To detect this particular circumstance of difference, we have but one practicable method, that of Concomitant Variations:
"'In the cases of polished metal and polished glass, the contrast shows evidently that the substance has much to do with the phenomenon; therefore let the substance alone be diversified as much as possible, by exposing polished surfaces of various kinds. This done, a scale of intensity becomes obvious. Those polished substances are found to be most strongly dewed which conduct heat worst, while those which conduct well resist dew most effectually....'
"The conclusion obtained is, that cœteris paribus the deposition of dew is in some proportion to the power which the body possesses of resisting the passage of heat; and that this, therefore (or something connected with this), must be at least one of the causes which assist in producing the deposition of dew on the surface.
"'But if we expose rough surfaces instead of polished, we sometimes find this law interfered with. Thus, roughened iron, especially if painted over or blackened, becomes dewed sooner than varnished paper: the kind of surface, therefore, has a great influence. Expose, then, the same material in very diversified states as to surface' (that is, employ the Method of Difference to ascertain concomitance of variations),' and another scale of intensity becomes at once apparent; those surfaces which part with their heat most readily by radiation, are found to contract dew most copiously....'
"The conclusion obtained by this new application of the method is, that cœteris paribus the deposition of dew is also in some proportion to the power of radiating heat; and that the quality of doing this abundantly (or some cause on which that quality depends) is another of the causes which promote the deposition of dew on the substance.
"'Again, the influence ascertained to exist of substance and surface, leads us to consider that of texture; and here, again, we are presented on trial with remarkable differences, and with a third scale of intensity, pointing out substances of a close firm texture, such as stones, metals, etc., as unfavourable, but those of a loose one, as cloth, velvet, wool, eiderdown, cotton, etc., as eminently favourable to the contraction of dew.' The Method of Concomitant Variations is here, for the third time, had recourse to; and, as before, from necessity, since the texture of no substance is absolutely firm or absolutely loose. Looseness of texture, therefore, or something which is the cause of that quality, is another circumstance which promotes the deposition of dew; but this third cause resolves itself into the first, viz., the quality of resisting the passage of heat: for substances of loose texture 'are precisely those which are best adapted for clothing, or for impeding the free passage of heat from the skin into the air, so as to allow their outer surfaces to be very cold, while they remain warm within....'
"It thus appears that the instances in which much dew is deposited, which are very various, agree in this, and, so far as we are able to observe, in this only, that they either radiate heat rapidly or conduct it slowly: qualities between which there is no other circumstance of agreement than that by virtue of either, the body tends to lose heat from the surface more rapidly than it can be restored from within. The instances, on the contrary, in which no dew, or but a small quantity of it, is formed, and which are also extremely various, agree (so far as we can observe) in nothing except in not having this same property....
"This doubt we are now able to resolve. We have found that in every such instance, the substance must be one which, by its own properties or laws, would, if exposed in the night, become colder than the surrounding air. The coldness, therefore, being accounted for independently of the dew, while it is proved that there is a connection between the two, it must be the dew which depends on the coldness; or, in other words, the coldness is the cause of the dew.
"This law of causation, already so amply established, admits, however, of efficient additional corroboration in no less than three ways. First, by deduction from the known laws of aqueous vapour when diffused through air or any other gas, and though we have not yet come to the Deductive Method, we will not omit what is necessary to render this speculation complete. It is known, by direct experiment, that only a limited quantity of water can remain suspended in the state of vapour at each degree of temperature, and that this maximum grows less and less, as the temperature diminishes. From this it follows deductively, that if there is already as much vapour suspended as the air will contain at its existing temperature, any lowering of that temperature will cause a portion of the vapour to be condensed, and become water. But, again, we know deductively, from the laws of heat, that the contact of the air with a body colder than itself, will necessarily lower the temperature of the stratum of air immediately applied to its surface; and will therefore cause it to part with a portion of its water, which accordingly will, by the ordinary laws of gravitation or cohesion, attach itself to the surface of the body, thereby constituting dew. This deductive proof, it will have been seen, has the advantage of proving at once causation as well as coexistence; and it has the additional advantage that it also accounts for the exceptions to the occurrence of the phenomenon, the cases in which, although the body is colder than the air, yet no dew is deposited, by showing that this will necessarily be the case when the air is so under-supplied with aqueous vapour, comparatively to its temperature, that even when somewhat cooled by the contact of the colder body, it can still continue to hold in suspension all the vapour which was previously suspended in it: thus, in a very dry summer there are no dews, in a very dry winter no hoar frost....
"The second corroboration of the theory is by direct experiment, according to the canon of the Method of Difference. We can, by cooling the surface of any body, find in all cases some temperature (more or less inferior to that of the surrounding air, according to its hygrometric condition) at which dew will begin to be deposited. Here, too, therefore, the causation is directly proved. We can, it is true, accomplish this only on a small scale; but we have ample reason to conclude that the same operation, if conducted in Nature's great laboratory, would equally produce the effect.
