its own motion, but it can modify the motion of other atoms. Thus, without leaving matter, we come to explain modifica- tions in the speed and direction of motion. God is eliminated from the world, in so far, at least, as He is considered to be an artist who produces by separate acts every detail of His work. Are we not, however, restoring the occult powers of the Schoolmen if we admit the existence of such a force ? Newton, as we know by his own declarations, does not regard attraction as a metaphysical force, analogous to a soul's activity, To him, this NATURAL LAW IN SCIENCE AND PHILOSOPHY is but an expression, a kind of metaphor, pointing to a phenomenal relationship. Force, as he interprets it, is none the less the cause of motion. Now, cause must be prior to effect. If, then, this is not an occult power, at least it is something metaphysical and invisible, which logically precedes phenomena. Mathematicians have taken it into account, and so we find them, nowadays, endeavour- ing to transform the relation between force and motion into a simple mutual dependence, a mere relation of solidarity. It is in this way that force is defined as the product of the mass into the velocity. Here, force and motion are two data related to each other, without there being any necessity to inquire whether it is force that is the cause of motion, or motion that is the cause of force : just as, in geometry, we have the relation of diameter to circumference. LIs force, as thus conceived, reduced to a purely mathematical notion, or does it contain some new element ? Doubtless, abstract mechanics does not differ from mathematics and consists solely of substitutions of formulae. But abstract mechanics does not suffice for the realization of the science of nature. This 52 THE MECHANICAL LAWS was clearly seen by Newton ; he tried to find in experience the mathematical principles of his natural philosophy. Now, what is that element which cannot be found in mathematics and which only experience can give us ? It is the measure of the action which bodies exercise upon one another:T In mathematics, consequences are analytically deduced from definitions ; we start with the identical and then diversify it. But, in nature, we start with things foreign to one another, such as the sun and the planets, and set up a definite, constant dependence between these things. We are really dealing, then, with a mathematical connexion, though it can neither be affirmed nor known d priori. Thus, what there is new in the notion of force, is, in short, the idea of physical causality, or, in more precise terms, the idea of natural law, strictly so called. /"Force is a uniform depend- ence, experimentally known, between things exterior to one another. Consequently it contains an extra-mathematical element^ But then, may it not be said that the affirmation of the natural laws results from a special necessity of the mind ? Followingl "J on Kant, profound philosophers maintain, | 53 NATURAL LAW IN SCIENCE AND PHILOSOPHY even nowadays, that the notion of law is the result of our mental make-up, and consists of a synthetic, d priori judgment. These philosophers justify their theory by setting forth how such an idea of causal law is neces- sary in order to think phenomena, i.e. to reduce them to unity within a consciousness. Phenomena, in themselves, are heterogeneous with regard to one another. The notion of law, by establishing universal and necessary relations between them, gives them the only unity of which a heterogeneous multiplicity admits. This theory, to our mind, is open to objections. At the outset, is it clear that we have an irresistible need to think phenomena, to reduce them all to unity, to set up between ourselves and them, in an absolute sense, the metaphysical relationship of subject and object ? No doubt we have need of unity ; but it is difficult to prove that this need takes precedence of all others and governs the whole of our intellectual life. Indeed, the history of philosophy offers us not only minds that aim at an explanation of the uniform by the multiple and the changing, but also logicians enamoured of a reduction to unity. 54 THE MECHANICAL LAWS Now, if unity in the conception of being is not necessary, neither are the means of obtaining it. But we may go farther. Even granting that we feel this absolute, imperious need to think things, is it certain that the categories of the understanding realize the end assigned to them, viz. the assimilation of things by the mind ? It would appear as though this point had been too readily granted to the Kantian doctrine. Indeed, to think things is to understand their particular affinities and connexions, to see how they unify and group together of themselves. Kant's cate- gories, however, leave things as they find them, exterior and alien to one another. They bring them together artificially, as stones are brought together in building a house. They reconcile nature which unites beings according to their consanguinity or kinship with art which brings them together in accordance with its own ideas of fitness. Is a bundle of sensations a thought taking possession of things ? This is not all, and we may enquire whether the position adopted by Kant can be main- tained as ultimate, or whether it must not 55 NATURAL LAW IN SCIENCE AND PHILOSOPHY of necessity be transcended in one direction or the other. The objection is frequently urged that, if Kant's categories are purely subjective, it is inexplicable that nature should conform to them. Stated thus, the objection is perhaps not well founded; for, in Kantianism, what we call nature is already the work of the mind, not perhaps of the individual thought, but of the universal human thought identical in each individual consciousness, and the individual mind only recognizes empirically and successively that which reason builds up and unifies d' priori. But it would seem that a somewhat similar objection might be raised. Either the laws, we may say, that the mind brings forward, will find analogous matter, obedient to their action, in which case how shall we know that the notion of these laws comes from ourselves rather than from the observation of things, that they are known to us d priori rather than d posteriori? Or else things will not conform to these laws, and in that case shall we claim that it is ourselves who are right and nature who is wrong ? It is clear that, as soon as it is proved that facts do not fit in .with the limits we wish to impose upon them, we shall 56 THE MECHANICAL LAWS make it our object to free ourselves of these limits and form conceptions more in accord with facts. Thus, the mechanical laws are not an ana- lytical succession of mathematical truths; neither do they rest on synthetic d priori judgments. Are they derived from experi- ence ? The ancients claimed to obtain from experience only the general and the probable, i.e. what happens in the ordinary way of things, W? eVJ TO TToXv ; what they wanted it to give them was universal and necessary rules, not laws. For the moderns, however induction is a kind of magic word, in virtu of which, fact is transmuted into law. B so-called scientific induction, which evi dently has scarcely anything in commo: with ancient induction, it is claimed tha the universal can be deduced from th contingent, the necessary from the partial lar. Still, however productive and methodical modern induction may be, it will never succeed, without superseding experience in bringing us to true laws. For instan we cannot possibly, by experience, beco acquainted with inertia and force ; to d this, we should have had to be present at th 57 NATURAL LAW IN SCIENCE AND PHILOSOPHY creation. We never observe the exactly uniform and rectilinear motion of a moving body, removed from all extraneous influence, any more than the continuance in rest of a body that has received no impulsion. The duality of inertia and force, the action of multiple forces, and the composition of these forces, are abstractions that cannot be verified. \ We may go even further and say that induction cannot even account for the most ' general characteristics of the mechanical laws. In fact, we observe only moments separate from one another, i.e. discontinuity, and yet ur laws give us continuity. Secondly, these aws imply precision, whereas experience gives us only approximations. Afterwards, we assume, as fundamental, definite relations between such and such phenomena, whereas experience offers us an infinite number of elations between which there is neither riority nor separation. Finally, we attri- bute to our laws, fixity, as an essential characteristic. Now, in this we cannot say that we are judging the future by the past, for only to an insignificant extent do we know the past. It is most seriously alleged nowadays that species are not eternal, but 58 THE MECHANICAL LAWS have a history of their own. Why also should not laws, those types of the relations that exist between phenomena, be subject to change ? The fixity we attribute to them is a characteristic that we add on to the data of experience, one that cannot be revealed to us from without. Nevertheless, if the mechanical laws are known neither d priori nor a posteriori, in their distinctive form, it does not therefore follow that they are fictitious. jThe concept of law results from the effort we make to adapt things to the mind. Law represents the characteristic we must attribute to things in order that they may be expressed by the symbols at our disposal, the matter that physics must offer to mathematics, so that mathematics may unite with it. And the result proves that certain phenomena of nature comply with this requirement, the consequence being that the notion of mechanical law dominates the whole of scientific research, as a guiding idea, at all events/) We have inquired into the nature of the mechanical laws ; now we must examine their objectivity and signification, i.e. we must see how far we are justified in believing 59 NATURAL LAW IN SCIENCE AND PHILOSOPHY that things realize mechanism, and to what extent we are included in this mechanism. These questions will be dealt with in the next chapter. 60 V THE MECHANICAL LAWS (Continued?) \ \X/E have seen that the mechanical laws V V are not a mere development and complication of mathematics ; in reality, they imply a new element which cannot be i^ reduced to mathematical intuition, viz. the solidarity of fact, the regular, constant depen- dence, empirically given and unknowable d priori, between two different magnitudes. \, We have shown that these laws are not purely experimental truths either. They result from the collaboration of mind and things ; they are products of mental activity and apply to extraneous matter ; they represent the effort which the mind makes to set up a coin- cidence between things and itself. Now we must inquire in what way the mechanical laws may be regarded as realized in nature. The first step taken by the creators of 61 NATURAL LAW IN SCIENCE AND PHILOSOPHY scientific mechanism was to grant objective existence to those laws that enable us to explain things in so rigorous a fashion, and the first doctrine we find on this subject is dogmatism. According to this doctrine, the mechanical laws, as such, are inherent in things considered per se, apart from the mind at work upon them. Descartes teaches this metaphysical mechanism ; he regards matter and motion, which are them- selves capable of expression in terms of space, as representing the entire essence of things other than mind, and so the mechanical laws exist as such in nature ; more than this, they are the fundamental laws of the whole of nature. Still, Cartesianism lends itself to serious objections. On what is it grounded ? On the clearness peculiar to the idea of extension. But, given that clearness of the idea of extension, does it follow that extension is the essence of matter, as Descartes states it to be ? Descartes himself succeeds only by having recourse to divine truth, as to some deus ex machina. But how are we to see in motion a thing that exists per se ? Motion is not self-sufficient. Common sense 62 THE MECHANICAL LAWS tells us that it presupposes something that moves, and common sense is right. To estab- lish a connexion between the different posi- tions of which motion consists, we must have either a permanent subject such as matter, or a mind that contains the representations of these positions in one and the same con- sciousness. In a word, motion, of itself, does not involve the principle of unity, of which it stands in need in order to be real. L Newt on corrected Descartes' mechanism, though he remained dogmatic. When he says Hypotheses non fingo, he means that he is not satisfied, as Descartes is, with merely possi- ble explanations, but that he aspires to find out the real, effective causes of things, the laws which God himself had in mind when he created and planned the universe. Newton introduces into nature that material subject which was lacking in Cartesian mechanism ; he admits of bodies, endowed with forces, as a condition of motion, and thereby thinks he is securing, far better than Cartesianism did, the objectivity of the mechanical laws.