EXPLANATION. What is meant by explaining a phe nomenon? There is no need to insist on the importance of this question. It is obvious that the entire structure of science will necessarily depend upon the reply given. The usual answer is that explanation consists in showing that a phenomenon obeys a law. This is the formula apparently first enunciated by Berkeley : Nana inventis semel naturae legibus, deinceps monstrandum est phi losopho, ex constanti harum legum observatione, hoc est, ex its principiis, phaenomenon quodvis necessario consequi: id quod est phaenomena explicare et solvere, causamque, id est rationem cur fiant, assignare. As is well known, Comte based his "Positivism" on this principle : Science seeks nothing but laws and, once these are discovered, science remains simply a collection of them. What ever is not law is vain or, at most, provisional scaff olding,—f or what science really aims at is simply preparation for action : "Science, whence prevision; prevision, whence action." This is almost a translation of Hobbes's statement : Scientia propter po tentiam . . . omnis denique speculatio actions vel operis alicuius gratin institute est.
Berkeley, as we have just seen, identified cause and law. Comte, on the contrary, saw that it is possible to investigate the cause of a phenomenon after having determined its law. But he severely forbade research of this kind. In his view, "only men absolutely devoid of the scientific spirit" are inclined to adopt such a procedure.
This way of conceiving scientific explanation is quite in accord ance with the etymological meaning of the term if we remember that this implies merely that what was not entirely "level" has now been made so. From the same order of ideas is derived the Ger man expression, erkldren, "to make clear," so that what was hidden may become visible. All this seems in harmony with the positivist view that to explain a phenomenon is to describe it.
The term "explanation" however has, for its synonym, explica tion (in French this latter alone has been retained), while, in Latin, explicare originally meant "to unroll," and is almost synony mous with evolvere (whence the modern concept "evolution"). Thinkers of the Middle Ages often gave this interpretation to it, and among moderns, Hegel, Wallace and Ward have followed them. So understood explanation appears to be something quite different from description; it implies the preformation of the consequent in the antecedent. A phenomenon will be explained only when it is shown that what is new, what is surprising in it, should not have surprised us, since it was already present in a disguised form. And it is precisely in this element of wonder and certainly not in the desire to prepare for action, that Plato and Aristotle saw the true motive force of science.
Might this, however, not be a vicious, chimerical form of the search for knowledge? Might not the orientation of present day science in fact run counter to that of the past (tainted according to Comte with the "metaphysical spirit"), in conformity with the positivist scheme? This is a question which cannot be settled without an investigation of science itself.
One must remember besides, that, as against Comte's formula, the dominant role in science is played not by law, but by causal hypotheses. Now, at bottom, the very existence of such theories is embarrassing for strict Positivism. Comte himself felt it and vacillated a little on their account, sometimes ruling them out entirely, at other times admitting them as a kind of provisional make-shift. Impelled by a strong scientific instinct, he even went so far as to declare the atomic theory "a good hypothesis." But Mach, who built his theory of science upon a basis com pletely analogous to that of Comte, was more logical, for he vio lently opposed the revival of atomistic conceptions since the end of the i9th century, declaring (during a well-known controversy with Planck) that if physicists affirmed the reality of atoms to constitute an essential point of their scientific credo, he (Mach) would cease to think as a physicist and would forego their ap proval of his work. The majority of positivists, however, main tain a less uncompromising attitude. They admit causal hypotheses, hoping that subsequent progress in knowledge will eliminate them and reduce science to a system of laws entirely freed from hy potheses. Now, it is sufficient to consider the actual evolution of knowledge to convince oneself how little its progress corresponds to these views. Never has a mechanistic hypothesis disappeared before a simple law ; like the priest of Nemi, it always had to be annihilated by some other theory that succeeded it. This fact seems sufficient to overthrow the positivist scheme.
