CHAPTER FIFTH

PHILOSOPHY—STUART MILL

Section I.—Lack of General Ideas

When at Oxford, some years ago, during the meeting of the British Association, I met, amongst the few students still in residence, a young Englishman, a man of intelligence, with whom I became intimate.[396] He took me in the evening to the New Museum, well filled with specimens. Here short lectures were delivered, new models of machinery were set to work; ladies were present and took an interest in the experiments; on the last day, full of enthusiasm, "God Save the Queen" was sung. I admired this zeal, this solidity of mind, this organization of science, these voluntary subscriptions, this aptitude for association and for labor, this great machine pushed on by so many arms, and so well fitted to accumulate, criticise, and classify facts. But yet in this abundance, there was a void; when I read the Transactions, I thought I was present at a congress of heads of manufactories. All these learned men verified details and exchanged recipes. It was as though I listened to foremen, busy in communicating their processes for tanning leather, or dyeing cotton: general ideas were wanting. I used to regret this to my friend; and in the evening, by his lamp, amidst that great silence in which the university town lay wrapped, we both tried to discover its reasons.

Section II.—Why Metaphysics are Lacking

One day I said to him: You lack philosophy—I mean, what the Germans call metaphysics. You have learned men, but you have no thinkers. Your God impedes you. He is the Supreme Cause, and you dare not reason on causes, out of respect for him. He is the most important personage in England, and I see clearly that he merits his position; for he forms part of your constitution, he is the guardian of your morality, he judges in final appeal on all questions whatsoever, he replaces with advantage the prefects and gendarmes with whom the nations on the Continent are still encumbered. Yet, this high rank has the inconvenience of all official positions; it produces a cant, prejudices, intolerance, and courtiers. Here, close by us, is poor Mr. Max Müller, who, in order to acclimatize the study of Sanscrit, was compelled to discover in the Vedas the worship of a moral God, that is to say, the religion of Paley and Addison. Some time ago, in London, I read a proclamation of the Queen, forbidding people to play cards, even in their own houses, on Sundays.[397] It seems that, if I were robbed, I could not bring my thief to justice without taking a preliminary religious oath; for the judge has been known to send a complainant away who refused to take the oath, deny him justice, and insult him into the bargain. Every year, when we read the Queen's speech in your papers, we find there the compulsory mention of Divine Providence, which comes in mechanically, like the invocation to the immortal gods on the fourth page of a rhetorical declamation; and you remember that once, the pious phrase having been omitted, a second communication was made to Parliament for the express purpose of supplying it. All these cavillings and pedantries indicate to my mind a celestial monarchy; naturally it resembles all others; I mean that it relies more willingly on tradition and custom than on examination and reason. A monarchy never invited men to verify its credentials. As yours is, however, useful, well adapted to you, and moral, you are not revolted by it; you submit to it without difficulty, you are, at heart, attached to it; you would fear, in touching it, to disturb the constitution and morality. You leave it in the clouds, amidst public homage. You fall back upon yourselves, confine yourselves to matters of fact, to minute dissections, to experiments in the laboratory. You go culling plants and collecting shells. Science is deprived of its head; but all is for the best, for practical life is improved, and dogma remains intact.

Section III.—Mill's Philosophical Method

You are truly French, he answered; you ignore facts, and all at once find yourself settled in a theory. I assure you that there are thinkers amongst us, and not far from hence, at Christ Church, for instance. One of them, the professor of Greek, has spoken so deeply on inspiration, the creation and final causes, that he is out of favor. Look at this little collection which has recently appeared, "Essays and Reviews;" your philosophic freedom of the last century, the latest conclusions of geology and cosmogony, the boldness of German exegesis, are here in abstract. Some things are wanting, amongst others the waggeries of Voltaire, the misty jargon of Germany, and the prosaic coarseness of Comte; to my mind, the loss is small. Wait twenty years, and you will find in London the ideas of Paris and Berlin.—But they will still be the ideas of Paris and Berlin. Whom have you that is original?—Stuart Mill.—Who is he?—A political writer. His little book "On Liberty" is as admirable as Rousseau's "Contrat Social" is bad.—That is a bold assertion.—No, for Mill decides as strongly for the independence of the individual as Rousseau for the despotism of the State.—Very well, but that is not enough to make a philosopher. What besides is he?—An economist who goes beyond his science, and subordinates production to man, instead of man to production.—Well, but this is not enough to make a philosopher. Is he anything else?—A logician.—Very good; but of what school?—Of his own. I told you he was original.—Is he Hegelian?—By no means; he is too fond of facts and proofs.—Does he follow Port-Royal?—Still less; he is too well acquainted with modern sciences.—Does he imitate Condillac?—Certainly not; Condillac has only taught him to write well.—Who, then, are his friends?—Locke and Comte in the first rank; then Hume and Newton.—Is he a system-monger, a speculative reformer?—He has too much sense for that; he only arranges the best theories, and explains the best methods. He does not attitudinize majestically in the character of a restorer of science; he does not declare, like your Germans, that his book will open up a new era for humanity. He proceeds gradually, somewhat slowly, often creepingly, through a multitude of particular facts. He excels in giving precision to an idea, in disentangling a principle, in discovering it amongst a number of different facts; in refuting, distinguishing, arguing. He has the astuteness, patience, method, and sagacity of a lawyer.—Very well, you admit that I was right. A lawyer, an ally of Locke, Newton, Comte, and Hume; we have here only English philosophy; but no matter. Has he reached a grand conception of the universe?—Yes.—Has he an individual and complete idea of nature and the mind?—Yes.—Has he combined the operations and discoveries of the intellect under a single principle which puts them all in a new light?—Yes; but we have to discover this principle.—That is your business, and I hope you will undertake it.—But I shall fall into abstract generalities.—There is no harm in that?—But this close reasoning will be like a quick-set hedge. We will prick our fingers with it.—But three men out of four would cast aside such speculations as idle.—So much the worse for them. For in what does the life of a nation or a century consist, except in the formation of such theories? We are not thoroughly men unless so engaged. If some dweller in another planet were to come down here to ask us the nature of our race, we should have to show him the five or six great ideas which we have formed of the mind and the world. That alone would give him the measure of our intelligence. Expound to me your theory, and I shall go away better instructed than after having seen the masses of brick, which you call London and Manchester.