^ And so he acknowledges the existence of real motion, whereas, according to Descartes, there existed only relative motions. We must 63 NATURAL LAW IN SCIENCE AND PHILOSOPHY [^carefully distinguish between Newtonianism as science and Newtonianism as metaphysics. Newtonianism as science is satisfied, as far, almost, as the human mind can be, with ex- perimental or mathematical notions. But if we would convert this science into a knowledge of nature as existing per se, we must realize space, mechanical causality, force, atoms, and even attraction, or any other mode in which the cause of motion operates. And here arise the difficulties so well demonstrated by Berkeley, whose system, from the very outset, is a refutation of Newtonianism regarded j as metaphysics^ If space, matter, atoms, mechanical causality, force, attraction and repulsion, says Berkeley, are looked upon as objective realities, we must first acknowledge that they are things which the human mind is incapable of knowing. It is only by a process of artificial abstraction that we detach them from the sensations of which we are conscious. They are never presented to us in themselves ; they cannot be. Nor is this all. Not only are such things, for us, if they exist, as though they were not, but we cannot even conceive that they do exist, in themselves. In fact, these con- 64 THE MECHANICAL LAWS cepts, set up as things per se, become contradictory. Infinite and homogeneous space devoid of quality, the extended, indi- visible atom, mechanical causality, wherein that which is powerless over itself, possesses power over something else, resulting in pro- gression ad infinitum, the action of one crude body upon another, in whatever way this action is brought before the mind : all these symbols, taken as absolute realities, become unintelligible ; nor need we be surprised if we remember that these concepts, when analysed, present elements with which thought cannot deal. A third form of dogmatism is that pro- fessed by Leibnitz. According to him, there is everywhere at the same time both the mechanical and the metaphysical ; the me- chanical laws exist, though not separately and in themselves, as the mechanician conceives them. Their reality consists in the fact that they are well founded, i.e. supported by a reality distinct from themselves, but one that really exists and contains the requisita of mechanical action. This subject of mechani- cal phenomena is force, i.e. a metaphysical essence which, at bottom, offers a certain 65 E NATURAL LAW IN SCIENCE AND PHILOSOPHY analogy with our souls. But this system also raises difficulties. LThe mathematical formulae of the mechanicians, from the time of Descartes right on to our own, have been so purged of all psychological or metaphysical content, that we no longer see any connexion 1 between force as metaphysics understands it and force as assumed by science. The latter is nothing but a measure of motions. It might with equal justice be conceived both as a con- sequence and as a condition of motion. The transition, then, from scientific to metaphysi- cal force is lacking. Leibnitz's metaphysics is superimposed from without upon science strictly so called. True or false, it is no longer scientific mechanism that it sets up as a reality .J The mechanical laws, therefore, cannot be considered realized, as such, in the nature of things. The concepts of which they are constituted become unintelligible when con- erted into beings. Must they therefore be denied all genuine reality, and regarded, along with idealism, as nothing else than a symbolical expression, a projection of the laws of mind iself ? Interpreted idealistically, the concepts of 66 THE MECHANICAL LAWS which the mechanical laws consist, avoid the contradictions that appear when they are interpreted realistically. Thus, space, a form of sensibility, is no longer contradictory, like space that exists per se. Mechanical causality, connecting representations with one another, no longer lends itself to the objections raised by this causality, conceived as con- necting things. [jBut idealism is unable to stand its ground; and, the more closely it pursues the problem, the more it is compelled to recognize destructive elements within itself. As a principle, idealism consists in explaining the unconscious by the conscious, things by thought. But the history of philo- sophy shows us that, in order to explain the given, idealism is forced to appeal to the unconscious and allot this latter a place along- side of or even above the conscious. In the case of Kant, deep within the mind appears the synthetic judgment d priori, which the intellect is compelled to accept as a sort of metaphysical fact, without really under- standing it. Beneath the conscious self, Fichte places the absolute self, the activity of which precedes the intellect, and it is this activity which, when subjected to an inexplicable 67 / NATURAL LAW IN SCIENCE AND PHILOSOPHY impact, explains the self as the not-self. In Schelling, the absolute becomes the identity of the self and the not-self ; in Hegel, it becomes the identity of the contradictories, that offence and stumbling-block to thought. Thus the self is more and more driven to leave itself and have recourse to some heterogeneous principle ; idealism more and more abjures ^ itself and approaches realism/) If then the mechanical laws do not exist objectively, neither are they mere projections of the conscious mind. They witness to the existence of something different from mind, and yet which must not be altogether j separated from it. lWe are foiled when we try to determine the substantial nature of things ; all the same, we cannot abolish them. JA11 we can say is that, in things, there is a mode of being which suggests to our minds the invention of the mechanical laws. In reality, how do things act in nature ? We can form a conjecture of this only by analogy, when / we consider what takes place within ourselves] In short, consciousness is the only sense of being that we have at our disposal. Now, the phenomena which, in man, affect the mind in its most intimate union with the body, are the 68 THE MECHANICAL LAWS phenomena of habit, and it would really seem as though its effects bore a certain resemblance to mechanical causality. (TTt first we have mental activity, in certain cases, at all events ; actions are related to thought, as their generating cause. By degrees, they fall away from thought, and jostle one another, as it were. Thus, in certain cases and with certain men, words follow one another without being determined by thought ; and so we find inertia and mechanical force in the persistence of our states of consciousness and in their mutual influence. This view may not follow from an induction based on the results of science, it is but a simple analogy ; still, it constitutes the only way in which we can point to the reality of mechanical action. 1 To our mind, it is the degradation of true action, it is activity as represented by a link between its products, and thereby released and set free for new tasks. If such actions exist, the mechanical laws are the form we attribute to them, for the purpose of subjecting them to mathematical calculation. And so we se that the scientist can nowhere find the conditions of science accurately realized in phenomena. 69 NATURAL LAW IN SCIENCE AND PHILOSOPHY One final question : do the mechanical laws establish an absolute determinism ? I There are few men, even amongst meta- physicians, who accept mechanical deter- minism as absolute. It is generally believed that man can produce movements in con- formity with his volitions. In the very countries where determinism is professed by eminent philosophers, teachers and all who appeal to conscience and claim to regulate conduct, affirm the existence of free-will and of its power over things. We find this the case in England as well as in Germany. Lit is more difficult, however, to prove one's opinion, than to convince oneself of its correct- ness.^ How -do we reason when we attempt to lay aside mechanical necessity ? Common sense acknowledges that the soul is capable of producing movements ; but that is simply appearance which will not bear investi- gation. I The soul, it is said, is a force ; but this is a much abused word. We pass without saying what right we have to do so from the notion of moral or metaphysical force to that of mechanical forceTf If the soul is a force, in the sense in which it must be for 70 THE MECHANICAL LAWS imparting motion to a body by virtue of the principle of inertia, it must modify the quantity of force wherever it intervenes. But this in itself is strange and contrary to experience and induction, which show us that the quantity of force in nature is constant. Are we to say that the soul cancels a quantity of force exactly equal to that it produces ? Such a conception would appear an entirely arbitrary one. We find philosophers offering us a subtler explanation : that the action of the soul upon the body is real, although of a metaphysical, not a mechanical nature. Descartes acknow- ledges that the quantity of motion remains constant throughout nature, but that the soul may change the direction of the motion. The mechanical laws remain secure, since, according to Descartes, they do not determine direction, which latter must come from some other source. In spite of the objections of Leibnitz, which in all probability are not decisive, this expedient, interpreted in more or less complicated ways, has frequently been reproduced. Of recent years, M. Cournot, ascertaining that the amount of power necessary for the starting of a machine may NATURAL LAW IN SCIENCE AND PHILOSOPHY be indefinitely diminished, recognizes a limit where this power would be nil. Then it would be replaced by a guiding force, belong- ing, for instance, to organisms or to thought. M. Boussinesq admitted that there were cases in which the initial state of a system does not wholly determine the course which the phenomenon must take. There would then be a greater or less number of bifurcations, making possible the intervention of a guiding force. Here the action attributed by Claude Bernard to life as a guiding idea, would find a place ; life does not violate the mechanical laws, but it communicates to movements a direction they would not of themselves have taken. This extremely seductive theory was up- held, as we see, by scientists of the first rank. It cannot be said, however, that it succeeded in becoming adopted. As regards passing to the limit, that is an expedient which offends the reason, and one which, in spite of appear- ances, does not seem to be authorized by mathematics. This latter declares A equal to B in so far as their difference may be made smaller than any given quantity only when A and B are both given as fixed, determinate 72 THE MECHANICAL LAWS quantities. A distinction is made between the true and the false use of the method of limits. Now, however small the force neces- sary for starting a machine may be conceived as being, this force is always required, it never becomes nil. The strange solutions of M. Boussinesq have been disputed by several mathematicians, and it would seem rash to regard the efficacy of freewill as depending upon speculations the proof of which is not perfectly evident. An important distinction, however, appears to dominate the whole question. As long as, with Descartes and even Leibnitz, we confine ourselves to laying down laws of invariability or constancy regarding quantity in general, there is necessarily room for indetermination. The constant as a rule may always be secured in several ways. Newton, however, looked upon the me- chanical laws as eliminating this element of indetermination. pFndeed, Newton is not satisfied with an abstract law, he deter- mines the quantity and direction of the motion which is to be realized in each case.] He envelops the law of conservation in a concrete law which indicates the mode of its 73 NATURAL LAW IN SCIENCE AND PHILOSOPHY application. If motion, then, is modified, it can only be by a formal derogation of law, by a miracle. There is a particularly metaphysical way of escaping mechanical determinism, and that consists whilst admitting this determinism for external phenomena in breaking the bond which links to these phenomena the higher forms of existence. We are given a relation between organic movements and intellectual states. Now, if a determinate movement corresponds with each thought, and if movements are necessarily linked to one another, the consequence is that thoughts also are necessarily linked to one another. It is this dependence of thought as regards movement that certain philosophers endeavour to weaken or to destroy altogether. Accord- ing to this view, Descartes acknowledged that when a passion is brought into being within us as the result of some external action, we are not condemned to become wedded to the thoughts called up by this passion. He maintained that we have the power to summon before the mind different thoughts, and to hold them there by means of attention. For instance, when the physical body impresses 74 THE MECHANICAL LAWS on us an impulse of anger, we can summon before the mind ideas of justice, moderation and duty, to replace ideas of vengeance. Thought, then, is not indissolubly connected with the physical organism. In one sense, Leibnitz goes much farther than Descartes ; he breaks off all communication between body and soul, and maintains that the life of souls would remain the same even if all bodies were annihilated. On the other hand, he recog- nizes that there exists pre-established harmony and exact parallelism between bodies and minds. The mind, however, is not therefore made dependent on the body. It is the contrary to this that Leibnitz has in view, for he regards efficient causes as dependent on final causes. Kant simply abolishes all connexion between the moral subject and the world of motion ; he regards the noumenon, which is entirely free from the fetters of mechanism, as having power to determine itself in an absolutely autonomous fashion. These various theories are either ingeni- ous or profound, still, hypothesis has a large share in them. In the first place, how is it known that the bond between 75 NATURAL LAW IN SCIENCE AND PHILOSOPHY the mechanical order and the higher orders is loose, or liable to be broken ? Then, too, who is to guarantee that the orders of things, thus superimposed on the mechanical order, will not themselves also be deter- minisms, different, it may be, but equally inflexible ? Still, even though this system were admitted, it would give us but little satisfaction, for it would leave quite out of our control the world of motion in space, i.e. the world in which we are living, after all, and on which it is primarily important that we should be able to act. Mechanical