Finally, there is observable in science the existence of a series of propositions (the most important, or, at any rate, the most general throughout the whole domain of our knowledge) the na ture of which is ill determined, namely, the principles of conser vation. Some thinkers have taken them to be simple empirical statements, while others have declared them to be a priori. But on a rather closer examination of these two opinions, it will be easily seen that neither has any solid foundation, and one wonders there fore how these principles met with such ready acceptance at the time they were proposed, and how they came to occupy such a high place in the hierarchy of dominant scientific truths.
So the positivist scheme is incapable of embracing the whole of science; it is quite vain to try to adjust the whole of science to this bed of Procrustes. What the positivist formula defines is only a part of science, the knowledge of laws; and if this part be sub tracted from the total (an operation which Comte's formula enables us to do—and in this lies his great merit) , there remains, so to speak, a residue. To use another image, the positivist key does indeed open many of the doors of science but not all of them ;—there still remains a whole series of locks which it does not fit.
Is the solution which we have just reached quite complete? On examination, the concept of cause is found to involve motions to which the solution does not seem directly applicable. First, there is the fact that we demand the cause not only of that which changes, but also of that which persists. Aristotle himself some times spoke of "cause" in such cases, and Leibniz declared that if it were proved that the ultimate particles of matter were spherical, we still should ask why they were not cubical. Would this tend ency be entirely alien to the nature of physics? It is easy to realize, on the contrary, that it exerts the most powerful influence upon it. On this tendency depends an essential idea of mechanism, namely, the unity of matter, which it has not ceased to proclaim from the time of Leucippus and Democritus up to our own day; also another equally characteristic idea, viz., that this matter, of which all "reality" is made, has no quality except that of occupy ing space, and is therefore identical with empty space. Descartes, who may be called the codifier of modern science, boldly pro claims this identification, although he expresses it in a rather different way. He declares that there is no space where there is no matter; but one realizes through his very deduction that this "matter," having only geometrical qualities, is, at bottom, nothing but space.
In modern physics (or more precisely, before the appearance of Einstein's "general relativity") this reduction was carried out by a more round-about route; a semi-material medium, the ether, was postulated, and it was sought to explain material particles by such peculiar properties of this medium as rings, vortices, etc. It was understood, however, that this ether must possess no "occult quality," and this requirement obviously ended by making it identical with empty space, as Maxwell recognized, or else a simple hypostasis of space, according to Helmholtz. The rela tivists, in this respect, resumed the Cartesian tradition by aban doning to a greater or less degree the hypothesis of an ether.
Paradoxes.—A very thorough scrutiny is hardly necessary in order to see that this train of thought leads to an exceedingly paradoxical conclusion. For space (at least, the three-dimen sional space of the pre-relativists) is evidently not susceptible of any change, and even if we suppose it filled with some quasi material substance everywhere identical with itself (such as the hypothetical ether), movement becomes impossible, for its suc cessive states cannot be distinguished one from another, "even by an angel," as Leibniz declared. Therefore, the outcome of all this labour of reduction, if by some miracle it might be brought to a successful conclusion, would be tantamount to reducing the real to nothing, to absolute annihilation. And we are driven to the conclusion that such aims, so paradoxical, so contrary to that which the physicist firmly believes to constitute his nearest and surest aim, namely, the understanding of the real, can only derive from a tendency rooted in the deepest part of the human mind— the intellectus ipse, whose existence is affirmed by Leibniz when to the scholastic formula, Nihil est in intellectu quod non fuerit pries in sensu, he adds the words nisi intellectus ipse. It will also be seen how far this tendency to discover the cause of the diver sity among the co-existent is connected with that which attacks the diversity of the changing. The solutions, further, resemble each other. A moment ago we explained change, by showing it to be merely apparent, and so concealing a basic identity. Now we en deavour to establish that the "real," whatever be the matter which seems to fill it, is everywhere identical with itself. Explanation is accomplished, then, in both cases, by the help of what has been called the principle of identity, but which might have been better named the schema of identification. Hegel, indeed, has justly pointed out that the formula of strict identity A=A, constitutes a tautology pure and simple and, therefore, cannot serve as an in strument for any progress in thought. In reality, the second A is always regarded as differing from the first in some respect, and the work of the mind consists in establishing, or at least affirm ing, identity in spite of this difference.
