[Section VI.—The Methods of Induction]
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.
[Section VII.—Experience and Abstraction]
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.
[Section VIII.—Idea and Limits of Metaphysics]
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.