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every assertion which is not merely | philosophy is but bad.ry-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.

the faculty of building up hypotheses

-Perhaps so.—But the systems which § 2.-ABSTRACTION

they have constructed have not beld

their ground before experience.- I do I.

not defend what they have done.—Bu:

their absolute, their subject, their ob An abývs of chance and an abyss of ject, and the rest, are but big words.georance. The prospect is gloomy : do not defend their style.- Whal no matter, if it be true. At all events, then, do you defend ?—Their idea oi this theory of science is a theory of Causation. —You believe with them English science. Rarely, I grant you, that causes are discovered by a revelahas a thinker better summed up in his tion of the reason !-By no means. teaching the practice of his country; You believe with us that our knowledge seldom has a man better represented of causes is based on simple experiby his negations and his discoveries the ence?-Still less.—You think, then, that limits and scope of his race. The op- there is a faculty, other than experience erations, of which he constructs science, and reason, capable of discovering are those in which the English excel all causes ?-Yes.—You think there is an others, and those which he excludes from intermediate course between intuition science are precisely those in which the and observation, capable of arriving at English are deficient more than any other principles, as it is affirmed that the nation. He has described the English first is, capable of arriving at truths, as mind whilst he thought to describe the we find that the second is ?-Yes.human mind. That is his glory, but it is What is it? Abstraction.

Let us realso his weakness. There is in your turn to your original idea ; I will enidea of knowledge a flaw of which the deavor to show in what I think it inincessant repetition ends by creating complete and how you seem to me to the gulf of chance, from which, accord. mutilate the human mind. But my arguing to him, all things arise, and the gulf ment will be the formal one of an advo of 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

II. from science the knowledge of first causes, that is, of divine things, you re- Your starting-point is good: man, in duce men to become skeptical, positive, fact, does not know any thing, of subutilitarian, if they are are cool-headed; stances ; he knows neither minds nor or mystical, enthusiastic, methodistical, bodies; he perceives only transient, if they have lively imaginations. In isolated, internal conditions; he makes this huge unknown void which you use of these to affirm and name ex: place beyond our little world, passion. terior states, positions, movements, ate men and uneasy consciences find changes, and avails himself of them for room for all their dreams; and men of nothing else. He can only attain to cold judgment, despairing of arriving facts, whether within or without, some at any certair. knowledge, have nothing times transient, when his impression is left but to sink down to the search for not repeated; sometimes permanent, practical means which may serve for when his impression many times ro the amelioration of our condition. It peated, makes him suppose that it will seems to me that these two dispositions be repeated as often as he wishes to are most frequently met with in an experience it. He only grasps colors, English mind." The religious and the sounds, resistances, movements, some positive spirit dwell there side by side, times momentary and variable, some but separate. This produces an odd times like one another, and renewed. medley, and I confess that I prefer the To group these facts more advanta: way in which the Germans have recon- geously, he supposes, by an artifice al ciled science with faith. But their language, qualities and properties

We go even further than you : we think I causes, laws, essences, prin itive prop, that there are neither minds nor bodies, erties. They are not new facts added but simply groups of present or possi- to the first, but an essence or extract ble movements or thoughts. We be- from them; they are contained in the lieve that there are no substances, but first, they have no existence apart from only systems of facts. We regard the the facts themselves. When we dis: idea of substance as a psychological cover them, we do not pass from one illusion. We consider substance, force, fact to another, but from one to another and all modern metaphysical existences, aspect of the same fact; from the whole as the remains of scholastic entities. to a part, from the compound to the We think that there exists nothing but components. We only see the same facts and laws, that is, events and the thing under two forms; first, as a whole relations between them; and we recog. then as divided : we only translate the nize, with you, that all knowiedge cour same idea from one language into an sists first of all in connecting or adding other, from the language of the senses fact to fact. But when this is done, a into abstract language, just as we exnew operation begins, the most fertile press a curve by an equation, or a cube ef all, which consists in reducing these as a function of its side. It signifies complex into simple facts. A splendid little whether this translation be diffifaculty appears, the source of language, cult or not; or that we generally need the interpreter of nature, the parent of the accumulation or comparison of a religions and philosophies, the only vast number of facts to arrive at it, and genuine distinction, which, according whether our mind may not often suc: to its degree, separates man from the cumb before accomplishing it. Howbrute, and great from little men. I ever this may be, in this operation, mean Abstraction, which is the power which is evidently fertile, instead of of isolating the elements of facts, and proceeding from one fact to another, of considering them one by one. My we go from the same to the same; ineyes follow the outline of a square, and stead of adding experiment to experiabstraction isolates its two constituent ment, we set aside some portion of the properties, the equality of its sides and first; instead of advancing, we pause angles. My fingers touch the surface to examine the ground we stand on. of a cylinder, and abstraction isolates There are, thus, fruitful judgments, its two generative elements, the idea of which, however, are not the results of a rectangle, and of the revolution of experience: there are essential propo this rectangle about one of its sides as sitions, which, however, are not merely an axis. A hundred thousand experi- verbal: there is, thus, an operation, ments develop for me, by an infinite differing from experience, which acts number of details, the series of physi- by cutting down instead of by addition ; ological operations which constitute which, instead of acquiring, devotes life; and abstraction isolates the law itself to acquired data; and which, of this series, which is a round of con- going farther than observation, openstant loss and continual reparation. ing a new field to the sciences, defines Twelve hundred pages teach me Mill's their nature, determines their progress, opinion on the various facts of science, completes their resources, and marks and abstraction isolates his fundamen: out their end. tal idea, namely, that the only fertile This is the great omission of your propositions are those which connect system. Abstraction is left in the ifact with another not contained in the background, barely mentioned, confirst. Everywhere the case is the same. cealed by the other operations of the A fact, or a series of facts, can always mind, treated as an appendage of Exbe resolved into its components. It is perience; we have but to re-establish this resolution which forms our prob- it in the general theory, in order to relem, when we ask what is the nature of form the part cular theories in which an object. It is these components we it is absent. look for when we wish to penetrate into