conjunction, it must be recog- nized, is the most perfect form of determin- ism, for it represents the coincidence of experi- mental reality with mathematics. But what we have to discover is whether this deter- minism should be transferred from the explan- ation of the phenomena it governs to the very beings whose manifestations we are endea- vouring to systematize. When we ask our- selves if the mode in which bodies act on one another compromises our freedom, we are mis- stating the question. Bodies do not act on one another. It is by a process of artificial construction and abstraction that we isolate 76 THE MECHANICAL LAWS a world of atoms and mechanical forces, and regard it as self-sufficient. In reality, this world is not self-sufficient. Not only cannot atoms and mechanical causality be conceived without a mind to think them, but mechanical movements themselves cannot be isolated from the physical and organic phenomena that exist in nature. Do we know whether the mechan- ical laws are the cause or the consequence of the other laws ? If, by chance, they were the consequence, could we still affirm that they are rigorous and immutable ? If there really are activities in nature, they are quite different from the so-called action of one body on another, which is nothing but a numerical relation. And as there is nothing to prove that the real support of so-called mechanical phenomena is itself mechanical and subject to determinism, there is no chain to be broken in order to enable a moral influence to permeate what is called the world of matter and motion. Bodies, in their reality, resemble us already, otherwise they are not for us. The distinc- tion between laws or relations and phenomena or elements, copied from that between precepts will, is a mental artifice for the reduction 77 NATURAL LAW IN SCIENCE AND PHILOSOPHY to ideas of the greatest possible amount of given reality. In being itself, this distinction disappears, and with it the determinism which implies it. 78 \/ VI THE PHYSICAL LAWS \X 7 E have seen that experience inter- V V venes, as an essential element, in the establishing of the mechanical laws. And yet these laws have a strictly mathematical form. 1 If they could exactly realize, without any sacrifice on either side, the synthesis of the rational and the experimental, they would express a really necessary determinism. The two elements, however, are not so much blended with, as set alongside of, each other : the mathematical element in the mechanical laws does not apply exactly to reality, and the experimental element in them remains unknown as regards its nature and cause. Anyhow, I the" harmony between mathematics and the experimental borders near enough on coincidence, in the mechanical laws, for these latter to be, in practice, the most perfect model we possess of necessary 79 NATURAL LAW IN SCIENCE AND PHILOSOPHY determination. We will now look into the < nature of the physical laws, and see whether they are but one particular instance of t mechanical determination, or possess an 1 originality and meaning of their ownj Man's first feeling was a consideration of the physical qualities which our senses reveal as inherent in bodies themselves ; evidently, when thus regarded, physical phenomena cannot be reduced to mechanical phenomena. From this point of view, change implies a destruction and a production of substantial forms that is opposed to the homogeneity and continuity of strictly mechanical pheno- mena. This method of enquiry, however, is very unfavourable to science ; for things, when envisaged in this light, lend themselves but feebly to the application of mathematics. [Consequently, the revolution that Descartes effected was useful in that it divested things of sensible qualities, which latter it attributed to the knowing sub j ect . Descartes regarded clear- ness of ideas as indicative of their truth. f Now, sensible quality is not an object of clear ideas ; consequently, it cannot exist as it appears to us. On the other hand, extension and mo- tion are objects of clear ideas. Besides, we 80 THE PHYSICAL LAWS have a natural tendency to refer our sensa- tions to things in extension as being their cause. In virtue, then, of divine truth, this tendency must be a law unto us, and so we will affirm, d priori, that exten- sion and motion must suffice to explain all the phenomena of nature. Physics is thus nothing more than a continuation of mechanics. This theory could not be applied off-hand to facts ; and so, in the eighteenth century, special physical agents were superimposed on motion. Electricity was explained by two contrary fluids ; light, heat, and magnetism were explained by distinct, separate fluids. [Still, the Cartesian principle was never alto- gether abandoned : it continued to indicate the ideal of perfect science. At the present time, we are once again tending to eliminate qualities and reduce the physical to the mechanical. This is proved by the mechanical theory of heat. In con- formity with the Cartesian tradition, many scientists regard motion as an all-sufficient explanation of every physical phenomenon ; as Tyndall said : heat is motion. Still, the most recent works of contemporary physicists 81 F ^ NATURAL LAW IN SCIENCE AND PHILOSOPHY / show a certain mistrust of this theory. The reproach is made that it leads the scientist too much to reason deductively and to be too / metaphysical^ When we say that heat is motion, are we not actually pronouncing on the very nature of heat ? Recognizing this, Lippmann was careful to substitute for the expression "mechanical theory of heat/' that of " thermodynamics," which does not forejudge the nature of heat; he also endeavoured to discover, not the essence of calorific phenomena, but simply their laws. We ought, then, to enquire whether, in accordance with the conclusions of modern science, there would appear to be in physics some element that cannot be re- duced to mechanics, or whether, in the object of these two sciences, there is anything more than a difference in complexity and degree. The essential character of a mechanical phenomenon is reversibility. In abstract or theoretical mechanics, a moving body which has just gone over the path A B must return exactly along the same positions, from B to A, if the direction of the motion is changed. The conditions of abstract mechanics being sensibly realized in celestial 82 THE PHYSICAL LAWS mechanics, it is possible to say that if the direction in which a heavenly body moves were to be changed, this heavenly body would return exactly along the same points ; it would describe, for instance, an identical ellipse. But in concrete mechanics, which is actually physics, since all power generates heat, reversibility is hindered or impeded by friction. Now, this difference is a general one : no physical phenomenon can be repro- duced in identical fashion if its direction is changed. For instance, in the ordinary atmosphere, a pendulum going from A to B, will have a certain resistance to overcome ; to do this, it will have to produce power ; in producing power, it will lose a portion of its energy. If, then, the direction of the motion is changed, this moving body will not return to the starting-point, since it has already lost energy on the outward track and will again lose energy on the return track. It may be set down as a rule without exception, that wherever there is expenditure of effort, there is both production of heat and irreparable loss of the original condition. This law introduces into physics an element quite different from those of mechanics. In 83 NATURAL LAW IN SCIENCE AND PHILOSOPHY mechanics, we are considering a force which always maintains the same nature and the same quality ; in physics, on the other hand, the quality is different : the expenditure of effort is higher in quality than heat, heat at 100 is higher in quality than heat at 99. Heat never wholly reconstitutes the expendi- ture of effort which gave birth to it ; the amount of energy is continually decreasing, according to the principle of Clausius ; the phenomena are irreversible, the ultimate result is always a falling off. What does all this mean, if not that physics cannot leave quality out of account, quality as thus understood, at all events ? This was Cornu's maxim : in physics, he said, we have to consider not only the quantity of energy, but also its quality. The physical laws, then, cannot be reduced to the mechanical laws ; a new element intervenes ; quality. Of course, this is no longer scholastic quality ; still, it is an element of differentiation and heterogeneity. Let us now try to discover what it is, in reality, that corresponds to the physical laws, and how far we may regard them as existing objectively. THE PHYSICAL LAWS When the mechanical theory of heat was established in science, philosophers thought they could turn it to considerable account. The law of the equivalence of effort-expendi- ture and heat was regarded as an instance of the general law governing the transformation of natural forces. They thought it would estab- lish continuity between the most seemingly heterogeneous things. f~ Indeed, if motion can be changed into heat, why should heat not be changed into vital force, and this latter into thought ? All can be changed into all, and the dream of Heraclitus is realized ; transmutation, which the alchemists sought after in metals alone, becomes the universal ^^ law of nature. Renouvier, 'with considerable precision, showed the superficiality of this interpreta- tion. The law in question, instead of prov- ing the possibility of transformations, ex- cludes them. Indeed, it is obtained only by eliminating the heterogeneous and consider- ing the homogeneous side of things. The physicist lays aside the best part of the essence of physical phenomena, leaving it to the physiologist, the psychologist or the metaphysician ; the laws he positsdeal 85 NATURAL LAW IN SCIENCE AND PHILOSOPHY only with the quantitative relations which- may be found on the surface of these phenomena. Instead of there being any transformation in physical production, as the scientist considers to be the case, there is a passing from the same to the same, a passing from one distribution of energy to another equivalent distribution. ^ [~Ajid y e *> what is it that is conserved in nature if not a force capable of assuming all kinds of forms ? Spencer regarded the reality of such a force as no less assured than the impossibility of becoming acquainted with its essence ; to establish this dual characteristic of universal force, he invoked the conditions of our consciousness and mental constitution. The force of which we assert persistence is that Absolute Force we are obliged to postulate as the necessary correlative of the force we are conscious of. . . . In asserting it, we assert an Unconditioned Reality, without beginning or end. Thus, quite unexpectedly, we come down once more to ... the continued existence of an Unknow- able as the necessary correlative of the Know- / able (First Principles, 62, etc.). j But then, as Dauriac stated in his remarkable work Des 86 THE PHYSICAL LAWS notions de mati&re et de force dans les sciences de la nature, if that which is conserved is unknowable, how do we know that it persists ? Either this transcendent principle has no- thing in common with the forces with which science deals, and its so-called persistence explains nothing ; or else it is the substance of the forces with which we are acquainted, and, in affirming its persistence, we are really affirming that transmutation of forces which there is nothing in science to warrant us in admitting. According to Renouvier, that which is conserved is, strictly speaking, kinetic energy. But then, as we have seen, physicists nowa- days are diffident of reducing phenomena to motion. There are even mathematicians who consider the two principles of thermo- dynamics as incompatible with mechanism. The energy, that is conserved, at the same time changes its nature, and its quality is continually diminishing. In reality, the principle of the conservation of energy is rather a mould or matrix of law than a single, determinate law. Whenever we con- sider a " closed-in ". system, there is some- thing conserved in it. This something will 87 NATURAL LAW IN SCIENCE AND PHILOSOPHY vary, according as the system is conceived as being formed of mechanical, of physical or of chemical forces. There remains to be explained the concept of permanence. In this connexion, Helm- holtz says that the question is not whether all the facts can really be reduced to constant causes, but rather that science, in so far as it insists on conceiving nature to be intelligible, must admit the possibility of such reduction, if only in order to acquire the unexception- able certainty that our knowledge is limited (Mem. sur la conservation de la force, Introd.). The principle of the conservation of force, therefore, is, for science, a guiding idea, necessary in a way. But there is nothing to warrant that this law, as such, is inherent in the nature of things. In its profitable form, *it is not known A priori, nor does it obtrude upon the mind. It was discovered by means of experiments and analyses, and conse- quently is essentially experimental and induc- tive. :There is something artificial about it, like \/ all induction, and it is difficult to conceive of it as being absolute. Indeed, given an ensemble of forces, either this system offers solutions of continuity, or it is shut in on all 88 . THE PHYSICAL LAWS sides. If it is open to external influences, these may thwart the law, which, in that case, will be realized only in so far as the external influences are feeble and negligible. On the other hand, if the system is " closed- in," the law of conservation is conceived only as co-existing with some cause of change. In order that energy may be conserved through the changes, then changes must take place. And if we would conceive things in their reality, we cannot separate conserva- tion and change from each