"And, finally, even on that great scale we are able to verify the result. The case is one of those rare cases, as we have shown them to be, in which nature works the experiment for us in the same manner in which we ourselves perform it; introducing into the previous state of things a single and perfectly definite new circumstance, and manifesting the effect so rapidly that there is not time for any other material change in the pre-existing circumstances. 'It is observed that dew is never copiously deposited in situations much screened from the open sky, and not at all in a cloudy night; but if the clouds withdraw even for a few minutes, and leave a clear opening, a deposition of dew presently begins, and goes on increasing.... Dew formed in clear intervals will often even evaporate again when the sky becomes thickly overcast.' The proof, therefore, is complete, that the presence or absence of an uninterrupted communication with the sky causes the deposition or non-deposition of dew. Now, since a clear sky is nothing but the absence of clouds, and it is a known property of clouds, as of all other bodies between which and any given object nothing intervenes but an elastic fluid, that they tend to raise or keep up the superficial temperature of the object by radiating heat to it, we see at once that the disappearance of clouds will cause the surface to cool; so that Nature, in this case, produces a change in the antecedent by definite and known means, and the consequent follows accordingly: a natural experiment which satisfies the requisitions of the Method of Difference."
These four are not all the scientific methods, but they lead up to the rest. They are all linked together, and no one has shown their connection better than Mill. In many cases these processes of isolation are powerless; namely, in those in which the effect, being produced by a concourse of causes, cannot be reduced into its elements. Methods of isolation are then impracticable. We cannot eliminate, and consequently we cannot perform induction. This serious difficulty presents itself in almost all cases of motion, for almost every movement is the effect of a concurrence of forces; and the respective effects of the various forces are found so mixed up in it that we cannot separate them without destroying it, so that it seems impossible to tell what part each force has in the production of the movement. Take a body acted upon by two forces whose directions form an angle: it moves along the diagonal; each part, each moment, each position, each element of its movement, is the combined effect of the two impelling forces. The two effects are so commingled that we cannot isolate either of them, and refer it to its source. In order to perceive each effect separately, we should have to consider the movements apart, that is, to suppress the actual movement, and to replace it by others. Neither the Method of Agreement, nor of Difference, nor of Residues, nor of Concomitant Variations, which are all decomposing and eliminative, can avail against a phenomenon which by its nature excludes all elimination and decomposition. We must, therefore, evade the obstacle; and it is here that the last key of nature appears, the Method of Deduction. We quit the study of the actual phenomenon to observe other and simpler cases; we establish their laws, and we connect each with its cause by the ordinary methods of induction. Then, assuming the concurrence of two or of several of these causes, we conclude from their known laws what will be their total effect. We next satisfy ourselves as to whether the actual movement exactly coincides with the movement foretold; and if this is so, we attribute it to the causes from which we have deduced it. Thus, in order to discover the causes of the planetary motions, we seek by simple induction the laws of two causes: first, the force of primitive impulsion in the direction of the tangent; next, an accelerative attracting force. From these inductive laws we deduce by calculation the motion of a body submitted to their combined influence; and satisfying ourselves that the planetary motions observed coincide exactly with the predicted movements, we conclude that the two forces in question are actually the causes of the planetary motions. "To the Deductive Method," says Mill, "the human mind is indebted for its most conspicuous triumphs in the investigation of nature. To it we owe all the theories by which vast and complicated phenomena are embraced under a few simple laws." Our deviations have led us further than the direct path; we have derived efficiency from imperfection.
If we now compare the two methods, their aptness, function, and provinces, we shall find, as in an abstract, the history, divisions, hopes, and limits of human science. The first appears at the beginning, the second at the end. The first, necessarily, gained ascendancy in Bacon's time,[423] and now begins to lose it; the second, necessarily, lost ascendancy in Bacon's time, and now begins to regain it. So that science, after having passed from the deductive to the experimental state, is now passing from the experimental to the deductive. Induction has for its province phenomena which are capable of being decomposed', and on which we can experiment. Deduction has for its province indecomposable phenomena, or those on which we cannot experiment. The first is efficacious in physics, chemistry, zoology, and botany, in the earlier stages of every science, and also whenever phenomena are but slightly complicated, within our reach, capable of being modified by means at our disposal. The second is efficacious in astronomy, in the higher branches of physics, in physiology, history, in the higher grades of every science, whenever phenomena are very complicated, as in animal and social life, or lie beyond our reach, as the motions of the heavenly bodies and the changes of the atmosphere. When the proper method is not employed, science is at a stand-still: when it is employed, science progresses. Here lies the whole secret of its past and its present. If the physical sciences remained stationary till the time of Bacon, it is because men used deduction when they should have used induction. If physiology and the moral sciences are now making slow progress, it is because we employ induction when deduction should be used. It is by deduction, and according to physical and chemical laws, that we shall be enabled to explain physiological phenomena. It is by deduction, and according to mental laws, that we shall be enabled to explain historical phenomena.[424] And that which has become the instrument of these two sciences, it is the object of all the others to employ. All tend to become deductive, and aim at being summed up in certain general propositions, from which the rest may be deduced. The less numerous these propositions are, the more science advances. The fewer suppositions and postulates a science requires, the more perfect it is become. Such a reduction is its final condition. Astronomy, acoustics, optics, present its models; we shall know nature when we shall have deduced her millions of facts from two or three laws.