we designate under the names of forces To begin with Definitions


teaches that there is no definition of define a chemical body by the notion things, and that when you define a of equivalent, and a living body by the sphere as the solid generated by the notion of type. We are striving to revolution of a semicircle about its transform every group of phenomeca diameter, you only define a name. into certain laws, forces, or abstract Doubtless you tell me by this the notions. We endeavor to attain in meaning of a name, but you also teach every object the generating elements, me a good deal more. You state that as we do attain them in the sphere, the all the properties of every sphere are cylinder, the circle, the cone, and in all derived from this generating formula; mathematical loci. We reduce natura rou reduce an infinitely complex sys- bodies to two or three kinds of movemeus tem of facts to two elements ; you -attraction, vibration, polarization.ransform sensible into abstract data ; as we reduce geometrical bodies to two you express the essence of the sphere, or three kinds of elements—the point, that is to say, the inner and primordial the movement, the line; and we con cause of all its properties. Such is the sider our science partial or complete, nature of every true definition; it is provisional or definite, according as not content with explaining a name, this reduction is approximate or abso it is not a mere description; it does lute, imperfect or complete. not simply indicate

distinctive prop erty; it does not limit itself to that

IV. ticketing of an object which will cause The same alteration is required in it to be distinguished from all others. the Theory of Proof. According to There are, besides its definition, sev. Mill, we do not prove that Prince Al. eral other ways of causing the object bert will die by premising that all men to be recognized; there are other are mortal, for that would be asserting properties belonging to it exclusively : the same thing twice over; but from we might describe a sphere by saying the facts that John, Peter, and others. that, of all bodies having an equal sur- in short, all men of whom we have face, it occupies the most space; or in ever heard, have died.— I reply that many other ways. But such descrip- the real source of our inference lies tions are not definitions ; they lay neither in the mortality of John, Peter, down a characteristic and derived and company, nor in the mortality of property, not a generating and primi- all men, but elsewhere. We prove a tive one; they do not reduce the thing fact, says Aristotle, * by showing its to its factors, and reconstruct it before

We shall therefore prove the our eyes ; they do not show its inner mortality of Prince Albert by showing nature and its irreducible elements. the cause which produces his death. A definition is a proposition which And why will he die? Because the humarks in an object that quality from man body, being an unstable chemical which its others are derived, but which compound, must in time be resolved; is not derived from others. Such a in other words, because mortality is proposition is not verbal, for it teaches added to the quality of man. Here the quality of a thing. It is not the is the cause and the proof. It is this affirmation of an ordinary quality, for abstract law which, present in nature, it reveals to us the quality which is the will cause the death of the prince, and source of the rest. It is an assertion which, being present to my mind, shows of an extraordinary kind, the most fer

me that he will die. It is this abstract cile and valuable of all, which sums up proposition which is demonstrative ; a whole science, and in which it is the it is neither the particular nor the gen. aim of every science to be summed up. eral propositions. In fact, the abstract There is a definition in every science, proposition proves the others. If John, and one for each object. We do not Peter, and others are dead, it is because in every case possess it, but we search mortality is added to the quality of man. for it everywhere. We have arrived If all men are dead, or will die, it is ai defining the planetary motion by the still because mortality is added to the tangential force and attraction which

• See the Posterior Analytics, which are much compose it; we can aiready partially magtrior to the Prior-si airiwv kai apotépwr.