Part I.—Experience

Section I.—The Object of Logic

Let us begin, then, at the beginning, like logicians. Mill has written on logic. What is logic? It is a science. What is its object? The sciences; for, suppose that you have traversed the universe, and that you know it thoroughly: stars, earth, sun, heat, gravity, chemical affinities, the species of minerals, geological revolutions, plants, animals, human events, all that classifications and theories explain and embrace, there still remain these classifications and theories to be learnt. Not only is there an order of beings, but also an order of the thoughts which represent them; not only plants and animals, but also botany and zoology; not only lines, surfaces, volumes, and numbers, but also geometry and arithmetic. Sciences, then, are as real things as facts themselves, and therefore, as well as facts, become the subject of study. We can analyze them as we analyze facts, investigate their elements, composition, order, relations, and object. There is, therefore, a science of sciences; this science is called logic, and is the subject of Mill's work. It is no part of logic to analyze the operations of the mind, memory, the association of ideas, external perception, etc.; that is the business of psychology. We do not discuss the value of such operations, the veracity of our consciousness, the absolute certainty of our elementary knowledge; this belongs to metaphysics. We suppose our faculties to be at work, and we admit their primary discoveries. We take the instrument as nature has provided it, and we trust to its accuracy. We leave to others the task of taking its mechanism to pieces, and the curiosity which criticises its results. Setting out from its primitive operations, we inquire how they are added to each other; how they are combined; how one is convertible into another; how, by dint of additions, combinations, and transformations, they finally compose a system of connected and developed truths. We construct a theory of science, as others construct theories of vegetation, of the mind, or of numbers. Such is the idea of logic; and it is plain that it has, as other sciences, a real subject-matter, its distinct province, its manifest importance, its special method, and a certain future

Section II.—Discussion of Ideas

Having premised so much, we observe that all these sciences which form the subject of logic are but collections of propositions, and that each proposition merely connects or separates a subject and an attribute, that is, two names, a quality and a substance; that is to say, a thing and another thing. We must then ask what we understand by a thing, what we indicate by a name; in other words, what it is we recognize in objects, what we connect or separate, what is the subject-matter of all our propositions and all our science. There is a point in which all our several items of knowledge resemble one another. There is a common element which, continually repeated, constitutes all our ideas. There is, as it were, a minute primitive crystal which, indefinitely and variously repeating itself, forms the whole mass, and which, once known, teaches us beforehand the laws and composition of the complex bodies which it has formed.

Now, when we attentively consider the idea which we form of anything, what do we find in it? Take first, substances: that is to say, Bodies and Minds.[398] This table is brown, long, wide, three feet high, judging by the eye: that is, it forms a little spot in the field of vision; in other words, it produces a certain sensation on the optic nerve. It weighs ten pounds: that is, it would require to lift it an effort less than for a weight of eleven pounds, and greater than for a weight of nine pounds; in other words, it produces a certain muscular sensation. It is hard and square, which means that, if first pushed, and then run over by the hand, it will excite two distinct kinds of muscular sensations. And so on. When I examine closely what I know of it, I find that I know nothing else except the impressions it makes upon me. Our idea of a body comprises nothing else than this: we know nothing of it but the sensations it excites in us; we determine it by the nature, number, and order of these sensations; we know nothing of its inner nature, nor whether it has one; we simply affirm that it is the unknown cause of these sensations. When we say that a body has existed in the absence of our sensations we mean simply that if, during that time, we had been within reach of it, we should have had sensations which we have not had. We never define it save by our present or past, future or possible, complex or simple impressions. This is so true, that philosophers like Berkeley have maintained, with some show of truth, that matter is a creature of the imagination, and that the whole universe of sense is reducible to an order of sensations. It is at least so, as far as our knowledge is concerned; and the judgments which compose our sciences have reference only to the impressions by which things are manifested to us.