I venture to say that the theory which you have just heard is perfect. I have omitted several of its characteristics, but you have seen enough to recognize that induction has nowhere been explained in so complete and precise a manner, with such an abundance of fine and just distinctions, with such extensive and exact applications, with such a knowledge of the practical methods and ascertained results of science, with so complete an exclusion of metaphysical principles and arbitrary suppositions, and in a spirit more in conformity with the rigorous procedure of modern experimental science. You asked me just now, what Englishmen have effected in philosophy; I answer, the theory of Induction. Mill is the last of that great line of philosophers, which begins at Bacon, and which, through Hobbes, Newton, Locke, Hume, Herschel, is continued down to our own times. They have carried our national spirit into philosophy; they have been positive and practical; they have not soared above facts; they have not attempted out-of-the-way paths; they have cleared the human mind of its illusions, presumptions, and fancies. They have employed it in the only direction in which it can act; they only wished to mark out and light up the already well-trodden ways of the progressive sciences. They have not been willing to spend their labor vainly in other than explored and verified paths; they have aided in the great modern work, the discovery of applicable laws; they have contributed, as men of special attainments do, to the increase of man's power. Can you find many philosophers who have done as much?
You will tell me that our philosopher has clipped his wings, in order to strengthen his legs. Certainly; and he has acted wisely. Experience limits the career which it opens to us; it has given us our goal, but also our boundaries. We have only to observe the elements of which our experience is composed, and the facts from which it sets out, to understand that its range is limited. Its nature and its method confine its progress to a few steps. And, in the first place,[425] the ultimate laws of nature cannot be less numerous than the several distinct species of our sensations. We can easily reduce a movement to another movement, but not the sensation of heat to that of smell, or of color, or of sound, nor either of these to a movement. We can easily connect together phenomena of different degrees, but not phenomena differing in species. We find distinct sensations at the bottom of all our knowledge, as simple indecomposable elements, separated absolutely one from another, absolutely incapable of being reduced one to another. Let experience do what she will, she cannot suppress these diversities which constitute her foundation. On the other hand, experience, do what she will, cannot escape from the conditions under which she acts. Whatever be her province, it is bounded by time and space; the fact which she observes is limited and influenced by an infinite number of other facts to which she cannot attain. She is obliged to suppose or recognize some primordial condition from whence she starts, and which she does not explain.[426] Every problem has its accidental or arbitrary data: we deduce the rest from these, but there is nothing from which these can be deduced. The sun, the earth, the planets, the initial impulse of the heavenly bodies, the primitive chemical properties of substances, are such data.[427] If we possessed them all we could explain everything by them, but we could not explain these themselves. Mill says:
"Why these particular natural agents existed originally and no others, or why they are commingled in such and such proportions, and distributed in such and such a manner throughout space, is a question we cannot answer. More than this: we can discover nothing regular in the distribution itself; we can reduce it to no uniformity, to no law. There are no means by which, from the distribution of these causes, or agents, in one part of space, we could conjecture whether a similar distribution prevails in another."[428]
And astronomy, which just now afforded us the model of a perfect science, now affords us an example of a limited science. We can predict the numberless positions of all the planetary bodies; but we are obliged to assume, beside the primitive impulse and its amount, not only the force of attraction and its law, but also the masses and distances of all the bodies in question. We understand millions of facts, but it is by means of a hundred facts which we do not comprehend; we arrive at necessary results, but it is only by means of accidental antecedents; so that if the theory of our universe were completed there would still remain two great voids: one at the commencement of the physical world, the other at the beginning of the moral world; the one comprising the elements of being, the other embracing the elements of experience; one containing primary sensations, the other primitive agents. "Our knowledge," says Royer-Collard, "consists in tracing ignorance as far back as possible."
Can we at least affirm that these irreducible data are so only in appearance, and in relation to our mind? Can we say that they have causes, like the derived facts of which they are the causes? Can we conclude that every event, always and everywhere, happens according to laws, and that this little world of ours, so well-regulated, is a sort of epitome of the universe? Can we by aid of the axioms, quit our narrow confines, and affirm anything of the universe? In no wise; and it is here that Mill pushes his principles to their furthest consequences: for the law which attributes a cause to every event, has to him no other foundation, worth, or scope, than what it derives from experience. It has no inherent necessity; it draws its whole authority from the great number of cases in which we have recognized it to be true; it only sums up a mass of observations; it unites two data, which, considered in themselves, have no intimate connection; it joins antecedents generally to consequents generally, just as the law of gravitation joins a particular antecedent to a particular consequent; it determines a couple, as do all experimental laws, and shares in their uncertainty and in their restrictions. Listen to this bold assertion:
"I am convinced that anyone accustomed to abstraction and analysis, who will fairly exert his faculties for the purpose, will, when his imagination has once learnt to entertain the notion, find no difficulty in conceiving that in some one, for instance, of the many firmaments into which sidereal astronomy now divides the universe, events may succeed one another at random, without any fixed law; nor can anything in our experience, or in our mental nature, constitute a sufficient, or indeed any, reason for believing that this is nowhere the case. The grounds, therefore, which warrant us in rejecting such a supposition with respect to any of the phenomena of which we have experience, must be sought elsewhere than in any supposed necessity of our intellectual faculties."[429]
Practically, we may trust in so well-established a law; but
"In distant parts of the stellar regions, where the phenomena may be entirely unlike those with which we are acquainted, it would be folly to affirm confidently that this general law prevails, any more than those special ones which we have found to hold universally on our own planet. The uniformity in the succession of events, otherwise called the law of causation, must be received not as a law of the universe, but of that portion of it only which is within the range of our means of sure observation, with a reasonable degree of extension to adjacent cases. To extend it further is to make a supposition without evidence, and to which, in the absence of any ground from experience for estimating its degree of probability, it would be idle to attempt to assign any."[430]
We are, then, irrevocably driven back from the infinite: our faculties and our assertions cannot attain to it; we remain confined in a small circle; our mind reaches not beyond its experience; we can establish no universal and necessary connection between facts; such a connection probably does not even exist. Mill stops here; but certainly, by carrying out his idea to its full extent, we should arrive at the conception of the world as a mere collection of facts; no internal necessity would induce their connection or their existence; they would be simple, arbitrary, accidentally-existing facts. Sometimes, as in our system, they would be found assembled in such a manner as to give rise to regular recurrences; sometimes they would be so assembled that nothing of the sort would occur. Chance, as Democritus taught, would be at the foundation of all things. Laws would be the result of chance, and sometimes we should find them, sometimes not. It would be with existences as with numbers—decimal fractions, for instance, which, according to the chance of their two primitive factors, sometimes recur regularly, and sometimes not. This is certainly an original and lofty conception. It is the final consequence of the primitive and dominant idea, which we have discovered at the beginning of the system, which has transformed the theories of Definition, of Propositions, and of the Syllogism; which has reduced axioms to experimental truths; which has developed and perfected the theory of induction; which has established the goal, the limits, the province, and the methods of science; which everywhere, in nature and in science, has suppressed interior connections; which has replaced the necessary by the accidental; cause by antecedent; and which consists in affirming that every assertion which is not merely verbal forms in effect a couple, that is to say, joins together two facts which were separate by their nature.