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quality of man. Here, again, the part, tangle which generated .t. It will not played by Abstraction has been over- do to say that a straight line is the looked. Mill has confounded it with shortest from one point to another, Experience : he has not distinguished for that is a derived property; but i the proof from the materials of the may say that it is the line described by proof, the abstract law from the finite a point, tending to approach towards or indefinite number of its applications. another point, and towards that point The applications contain the law, and only: which amounts to saying that two the proof, but are themselves nei. points suffice to determine a straight ther law nor proof. The examples of line ; in other words, that two straight Peter, John, and others, contain the lines, having two points in comcause, but they are not the ca'ise. mon, coincide in their entire length; It is not sufficient to add up the from which we see that if two straight cases, we must extract from them lines approach to enclose a space, they

he law. It is not enough to experi- would form but one straight line, and mentalize, we must abstract. This is enclose nothing at all. Here is a second the great scientific operation. Syllo method of arriving at a knowledge of gism does not proceed from the par- the axiom, and it is clear that it differs ticular to the particular, as Mill says, much from the first. In the first we nor from the general to the particular, verify; in the second we deduce it. In as the ordinary logicians teach, but the first we find by experience that it from the abstract to the concrete ; that is true ; in the second we prove it to is to say, from cause to effect. It is be true. In the first we admit the on this ground that it forms part of truth ; in the second we explain it. In science, the links of which it makes the first we merely remark that the conand marks out ; it connects principles trary of the axiom is inconceivable; in with effects; it brings together defini- the second we discover in addition that tions and phenomena. It diffuses the contrary of the axiom is contradic: through the whole range of science tory Having given the definition of that Abstraction which definition has the straight line, we find that the axiom carried to its summit.

that two straight lines cannot enclose a

space is comprised in it, and may be V.

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. It 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 rerent a straight line in imagination, and solve the notions of equality, cause, se may also form a conceptior of it by substance, time, and space into their

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 e ements. I can go back to its for- quences. When this is admitted, we matior, 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


knowledge ; we posses in axioms facts produced by all varieties of texture, al which not only accompany one another, diversities of substance all inequalities but one of which includes the other. If, of temperature, all cumplications of as Mill says, they merely accompanied circumstances. I join an abstract an. one another, we should be obliged to tecedent to an abstract consequent, and conclude with him, that perhaps this I connect them, as Mill himself shows, might not always be the case. We by subtractions, suppressions, elimina should not see the inner necessity for tions; I expel from the two groups their connection, and should only admit containing them, all the proximate cir it as far as our experience went; we cumstances ; I discover the couple un should say that, the two facts being der the surroundings which obscure it ; isolated in their nature, circumstances I detach, by a series of comparisons might arise in which they would be and experiments, all the subsidiary separate ; we should affirń the truth accidental circumstances which have of axioms only in reference to our clung to it, and thus I end hy laying it world and mind. If, on the contrary, bare. I seem to be considering twenty the two facts are such that the first different cases, and in reality I only contains the second, we should estab- consider one ; I appear to proceed by lish on this very ground the necessity addition, and in fact I am performing of their connection; wheresoever the subtraction. All the methods of In. first may be found, it will carry the duction, therefore, are methods of Absecond with it, since the second is a straction, and all the work of Induction part of it, and cannot be separated is the connection of abstract facts. from it. Nothing can exist between them and divide them, for they are but

VII. one thing under different aspects. Their connection is therefore absolute We see now the two great moving and universal; and we possess truths powers of science, and the two great which admit neither doubt nor limita manifestations of nature. There are tion, nor condition, nor restriction. Ab- two operations, experience and abstracstraction restores to axioms their value, tion; there are two kingdoms, that of whilst it shows their origin; and we complex facts and that of simple ele. restore to science her dispossessed ments. The first is the effect, the dominion, by restoring to the mind the second the cause. The first is confaculty of which it had been deprived. tained in the second, and is deduce

from it, as a consequent from its prir. VI.

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 in. triumph of abstraction. When I dis- cessant life, infinitely varied and multicover by induction hat 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 Lae 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 woof of existence. If they were differdew in general from all local, tempo- ently constituted, they would intercept rary, special dews which I observe; I other fragments; it is the chance of isolate cold in general from all special, their structure which determines what various, distinct colds which may be lis actually perceive I. They are like

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