other, as we do the ingredients of a purely physical mixture. True, along with the laws of conservation we have laws of change, such as the principle of Clausius. These laws, however, are neither reducible to the law of conservation nor adequate for determining the phenomena with any degree of precision. The negative form of the principle of Clausius actually prevents this principle from generating a complete determination. What, in short, as regards the problem of necessity, is the meaning of the physical laws ? To answer this question, let us return to the distinction drawn between the laws of conservation and those of change. The for- 89 NATURAL LAW IN SCIENCE AND PHILOSOPHY mer are built up on the type of the mathema- tical laws ; they are absolute, they set forth precise conditions, they are or they are not. They establish only a negative necessity, however. They are, in our opinion, barriers analogous to those formed by the logical laws, only closer and nearer to things : they leave the phenomena partially indeterminate. Indeed, we must guard against confusing determinism with necessity : necessity expresses the im- J possibility of a thing being different from what it is ; determinism expresses the sum total of the conditions which make it necessary for the phenomenon to be stated just as it is, with all its modes of being. The law of conservation is one of abstract necessity, not a law of determinism ; on the other hand, any law which, like the principle of Clausius, governs the distribution of force, is really a law of determinism, though it is and remains exclusively experimental. Such a law is no longer, like the law of conserva- / tion, a condition of intelligibility. (""There would be nothing shocking to the mind if bodies were to attract one another in inverse ratio to their distance, instead of doing this in inverse ratio to the square of the distance. j 9 THE PHYSICAL LAWS The laws of determinism, purely experi- mental as they are, do not claim to be abso- lutely exact and rigid. Of themselves, they cannot denote a necessary concatenation. They would become laws of necessity only if they were reducible to the laws of conserva- tion, and finally to the formula A is A ; or, at all events, if we had solid grounds for believing that they could, by right, be reduced thereto. This reduction, however, to unity, of the experimental and the logical, we find impossible. Either necessity without deter- minism or determinism without necessity ; such is the dilemma confronting us. Still, it will be urged, since our laws can be verified, it is at least natural and morally necessary to regard them as immutable. Such a conclusion, most certainly, super- sedes experience. We do not know whether the physical laws are fundamental V and primal or whether they are merely resul- tants. When questioned on this point, the physicists would either refuse to answer or would incline to the latter view. The very law of gravitation itself was not regarded by Newton as a primary law. He refused, however, to investigate its causes, alleging NATURAL LAW IN SCIENCE AND PHILOSOPHY that he had no hypotheses to set up. We isolate these laws for convenience of study, and because experience obviously authorizes us to do so. But how are we to know that they form an absolute, that thus we have a self-sufficient side of nature, one that is not influenced by the rest ? Are all these ele- ments of reality, the qualities and forms of being, which have had to be eliminated in establishing physics as a science, really inactive, high above the measurable magni- tudes isolated by science, like the gods of Epicurus, far above this world of ours ? Does not thought, as well as the sense of reality, require that the different elements of the world should condition one another, for the world to be a unity ? And if, in reality, the physical laws are not independent of the other laws that may lie concealed in nature, how can we affirm that they are immutable and inflexible ? Possibly they are formed by evolution, as is said nowadays regarding animal species ; possibly their fixity is a contingent state of things, not a necessity. It is not legiti- mate to take literally this determinism, which recognizes no cause for a physical phenomenon, other than some equally physical phenomenon, 92 THE PHYSICAL LAWS since such phenomena are but abstractions, and true action, if it does exist in nature, is something very much more complex. To sum up, consideration of the physic* laws, when compared with that of the purel] mechanical laws, marks a certain pr ogres in determinism, in the sense that modes oi being which mechanics left indeterminate, are now explained according to laws. In becoming narrower, however, determinism becomes more complex and obscure, and less reducible to that analytical relationship which alone would appear to constitute necessity. 93 VII THE CHEMICAL LAWS THE sciences with which we have hitherto dealt had all, though in differing de- grees, an abstract object ; they considered existing properties, but not beings of nature. Chemistry, on the other hand, takes account of concrete bodies existing in themselves. The result would seem to be that this science, from the philosophical point of view, has a wider range than the former ones, and that the determinism of the chemical laws pene- trates more deeply into the essence of things. Let us now see if this is really so. Chemistry is a comparatively recent science. As shown in the profound and learned work of Berthelot on Les Origines de I'Alchimie, the transformations of bodies were first explained by the spontaneous action, either of supernatural powers, or of a (f)utrt9 which again was a kind of divine instinct, working apart from the mechanical 94 THE CHEMICAL LAWS laws. We find alchemy intervening between this more or less theological period and the present scientific period. According to the alchemists, man must be permitted, by every human and divine law, to utilize the forces of nature, and this is possible for him. The way to do it is to rely on nature her- self : Natum a natura vincitur. Their theory is as follows. On the one hand, the corporeal elements are susceptible of transmutation ; on the other, this transmutation admits of rotation, a circular process which returns to its starting-point. A serpent biting its tail is the symbol adopted by the alchemists. The former of these two principles may be confirmed by immediate experience ; in a chemical transformation, we note a complete change of qualitative properties. /"But the alchemists, confining themselves to immediate observation, were mistaken as regards the simple and the compound. They looked upon the simple as that which is given, and the compound as that which is formed from the given. This identification of the given with the simple is an error identical to that which we find in the philosophy of Locke, for whom the simple was the given sensation, and the 95 NATURAL LAW IN SCIENCE AND PHILOSOPHY compound the idea resulting from it. The second principle of the alchemists also con- forms with crude experience. Indeed, start- ing with metallic oxide, metal can be ob- tained ; and, in the same way, if we heat the metal, the latter becomes an oxide once again.] It was Lavoisier who, when tracing the real principles of chemistry, brought this science to its present condition (see Berthe- lot's Notice historique sur Lavoisier'). In the first place, he established the fact that, in chemical transformations, not only does matter generally remain constant in quantity, but that even the special bodies on which the chemist operates remain unchanged in weight. (Showing that the calcination of metals re- sulted from the union of the metal with a por- tion of the surrounding air, and not from a loss of phlogiston, he proved the metal to be the simple and the oxide the compound, thus changing the very foundations of the science. And in the second place, according to Lavoi- sier, special simple bodies, defined by their weight, must suffice to explain the forma- tion of compounds. He offered a notable instance of this, explaining the composition of water by the combination of hydrogen 96 / THE CHEMICAL LAWS and oxygen. Such mysterious substances as phlogiston were altogether eliminated. Thus, the so-called simple bodies set a limit on the decomposition and suffice for the reconstitution of the given bodies."! And so chemistry transfers to the species of bodies that permanence which mechanics attributed only to force considered generally. The result is a most important difference between physics and chemistry. Is this irre- ducibility an absolute one ? The different theories aim at lessening it as much as possible. According to the atomic theory, atoms, differing simply in weight, form and valence, by their various arrangements suffice to account for chemical phenomena. But these differences, especially that of valence, still constitute specific differences. This latter difference, which concerns the number of atoms susceptible of associating to form a molecule, cannot be reduced to physical or mechanical properties. For instance, in gravitation, a mechanical force, mass and dis- tance alone enter into account. Moreover, the atomic theory of itself is powerless to reproduce the variety and complication of nature. Its complications are all to no pur- 97 G NATURAL LAW IN SCIENCE AND PHILOSOPHY pose : the possibility of atoms exchanging semi-valences with one another, of atoms possessing four dimensions (that of azote, for instance), the mutual incommensurability of their weights. There is continually hover- ing above the atomic theory that dim mist of approximation which, according to Berthe- lot, casts a shadow over the whole system. For the present, we may conclude that chemis- try is really distinct from physics, in so far as it admits of distinct species of bodies, the substratum of that profound chemical change which observation distinguishes from mere physical change. What is the objective value of the chemical laws ? If some day chemistry comes to be wholly reducible to physics, the reproach to which this latter lays itself open, that it is an abstract science when regarded as a science of being, will be brought against the former also. But the atomic theory claims, as interpreted by some philosophers who have adopted it, to explain, as regards its general form, the real constitution of matter. Let us examine if such a claim can be made for it. Modern atomists take for their starting-point Newton's principle : " By effects to come to know 98 THE CHEMICAL LAWS causes," and, basing their conclusions on ex- perience and induction, they think they can proceed from phenomena to being. But then, the atomic theory would first have to be pre- cise and homogeneous for it to be capable of being regarded as a doctrine of being itself. Now, the difficulties we have mentioned above, especially as regards valence, show that the very idea of atom has not been definitely established. Stallo, the author of a learned work on La matiere et la physique moderne, shows that chemists cannot guarantee the homogeneity, hardness and inertia of the atom, though these are all essential elements in its definition. Chemists also tell us of an energy of position, distinct from kinetic energy, and the reality of which it is no easy matter to reconcile with the principles of atomism. The truth would appear to be that this theory has been of great service, that it is valuable as a symbolic representation and doubtless the best we possess, but that it has no claim to determine metaphysically the nature of things. We may go further and say : even were there a more complete coincidence between facts and theory, we should still have no right 99 NATURAL LAW IN SCIENCE AND PHILOSOPHY to regard atomism as a theory of being. In- deed, the principle ab effectibus ad causas never offers anything but a subjective expla- nation. The atom cannot be known by the senses : it is conceived of only by the aid of hypothetical reasoning. Now, such reasoning never attains to anything more than pos- sibility, the sufficient, or apparently sufficient condition, given the facts at our disposal ; it never reaches the necessary condition. Speak- ing of the objections to which the atomic theory may give rise, M. Friedel alleges that no physicist is as yet disposed to throw over- board the undulatory theory of light, on account of the grave difficulties, and even con- tradictions, which the conception of luminous ether offers. In the same way, he said, it is better to continue to use a theory which has enabled a vast number of facts to be grouped together, and which daily leads to the discovery of fresh ones. Such language is a tolerably clear indication that there is no intention, in the name of science, of setting up atomism as absolute truth. Metaphysics, however, supports this theory, and claims to bring it the aid which science neither can nor will afford. In a general 100 THE CHEMICAL LAWS way, it is maintained that the atom is the element which unites reality and intel- ligibility in the highest possible degree. The atom, it is said, is real, for it is determi- nate, both in bulk, in magnitude and in shape ; it is intelligible, for it is defined by the qualities we conceive most clearly : the geometrical qualities. Moreover, we need only conceive of the sensible qualities as connected with the properties of atoms, to explain, by means of these latter, the changes which seem to be effected in the nature of bodies. The atom, then, is both intelligible and a principle of intelligibility. But these affirmations are open to criti- cism. First of all, we cannot explain the endless variety of things by means' of the atom, without making of this latter a more or less extra-scientific notion. Thus, some scientists consider that the extended atom cannot be reconciled with the centrifugal force implied in the relations between atoms at short distances from one another ; they reduce the atom to nothing more than a centre of force, devoid of extension