So, again, with the mind. We may well admit that there is in us a soul, an "ego," a subject or recipient of our sensations, and of our other modes of being, distinct from those sensations and modes of existence; but we know nothing of it. Mr. Mill says:

"For, as our conception of a body is that of an unknown exciting cause of sensations, so our conception of a mind is that of an unknown recipient, or percipient, of them; and not of them alone, but of all our other feelings. As body is the mysterious something which excites the mind to feel, so mind is the mysterious something which feels, and thinks. It is unnecessary to give in the case of mind, as we gave in the case of matter, a particular statement of the sceptical system by which its existence as a Thing in itself, distinct from the series of what are denominated its states, is called in question. But it is necessary to remark, that on the inmost nature of the thinking principle, as well as on the inmost nature of matter, we are, and with our faculties must always remain, entirely in the dark. All which we are aware of, even in our own minds, is a certain 'thread of consciousness'; a series of feelings, that is, of sensations, thoughts, emotions, and volitions, more or less numerous and complicated."[399]

We have no clearer idea of mind than of matter; we can say nothing more about it than about matter. So that substances, of whatever kind, bodies or minds, within or without us, are never for us more than tissues, more or less complex, more or less regular, of which our impressions and modes of being form all the threads.

This is still more evident in the case of attributes than of substances. When I say that snow is white, I mean that, when snow is presented to my sight, I have the sensation of whiteness. When I say that fire is hot, I mean that, when near the fire, I have the sensation of heat. We call a mind devout, superstitious, meditative, or gay, simply meaning that the ideas, the emotions, the volitions, designated by these words, recur frequently in the series of its modes of being.[400] When we say that bodies are heavy, divisible, movable, we mean simply that, left to themselves, they will fall; when cut, they will separate; or, when pushed, they will move: that is, under such and such circumstances they will produce such and such a sensation in our muscles, or our sight. An attribute always designates a mode of our being, or a series of our modes of being. In vain we disguise these modes by grouping, concealing them under abstract words, dividing and transforming them, so that we are frequently puzzled to recognize them: whenever we pierce to the basis of our words and ideas, we find them and nothing but them. Mill says:

"Take the following example: A generous person is worthy of honour. Who would expect to recognize here a case of coexistence between phenomena? But so it is. The attribute which causes a person to be termed generous is ascribed to him on the ground of states of his mind, and particulars of his conduct; both are phenomena; the former are facts of internal consciousness, the latter, so far as distinct from the former, are physical facts, or perceptions of the senses. Worthy of honour, admits of a similar analysis. Honour, as here used, means a state of approving and admiring emotion, followed on occasion by corresponding outward acts. 'Worthy of honour' connotes all this, together with an approval of the act of showing honour. All these are phenomena; states of internal consciousness, accompanied or followed by physical facts. When we say, A generous person is worthy of honour, we affirm coexistence between the two complicated phenomena connoted by the two terms respectively. We affirm, that wherever and whenever the inward feelings and outward facts implied in the word generosity have place, then and there the existence and manifestation of an inward feeling, honour, would be followed in our minds by another inward feeling, approval."[401]

In vain we turn about as we please, we remain still in the same circle. Whether the object be an attribute or a substance, complex or abstract, compound or simple, its material is to us always the same; it is made up only of our modes of being. Our mind is to nature what a thermometer is to a boiler: we define the properties of nature by the impressions of our mind, as we indicate the conditions of the boiling water by the changes of the thermometer. Of both we know but condition and changes; both are made up of isolated and transient facts; a thing is for us but an aggregate of phenomena. These are the sole elements of our knowledge: consequently the whole effort of science will be to link facts to facts.

Section III.—The Two Corner-Stones of Logic

This brief phrase is the abstract of the whole system. Let us master it, for it explains all Mill's theories. He has defined and restated everything, from this starting-point. In all forms and all degrees of knowledge, he has recognized only the knowledge of facts, and of their relations.

Now we know that logic has two corner-stones: the Theories of Definition and of Proof. From the days of Aristotle logicians have spent their time in polishing them. They have only dared to touch them respectfully, as if they were sacred. At most, from time to time, some innovator ventured to turn them over cautiously, to put them in a better light. Mill shapes, cuts, turns them over, and replaces them both in a similar manner and by the same means.