An abyss of chance and an abyss of ignorance. The prospect is gloomy: no matter, if it be true. At all events, this theory of science is a theory of English science. Rarely, I grant you, has a thinker better summed up in his teaching the practice of his country; seldom has a man better represented, by his negations and his discoveries, the limits and scope of his race. The operations, of which he constructs science, are those in which the English excel all others, and those which he excludes from science are precisely those in which the English are deficient, more than any other nation. He has described the English mind, whilst he thought to describe the human mind. That is his glory, but it is also his weakness. There is in your idea of knowledge a flaw, of which the incessant repetition ends by creating the gulf of chance, from which, according to him, all things arise, and the gulf of ignorance, at whose brink, according to him, our knowledge ends. And see what comes of it. By cutting away from science the knowledge of first causes, that is, of divine things, you reduce men to become sceptical, positive, utilitarian, if they are cool-headed; or mystical, enthusiastic, methodistical, if they have lively imaginations. In this huge unknown void, which you place beyond our little world, passionate men and uneasy consciences find room for all their dreams; and men of cold judgment, despairing of arriving at any certain knowledge, have nothing left but to sink down to the search for practical means which may serve for the amelioration of our condition. It seems to me that these two dispositions are most frequently met with in an English mind. The religious and the positive spirit dwell there side by side, but separate. This produces an odd medley, and I confess that I prefer the way in which the Germans have reconciled science with faith.—But their philosophy is but badly written poetry.—Perhaps so.—But what they call reason, or intuition of principles, is only the faculty of building up hypotheses.—Perhaps so.—But the systems which they have constructed have not held their ground before experience.—I do not defend what they have done.—But their absolute, their subject, their object, and the rest, are but big words.—I do not defend their style.—What, then, do you defend?—Their idea of Causation.—You believe with them that causes are discovered by a revelation of the reason?—By no means.—You believe with us that our knowledge of causes is based on simple experience?—Still less.—You think, then, that there is a faculty, other than experience and reason, capable of discovering causes?—Yes.—You think there is an intermediate course between intuition and observation, capable of arriving at principles, as it is affirmed that the first is, capable of arriving at truths, as we find that the second is?—Yes.—What is it? Abstraction. Let us return to your original idea; I will endeavor to show in what I think it incomplete, and how you seem to me to mutilate the human mind. But my argument will be the formal one of an advocate, and requires to be stated at length.