and yet situated in space. Such was the hypothesis of Boscovich, revived by scientists like Ampere, 10 1 NATURAL LAW IN SCIENCE AND PHILOSOPHY Cauchy and Carnot (see Pillon's fine article on " I'Evolution historique de Tatomisme/' in the Annee philosophique for 1891). On the other hand, in order to explain by the combi- nation of atoms the phenomena of sensation and thought, certain metaphysicians endow the atom with psychic as well as with mechani- cal and physical properties. For instance, in the system of Epicurus, we find the clinamen, which, after all, is no more than an ebauche of free-will. In modern times, atomism entered on a new phase with Locke, as Pillon has shown in the above-mentioned article. God is omnipotent, says Locke, and therefore, without contradicting himself, he can endow the atom with both extension and thought. Following the lead that Locke gave to atomism, Maupertuis attributes to the atom a rudiment of sensibility and thought, apart from physical qualities. This point of view is also seen in a scientist like Haeckel, who regards the atom as animated, and looks upon the elective affinity of bodies as a manifestation of tendencies, sensations and volitions. And so, by varying at will our idea of the atom, we have come to regard it as explain- 102 THE CHEMICAL LAWS ing everything ; though at the same time we have made this explanation anything but con- vincing. ["Speaking generally, atomism can give a reason for everything, provided it endow the atom with the very thing that has to be explained!] Now, this way of developing ato- mism contradicts its principle, which is essen- tially one of economy, in more precise terms, the idea of explaining the higher by the lower, the appearance of finality by mechanism, mind by matter. To return to atomism strictly so called, i.e. to geometrical atomism, are we certain that it reconciles intelligibility with reality ? The starting-point of modern atomism is the Newtonian distinction between space and bodies. Space is nothing else than a vacuum, and a vacuum is unthinkable. Bodies are magnitudes, but they cannot be measured absolutely, for we have no absolute unit of measurement and we cannot compare the atom with the point in mathematics, without falling into the insuperable difficulties of the infinite. Extension is never anything but a relation. It is the same with weight : weight is a relation depending on terrestrial attrac- tion. In a general way, we only make use of 103 NATURAL LAW IN SCIENCE AND PHILOSOPHY experience in order to determine the size or the mass of atoms. Now, experience can offer us no more than the relative. Thus, doubt- less, the notion of the atom is clear and evi- dent, so long as we are dealing with the abstract, but when we wish to determine the atom with reference to its location in space, its form, extension or weight, thought finds itself faced with a mere relationship, pro- ceeding from an insuperable indetermination. f After all, the atomic theory offers us no- thing else than the imaginative scheme of the notion of law, just as a curve represents to the eye the variations in temperature or the increase or diminution of the popula- tion. By definition, a natural law is a con- stant relation between two definite, immu- table terms ; a couple of atoms whose mutual action depends solely on their distance well represents this relation. Adequately deter- mined, the atom supplies schemes that cor- respond to the physical and chemical laws, which are conceived after the model of the mechanical laws. This representation is a very natural and convenient one, though relative to our imagination, for which it has been constructed. A metaphor is not a being. 104 THE CHEMICAL LAWS What, in short, is the meaning of the prin- ciples of chemistry as regards determinism ? It is noteworthy that, in antiquity, atomism was a doctrine of atheism, or, at all events, of the non-intervention of the gods ; whereas, in the case of the moderns, it does not, as a rule, exclude religious beliefs. Newton closely connects the idea of God with the nature of space and of the mechanical laws of the universe. Boscovich is a spiritualist ; he subordinates the existence of the world, which he regards as contingent, to the will or arbitrament of an infinite power. This difference would appear to result from the notion that has been formed of inertia. iTn- deed, the atomists of old admitted that matter possesses within itself a principle of motion : therefore they had no need of the workings of a God. The moderns, on the other hand, consider mass and motion separately, and look upon them as independent of each other. Therefore their union may seem to require the intervention of a supernatural power. A God is needed to give a start, an impetus/] In spite of numerous examples of recon- ciliation between atomism and religious be- liefs, it seems correct to say that atomism, 105 NATURAL LAW IN SCIENCE AND PHILOSOPHY speaking generally, remains hostile to ideas of providence and freedom. Indeed, its tendency is to explain the more by the less ; and so it endows atoms with the fewest possible qualities, those, too, that are farthest removed from mind ; and in this philosophy, even when it is thought that God must be appealed to for an explanation of the exis- tence of atoms, divine action is reduced to a minimum ; it is admitted only in so far as it cannot be dispensed with. Still, let us consider not atomism but simply the general idea of the chemical laws, to wit, the principle of the permanence of the \weight of bodies. Physics and chemistry Jshow us everything seemingly permanent in i nature, mass and energy alike. What is this permanence ? We are inclined to think that everything we attribute to permanence we withdraw from contingence and free- dom. But this may be no more than a pre- judice, the origin of which would seem to date back to antiquity. The ancients re- garded fixity, immutability, as the ideal. Epicurus considers the gods as being eternally unoccupied, for work is a change of state, it implies fatigue. But these ideas are not so 106 THE CHEMICAL LAWS current amongst the moderns as they were amongst the ancients. Many of us look upon motion as superior to repose. For aesthetic and moral reasons, perhaps, as well as scientific, our conception of being and of the ideal has changed ; nowadays, it admits of even if it does not exact pro- gress, improvement, flexibility. And there- fore immutability is no longer the mark of the absolute, but rather of the relative. Mass and energy are immutable, therefore they are only phenomena. We conceive of permanence either as a state or as a limit, no longer as a necessity inherent in being. Moreover, we may note that determinism becomes obscure the more it contracts. Mechanics has actually had to substitute for mathematical intuition a relation of simple phenomenal causality, incapable of being reduced to this intuition. Physics has complicated this relation by introduc- ing a notion of quality, that of energy. Chemistry adds the idea of special bodies, relatively permanent in nature. Progress takes place from the homogeneous to the heterogeneous, consequently from the intel- ligible to the obscure. 107 NATURAL LAW IN SCIENCE AND PHILOSOPHY On the other hand, every one admits that physico-chemical determinism may act upon mechanical determinism without the former being reducible to the latter. A priori, then, there is nothing to prevent physico- chemical determinism, in its turn, from ad- mitting of the intervention of some superior determinism, biological determinism, for in- stance, if it were to happen that it could not be reduced to physico-chemical determinism. 108 VIII THE BIOLOGICAL LAWS IN his Nouveaux Elements de Physiologic humaine, M. Beaunis reduces the biological laws to two principles : first, the correlation of physical with vital movements ; second, the evolution of living beings. Conformably with this division, we will now study the relations between physiology and physics ; and, in the next chapter, take up the rela- tions of species with one another, and the question of evolution. Are the general laws of life reducible to the physico-chemical laws ? Let us first examine the matter from the historical point of view. Descartes declared that every science, the science of life as well as those of matter, must be reducible to mechanics ; he him- self made attempts in physiology, along 109 NATURAL LAW IN SCIENCE AND PHILOSOPHY these lines. Modern science, however, did not originate immediately in this synthetic view. M. Gley * dates the beginnings of modern physiology from the English doctor, Glisson. Now, the latter bases this science on the notion of irritability, which he regards not as reducible to mechanism, but as a special property, peculiar to living beings ; a lower ^' form of the very faculties that constitute the human mind : appetition and per- ception. In a second period, comprising Haller and Bichat, vital phenomena are clearly distinguished from physical ones, but more attention is bestowed on their analysis and division into categories than on the inquiry as to whether or not they have any special basis. This analytical period offers a striking analogy with the psychological period mainly represented by Jouffroy. A third period begins with Broussais : its main representative is Claude Bernard. We work up from phenomena to their prin- ciples ; we ascend from vital faculties to irritability, doing away, however, with the idea of mysterious powers and attempting 1 Dictionnaire encyclopedique des sciences medicates, article on " Irritabilit6." no THE BIOLOGICAL LAWS to reduce this very irritability to mechanism, in accordance with the Cartesian principle. Thus we introduce a strict determinism into physiology. In examining what this reduc- tion consists of essentially, we will base our argument on the Elements de Physiologie of M. Beaunis and on Dr. Gley's remarkable article just mentioned. Present-day science teaches that in the living being : i, there is no spontaneity ; 2, reaction is equal to action. Protoplasm is the common element of all tissues. It enters into motion only when subjected to some particular mechanical, physical or chem- ical excitant. What is true of the element must be true of the compounds. Again, in living beings and in the organic world alike, there is equality between action and reaction. Of this we become more and more conscious,*/ as we consider, with increasing precision, the amount of material supplied and of effort and heat expended, in the case of living beings. The law of the mechanical equivalent of heat applies to living beings. The reason they appear to expend more force than they receive is that they have reserve forces of tension which are suddenly released beneath in NATURAL LAW IN SCIENCE AND PHILOSOPHY the influence of the exciting agent. Strictly speaking, they are machines capable of stor- ing force. No doubt every kind of tissue appears to have special irritability, but this difference in manifestation results from the complexity of the tissues and the different way in which their cells are arranged. The final reason for irritability lies in the nature of the substances which compose protoplasm ; these admit of a great variety of combinations : carbon, for instance, which is tetravalent. Impermanence of protoplas- mic substance is the essential condition of irritability. And the progress of organization! is nothing but the increase of this very im- \ permanence. It would thus appear that the * reduction of physiology to physico-chemis- try, if not actually effected in detail, is at all events certain in principle and assured in the future. Still, if we consider the usual language of the physiologists who are labouring to justify this induction, it would seem that results have not yet come up to intentions. Claude Bernard wrote : " It is clear that this evolu- tive property of the egg, which will produce a mammifer, a bird or a fish, belongs neither 112 THE BIOLOGICAL LAWS to physics nor to chemistry. " * And M. Beaunis said : " There is always a certain constancy in the outer form of living beings. Each organism is built up according to a morphological type, from which, in the course of its existence, it can only deviate within restricted limits." 2 M. Gley said : " Not only does the being or the tissue react, when V affected by an excitation in its environment, but it appropriates its elements to this reac- tion ; for, under penalty of deposition, perhaps of death, it is compelled to adapt its physical nature and chemical constitution to this change in the conditions of existence." 3 j Do not such words as these seem to indicate s that the living element tends to subsist in its individuality and employs the appro- priate means of realizing this end ? Still, it is quite possible that these scientists merely continue, as a matter of habit, to use ordinary language, just as the astronomer speaks of the sun's motion round the earth, or of its rising and setting. Let us consider things in themselves. 1 Claude Bernard, La science experimentale, p. 210 ; Gley, art. " Irritability" p. 487. 2 Beaunis, Tvaite de Physiologie, 2nd ed., 17. 3 Gley, article on " Irritabilite," p. 489. 113 H NATURAL LAW IN SCIENCE AND PHILOSOPHY It cannot be doubted but that life, to Claude Bernard, is really a " controlling idea/' distinct from mechanism. He regards this theory as playing too important a role for it to be looked upon as only a metaphor, a way of speaking. Claude Bernard attri- butes to living beings, in their own right, the following characteristics : organization, v generation, evolution, nutrition, decay, sick- \* ness and death. These phenomena he regards as inexplicable apart from life as a special principle. " Vital force/' he says, " con- trols phenomena which it does not produce ; physical agents produce phenomena which they do not control." * M. Marey writes : " For myself, I am not acquainted with the phenomena of life ; I acknowledge only two kinds of manifestations of life : those intelli- gible to us, which are all of a physical or chemical order ; and those that are unintelligible/' 2 There are gaps, then, in mechanism ; certain aspects of the living being, in the present state of science, appear to be unintelligible, i.e. irreducible to physico- 1 Claude Bernard, Lepon sur Us phenomtnes de la vie, i. 51. * Marey, Du mouvement dans les fonctions de la vie, 3rd lesson. Gley, article on " Irritability" p. 486. 