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."

To detect this particular circumstance of difference, we have but one practicable method, that of Concomitant Variations:

"'In the cases of polished metal and polished glass, the contrast shows evidently that the substance has much to do with the phenomenon; therefore let the substance alone be diversified as much as possible, by exposing polished surfaces of various kinds. This done, a scale of intensity becomes obvious. Those polished substances are found to be most strongly dewed which conduct heat worst, while those which conduct well resist dew most effectually....'

"The conclusion obtained is, that _cœteris paribus_ the deposition of dew is in some proportion to the power which the body possesses of resisting the passage of heat; and that this, therefore (or something connected with this), must be at least one of the causes which assist in producing the deposition of dew on the surface.

"'But if we expose rough surfaces instead of polished, we sometimes find this law interfered with. Thus, roughened iron, especially if painted over or blackened, becomes dewed sooner than varnished paper: the kind of surface, therefore, has a great influence. Expose, then, the same material in very diversified states as to surface' (that is, employ the Method of Difference to ascertain concomitance of variations),' and another scale of intensity becomes at once apparent; those surfaces which part with their heat most readily by radiation, are found to contract dew most copiously....'

"The conclusion obtained by this new application of the method is, that _cœteris paribus_ the deposition of dew is also in some proportion to the power of radiating heat; and that the quality of doing this abundantly (or some cause on which that quality depends) is another of the causes which promote the deposition of dew on the substance.

"'Again, the influence ascertained to exist of substance and surface, leads us to consider that of texture; and here, again, we are presented on trial with remarkable differences, and with a third scale of intensity, pointing out substances of a close firm texture, such as stones, metals, etc., as unfavourable, but those of a loose one, as cloth, velvet, wool, eiderdown, cotton, etc., as eminently favourable to the contraction of dew.' The Method of Concomitant Variations is here, for the third time, had recourse to; and, as before, from necessity, since the texture of no substance is absolutely firm or absolutely loose. Looseness of texture, therefore, or something which is the cause of that quality, is another circumstance which promotes the deposition of dew; but this third cause resolves itself into the first, viz., the quality of resisting the passage of heat: for substances of loose texture 'are precisely those which are best adapted for clothing, or for impeding the free passage of heat from the skin into the air, so as to allow their outer surfaces to be very cold, while they remain warm within....'

"It thus appears that the instances in which much dew is deposited, which are very various, agree in this, and, so far as we are able to observe, in this only, that they either radiate heat rapidly or conduct it slowly: qualities between which there is no other circumstance of agreement than that by virtue of either, the body tends to lose heat from the surface more rapidly than it can be restored from within. The instances, on the contrary, in which no dew, or but a small quantity of it, is formed, and which are also extremely various, agree (so far as we can observe) in nothing except in not having this same property....

"This doubt we are now able to resolve. We have found that in every such instance, the substance must be one which, by its own properties or laws, would, if exposed in the night, become colder than the surrounding air. The coldness, therefore, being accounted for independently of the dew, while it is proved that there is a connection between the two, it must be the dew which depends on the coldness; or, in other words, the coldness is the cause of the dew.

"This law of causation, already so amply established, admits, however, of efficient additional corroboration in no less than three ways. First, by deduction from the known laws of aqueous vapour when diffused through air or any other gas, and though we have not yet come to the Deductive Method, we will not omit what is necessary to render this speculation complete. It is known, by direct experiment, that only a limited quantity of water can remain suspended in the state of vapour at each degree of temperature, and that this maximum grows less and less, as the temperature diminishes. From this it follows deductively, that if there is already as much vapour suspended as the air will contain at its existing temperature, any lowering of that temperature will cause a portion of the vapour to be condensed, and become water. But, again, we know deductively, from the laws of heat, that the contact of the air with a body colder than itself, will necessarily lower the temperature of the stratum of air immediately applied to its surface; and will therefore cause it to part with a portion of its water, which accordingly will, by the ordinary laws of gravitation or cohesion, attach itself to the surface of the body, thereby constituting dew. This deductive proof, it will have been seen, has the advantage of proving at once causation as well as coexistence; and it has the additional advantage that it also accounts for the exceptions to the occurrence of the phenomenon, the cases in which, although the body is colder than the air, yet no dew is deposited, by showing that this will necessarily be the case when the air is so under-supplied with aqueous vapour, comparatively to its temperature, that even when somewhat cooled by the contact of the colder body, it can still continue to hold in suspension all the vapour which was previously suspended in it: thus, in a very dry summer there are no dews, in a very dry winter no hoar frost....