An "irrational" of a different order from that which Carnot's principle has brought to light, becomes apparent if we consider sensation. This, without doubt, is the ultimate source of all our knowledge of the real, but it is easy to see that our modern science excludes that which is its characteristic element. This science does by a somewhat indirect route, banishing it first of all into one of its most complex and least advanced branches, namely, physiology. Once there, it is enveloped in mystery, shut up in the nerve and in the specific energy of the nerve. Leucippus and Democritus had already allowed this exclusion, and Descartes (and all modern science with him) maintained it. Aristotle cer tainly attempted to create a different system of physics, a qual itative physics, and the middle ages docilely followed his lead. But we know that this attempt has been absolutely ineffectual. However magnificent it may have appeared at the time, at the present day the edifice is an irremediable ruin : absolutely nothing can be saved from it. And even those who have occasionally tried to incorporate a few fragments of it into modern physics have had to recognize the vanity of their efforts. (The loyal attempts of Duhem were the most brilliant and persevering of this kind ever made.) Vain too have proved to be the objections of philosophers against what they considered unjustifiable prejudice on the part of physicists, as well as the efforts during the first part of the i9th century (especially in Germany) which were directed to elaborat ing—alongside the physics of physicists, nay, in opposition to it— a different science incorporating and explaining the quid proprium of sensation. And, what is more remarkable, is that even in Ger many, scientists did not take the trouble to refute these attempts, but simply disdained them, passing them by unnoticed, despite the great authority which their authors—we need only mention the names of Hegel and Goethe—enjoyed at the time.
Another "irrational" arises if we consider the explanation of the persistent, of which we have just spoken. This explanation amounts in the last resort to dissolving the whole of reality into the undifferentiated whole of space. It is clear therefore that what ever opposes such a dissolution must play the role of an obstacle. In this way, all diversity inevitably appears as an irrational. Per haps it will not be pointless to make the significance of this as sertion more precise by the aid of an example. We know that chemistry has for a long time been constituted as a science dis tinct from the other physical sciences, and that what differentiates it is its affirmation of the qualitative diversity of substances. Under the name of Mendeleeff's theory, this diversity has been questioned, for it seemed to be demonstrated that the various elementary substances themselves should not be considered corn pletely isolated from each other, but, on the contrary, as deriva tive from a more general system. As a consequence, on the one hand, of the discovery of radio-active bodies and other discoveries connected therewith, and, on the other, of a series of researches which better enable us to understand the nature of the chemical atom, this current has acquired great strength, and, it may be said to dominate chemical theory at the moment. Clearly, were these efforts to prove completely successful,—in other words, were it possible to reach an explanation of the entire behaviour of chemical substances through the spatial configuration of ele mentary particles (electrons and protons, according to the dom inant conception), the specific nature of chemistry would vanish. But, on the other hand, to encounter phenomena fundamentally inexplicable by such configuration, would be to discover the pres ence of an "irrational." We can realize, then, that such a situation is particularly liable to arise wherever we admit the existence of separate sciences. Thus, it is most probable that when our knowl edge of biological phenomena is more advanced, and when we are in a position actually to reduce a great number of them to physi cal chemistry, there will remain, nevertheless, something which we shall not be able fully to account for, and then science will be compelled to admit one or more "irrationals" as being related to the manifestations of organic matter.
