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every assertion which is not merely | philosophy is but bad y-written poetry verba. forms in effect a couple, that is -Perhaps so.-But what they call rea to say, joins together two facts which, son, or intuition of principles, is only were separate by their nature.
§ 2. ABSTRACTION
the faculty of building up hypotheses
An abyss of chance and an abyss of gnorance. 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 gulfment will be the formal one of an advoof ignorance, at whose brink, according cate, and requires to be stated at length. 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 skeptical, positive, utilitarian, if they are 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
Your starting-point is good: man, in fact, does not know any thing 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, some times transient, when his impression is not repeated; sometimes permanent, when his impression many times re peated, 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, some times like one another, and renewed. To group these facts more advanta geously, he supposes, by an artifice of language, qualities and properties.
erties. 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 dis cover 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 sam thing under two forms; first, as a whole then as divided: we only translate the same idea from one language into an other, 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 suc cumb 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 farther than observation, opening a new field to the sciences, defines their nature, determines their progress, completes their resources, and marks out their end.
We go even further than you: we think | causes, laws, essences, prin itive prop 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 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 cosists 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 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,
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 part cular 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 ransform 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 ferale 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 aiready 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 natura bodies to two or three kinds of movement attraction, vibration, polarizationas we reduce geometrical bodies to twe or three kinds of elements-the point, the movement, the line; and we con sider 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 Al bert 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 gen. eral 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
* See the Posterior Analytics, which are much prior to the Prior-di airíwv kai #potéрwv.
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 he 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.
tangle which generated .t. 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 1 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 contradic tory 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 Abstraction explains also axioms. than an identical proposition, which According to Mill, if we know that means that the subject contains its when equal magnitudes are added to attribute; it does not connect two sepequal magnitudes the wholes are equal, arate terms, irreducible one to the or that two straight lines cannot en- other; it unites two terms, of which close a space, it is by external ocular ex- the second is a part of the first. periment, or by an internal experiment is a simple analysis, and so are all by the aid of imagination. Doubtless we axioms. We have only to decompose may thus arrive at the conclusion that them, in order to see that they do not two straight lines cannot enclose a proceed from one object to a differspace, but we might recognize it also ent one, but are concerned with one in another manner. We might repre- object only. We have but to resent a straight line in imagination, and solve the notions of equality, cause, we may also form a conceptior of it by substance, time, and space into their reason. We may either study its form abstracts, in order to demonstrate the or its definition. We can observe it axioms of equality, substance, cause, in itself, or in its generating elements. time, and space. There is but one I can represent to myself a line ready axiom, that of identity. The others drawn, but I can also resolve it into are only its applications or its conseits elements. I can go back to its for- quences. When this is admitted, we mation, and discover the abstract ele- at once see that the range of our mind ments which produce it, as I have is altered. We are no longer merely watched the formation of the cylinder capable of relative and limited knowl and discover the revolution of the rec-edge, but also of absolute and infinite
diversities of substance all inequalities of temperature, all complications of circumstances. I join an abstract an tecedent to an abstract consequent, and I connect them, as Mill himself shows, by subtractions, suppressions, elimina tions; I expel from the two groups containing them, all the proximate cir cumstances; I discover the couple un der 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 Ab straction, and all the work of Induction is the connection of abstract facts.
knowledge; we posses in axioms facts | produced by all varieties of texture, all 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.
We see now the two great moving powers of science, and the two great manifestations of nature. There are two operations, experience and abstrac tion; 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 deduce from it, as a consequent from its prir. ciple. The two are equivalent, they are one and the same thing considered Induction remains to be considered, under two aspects. This magnificen. which seems to be the triumph of pure moving universe, this tumultuous chaos experience, while it is, in reality, the of mutually dependent events, this intriumph of abstraction. When I dis- cessant life, infinitely varied and multicover by induction that coid produces plied, may be all reduced to a few dew, or that the passage from the li- elements and their relations. Our quid to the solid state produces crys- whole efforts result in passing from one tallization, I establish a connection be- to the other, from the complex to the tween two abstract facts. Neither simple, from facts to laws, from expeold, nor dew, nor the passage from riences to formulæ. And the reason the liquid to the solid state, nor crys- of this is evident; for this fact which I tallization, exist in themselves. They perceive by the senses or the conscious are parts of phenomena, extracts from ness is but a fragment arbitrarily complex cases, simple elements in- severed by my senses or my conscious cluded in compound aggregates. Iness from the infinite and continuous 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
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 perceive 1. They are like