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." 6

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 Mill's "Logic," ii. 104.

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.

PART II.-ABSTRACTION

Section I.-Agreement of this Philosophy with the English Mind

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 coolheaded; 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.

Section II.-The Nature of Abstraction

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.

Section III.-Definitions Explain the Abstract Generating Elements of Things

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