However, it should be realized that not all irrationals could be foreseen in this way, by even the boldest speculation. Indeed, from those very phenomena which we believe to be the most fully understood, something inexplicable may arise. This is just what happened during the first decades of this century. We refer to the observations concerning radiation which led to Planck's theory of quanta,—a theory so strange and disturbing, because it is so difficult to reconcile it with the remaining hypotheses of physics. And who can say that this surprise will be the last, and that science will not encounter in the future other anomalies just as disagreeable? The Real and the Necessary.—If now we take a comprehen sive survey of this great effort of science to explain and to identify, we see that it aims at a rationalization of the real, that is to say, at its reduction to purely rational elements. The real appears to us as a fact,—a datum. Now reason would like to conceive it as necessary. Hence the extravagant attempt to reduce it to space, namely, to nothingness,—or (what amounts to the same thing), to reconstitute it with the aid of space alone. Newton, who had before him the attempts of Descartes, admirably discerned that such an effort could only end in failure. "A coeca necessitate metaphysica," he says at the end of the third edition of his Prin cipia, "quae utique eadem est semper et ubique, nulla oritur rerum variatio." One sees, none the less, that the effort has been renewed in our own day by the physics of relativity. But by the very fact that space is there supposed capable of modifying its curvature, of disclosing "wrinkles," it ceases to be always and everywhere homogeneous, and this construction thus escapes Newton's ob jection to some extent.
This notion of the irrational, as an obstacle which mind con stantly encounters in its advance towards an explanation of nature, shows that we should be wrong in charging science with the tend ency to dissolve the real into nothingness. For this tendency is quite obviously something which precedes science, something by the aid of which science itself has been created. We begin the penetration of the real with the profound conviction that it should prove itself everywhere penetrable. It might be objected, it is true, that a science confined to the discovery of laws, according to the formula of Comte, seems practically to rule out any intel ligibility strictly so-called, by contenting itself with the supposi tion that nature obeys laws. But apart from the fact that there never has been such a type of science, and in all probability never will be, it is easy to see that even if, in an exposition of science already made, it could in strictness, be made to appear as simply a tissue of laws, this would become absolutely impossible so soon as it became a question of science in the making, of science in process of development. Francis Bacon believed it possible to establish laws by means of experiments undertaken at random, and summed up later by a sort of mechanical book-keeping. But Liebig has declared that between this variety of science and real science the same relation holds as between the noise made by a child beat ing a drum and music, and in this the unanimous opinion of scien tists would agree with him. In reality, when trying to discover a law the scientist is compelled to select among the conditions of phe nomena which are infinite in number, in order to observe those which seem to be more closely connected with each other. What he is intent upon determining is what Lord Balfour calls the fibre, that is to say, one of the fibres of which the real is constituted. And simply this fact, that the whole body of the real is not chaotic, but actually consists of a tissue of such fibres, allows us not only to penetrate into it but even to live in it. Now it is only by means of hypotheses concerning the nature and essence of the real that we can seek out this fibre and make a supposition as to its exist ence and precise place in the scheme of things. Thus, a science directed to the discovery of laws is itself ultimately based- upon the conception that nature is intelligible.
The schema of identity constitutes the eternal framework of the mind, and science as a product of the mind, cannot be other than pervaded by it. But, far from submitting to it passively, it re acts, because the real itself reacts, in showing that it is not com pletely penetrable. The idea of the irrational is the manifesta tion of reality's resistance to intellect. Hence in science, the two tendencies which might be thought opposed to each other,—the idealist tendency toward a negation of the real by rationalization of the diverse, and the realist tendency toward an affirmation of the fundamental irreducibility of the diverse,—co-exist peacefully. It should be noticed that if idealist negation is at the end of its course, physics does not cease for a moment to be fundamentally realistic. The "vortices" of Kelvin, like the "wrinkles" of the relativity theory, show themselves the very moment we try to bring them nearer to ether or space, just as real, just as independ ent of our own selves, as any common-sense objects. Even more independent, indeed, for, as Planck has shown, science tends in its progress to draw further and further away from the anthro pomorphism that common-sense imposes on us.