Your starting-point is good: man, in fact, does not know anything of substances; he knows neither minds nor bodies; he perceives only transient, isolated, internal conditions; he makes use of these to affirm and name exterior states, positions, movements, changes, and avails himself of them for nothing else. He can only attain to facts, whether within or without, sometimes transient, when his impression is not repeated; sometimes permanent, when his impression, many times repeated, makes him suppose that it will be repeated as often as he wishes to experience it. He only grasps colors, sounds, resistances, movements: sometimes momentary and variable, sometimes like one another, and renewed. To group these facts more advantageously, he supposes, by an artifice of language, qualities and properties. We go even further than you: we think that there are neither minds nor bodies, but simply groups of present or possible movements or thoughts. We believe that there are no substances, but only systems of facts. We regard the idea of substance as a psychological illusion. We consider substance, force, and all the modern metaphysical existences, as the remains of scholastic entities. We think that there exists nothing but facts and laws, that is, events and the relations between them; and we recognize, with you, that all knowledge consists, first of all, in connecting or adding fact to fact. But when this is done, a new operation begins, the most fertile of all, which consists in reducing these complex into simple facts. A splendid faculty appears, the source of language, the interpreter of nature, the parent of religions and philosophies, the only genuine distinction, which according to its degree, separates man from the brute, and great from little men. I mean Abstraction, which is the power of isolating the elements of facts, and of considering them one by one. My eyes follow the outline of a square, and abstraction isolates its two constituent properties, the equality of its sides and angles. My fingers touch the surface of a cylinder, and abstraction isolates its two generative elements, the idea of a rectangle, and of the revolution of this rectangle about one of its sides as an axis. A hundred thousand experiments develop for me, by an infinite number of details, the series of physiological operations which constitute life; and abstraction isolates the law of this series, which is a round of constant loss and continual reparation. Twelve hundred pages teach me Mill's opinion on the various facts of science, and abstraction isolates his fundamental idea, namely, that the only fertile propositions are those which connect a fact with another not contained in the first. Everywhere the case is the same. A fact, or a series of facts, can always be resolved into its components. It is this resolution which forms our problem, when we ask what is the nature of an object. It is these components we look for when we wish to penetrate into the inner nature of a being. These we designate under the names of forces, causes, laws, essences, primitive properties. They are not new facts added to the first, but an essence or extract from them; they are contained in the first, they have no existence apart from the facts themselves. When we discover them, we do not pass from one fact to another, but from one to another aspect of the same fact; from the whole to a part, from the compound to the components. We only see the same thing under two forms; first, as a whole, then as divided: we only translate the same idea from one language into another, from the language of the senses into abstract language, just as we express a curve by an equation, or a cube as a function of its side. It signifies little whether this translation be difficult or not; or that we generally need the accumulation or comparison of a vast number of facts to arrive at it, and whether our mind may not often succumb before accomplishing it. However this may be, in this operation, which is evidently fertile, instead of proceeding from one fact to another, we go from the same to the same; instead of adding experiment to experiment, we set aside some portion of the first; instead of advancing, we pause to examine the ground we stand on. There are, thus, fruitful judgments, which, however, are not the results of experience: there are essential propositions, which, however, are not merely verbal: there is, thus, an operation, differing from experience, which acts by cutting down, instead of by addition; which, instead of acquiring, devotes itself to acquired data; and which, going further than observation, opening a new field to the sciences, defines their nature, determines their progress, completes their resources, and marks out their end.
This is the great omission of your system. Abstraction is left in the background, barely mentioned, concealed by the other operations of the mind, treated as an appendage of Experience; we have but to re-establish it in the general theory, in order to reform the particular theories in which it is absent.
To begin with Definitions. Mill teaches that there is no definition of things, and that when you define a sphere as the solid generated by the revolution of a semicircle about its diameter, you only define a name. Doubtless you tell me by this the meaning of a name, but you also teach me a good deal more. You state that all the properties of every sphere are derived from this generating formula; you reduce an infinitely complex system of facts to two elements; you transform sensible into abstract data; you express the essence of the sphere, that is to say, the inner and primordial cause of all its properties. Such is the nature of every true definition; it is not content with explaining a name, it is not a mere description; it does not simply indicate a distinctive property; it does not limit itself to that ticketing of an object which will cause it to be distinguished from all others. There are, besides its definition, several other ways of causing the object to be recognized; there are other properties belonging to it exclusively: we might describe a sphere by saying that, of all bodies having an equal surface, it occupies the most space; or in many other ways. But such descriptions are not definitions; they lay down a characteristic and derived property, not a generating and primitive one; they do not reduce the thing to its factors, and reconstruct it before our eyes; they do not show its inner nature and its irreducible elements. A definition is a proposition which marks in an object that quality from which its others are derived, but which is not derived from others. Such a proposition is not verbal, for it teaches the quality of a thing. It is not the affirmation of an ordinary quality, for it reveals to us the quality which is the source of the rest. It is an assertion of an extraordinary kind, the most fertile and valuable of all, which sums up a whole science, and in which it is the aim of every science to be summed up. There is a definition in every science, and one for each object. We do not, in every case, possess it, but we search for it everywhere. We have arrived at defining the planetary motion by the tangential force and attraction which compose it; we can already partially define a chemical body by the notion of equivalent, and a living body by the notion of type. We are striving to transform every group of phenomena into certain laws, forces, or abstract notions. We endeavor to attain in every object the generating elements, as we do attain them in the sphere, the cylinder, the circle, the cone, and in all mathematical loci. We reduce natural bodies to two or three kinds of movement—attraction, vibration, polarization—as we reduce geometrical bodies to two or three kinds of elements—the point, the movement, the line; and we consider our science partial or complete, provisional or definite, according as this reduction is approximate or absolute, imperfect or complete.
The same alteration is required in the Theory of Proof. According to Mill, we do not prove that Prince Albert will die by premising that all men are mortal, for that would be asserting the same thing twice over; but from the facts that John, Peter, and others, in short, all men of whom we have ever heard, have died.—I reply that the real source of our inference lies neither in the mortality of John, Peter, and company, nor in the mortality of all men, but elsewhere. We prove a fact, says Aristotle,[431] by showing its cause. We shall therefore prove the mortality of Prince Albert, by showing the cause which produces his death. And why will he die? Because the human body, being an unstable chemical compound, must in time be resolved; in other words, because mortality is added to the quality of man. Here is the cause and the proof. It is this abstract law which, present in nature, will cause the death of the prince, and which, being present to my mind, shows me that he will die. It is this abstract proposition which is demonstrative; it is neither the particular nor the general propositions. In fact the abstract proposition proves the others. If John, Peter, and others, are dead, it is because mortality is added to the quality of man. If all men are dead, or will die, it is still because mortality is added to the quality, of man. Here, again, the part played by Abstraction has been overlooked. Mill has confounded it with Experience: he has not distinguished the proof from the materials of the proof, the abstract law from the finite or indefinite number of its applications. The applications contain the law and the proof, but are themselves neither law nor proof. The examples of Peter, John, and others, contain the cause, but they are not the cause. It is not sufficient to add up the cases, we must extract from them the law. It is not enough to experimentalize, we must abstract. This is the great scientific operation. Syllogism does not proceed from the particular to the particular, as Mill says, nor from the general to the particular, as the ordinary logicians teach, but from the abstract to the concrete; that is to say, from cause to effect. It is on this ground that it forms part of science, the links of which it makes and marks out; it connects principles with effects; it brings together definitions and phenomena. It diffuses through the whole range of science that Abstraction which definition has carried to its summit.