114 THE BIOLOGICAL LAWS chemical forces. What is it that shrinks from mechanical explanation in this way ? It would seem to be a principle of finality, inherent, in spite of everything, in the most elementary vital phenomenon. The living being is re- duced to protoplasm, whose function it is to react under the influence of external activities. In it, we say, spontaneity is nil, reaction is equal to action. But, it may be remarked, this reaction is not any kind of a reaction ; it is incompletely characterized when defined from the sole standpoint of quantity, for it possesses the unexpected property of favouring not only the conserva- tion, but also the development and propaga- tion of the very individual that reacts. The exercise of irritability is expressed by losses ; now, organic matter reacts exactly in such a way as to make good these losses. Besides, it reacts so as to adapt itself to environment, to make life possible for itself in the various conditions in which it happens to be placed. In short, by a process of reproduction, it en- v sures the perpetuity of the form it represents. It has frequently been said that life is essen- tially a vicious circle. The^ organjnakes the function possible, and the function is the NATURAL LAW IN SCIENCE AND PHILOSOPHY organ ; muscular contraction accelerates the circulation of the blood, and the circulation of the blood keeps up muscular contraction. In every important physiological phenomenon we find the vicious circle. In the living being, then, there would appear to be an internal finality. The living being, re- garded as an individual, makes use of that which is around it to ensure its own subsis- tence. The reflex action that characterizes it offers two aspects : the one, which con- cerns physics and chemistry ; the other, which has no analogy in the objects of these sciences. There is one phenomenon which emphasizes this difference, and that is death. Death finds no explanation in mechanism : this was why Descartes dreamt of an indefinite development of human life ; and those who maintained the theory of mechanism, for the most part, saw no radical impossibility in the immortality of the living being, repara- tion always exactly making up for the wear- ing away of tissue. M. Sabatier * thinks that death is intimately connected with the 1 Essai sur la vie et la mort ; 1892. 116 THE BIOLOGICAL LAWS use made, by the living being, of the cells of which it consists. At first, the living being had no other function than to continue to live. It was then very slightly differ- entiated. To render higher faculties possi- ble, the cells have become differentiated and have acquired complicated structures. Loss of their potential immortality has been the consequence of this progress. At the pre- sent time, only the reproductive cells, which are relatively simple, retain comparative immortality, which is realized either imme- diately by scissiparity and gemmation ; or in- directly, by way of a plasmocaryogamic reju- venation. The cause of death is dual. There is an internal cause, the aspiration to rise, to supersede life pure and simple in order to attain to knowledge and feeling : it was to satisfy this tendency that differentiation of tissues, the origin of their mortality, came about. There is also an external cause : the outer appeals beneath the influence of which the tendency is realized. The biblical account of how man loses immortality when he tastes the fruit of the tree of knowledge is, according to M. Sabatier, an exact sym- bol of the cause of death. Thus, when 117 NATURAL LAW IN SCIENCE AND PHILOSOPHY Pascal proclaimed that man is greater than nature because he knows that he dies, he was propounding a view which was not only metaphysical and moral, it was also scientific. The best men in a nation, said Renan, are those it crucifies. Martyrdom is the ransom of superiority. Death, then, is a witness to the effort made by the living being to rise above' the environment in which he was born. Defeat is the mark of his greatness. All these considerations are both poetical and religious ; and yet scientists, as well as the rest of mankind, are influenced by them. Then what is the relation between vital faculties and physico-chemical proper- ties ? Can physiology be established, like chemis- try, by eliminating purely and simply every- thing that does not appear susceptible of strictly scientific determinations ? The chemist does not deny that there are sen- sible qualities, but he relegates them either to physiology or to metaphysics : he finds a relatively isolable object of science in the relations of molecular composition. In the same way, it may be alleged, when studying living beings, we distinguish, on the one 118 THE BIOLOGICAL LAWS hand, physico-chemical phenomena, and, on the other, an indescribable something which resembles finality : this latter element is relegated to psychology or metaphysics, or even to the unknowable ; and physiology is established as a science, no account being taken of any but physico-chemical manifest- ations. But is the separation, that was possible in chemistry, possible also in physiology ? It would appear that this triumphant adap- tation to . the conditions of existence, this choice of means suited to ensure the persis- tence of the individual, this tendency to expand and rise that we have remarked, here form one with the object of science. The amoeba, one of the simplest of beings, a homogeneous and almost diffluent substance, has these properties to a striking extent. If an amoeba is plunged into a liquid, and it there encoun- ters a foreign body on which it is able to feed, for instance, a particle of vegetation, we find its prolongations gradually extend around the grain, finally surrounding it completely and uniting with it, so that the latter forms one with its own bulk. Then follows a certain period during which digestion takes place. In the 119 NATURAL LAW IN SCIENCE AND PHILOSOPHY end, the useless portion of the foreign body is expelled, by a process the inverse of that by which it entered. This is not a mere chemical combination. Still, the amoeba is a very elementary organism. It is not given to us to see the physico-chemical pro- perties become vital properties by a process of simple particularization. Such is the present state of our knowledge ; but it may seem as though the future were destined to realize this exact reduction, which is, so far, only an ideal. M. Sabatier, in the above-mentioned work, makes a strong effort to compare living substance with inorganic substances. He regards the essential pro- perty of protoplasm, by which it effects self- restoration and communicates life, as being, after all, only a " baiting " kind of power. Now, we have instances of similar powers in inorganic matter. Such is the phenomenon of superfusion. Phosphorus melts at 40 Centigrade ; its temperature may gradually be diminished below 40 without any cessation of its liquid state ; but if a solid piece of phosphorus is introduced, the entire mass immediately becomes solidified. We find that a similar thing happens in the case of syn- 120 THE BIOLOGICAL LAWS chronous oscillations. If any one string of a violin is set vibrating and a second violin happens to be near the first, the correspond- ing string of the second instrument vibrates in unison. In like fashion, the explosion of a dynamite cartridge provokes the explosion of other cartridges in the neighbourhood. But these are only comparisons, since living matter must always be presented as such. And, in a general way, the intercalation of intermediaries could not be mistaken for proof of identity or of causality. Ascending by shorter stages is by no means a cessation of ascending. In reality, there is but one possible demons- tration of this reduction : the artificial pro- duction of an organic substance from inorganic matter and physico-chemical forces ; but such a process is still far from being realized. Pasteur declared most emphati- cally that the living never springs from any- thing but the living. No doubt this refers to the present state of things. It must be considered, however, that in itself the proof in question is very difficult to rea- lize ; for we must be very certain that the materials from which we think we see life 121 NATURAL LAW IN SCIENCE AND PHILOSOPHY emerging are really inorganic. If matter, says M. Sabatier, produces life, then it is not matter, pure and simple. Life is every- where, he thinks, in so-called inanimate matter as well as in living matter. Still, from the philosophical point of view, can we adhere to these assertions ? The mind pursues the reduction to the universal of everything that appears as new and hetero- geneous. Now, finality is heterogeneous to mechanism. However indispensable it seem, may not the finalistic point of view be relative to our intellectual constitu- tion ? This was the opinion of Kant, and it is a very tenable one. We must remark, however, along with Kant himself, that the extension of mechanism to everything that is, is not philosophically imperative. How is this extension brought about ? We note the extreme fertility of mechanism which, by degrees, explains the phenomena for which, moreover, it was thought right to infer occult qualities, and we are inclined to believe that, in time, everything will have a kind of mechani- cal appearance. But, admitting that every- thing must some day be reducible to unity, what is there to prove that absolute science 122 THE BIOLOGICAL LAWS will be only an extension of mechanical science, and not a superior science, into which mechanism itself enters, as a species into a genus ? At bottom, it is here implied that all is in all, that a given phenomenon contains all the laws of nature, and that, if there exists a science whose form is henceforth perfect, that science must contain all the rest in embryo. Mechanics, or the science of motion, possesses this relatively perfect form ; there- fore, it is hoped that mechanics will succeed in explaining everything. Our mechanics, however, is not absolutely intelligible, as it is believed to be ; indeed, applied mechanics must be considered apart from rational mechanics. / Now, experience is indispen- sable in applied mechanics, and, since all experience is limited, the results it gives us are nothing but approximations. In the final analysis, our reason for believing in universal mechanism is, as Descartes saw, our confidence in the truth of clear ideas and in their connexion with reality. We claim that the mind, freed from the influence of the senses, is the standard by which we measure things ;J we also consider that, if everything is motion, we have power over 123 NATURAL LAW IN SCIENCE AND PHILOSOPHY everything, since we can produce motion. But Descartes clearly saw also that, if we would prove for ourselves the legitimacy of this point of view, we must fall back on the idea , of a powerful, benevolent God, who has pro- portioned things to our means of knowledge and action. And so, the more we wish to rise from phenomenon to being, the more we are com- pelled to find room for feeling : it has a part in the affirmation of universal mechan- ism. But feeling also supplies us with data opposed to mechanism. For, though con- sciousness may not have arrived at physico- chemical forces, it actually does lay hold upon life. We are conscious of living ; a purely illusory consciousness, if mechanism is truth ; for, to mechanism, the elements alone exist and their rapprochement is nothing. Now, life shows forth as the effective synthesis of an extremely rich multiplicity. To believe the testimony of consciousness on this point is to doubt the absolute value of mechan- ism. But, it will be urged, how are we to look upon the relation between life and physico- chemical phenomena ? Either life will break 124 THE BIOLOGICAL LAWS the chain of movements, or it will find itself banished to intermundane spaces. rWe^seem * to have escaped from Cartesian mechanism only to fall back upon miracles or a state > of pre-established harmony^] It may be that this difficulty in our way of representing life and its relation to mechanism arises from the fact that the question is imperfectly stated. Life and mechanism are both re- garded as being things per se. Between life and mechanism we endeavour to find some relation which is still mechanical. The two, however, have no existence sepa- rate from each other ; they are artificial entities ; and the struggle which seems to result from their opposition is due to the fact that the human mind is incapable of grasping reality in its unity. To sum up, the laws of physiology appear to be irreducible. Physiological determinism, con- sidered in itself, differs from physico-chemical determinism, just as the latter differed from a purely mechanical determinism. It is stricter, for it governs phenomena which the physico- chemical laws left indeterminate. It is based, however, on a more complex and obscure idea of law : the relation of one fact not only 125 NATURAL LAW IN SCIENCE AND PHILOSOPHY to another, but to a fact presented as an end, an object to be realized. Determinism, as it contracts, becomes more impenetrable, more irreducible to necessity. 