IV.

According

The same alteration is required in the Theory of Proof. 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,' 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 experimentalise, 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.

V.

Abstraction explains also axióms. 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

'See the Posterior Analytics, which are much superior to the Prior-di' alias καὶ προτέρων.

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 recognise 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 apprcach 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. No circumstance 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.

VI.

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 crystallisation, I establish a connection between two abstract facts. Neither cold, nor dew, nor the passage from the liquid to the solid state, nor crystallisation, 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.

VII.

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

1

from its principle. Both 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 amount in passing from one to the other, from the complex to the simple, from facts to laws, from experiences to formulæ. 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 colour, 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; 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 practise 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

1 An eminent student of physical science said to me: 'A fact is a superposition

of laws.'

VOL. II.

2 K

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.

VIII.

For my

Can we arrive at a knowledge of these primary elements? 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 motions, 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 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