Abstraction explains also axioms. According to Mill, if we know that when equal magnitudes are added to equal magnitudes the wholes are equal, or that two straight lines cannot enclose a space, it is by external ocular experiment, or by an internal experiment, by the aid of imagination. Doubtless we may thus arrive at the conclusion that two straight lines cannot enclose a space, but we might recognize it also in another manner. We might represent a straight line in imagination, and we may also form a conception of it by reason. We may either study its form or its definition. We can observe it in itself, or in its generating elements. I can represent to myself a line ready drawn, but I can also resolve it into its elements. I can go back to its formation, and discover the abstract elements which produce it, as I have watched the formation of the cylinder and discover the revolution of the rectangle which generated it. It will not do to say that a straight line is the shortest from one point to another, for that is a derived property; but I may say that it is the line described by a point, tending to approach towards another point, and towards that point only: which amounts to saying that two points suffice to determine a straight line; in other words, that two straight lines, having two points in common, coincide in their entire length; from which we see that if two straight lines approach to enclose a space, they would form but one straight line, and enclose nothing at all. Here is a second method of arriving at a knowledge of the axiom, and it is clear that it differs much from the first. In the first we verify; in the second we deduce it. In the first we find by experience that it is true; in the second we prove it to be true. In the first we admit the truth; in the second we explain it. In the first we merely remark that the contrary of the axiom is inconceivable; in the second we discover, in addition, that the contrary of the axiom is contradictory. Having given the definition of the straight line, we find that the axiom that two straight lines cannot enclose a space is comprised in it, and may be derived from it, as a consequent from a principle. In fact, it is nothing more than an identical proposition, which means that the subject contains its attribute; it does not connect two separate terms, irreducible one to the other; it unites two terms, of which the second is a part of the first. It is a simple analysis, and so are all axioms. We have only to decompose them, in order to see that they do not proceed from one object to a different one, but are concerned with one object only. We have but to resolve the notions of equality, cause, substance, time, and space into their abstracts, in order to demonstrate the axioms of equality, substance, cause, time, and space. There is but one axiom, that of identity. The others are only its applications or its consequences. When this is admitted, we at once see that the range of our mind is altered. We are no longer merely capable of relative and limited knowledge, but also of absolute and infinite knowledge; we possess in axioms facts which not only accompany one another, but one of which includes the other. If, as Mill says, they merely accompanied one another, we should be obliged to conclude with him, that perhaps this might not always be the case. We should not see the inner necessity for their connection, and should only admit it as far as our experience went; we should say that, the two facts being isolated in their nature, circumstances might arise in which they would be separate; we should affirm the truth of axioms only in reference to our world and mind. If, on the contrary, the two facts are such that the first contains the second, we should establish on this very ground the necessity of their connection; wheresoever the first may be found, it will carry the second with it, since the second is a part of it, and cannot be separated from it. Nothing can exist between them and divide them, for they are but one thing under different aspects. Their connection is therefore absolute and universal; and we possess truths which admit neither doubt nor limitation, nor condition, nor restriction. Abstraction restores to axioms their value, whilst it shows their origin; and we restore to science her dispossessed dominion, by restoring to the mind the faculty of which it had been deprived.
Induction remains to be considered: which seems to be the triumph of pure experience, while it is in reality, the triumph of abstraction. When I discover, by induction, that cold produces dew, or that the passage from the liquid to the solid state produces crystallization, I establish a connection between two abstract facts. Neither cold, nor dew, nor the passage from the liquid to the solid state, nor crystallization, exist in themselves. They are parts of phenomena, extracts from complex cases, simple elements included in compound aggregates. I withdraw and isolate them; I isolate dew in general from all local, temporary, special dews which I observe; I isolate cold in general from all special, various distinct colds, which may be produced by all varieties of texture, all diversities of substance, all inequalities of temperature, all complications of circumstances. I join an abstract antecedent to an abstract consequent, and I connect them, as Mill himself shows, by subtractions, suppressions, eliminations; I expel from the two groups, containing them, all the proximate circumstances; I discover the couple under the surroundings which obscure it; I detach, by a series of comparisons and experiments, all the subsidiary accidental circumstances which have clung to it, and thus I end by laying it bare. I seem to be considering twenty different cases, and in reality I only consider one; I appear to proceed by addition, and in fact I am performing subtraction. All the methods of Induction, therefore, are methods of Abstraction, and all the work of Induction is the connection of abstract facts.