"The second corroboration of the theory is by direct experiment, according to the canon of the Method of Difference. We can, by cooling the surface of any body, find in all cases some temperature (more or less inferior to that of the surrounding air, according to its hygrometric condition) at which dew will begin to be deposited. Here, too, therefore, the causation is directly proved. We can, it is true, accomplish this only on a small scale; but we have ample reason to conclude that the same operation, if conducted in Nature's great laboratory, would equally produce the effect.

"And, finally, even on that great scale we are able to verify the result. The case is one of those rare cases, as we have shown them to be, in which nature works the experiment for us in the same manner in which we ourselves perform it; introducing into the previous state of things a single and perfectly definite new circumstance, and manifesting the effect so rapidly that there is not time for any other material change in the pre-existing circumstances. 'It is observed that dew is never copiously deposited in situations much screened from the open sky, and not at all in a cloudy night; but if the clouds withdraw even for a few minutes, and leave a clear opening, a deposition of dew presently begins, and goes on increasing.... Dew formed in clear intervals will often even evaporate again when the sky becomes thickly overcast.' The proof, therefore, is complete, that the presence or absence of an uninterrupted communication with the sky causes the deposition or non-deposition of dew. Now, since a clear sky is nothing but the absence of clouds, and it is a known property of clouds, as of all other bodies between which and any given object nothing intervenes but an elastic fluid, that they tend to raise or keep up the superficial temperature of the object by radiating heat to it, we see at once that the disappearance of clouds will cause the surface to cool; so that Nature, in this case, produces a change in the antecedent by definite and known means, and the consequent follows accordingly: a natural experiment which satisfies the requisitions of the Method of Difference."

Section IX.--The Province and Method of Deduction

These four are not all the scientific methods, but they lead up to the rest. They are all linked together, and no one has shown their connection better than Mill. In many cases these processes of isolation are powerless; namely, in those in which the effect, being produced by a concourse of causes, cannot be reduced into its elements. Methods of isolation are then impracticable. We cannot eliminate, and consequently we cannot perform induction. This serious difficulty presents itself in almost all cases of motion, for almost every movement is the effect of a concurrence of forces; and the respective effects of the various forces are found so mixed up in it that we cannot separate them without destroying it, so that it seems impossible to tell what part each force has in the production of the movement. Take a body acted upon by two forces whose directions form an angle: it moves along the diagonal; each part, each moment, each position, each element of its movement, is the combined effect of the two impelling forces. The two effects are so commingled that we cannot isolate either of them, and refer it to its source. In order to perceive each effect separately, we should have to consider the movements apart, that is, to suppress the actual movement, and to replace it by others. Neither the Method of Agreement, nor of Difference, nor of Residues, nor of Concomitant Variations, which are all decomposing and eliminative, can avail against a phenomenon which by its nature excludes all elimination and decomposition. We must, therefore, evade the obstacle; and it is here that the last key of nature appears, the Method of Deduction. We quit the study of the actual phenomenon to observe other and simpler cases; we establish their laws, and we connect each with its cause by the ordinary methods of induction. Then, assuming the concurrence of two or of several of these causes, we conclude from their known laws what will be their total effect. We next satisfy ourselves as to whether the actual movement exactly coincides with the movement foretold; and if this is so, we attribute it to the causes from which we have deduced it. Thus, in order to discover the causes of the planetary motions, we seek by simple induction the laws of two causes: first, the force of primitive impulsion in the direction of the tangent; next, an accelerative attracting force. From these inductive laws we deduce by calculation the motion of a body submitted to their combined influence; and satisfying ourselves that the planetary motions observed coincide exactly with the predicted movements, we conclude that the two forces in question are actually the causes of the planetary motions. "To the Deductive Method," says Mill, "the human mind is indebted for its most conspicuous triumphs in the investigation of nature. To it we owe all the theories by which vast and complicated phenomena are embraced under a few simple laws." Our deviations have led us further than the direct path; we have derived efficiency from imperfection.