Section IV.—Theory of Definitions

I am quite aware that nowadays men laugh at those who reason on definitions; the laughers deserve to be laughed at. There is no theory more fertile in universal and important results; it is the root by which the whole tree of human science grows and lives. For to define things is to mark out their nature. To introduce a new idea of definition is to introduce a new idea of the nature of things; it is to tell us what beings are, of what they are composed, into what elements they are capable of being resolved. In this lies the merit of these dry speculations; the philosopher seems occupied with arranging mere formulas; the fact is, that in them he encloses the universe.

Take, say logicians, an animal, a plant, a feeling, a geometrical figure, an object or group of objects of any kind. Doubtless the object has its properties, but it has also its essence. It is manifested to the outer world by an indefinite number of effects and qualities; but all these modes of being are the results or products of its inner nature. There is within it a certain hidden substratum which alone is primitive and important, without which it can neither exist nor be conceived, and which constitutes its being and our notion of it.[402] They call the propositions which denote this essence definitions, and assert that the best part of our knowledge consists of such propositions.

On the other hand, Mill says that these kinds of propositions teach us nothing; they show the mere sense of a word, and are purely verbal.[403] What do I learn by being told that man is a rational animal, or that a triangle is a space contained by three lines? The first part of such a phrase expresses, by an abbreviative word, what the second part expresses in a developed phrase. You tell me the same thing twice over; you put the same fact into two different expressions; you do not add one fact to another, but you go from one fact to its equivalent. Your proposition is not instructive. You might collect a million such, my mind would remain entirely void; I should have read a dictionary, but not have acquired a single piece of knowledge. Instead of saying that essential propositions are important, and those relating to qualities merely accessory, you ought to say that the first are accessory, and the second important. I learn nothing by being told that a circle is a figure formed by the revolution of a straight line about one of its points as centre; I do learn something when told that the chords which subtend equal arcs in the circle are themselves equal, or that three given points determine the circumference. What we call the nature of a being is the connected system of facts which constitutes that being. The nature of a carnivorous mammal consists in the fact that the property of giving milk, and all its implied peculiarities of structure, are combined with the possession of sharp teeth, instincts of prey, and the corresponding faculties. Such are the elements which compose its nature. They are facts linked together as mesh to mesh in a net. We perceive a few of them; and we know that beyond our present knowledge and our future experience, the network extends to infinity its interwoven and manifold threads. The essence or nature of a being is the indefinite sum of its properties. Mill says:

"The definition, they say, unfolds the nature of the thing: but no definition can unfold its whole nature; and every proposition in which any quality whatever is predicated of the thing, unfolds some part of its nature. The true state of the case we take to be this: All definitions are of names, and of names only; but in some definitions it is clearly apparent, that nothing is intended except to explain the meaning of the word; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing, corresponding to the word."[404]

Abandon, then, the vain hope of eliminating from properties some primitive and mysterious being, the source and abstract of the whole; leave entities to Duns Scotus; do not fancy that, by probing your ideas in the German fashion, by classifying objects according to genera and species like the schoolmen, by reviving the nominalism of the Middle Ages or the riddles of Hegelian metaphysics, you will ever supply the want of experience. There are no definitions of things; if there are definitions, they only define names. No phrase can tell me what a horse is; but there are phrases which will inform me what is meant by these five letters. No phrase can exhaust the inexhaustible sum of qualities which make up a being; but several phrases may point out the facts corresponding to a word. In this case definition is possible, because we can always make an analysis, which will enable us to pass from the abstract and summary term to the attributes which it represents, and from these attributes to the inner or concrete feelings which constitute their foundation. From the term "dog" it enables us to rise to the attributes "mammiferous, carnivorous," and others which it represents; and from these attributes to the sensations of sight, of touch, of the dissecting knife, on which they are founded. It reduces the compound to the simple, the derived to the primitive. It brings back our knowledge to its origin. It transforms words into facts. If some definitions, such as those of geometry, seem capable of giving rise to long sequences of new truths,[405] it is because, in addition to the explanation of a word, they contain the affirmation of a thing. In the definition of a triangle there are two distinct propositions—the one stating that "there may exist a figure bounded by three straight lines"; the other, that "such a figure may be termed a triangle." The first is a postulate, the second a definition. The first is hidden, the second evident; the first may be true or false, the second can be neither. The first is the source of all possible theorems as to triangles, the second only resumes in a word the facts contained in the other. The first is a truth, the second is a convention; the first is a part of science, the second an expedient of language. The first expresses a possible relation between three straight lines, the second gives a name to this relation. The first alone is fruitful, because it alone conforms to the nature of every fruitful proposition, and connects two facts. Let us, then, understand exactly the nature of our knowledge: it relates either to words or to things, or to both at once. If it is a matter of words, as in the definition of names, it attempts to refer words to our primitive feelings: that is to say, to the facts which form their elements. If it relates to beings, as in propositions about things, its whole effort is to link fact to fact, in order to connect the finite number of known properties with the infinite number to be known. If both are involved, as in the definitions of names which conceal a proposition relating to things, it attempts to do both. Everywhere its operation is the same. The whole matter, in any case, is to understand each other—that is, to revert to facts, or to learn—that is, to add facts to facts.