We see now the two great moving powers of science, and the two great manifestations of nature. There are two operations, experience and abstraction; there are two kingdoms, that of complex facts, and that of simple elements. The first is the effect, the second the cause. The first is contained in the second, and is deduced from it, as a consequent from its principle. The two are equivalent: they are one and the same thing considered under two aspects. This magnificent moving universe, this tumultuous chaos of mutually dependent events, this incessant life, infinitely varied and multiplied, may be all reduced to a few elements and their relations. Our whole efforts result in passing from one to the other, from the complex to the simple, from facts to laws, from experiences to formulas. And the reason of this is evident; for this fact, which I perceive by the senses or the consciousness, is but a fragment, arbitrarily severed by my senses or my consciousness, from the infinite and continuous woof of existence. If they were differently constituted, they would intercept other fragments; it is the chance of their structure which determines what is actually perceived. They are like open compasses, which might be more or less extended; and the area of the circle which they describe is not natural, but artificial. It is so in two ways, both externally and internally. For, when I consider an event, I isolate it artificially from its natural surroundings, and I compose it artificially of elements which do not form a natural group. When I see a falling stone, I separate the fall from the anterior circumstances which are really connected with it; and I put together the fall, the form, the structure, the color, the sound, and twenty other circumstances which are really not connected with it. A fact, then, is an arbitrary aggregate, and at the same time an arbitrary severing;[432] that is to say, a factitious group, which separates things connected, and connects things that are separate. Thus, so long as we only regard nature by observation, we do not see it as it is: we have only a provisional and illusory idea of it. Nature is, in reality, a tapestry, of which we only see the reverse; this is why we try to turn it. We strive to discover laws; that is, the natural groups which are really distinct from their surroundings, and composed of elements really connected. We discover couples; that is to say, real compounds and real connections. We pass from the accidental to the necessary, from the relative to the absolute, from the appearance to the reality; and having found these first couples, we practice upon them the same operation as we did upon facts, for, though in a less degree, they are of the same nature. Though more abstract, they are still complex. They may be decomposed and explained. There is some ulterior reason for their existence. There is some cause or other which constructs and unites them. In their case, as well as for facts, we can search for generating elements into which they may be resolved, and from which they may be deduced. And this operation may be continued until we have arrived at elements wholly simple; that is to say, such that their decomposition would involve a contradiction. Whether we can find them or not, they exist; the axiom of causation would be falsified if they were absent. There are, then, indecomposable elements, from which are derived more general laws; and from these, again, more special laws; and from these the facts which we observe; just as in geometry there are two or three primitive notions, from which are deduced the properties of lines, and from these the properties of surfaces, solids, and the numberless forms which nature can produce, or the mind imagine. We can now comprehend the value and meaning of that axiom of causation which governs all things, and which Mill has mutilated. There is an inner constraining force which gives rise to every event, which unites every compound, which engenders every actual fact. This signifies, on the one hand, that there is a reason for everything; that every fact has its law; that every compound can be reduced to simple elements; that every product implies factors; that every quality and every being must be reducible from some superior and anterior term. And it signifies, on the other hand, that the product is equivalent to the factors, that both are but the same thing under different aspects; that the cause does not differ in nature from the effect; that the generating powers are but elementary properties; that the active force, by which we represent Nature to our minds, is but the logical necessity which mutually transforms the compound and the simple, the fact and the law. Thus we determine beforehand the limits of every science; and we possess the potent formula, which, establishing the invincible connection and the spontaneous production of existences, places in Nature the moving spring of Nature, whilst it drives home and fixes in the heart of every living thing the iron fangs of necessity.
Can we arrive at a knowledge of these primary elements? For my part, I think we can; and the reason is, that, being abstractions, they are not beyond the region of facts, but are comprised in them, so that we have only to extract them from the facts. Besides, being the most abstract, that is, the most general of all things, there are no facts which do not comprise them, and from which we cannot extract them. However limited our experience may be, we can arrive at these primary notions; and it is from this observation that the modern German metaphysicians have started, in attempting their vast constructions. They understood that there are simple notions, that is to say, indecomposable abstract facts, that the combinations of these engender all others, and that the laws for their mutual union or contrarieties, are the primary laws of the universe. They tried to attain to these ideas, and to evolve, by pure reason, the world as observation shows it to us. They have partly failed; and their gigantic edifice, factitious and fragile, hangs in ruins, reminding one of those temporary scaffoldings which only serve to mark out the plan of a future building. The reason is, that with a high notion of our powers, they had no exact view of their limits. For we are outflanked on all sides by the infinity of time and space; we find ourselves thrown in the midst of this monstrous universe like a shell on the beach, or an ant at the foot of a steep slope. Here Mill is right. Chance is at the end of all our knowledge, as on the threshold of all our postulates: we vainly try to rise, and that by conjecture, to an initial state; but this state depends on the preceding one, which depends on another, and so on; and thus we are forced to accept it as a pure postulate, and to give up the hope of deducing it, though we know that it ought to be deduced. It is so in all sciences, in geology, natural history, physics, chemistry, psychology, history, and the primitive accidental fact extends its effects into all parts of the sphere in which it is comprised. If it had been otherwise, we should have neither the same planets, nor the same chemical compounds, nor the same vegetables, nor the same animals, nor the same races of men, nor, perhaps, any of these kinds of beings. If an ant were taken into another country, it would see neither the same trees, nor insects, nor dispositions of the soil, nor changes of the atmosphere, nor, perhaps, any of these forms of existence. There is, then, in every fact and in every object, an accidental and local part, a vast portion, which, like the rest, depends on primitive laws, but not directly, only through an infinite circuit of consequences in such a way that between it and the primitive laws there is an infinite hiatus, which can only be bridged over by an infinite series of deductions.