126 IX THE BIOLOGICAL LAWS (Continued) IN the last chapter, we saw that the reflex act to which contemporary science endeavours to reduce all physiological pheno- mena is a sort of dual-faced phenomenon : on the one hand, it comes within the scope of physico-chemistry ; on the other, presenting strictly the physiological aspect, it shows forth characteristics that are irreducible. Each order of science thus implies postulates proper to itself. We will now study, not the living being taken by itself, but rather the re- lations which living beings have with one another, that is to say, the laws which bind organic forms together. We will simply set forth an historical statement of the main phases through which zoology has passed, disentangling the philosophical ideas that have guided its development. 127 .' NATURAL LAW IN SCIENCE AND PHILOSOPHY Aristotle is the founder of natural history ; and his scientific conceptions may be traced back to the general principles of his philosophy. Speaking generally, he made it his business to investigate the first causes of order in the world. Now, according to the Aristotelian doctrine, the world consists of two elements : jnatter, whose distinctive nature is a lawless mobility ; and a principle 'which fixes and regulates this impermanent, capricious matter. As species present a striking permanence and harmony, they must depend on principles superior to matter. These principles are metaphysical entities, immutable types, per- fect forms, acting on matter as final causes, as models to be realized, in so far as the nature of the elements permits. From these principles result the grada- tions of living beings. There is not exactly amongst them unity of composition and a simple difference in degree ; they rise in tiers, so to speak, one above the other, the upper ones possessing more qualities and greater perfection than the lower. The more implies the less, but it does so by adding to it. Thus, the lower orders of living beings possess nutritiveness ; animals possess nutritiveness 128 THE BIOLOGICAL LAWS and sensibility ; man possesses nutritiveness, sensibility and intelligence. At the same time, however, nature, through the continu- ous matter at her disposal, multiplies the intermediate stages between these forms and proceeds from one to the other by scarcely perceptible transitions. Are species fixed ? Not altogether ; ideal types, indeed, neither are nor can be exactly realized by matter ; they represent models round which nature gravitates, which she tends to reach but never perfectly realizes. Fixity of species, then, is an altogether ideal immobility, permitting and even requiring a real and in a sense indefinite variability, whilst opposed to any being altogether over- stepping the limits of the species to which it belongs. In this doctrine, even teratological cases can be explained by natural causes. These are extreme dissimilarities, the result of excess or defect. They are connected with the dualism of end and of conditions, and with the capricious mobility of matter. Matter never fully realizes form ; at times it deviates considerably from it. If this was the doctrine of Aristotle, was it 129 T 1= NATURAL LAW IN SCIENCE AND PHILOSOPHY owing to the fact that he had no idea of a mechanical explanation in zoology ? To con- vince ourselves that this was not so, we need only quote a few lines from the Physics : tl OTTOV /uiev ovv airavra ble to determine causes, but that all idea of discovering laws must be abandoned. In- 196 THE SOCIOLOGICAL LAWS deed, according to his view, a law implies the reappearance of one and the same ante- ' cedent. Now, where do we find history re- peating itself ? The essential feature of the historical mind, Jules Zeller was fond of saying, is the discernment of the charac- teristics peculiar to each epoch ; we are generally mistaken when we judge the past ; by the present, or vice versa. Historical facts are too complex and unstable intermix-\ >< tures to be reproduced as they are. If they exhibit laws, it is in their elements, not in their concrete sequence, that we must seek them. Hence we have a second point of view, which may be called the physico-sociologi- cal : we endeavour to connect social facts, not with their equally social antecedents, but with external conditions that are capa- ble of being observed and measured, such as geographical circumstances, density of population, amount of sustenance. Here, however, a distinction must be made. Population and amount of sustenance are not crude facts like climatic conditions. Man, the social human being, intervenes in the former class of conditions : therefore they are, to a certain extent, social facts ; 197 NATURAL LAW IN SCIENCE AND PHILOSOPHY to demand from society an explanation of them is partly to take for granted what we purpose to explain. Nor is this all ; we require that social phenomena, as well as physical phenomena, should derive from external conditions ; but it is very difficult to demonstrate this derivation. Suppose, for instance, we ex- plain the development of the division of labour by the progress of social density, the interdependence of the members of a so- ciety. The saying of Darwin is recalled, that different beings live side by side more easily than similar beings : they inconve- nience one another in a less degree and the struggle for life amongst them is not so keen. Man obtains this salutary diversity by developing division of labour, and so this division of labour shows itself as the necessary result of the struggle for life. Vital com- petition : a physical cause, thus explains division of labour : a social fact. But does the law stated by Darwin neces- sarily apply when we are dealing with man ? Is it correct to say that, in a human society, diversity of functions is in variably a principle of mutual tolerance ? Look at capital and 198 THE SOCIOLOGICAL LAWS labour : the difference that separates them does not prevent them from combating each other. It often happens that diver- sity of education and occupation inclines men to misunderstand and despise one ano- ther. If men are to agree, it is not enough that they cannot understand one another. Let us admit, however, that division of labour is a solution of the struggle for life. In what way will this antecedent determine this consequent ? Have we here some rela- tion of necessity, similar to that which con- nects the attraction of bodies to their mass and their distance from each other ? Division of labour appears to be necessary, if men are to live at all. But here, necessary means indispensable, i.e. a condition of the realization of a certain end, viz. the cessa- tion of the struggle for life. This is by no means a mechanical and inevitable neces- sity. Must we even translate, in this case, the word necessary by indispensable ? The struggle for life, indeed, admits of other solutions, the simplest of which is the eat- ing of one another. That is really the law of nature, and division of labour is in- stituted for the very purpose of impeding 199 NATURAL LAW IN SCIENCE AND PHILOSOPHY the fulfilment of this law. Indispensable, then, in turn, really means, preferable, i.e. more in conformity with the idea of human- ity, responding more completely to that sympathy with the weak which we assume to exist in man. As Aristotle said, we do not wish merely 5", but eu ty. Division of labour is a more or less intelligently con- ceived means of realizing this ideal. What does this mean, except that what we took to be a crude law of causality involves a relation of finality, and that we are assum- ing the intervention of the human intellect and will where we think we are bringing into action none but external and material conditions ? Thus the physico-social law does not satisfy :he conditions of a strictly positive science. To bring sociology really within the sphere of the physical sciences, we should have to discover, for social facts, legitimate substi- tutes, in their mechanical equivalents. The physicist therefore looks upon physical agents only in their measurable manifestations. But do such equivalents, so difficult to find in psychology, exist in sociology ? We imagine that statistics will supply them, but do not 200 THE SOCIOLOGICAL LAWS statistics constantly need to be supple- mented by judgment ? Where do we meet with figures that admit only of one inter- pretation, and immediately express the social reality with which we are dealing ? Is the number of persons who can read and write a faithful standard by which to judge; of the development of instruction in a coun-f try ? Can religious feeling be gauged by the business carried on in the various articles used in public worship ? It is a fact that, in this order of things, men of tact and experi- ence, by means of literary descriptions anc without using figures, often hit upon a truth which cannot be acquired by mathemati- cal quantification. If some day we succeec in bringing social facts within the scope of physical facts, it will be by intercala- ting between the latter and the former an infinite number of intermediaries of whose existence we have now not the faintest sus- picion. At present, mathematics and society form two extremes with an abyss between them; by attempting to make them coincide, we run the risk of dwarfing and distorting the social reality. 201 NATURAL LAW IN SCIENCE AND PHILOSOPHY (I In the determination, then, of the socio- logical laws, we cannot possibly leave man out of account, he must be included as an agent, with his own nature, his powers of intellect and will. These are perhaps data that are partially irreducible and impossi- ble of analysis ; but when we look more closely, the inferior sciences actually imply such data. Moreover, there are degrees in the social laws. Some of them express the conditions of a society in which man scarcely acts at all as a man and does little more than follow the promptings of his animal nature. Others have reference to the more strictly human societies, wherein man makes a greater or less use of his reason and energy. The former are in existence before the second, they form the substratum, so to speak upon which human activity works. The animal state is first necessary before one can become a man. Man, however, in a certain measure, controls the animal on which his human nature is based. No doubt this view takes for granted that an idea, as such, may be efficacious. Still, though the immediate sway which an idea holds over matter may be unintelligible, is it so 202 THE SOCIOLOGICAL LAWS with activity exercised through an infinite number of intermediaries, affecting mind on the one hand, and matter on the other ? Let us not forget that pure mind and pure matter are but abstractions and fancies. When thoroughly understood, mechanism, instead of shutting us in on every hand, constitutes the means at our disposal for acting upon things and for obtaining power over them. Through the psychic and sociological mechanism, which depend on ourselves, we have a hold on the physical mechanism. A knowledge of the laws of things enables us to control them ; consequently, instead of checking our freedom, mechanism makes it efficacious. 203 XIV CONCLUSION WE have analysed ; the various types of natural laws offered us by the sciences, from the standpoint of these sciences themselves. In the physical laws, we have seen the data supplied to philoso- phy by the sciences, just as science sees in facts the data supplied to it by nature. In conclusion, we ask ourselves what becomes of human freedom and responsibility, over against these laws, which, to us, represent the nature of things. The problem is a more urgent one now than it was a century ago. When the domain of science, strictly so- called, was not so wide-spread, it was pos- sible to admit that, outside this domain, there was room for freedom. Science, how- ever, is daily gaining both in precision and in extent of influence. It is bringing under its sway the very manifestations which seemed most hostile to its influence. 204 CONCLUSION May it not be, then, that everything, de jure, belongs to it ; that everything, con- sequently, is determined and rendered neces- sary ? As the sense of freedom, in spite of this progress on the part of science, exists, de facto, in the human soul, it is expedient to find out whether there is any contradiction between these two facts, and whether the second must be attributed to illusion resulting from ignorance. There are weighty reasons why determin- ^ ism should nowadays appear more limited than it must have seemed to the men of the past. No doubt the latter saw above them a Destiny which was crushing them ; but, as Pascal says, even though he suc- cumbs, man is still nobler than that which / slays him, because he knows that he dies. Ancient philosophy, in its classic manifes- tations, is based on a dualism which prevents , determinism from being absolute. Being consists of two elements : truth, the abode of the eternal and the necessary ; and phenomenon, impermanent matter, incapable of being definitely fixed in any form. This quality of being ensures the possibility of the contraries, the condition of freedom. 