Section V.—Theory of Proof

The first rampart is destroyed; our adversaries take refuge behind the second—the Theory of Proof. This theory has passed for two thousand years for a substantiated, definite, unassailable truth. Many have deemed it useless, but no one has dared to call it false. On all sides it has been considered as an established theorem. Let us examine it closely and attentively. What is a proof? According to logicians, it is a syllogism. And what is a syllogism? A group of three propositions of this kind: "All men are mortal; Prince Albert is a man; therefore Prince Albert is mortal." Here we have the type of a proof, and every complete proof is conformable to this type. Now what is there, according to logicians, in this proof? A general proposition concerning all men, which gives rise to a particular proposition concerning a certain man. From the first we pass to the second, because the second is contained in the first; from the general to the particular, because the particular is comprised in the general. The second is but an instance of the first; its truth is contained beforehand in that of the first, and this is why it is a truth. In fact, as soon as the conclusion is no longer contained in the premises, the reasoning is false, and all the complicated rules of the Middle Ages have been reduced by the Port-Royalists to this single rule, "The conclusion must be contained in the premises." Thus the entire process of the human mind in its reasonings, consists in recognizing in individuals what is known of a whole class; in affirming in detail what has been established for the aggregate; in laying down a second time, and piecemeal, what has been laid down once for all at first.

By no means, replies Mill; for if it were so, our reasoning would be good for nothing. It would not be a progress, but a repetition. When I have affirmed that all men are mortal, I have affirmed implicitly that Prince Albert is mortal. In speaking of the whole class, that is to say, of all the individuals of the class, I have spoken of each individual, and therefore of Prince Albert, who is one of them. I say nothing new, then, when I now mention him expressly. My conclusion teaches me nothing; it adds nothing to my positive knowledge; it only puts in another shape a knowledge which I already possessed. It is not fruitful, but purely verbal. If, then, reasoning be what logicians represent it, it is not instructive. I know as much of the subject at the beginning of my reasoning as at the end. I have transformed words into other words; I have been moving, without gaining ground. Now this cannot be the case; for, in fact, reasoning does teach us new truths. I learn a new truth when I discover that Prince Albert is mortal, and I discover it by dint of reasoning; for, since he is still alive, I cannot have learnt it by direct observation. Thus logicians are mistaken; and beyond the scholastic theory of syllogism, which reduces reasoning to substitutions of words, we must look for a positive theory of proof, which shall explain how it is that, by the process of reasoning, we discover facts.

For this purpose, it is sufficient to observe that general propositions are not the true proof of particular propositions. They seem so, but are not. It is not from the mortality of all men that I conclude Prince Albert to be mortal; the premises are elsewhere, and in the background. The general proposition is but a memento^ a sort of abbreviative register, to which I have consigned the fruit of my experience. This memento may be regarded as a notebook, to which we refer to refresh our memory; but it is not from the book that we draw our knowledge, but from the objects which we have seen. My memento is valuable, only for the facts which it recalls. My general proposition has no value, except for the particular facts which it sums up.

"The mortality of John, Thomas, and company, is, after all, the whole evidence we have for the mortality of the Duke of Wellington. Not one iota is added to the proof by interpolating a general proposition. Since the individual cases are all the evidence we can possess, evidence which no logical form into which we choose to throw it can make greater than it is; and since that evidence is either sufficient in itself, or, if insufficient for the one purpose, cannot be sufficient for the other; I am unable to see why we should be forbidden to take the shortest cut from these sufficient premisses to the conclusion, and constrained to travel the 'high priori road' by the arbitrary fiat of logicians."[406]

"The true reason which makes us believe that Prince Albert will die is, that his ancestors, and our ancestors, and all the other persons who were their contemporaries, are dead. These facts are the true premises of our reasoning." It is from them that we have drawn the general proposition; they have taught us its scope and truth; it confines itself to mentioning them in a shorter form; it receives its whole substance from them; they act by it and through it, to lead us to the conclusion to which it seems to give rise. It is only their representative, and on occasion they do without it. Children, ignorant people, animals, know that the sun will rise, that water will drown them, that fire will burn them, without employing this general proposition. They reason, and we reason, too, not from the general to the particular, but from particular to particular:

"All inference is from particulars to particulars; general propositions are merely registers of such inferences already made, and short formulæ for making more: The major premiss of a syllogism, consequently, is a formula of this description: and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula: the real logical antecedent, or premisses, being the particular facts from which the general proposition was collected by induction. Those facts, and the individual instances which supplied them, may have been forgotten; but a record remains, not indeed descriptive of the facts themselves, but showing how those cases may be distinguished respecting which the facts, when known, were considered to warrant a given inference. According to the indications of this record we draw our conclusion; which is to all intents and purposes, a conclusion from the forgotten facts. For this it is essential that we should read the record correctly: and the rules of the syllogism are a set of precautions to ensure our doing so."[407]

"If we had sufficiently capacious memories, and a sufficient power of maintaining order among a huge mass of details, the reasoning could go on without any general propositions; they are mere formulae for inferring particulars from particulars."[408]

Here, as before, logicians are mistaken: they gave the highest place to verbal operations, and left the really fruitful operations in the background. They gave the preference to words over facts. They perpetuated the nominalism of the Middle Ages. They mistook the explanation of names for the nature of things, and the transformation of ideas for the progress of the mind. It is for us to overturn this order in logic, as we have overturned it in science, to exalt particular and instructive facts, and to give them in our theories that superiority and importance which our practice has conferred upon them for three centuries past.

Section VI.—Theory of Axioms

There remains a kind of philosophical fortress in which the Idealists have taken refuge. At the origin of all proof are Axioms, from which all proofs are derived. Two straight lines cannot enclose a space; two things, equal to a third, are equal to one another; if equals be added to equals, the wholes are equal. These are instructive propositions, for they express, not the meanings of words, but the relations of things. And, moreover, they are fertile propositions; for arithmetic, algebra, and geometry are all the result of their truth. On the other hand, they are not the work of experience, for we need not actually see with our eyes two straight lines in order to know that they cannot enclose a space; it is enough for us to refer to the inner mental conception which we have of them: the evidence of our senses is not needed for this purpose; our belief arises wholly, with its full force, from the simple comparison of our ideas. Moreover, experience follows these two lines only to a limited distance, ten, a hundred, a thousand feet; and the axiom is true for a thousand, a hundred thousand, a million miles, and for an unlimited distance. Thus, beyond the point at which experience ceases, it is no longer experience which establishes the axiom. Finally, the axiom is a necessary truth; that is to say, the contrary is inconceivable. We cannot imagine a space enclosed by two straight lines: as soon as we imagine the space enclosed, the two lines cease to be straight; and as soon as we imagine the two lines to be straight, the space ceases to be enclosed. In the assertion of axioms, the constituent ideas are irresistibly drawn together. In the negation of axioms, the constituent ideas inevitably repel each other. Now this does not happen with truths of experience: they state an accidental relation, not a necessary connection; they lay down that two facts are connected, and not that they must be connected; they show us that bodies are heavy, not that they must be heavy. Thus, axioms are not, and cannot be the results of experience. They are not so, because we can form them mentally without the aid of experience; they cannot be so, because the nature and scope of their truths lie beyond the limits of experience. They have another and a deeper source. They have a wider scope, and they come from elsewhere.

Not so, answers Mill. Here again you reason like a schoolman; you forget the facts concealed behind your conceptions; for examine your first argument. Doubtless you can discover, without making use of your eyes, and by purely mental contemplation, that two straight lines cannot enclose a space; but this contemplation is but a displaced experiment. Imaginary lines here replace real lines: you construct the figure in your mind instead of on paper: your imagination fulfils the office of a diagram on paper: you trust to it as you trust to the diagram, and it is as good as the other; for in regard to figures and lines the imagination exactly reproduces the sensation. What you have seen with your eyes open, you will see again exactly the same a minute afterwards with your eyes closed; and you can study geometrical properties, transferred to the field of mental vision, as accurately as if they existed in the field of actual sight. There are, therefore, experiments of the brain as there are ocular ones; and it is after just such an experiment that you deny to two straight lines, indefinitely prolonged, the property of enclosing a space. You need not, for this purpose, pursue them to infinity: you need only transfer yourself in imagination to the point where they converge, and there you have the impression of a bent line, that is of one which ceases to be straight.[409] Your presence there, in imagination, takes the place of an actual presence; you can affirm by it what you affirmed by your actual presence, and as positively. The first is only the second in a more commodious form, with greater flexibility and scope. It is like using a telescope instead of the naked eye; the revelations of the telescope are propositions of experience; so are those of the imagination. As to the argument which distinguishes axioms from propositions of experience under the pretext that the contraries of the latter are conceivable, while the contraries of axioms are inconceivable, it is nugatory, for this distinction does not exist. Nothing prevents the contraries of certain propositions of experience from being conceivable, and the contraries of others inconceivable. That depends on the constitution of our minds. It may be that in some cases the mind may contradict its experience, and in others not. It is possible that in certain cases our conceptions may differ from our perceptions, and sometimes not. It may be that, in certain cases, external sight is opposed to internal, and in certain others not. Now, we have already seen that in the case of figures, the internal sight exactly reproduces the external. Therefore, in axioms of figures, the mental sight cannot be opposed to the actual; imagination cannot contradict sensation. In other words, the contraries of such axioms will be inconceivable. Thus axioms, although their contraries are inconceivable, are experiments of a certain class, and it is because they are so that their contraries are inconceivable. At every point there results this conclusion, which is the abstract of the system: every instructive or fruitful proposition is derived from experience, and is simply a connecting together of facts.