Such is the inexplicable part of phenomena, and this is what the German metaphysicians tried to explain. They wished to deduce from their elementary theorems the form of the planetary system, the various laws of physics and chemistry, the main types of life, the progress of human civilizations and thought. They contorted their universal formulae with the view of deriving from them particular cases; they took indirect and remote consequences as direct and proximate ones; they omitted or suppressed the great work which is interposed between the first laws and the final consequences; they discarded Chance from their construction, as a basis unworthy of science; and the void so left, badly filled up by deceptive materials, caused the whole edifice to fall to ruins.
Does this amount to saying, that in the facts with which this little corner of the universe furnishes us, everything is local? By no means. If an ant were capable of making experiments, it might attain to the idea of a physical law, a living form, a representative sensation, an abstract thought; for a foot of ground, on which there is a thinking brain, includes all these. Therefore, however limited be the field of the mind, it contains general facts; that is, facts spread over very vast external territories, into which its limitation prevents it from penetrating. If the ant were capable of reasoning, it might construct arithmetic, algebra, geometry, mechanics; for a movement of half an inch contains in the abstract, time, space, number, and force: all the materials of mathematics: therefore, however limited the field of a mind's researches be, it includes universal data; that is, facts spread over the whole region of time and space. Again, if the ant were a philosopher, it might evolve the ideas of existence, of nothingness, and all the materials of metaphysics; for any phenomenon, interior or exterior, suffices to present these materials: therefore, however limited the field of a mind be, it contains absolute truths; that is, such that there is no object from which they could be absent. And this must necessarily be so; for the more general a fact is, the fewer objects need we examine to meet with it. If it is universal, we meet with it everywhere; if it is absolute, we cannot escape meeting it. This is why, in spite of the narrowness of our experience, metaphysics, I mean the search for first causes, is possible, but on condition that we remain at a great height, that we do not descend into details, that we consider only the most simple elements of existence, and the most general tendencies of nature. If anyone were to collect the three or four great ideas in which our sciences result, and the three or four kinds of existence which make up our universe; if he were to compare those two strange quantities which we call duration and extension, those principal forms or determinations of quantity which we call physical laws, chemical types, and living species, and that marvellous representative power, the Mind, which, without falling into quantity, reproduces the other two and itself; if he discovered among these three terms—the pure quantity, the determined quantity, and the suppressed quantity[433]—such an order that the first must require the second, and the second the third; if he thus established that the pure quantity is the necessary commencement of Nature, and that Thought is the extreme term at which Nature is wholly suspended; if, again, isolating the elements of these data, he showed that they must be combined just as they are combined, and not otherwise: if he proved, moreover, that there are no other elements, and that there can be no other, he would have sketched out a system of metaphysics without encroaching on the positive sciences, and have attained the source, without being obliged to descend to trace the various streams.
In my opinion, these two great operations, Experience as you have described it, and Abstraction, as I have tried to define it, comprise in themselves all the resources of the human mind, the one in its practical, the other in its speculative direction. The first leads us to consider nature as an assemblage of facts, the second as a system of laws: the exclusive employment of the first is English; that of the second, German. If there is a place between these two nations, it is ours. We have extended the English ideas in the eighteenth century; and now we can, in the nineteenth, add precision to German ideas. Our business is to restrain, to correct, to complete the two types of mind, one by the other, to combine them together, to express their ideas in a style generally understood, and thus to produce from them the universal mind.
We went out. As it ever happens in similar circumstances, each had caused the other to reflect, and neither had convinced the other. But our reflections were short: in the presence of a lovely August morning, all arguments fall to the ground. The old walls, the rain-worn stones, smiled in the rising sun. A fresh light rested on their embrasures, on the keystones of the cloisters, on the glossy ivy leaves. Roses and honeysuckles climbed the walls, and their flowers quivered and sparkled in the light breeze. The fountains murmured in the vast lonely courts. The beautiful town stood out from the morning's mist, as adorned and tranquil as a fairy palace, and its robe of soft rosy vapor was indented, as an embroidery of the Renaissance, by a border of towers, cloisters, and palaces, each enclosed in verdure and decked with flowers. The architecture of all ages had mingled their arches, trefoils, statues, and columns; time had softened their tints; the sun united them in its light, and the old city seemed a shrine to which every age and every genius had successively added a jewel. Beyond this, the river rolled its broad sheets of silver: the mowers stood up to the knee in the high grass of the meadows. Myriads of buttercups and meadow-sweets; grasses, bending under the weight of their gray heads, plants sated with the dew of the night, swarmed in the rich soil. Words cannot express this freshness of tints, this luxuriance of vegetation. The more the long line of shape receded, the more brilliant and full of life the flowers appeared. On seeing them, virgin and timid in their gilded veil, I thought of the blushing cheeks and fine modest eyes of a young girl who puts on for the first time her necklace of jewels. Around, as though to guard them, enormous trees, four centuries old, extended in regular lines; and I found in them a new trace of that practical good sense which has effected revolutions without committing ravages; which, while reforming in all directions, has destroyed nothing; which has preserved both its trees and its constitution, which has lopped off the dead branches without levelling the trunk; which alone, in our days, among all nations, is in the enjoyment not only of the present, but of the past.