205 NATURAL LAW IN SCIENCE AND PHILOSOPHY And so, even in the case of the Stoics, who were rationalistic pantheists, the wise man retains, deep in his soul, the free power to acquiesce in destiny or to resist it. There-/ fore the ancients maintain that there an two sciences, the second of which canno* be included in the first : the science of being strictly so-called, perfect and permanent like its object, and the science of becoming imperfect and impermanent like becoming itself. Now, the essential characteristic of modern science is a tendency to do away with this duality. Its fundamental idea, ormulated by Descartes, consists in admit- ting that there is a point at which the sensible . coincides with the mathematical, and becoming / coincides with being ; that things are not more or less imperfect copies of transcendent para- digms, but rather particular determinations of the mathematical essences themselves. Hence, we have an altogether new compass or range attributed to inductive reasoning. In Aristotle's mind, no empirical knowledge, as such, might lay claim to universality and necessity. Experience was inevitably limited to the relative. But if all the pro- 206 CONCLUSION perties of things are, in their essence, mathe- matical, even experience may attain to the necessary, provided it succeeds in discerning and unravelling or extricating this interior warp and woof of reality. Distinct as they were in the minds of the ancients, mathematics and experience remained, the former, transcen- dent ; the latter, uncertain. Closely united, they are the foundation of a complete science of sensible reality itself. Mathematics im- parts to science, necessity ; experience im- parts conformity with facts. Such is the root of modern determinism. We believe everything to be necessarily determined, because we believe everything, in essence to be mathematical. This belief is the spring, manifest or unperceived, of scien-i tific investigation. What we have to find} out is whether this is a truly constitu- tive principle, or simply a regulating prin- ciple and a guiding idea. Does science prove that the basis of things is exclusively mathematical, or does it only assume this ? Modern determinism is based on the two following assertions : (i) mathematics is per- fectly intelligible and is the expression of an absolute determinism ; (2) mathematics 207 NATURAL LAW IN SCIENCE AND PHILOSOPHY applies to reality in the most precise manner ; de jure, at all events, and in the essence of things. Let us begin with the first of these two theories. It regards mathematics as simply a special development of logic. Now, logic, real logic, at any rate, including the theory of concept, judgment and reasoning, actu- ally presupposes data that are irreducible to a strictly analytical relationship : the only type of perfect intelligibility. Concept, judgment and syllogism have ever given rise to controversy. The reproach of barren tautology, as regards their importance, is removed only by the introduction of con- siderations that have nothing to do with pure logic. Such is the notion of the implicit and the explicit, which meets the difficulty, in a fashion, though only by appealing to the obscure metaphysical distinction between act and potency. PWhile logic contains elements that cannot be reduced to pure thought, mathematics con- tains a greater number of these elements. In spite of all their efforts, mathematicians have not succeeded in bringing mathematics within the compass of simple logic . Descartes, by means of his theory of intuition and deduc- 208 CONCLUSION tion makes a radical distinction between mathematical method and syllogistic reason- ing. Mathematical knowledge, to his mind, compasses principles that have a content ; it proceeds from the simple to the com- pound, which logic does not do. Under the various names of synthetic d priori judg- ments, postulates, definitions, axioms and fundamental facts, philosophical mathema- ticians admit, either as coming from experi- ence or from the intellect, given and in- scrutable principles ."J In effect, mathematics has been established and is moving towards perfection by a process of generalization which consists in imagining axioms and definitions that allow of the development of demonstra- tions with the utmost possible continuity and the fewest possible gaps. How are we to affirm that principles thus received for the needs of the cause are all necessary and perfectly intelligible ? The philoso- phical analysis of principles and of mathe- matical methods reveals therein many a contin- gent determination, many an artifice accepted mainly because it is successful. And so mathematical necessity itself is no longer unconditioned in our minds, as it may 209 o NATURAL LAW IN SCIENCE AND PHILOSOPHY have been in the minds of/Jhe ancients, who regarded mathematics as entirely d priori. J On the other hand, this necessity has lost the aesthetic character it possessed for the Pythagoreans and the Platonists. To us, it is a blind and brutal necessity which goes straight ahead, without either goal or check. Is this necessity, such as it is con- ceived to be, really part and parcel of things ? Is the complete fusion of mathe- matics and experience, the object of modern science, effectually realized ? Does it appear as though some day it will have to be realized ? To enable mathematics and experience to become closely united, it has been assumed that everything given may be split up into two elements incapable of permeating each other : movements and states of consciousness ; and that the first of these two elements is, as regards knowledge, the legitimate substi- tute of the second. In so far as things may be looked upon as consisting of movements, they fulfil the conditions of a mathematico- experimental science. Can this separation so precise and strict in philosophy between quantity and quality, be accurately realized in the sciences ? This 210 CONCLUSION r is more than we can affirm. (^Mechanics, the concrete science which must be the basis of all the rest, offers elements that are irre- ducible to pure mathematical determina- tions ; it is incapable of entirely transform- ing its experimental data into rational truths. Known by experience alone, the most general connexions between things remain, so far as we are concerned, radically con- tingent, as Newton said. Why are bodies attracted to each other in the ratio of their mass and not of the square of their mass ? This is a fact, nothing more. Celestial mechanics, after all, implies the very idea of natural law, in so far as this law is distinct from purely mathematical relations, i.e. in so far as it brings together two terms, one of which can in no way be deduced from the other.] Moreover, it would be incorrect to say that mechanics, of itself alone, de jure, at all events, constitutes the entire science of the real. For, in the present state of our knowledge, science is not one, it is multi- ple. Science, regarded as including all the sciences, is but an abstraction. That which is given consists of sciences, each 211 o* NATURAL LAW IN SCIENCE AND PHILOSOPHY of which, whilst remaining connected with the rest, has its own distinctive aspect and evidence. In proportion as we advance from the study of the motions of the heavenly bodies the most external reality with which we are acquainted to the study of life and thought, the postulates required are the more numerous and in- accessible. Physics, by regarding work as superior to heat, actually makes an open appeal to the notion of quality. Chemistry is based upon the postulate that elements of different kinds exist and are maintained in existence. The reflex act of biology is no simple mechani- cal reaction, for it has the property of en- suring the conservation, evolution and re- production of a determinate organization. Psychic reaction is something more, since it tends to provide an individual with the science of things, i.e. the knowledge of laws, and thereby with an indefinite power to utilize them for ends laid down by himself. [To sum up, in sociology, the action of en- i vironment is not sufficient to explain pheno- \mena ; we must introduce man, with his know- ledge and prejudices, his power of sympathy 212 CONCLUSION with other men, and his ideas of happiness/ and progress, justice and harmony. Thus, the objects of the various sciences are not wholly permeated by mathematics, and we look upon the fundamental laws of each science as the least def ective^comgromisfiathat the mind has succeeded in finding for bring- ing together mathematics and experience. Moreover, we must distinguish between the physical sciences, which readily unite with mathematics, and the biological sciences, for which this union is far more artificial. In the former, man himself limits his field of investigation ; he purposes to take into consideration only a certain order of manifestations of nature that which is amenable to measure and number and to neglect the rest. Owing to this partially arbitrary delimitation, we have to deal with something that sensibly admits of mathe- matical determination. In the biological sciences this method may still be employed ; but here we are manifestly leaving out of our investigation the best and most character- istic part of the phenomena^ The more we resolve to grasp or understand being in its concrete reality, the more we must be con- 213 NATURAL LAW IN SCIENCE AND PHILOSOPHY tent with observing and inferring, and must refrain from using mathematical analysis. Thus the mathematical form gives the sciences a certain character of abstraction. The con- crete living being refuses to be confined therein. In a general way, then, there are two inds of laws : the first, which are more akin to mathematical conjunction and imply considerable elaboration and purification of concepts ; the second, which are nearer to >bservation and induction, pure and simple. The former express a rigorous, if not absolute, necessity, but they remain abstract and in- capable of determining the details and the mode of effective realization of the phenomena. The latter treat of the details and the rela- tions which complex and organized wholes have with one another : consequently they are far more determinative than the former ; but as they have no other basis than experi- ence and connect together wholly hetero- geneous terms, they cannot be regarded as necessitative. Possible prediction does not imply necessity, since free acts may admit >f it. Thus, necessity and determination ire distinct from each other ; our science :annot blend them into one. 214 CONCLUSION r To sum up, on the one hand, mathema- tics is necessary only with reference to pos- tulates whose necessity cannot be demon- strated, and so is only hypothetical after all. On the other hand, the application of mathematics to reality is only approxi- mate, and seems as though it could be nothing else. Under these conditions, what is the doctrine of determinism ? It is a generalization and a passing over to the limit. Certain concrete sciences approach mathematical rigidity ; the inference is that they are all destined to attain to the same per- fection. The distance that separates us from the goal may be increasingly lessened: the inference is that it may become nil. This generalization, however, is a theoretical view. As a matter of fact, the distance between mathematics and reality is not on the point of being abolished ; and, if it is les- sening, the number of intermediaries which would have to be intercalated to effect the junction of the two, appears more and more to be infinite. Historically, the idea of reducing the real to the mathematical is due to ignorance of this incommensurability of the real and of the mathematical ; iguor- i/ 215 NATURAL LAW IN SCIENCE AND PHILOSOPHY ance, in this case, has had good results ; for less eagerness would have been shown in making for a goal known to be inaccessible. The application of the Cartesian idea not only demonstrated its fertility, it also transformed into a transcendent ideal what, to Descartes, was a principle and a starting-point, f But if we compare with the present state of science the testimony of consciousness in favour of freedom, we shall find this testi- mony far more acceptable now than it was in Cartesian dualism, for instance. When things were reduced to matter and thought, to assume man to be free and his freedom to be efficacious, was to admit that spirit, as sub- stance, moves matter, as discrete substance. Now, this is incomprehensible, whether we assume that spirit creates motor force, or admit that what is not itself motion can directly determine motion. Science, how- ever, by no means establishes the reality of this dualism. It rather shows us a hierarchy of sciences, a hierarchy of laws, which we can compare with one another 1 but not blend into a single science of exter- \ nal things and into a single law. It shows us, besides, along with the relative heterogeneity 216 CONCLUSION of laws, their influence upon one another. The physical laws involve living beings, and the biological laws combine their action with that of the physical laws. In presence of these results, we are led to enquire whether thought and motion, along with the abyss that separ- ates them, might not be our mode of bring- ing things clearly before the mind, rather than their real mode of being. Motion, per se, it would appear, is but an abstrac- tion, as also is thought, per se. What exists are beings, whose nature is inter- mediate between the pure idea of thought and of motion. These beings form a hier- archy, and action moves amongst them from above, downwards, and from below, upwards. Spirit moves matter neither im- mediately, nor even mediately. There is no crude matter, however, and what constitutes the being of matter is in communication with what constitutes the being of spirit. Thafj which we call the laws of nature is the sum total of the methods we have discovered for adapting things to the mind, and subjecting them to be moulded by the will / In the beginning, man saw nothing but supernatural caprice and arbitrariness every- 217 NATURAL LAW IN SCIENCE AND PHILOSOPHY where. Consequently, the freedom he attri- buted unto himself had nothing on which it could lay hold. Modern science showed him physical law everywhere, and he imagined he saw his freedom being engulfed in universal determinism. A correct idea, however, of the natural laws, restores him to true self-posses- sion, and at the same time assures him that his freedom may be efficacious and control phenomena. Of things without and things within, the latter alone, said Epictetus, depend on ourselves, and he was right at the time he spoke. The mechanical laws of nature, revealed by modern science, form, in reality, the chain that binds the without to the within. Instead of being a necessity, they set us free ; they enable us to supple- ment, by active science, that state of contem- plation in which the ancients were plunged. THE END Printed by BUTLER & TANNER, Frame and London. 218 14 DAY USE ETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. REC'OLO DEC H72-5 PM 9 MAR 619tft> JAN 81986 Sp 1 ? 7988 nrPFIVPn Rtuti vcu MAR I 9 1996 AUTO JUN jggg General Library University of California 22487 GENERAL LIBRARY - U.C. BERKELEY