Section VII.—Theory of Induction

Hence it follows that Induction is the only key to nature. This theory is Mill's masterpiece. Only so thorough-going a partisan of experience could have constructed the theory of Induction.

What, then, is Induction?

"Induction is that operation of the mind by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times."[410]

This is the reasoning by which, having observed that Peter, John, and a greater or less number of men have died, we conclude that all men will die. In short, induction connects "mortality" with the quality of "man"; that is to say, connects two general facts ordinarily successive, and asserts that the first is the Cause of the second.

This amounts to saying that the course of nature is uniform. But induction does not set out from this axiom, it leads up to it; we do not find it at the beginning, but at the end of our researches.[411] Fundamentally, experience presupposes nothing beyond itself. No à priori principle comes to authorize or guide her. We observe that this stone has fallen, that this hot coal has burnt us, that this man has died, and we have no other means of induction except the addition and comparison of these little isolated and transient facts. We learn by simple practical experience that the sun gives light, that bodies fall, that water quenches thirst, and we have no other means of extending or criticising these inductions than by other like inductions. Every observation and every induction draws its value from itself, and from similar ones. It is always experience which judges of experience, and induction of induction. The body of our truths has not, then, a soul distinct from it, and vivifying it; it subsists by the harmony of all its parts taken as a whole, and by the vitality of each part taken separately.

"Why is it that, with exactly the same amount of evidence, both negative and positive, we did not reject the assertion that there are black swans, while we should refuse credence to any testimony which asserted that there were men wearing their heads underneath their shoulders? The first assertion was more credible than the latter. But why more credible? So long as neither phenomenon had been actually witnessed, what reason was there for finding the one harder to be believed than the other? Apparently because there is less constancy in the colours of animals than in the general structure of their internal anatomy. But how do we know this? Doubtless from experience. It appears, then, that we need experience to inform us in what degree, and in what cases, or sorts of cases, experience is to be relied on. Experience must be consulted in order to learn from it under what circumstances arguments from it will be valid. We have no ulterior test to which we subject experience in general; but we make experience its own test. Experience testifies, that among the uniformities which it exhibits, or seems to exhibit, some are more to be relied on than others; and uniformity, therefore, may be presumed, from any given number of instances, with a greater degree of assurance, in proportion as the case belongs to a class in which the uniformities have hitherto been found more uniform."[412]

Experience is the only test, and it is to be found everywhere.

Let us then consider how, without any help but that of experience, we can form general propositions, especially the most numerous and important of all, those which connect two successive events, by saying that the first is the cause of the second.

Cause is a great word; let us examine it. It carries in itself a whole philosophy. From the idea we have of Cause depend all our notions of nature. To give a new idea of Causation is to transform human thought; and we shall see how Mill, like Hume and Comte, but better than they, has put this idea into a new shape.

What is a cause? When Mill says that the contact of iron with moist air produces rust, or that heat dilates bodies, he does not speak of the mysterious bond by which metaphysicians connect cause and effect. He does not busy himself with the intimate force and generative virtue which certain philosophers insert between the thing producing and the product. Mill says:

"The only notion of a cause, which the theory of induction requires, is such a notion as can be gained from experience. The Law of Causation, the recognition of which is the main pillar of inductive science, is but the familiar truth, that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it; independently of all consideration respecting the ulterior mode of production of phenomena, and of every other question regarding the nature of 'Things in themselves.'"[413]

No other foundation underlies these two expressions. We mean simply, that everywhere, always, the contact of iron with the moist air will be followed by the appearance of rust; the application of heat by the dilatation of bodies: "The real cause is the whole of these antecedents."[414] "There is no scientific foundation for distinguishing between the cause of a phenomenon and the conditions of its happening.... The distinction drawn between the patient and the agent is purely verbal. The cause, then, philosophically speaking, is the sum total of the conditions, positive and negative, taken together; the whole of the contingencies of every description, which being realized, the consequent invariably follows."[415] Much argument has been expended on the word necessary: "If there be any meaning which confessedly belongs to the term necessity, it is unconditionalness. That which is necessary, that which must be, means that which will be, whatever supposition we may make in regard to all other things."[416] This is all we mean, when we assert that the notion of cause includes the notion of necessity. We mean that the antecedent is sufficient and complete, that there is no need to suppose any additional antecedent, that it contains all requisite conditions, and that no other condition need exist. To follow unconditionally, then, is the whole notion of cause and effect. We have none else. Philosophers are mistaken when they discover in our will a different type of causation, and declare it an example of efficient cause in act and in exercise. We sec nothing of the kind, but there, as elsewhere, we find only continuous successions. We do not see a fact engendering another fact, but a fact accompanying another. "Our will," says Mill, "produces our bodily actions as cold produces ice, or as a spark produces an explosion of gunpowder." There is here, as elsewhere, an antecedent, the resolution or state of mind, and a consequent, the effort or physical sensation. Experience connects them, and enables us to foresee that the effort will follow the resolution, as it enables us to foresee that the explosion of gunpowder will follow the contact of the spark. Let us then have done with all these psychological illusions, and seek only, under the names of cause and effect, for phenomena which form pairs without exception or condition.

Now, to establish these connections of phenomena, Mill discovers four methods, and only four—namely, the Methods of Agreement,[417] of Difference,[418] of Residues,[419] and of Concomitant Variations.[420] These are the only ways by which we can penetrate into nature. There are no other, and these are everywhere. And they all employ the same artifice, that is to say, elimination; for, in fact, induction is nothing else. You have two groups, one of antecedents, the other of consequents, each of them containing more or fewer elements, ten, for example. To what antecedent is each consequent joined? Is the first consequent joined to the first antecedent, or to the third, or sixth? The whole difficulty and the only possible solution lie there. To resolve the difficulty, and to effect the solution, we must eliminate, that is, exclude those antecedents which are not connected with the consequent we are considering.[421] But as we cannot exclude them effectually, and as in nature the pair of phenomena we are seeking is always surrounded with circumstances, we collect collect various cases, which by their diversity enable the mind to lop off these circumstances, and to discover the pair of phenomena distinctly. In short, we can only perform induction by discovering pairs of phenomena; we form these only by isolation; we isolate only by means of comparisons.

Section VIII.—Applications of the Theory of Induction

These are the rules; an example will make them clearer. We will show you the methods in exercise; here is an example which combines nearly the whole of them, namely, Dr. Well's theory of dew. I will give it to you in Mill's own words, which are so clear that you must have the pleasure of pondering over them: "We must separate dew from rain and the moisture of fogs, and limit the application of the term to what is really meant, which is, the spontaneous appearance of moisture on substances exposed in the open air when no rain or visible wet is falling."[422] What is the cause of the phenomena we have thus defined, and how was that cause discovered?

"'Now, here we have analogous phenomena, in the moisture which bedews a cold metal or stone when we breathe upon it; that which appears on a glass of water fresh from the well in hot weather; that which appears on the inside of windows when sudden rain or hail chills the external air; that which runs down our walls when, after a long frost, a warm moist thaw comes on.' Comparing these cases, we find that they all contain the phenomenon which was proposed as the subject of investigation. Now 'all these instances agree in one point: the coldness of the object dewed, in comparison with the air in contact with it.' But there still remains the most important case of all, that of nocturnal dew: does the same circumstance exist in this case? 'Is it a fact that the object dewed is colder than the air? Certainly not, one would at first be inclined to say; for what is to make it so? But ... the experiment is easy; we have only to lay a thermometer in contact with the dewed substance, and hang one at a little distance above it, out of reach of its influence. The experiment has been therefore made; the question has been asked, and the answer has been invariably in the affirmative. Whenever an object contracts dew, it is colder than the air.'

"Here then is a complete application of the Method of Agreement, establishing the fact of an invariable connection between the deposition of dew on a surface, and the coldness of that surface, compared with the external air. But which of these is cause, and which effect? or are they both effects of something else? On this subject the Method of Agreement can afford us no light: we must call in a more potent method. 'We must collect more facts, or, which comes to the same thing, vary the circumstances; since every instance in which the circumstances differ is a fresh fact: and especially, we must note the contrary or negative cases, i.e., where no dew is produced': for a comparison between instances of dew and instances of no dew, is the condition necessary to bring the Method of Difference into play.

"'Now, first, no dew is produced on the surface of polished metals, but it is very copiously on glass, both exposed with their faces upwards, and in some cases the under side of a horizontal plate of glass is also dewed.' Here is an instance in which the effect is produced, and another instance in which it is not produced; but we cannot yet pronounce, as the canon of the Method of Difference requires, that the latter instance agrees with the former in all its circumstances except one: for the differences between glass and polished metals are manifold, and the only thing we can as yet be sure of is, that the cause of dew will be found among the circumstances by which the former substance is distinguished from the latter."