Section X.--Comparison of the Methods of Induction and Deduction

If we now compare the two methods, their aptness, function, and provinces, we shall find, as in an abstract, the history, divisions, hopes, and limits of human science. The first appears at the beginning, the second at the end. The first, necessarily, gained ascendancy in Bacon's time,[423] and now begins to lose it; the second, necessarily, lost ascendancy in Bacon's time, and now begins to regain it. So that science, after having passed from the deductive to the experimental state, is now passing from the experimental to the deductive. Induction has for its province phenomena which are capable of being decomposed', and on which we can experiment. Deduction has for its province indecomposable phenomena, or those on which we cannot experiment. The first is efficacious in physics, chemistry, zoology, and botany, in the earlier stages of every science, and also whenever phenomena are but slightly complicated, within our reach, capable of being modified by means at our disposal. The second is efficacious in astronomy, in the higher branches of physics, in physiology, history, in the higher grades of every science, whenever phenomena are very complicated, as in animal and social life, or lie beyond our reach, as the motions of the heavenly bodies and the changes of the atmosphere. When the proper method is not employed, science is at a stand-still: when it is employed, science progresses. Here lies the whole secret of its past and its present. If the physical sciences remained stationary till the time of Bacon, it is because men used deduction when they should have used induction. If physiology and the moral sciences are now making slow progress, it is because we employ induction when deduction should be used. It is by deduction, and according to physical and chemical laws, that we shall be enabled to explain physiological phenomena. It is by deduction, and according to mental laws, that we shall be enabled to explain historical phenomena.[424] And that which has become the instrument of these two sciences, it is the object of all the others to employ. All tend to become deductive, and aim at being summed up in certain general propositions, from which the rest may be deduced. The less numerous these propositions are, the more science advances. The fewer suppositions and postulates a science requires, the more perfect it is become. Such a reduction is its final condition. Astronomy, acoustics, optics, present its models; we shall know nature when we shall have deduced her millions of facts from two or three laws.

I venture to say that the theory which you have just heard is perfect. I have omitted several of its characteristics, but you have seen enough to recognize that induction has nowhere been explained in so complete and precise a manner, with such an abundance of fine and just distinctions, with such extensive and exact applications, with such a knowledge of the practical methods and ascertained results of science, with so complete an exclusion of metaphysical principles and arbitrary suppositions, and in a spirit more in conformity with the rigorous procedure of modern experimental science. You asked me just now, what Englishmen have effected in philosophy; I answer, the theory of Induction. Mill is the last of that great line of philosophers, which begins at Bacon, and which, through Hobbes, Newton, Locke, Hume, Herschel, is continued down to our own times. They have carried our national spirit into philosophy; they have been positive and practical; they have not soared above facts; they have not attempted out-of-the-way paths; they have cleared the human mind of its illusions, presumptions, and fancies. They have employed it in the only direction in which it can act; they only wished to mark out and light up the already well-trodden ways of the progressive sciences. They have not been willing to spend their labor vainly in other than explored and verified paths; they have aided in the great modern work, the discovery of applicable laws; they have contributed, as men of special attainments do, to the increase of man's power. Can you find many philosophers who have done as much?

Section XI.--Limits of Our Knowledge

You will tell me that our philosopher has clipped his wings, in order to strengthen his legs. Certainly; and he has acted wisely. Experience limits the career which it opens to us; it has given us our goal, but also our boundaries. We have only to observe the elements of which our experience is composed, and the facts from which it sets out, to understand that its range is limited. Its nature and its method confine its progress to a few steps. And, in the first place,[425] the ultimate laws of nature cannot be less numerous than the several distinct species of our sensations. We can easily reduce a movement to another movement, but not the sensation of heat to that of smell, or of color, or of sound, nor either of these to a movement. We can easily connect together phenomena of different degrees, but not phenomena differing in species. We find distinct sensations at the bottom of all our knowledge, as simple indecomposable elements, separated absolutely one from another, absolutely incapable of being reduced one to another. Let experience do what she will, she cannot suppress these diversities which constitute her foundation. On the other hand, experience, do what she will, cannot escape from the conditions under which she acts. Whatever be her province, it is bounded by time and space; the fact which she observes is limited and influenced by an infinite number of other facts to which she cannot attain. She is obliged to suppose or recognize some primordial condition from whence she starts, and which she does not explain.[426] Every problem has its accidental or arbitrary data: we deduce the rest from these, but there is nothing from which these can be deduced. The sun, the earth, the planets, the initial impulse of the heavenly bodies, the primitive chemical properties of substances, are such data.[427] If we possessed them all we could explain everything by them, but we could not explain these themselves. Mill says:

"Why these particular natural agents existed originally and no others, or why they are commingled in such and such proportions, and distributed in such and such a manner throughout space, is a question we cannot answer. More than this: we can discover nothing regular in the distribution itself; we can reduce it to no uniformity, to no law. There are no means by which, from the distribution of these causes, or agents, in one part of space, we could conjecture whether a similar distribution prevails in another."[428]

And astronomy, which just now afforded us the model of a perfect science, now affords us an example of a limited science. We can predict the numberless positions of all the planetary bodies; but we are obliged to assume, beside the primitive impulse and its amount, not only the force of attraction and its law, but also the masses and distances of all the bodies in question. We understand millions of facts, but it is by means of a hundred facts which we do not comprehend; we arrive at necessary results, but it is only by means of accidental antecedents; so that if the theory of our universe were completed there would still remain two great voids: one at the commencement of the physical world, the other at the beginning of the moral world; the one comprising the elements of being, the other embracing the elements of experience; one containing primary sensations, the other primitive agents. "Our knowledge," says Royer-Collard, "consists in tracing ignorance as far back as possible."

Can we at least affirm that these irreducible data are so only in appearance, and in relation to our mind? Can we say that they have causes, like the derived facts of which they are the causes? Can we conclude that every event, always and everywhere, happens according to laws, and that this little world of ours, so well-regulated, is a sort of epitome of the universe? Can we by aid of the axioms, quit our narrow confines, and affirm anything of the universe? In no wise; and it is here that Mill pushes his principles to their furthest consequences: for the law which attributes a cause to every event, has to him no other foundation, worth, or scope, than what it derives from experience. It has no inherent necessity; it draws its whole authority from the great number of cases in which we have recognized it to be true; it only sums up a mass of observations; it unites two data, which, considered in themselves, have no intimate connection; it joins antecedents generally to consequents generally, just as the law of gravitation joins a particular antecedent to a particular consequent; it determines a couple, as do all experimental laws, and shares in their uncertainty and in their restrictions. Listen to this bold assertion:

"I am convinced that anyone accustomed to abstraction and analysis, who will fairly exert his faculties for the purpose, will, when his imagination has once learnt to entertain the notion, find no difficulty in conceiving that in some one, for instance, of the many firmaments into which sidereal astronomy now divides the universe, events may succeed one another at random, without any fixed law; nor can anything in our experience, or in our mental nature, constitute a sufficient, or indeed any, reason for believing that this is nowhere the case. The grounds, therefore, which warrant us in rejecting such a supposition with respect to any of the phenomena of which we have experience, must be sought elsewhere than in any supposed necessity of our intellectual faculties."[429]

Practically, we may trust in so well-established a law; but

"In distant parts of the stellar regions, where the phenomena may be entirely unlike those with which we are acquainted, it would be folly to affirm confidently that this general law prevails, any more than those special ones which we have found to hold universally on our own planet. The uniformity in the succession of events, otherwise called the law of causation, must be received not as a law of the universe, but of that portion of it only which is within the range of our means of sure observation, with a reasonable degree of extension to adjacent cases. To extend it further is to make a supposition without evidence, and to which, in the absence of any ground from experience for estimating its degree of probability, it would be idle to attempt to assign any."[430]

We are, then, irrevocably driven back from the infinite: our faculties and our assertions cannot attain to it; we remain confined in a small circle; our mind reaches not beyond its experience; we can establish no universal and necessary connection between facts; such a connection probably does not even exist. Mill stops here; but certainly, by carrying out his idea to its full extent, we should arrive at the conception of the world as a mere collection of facts; no internal necessity would induce their connection or their existence; they would be simple, arbitrary, accidentally-existing facts. Sometimes, as in our system, they would be found assembled in such a manner as to give rise to regular recurrences; sometimes they would be so assembled that nothing of the sort would occur. Chance, as Democritus taught, would be at the foundation of all things. Laws would be the result of chance, and sometimes we should find them, sometimes not. It would be with existences as with numbers--decimal fractions, for instance, which, according to the chance of their two primitive factors, sometimes recur regularly, and sometimes not. This is certainly an original and lofty conception. It is the final consequence of the primitive and dominant idea, which we have discovered at the beginning of the system, which has transformed the theories of Definition, of Propositions, and of the Syllogism; which has reduced axioms to experimental truths; which has developed and perfected the theory of induction; which has established the goal, the limits, the province, and the methods of science; which everywhere, in nature and in science, has suppressed interior connections; which has replaced the necessary by the accidental; cause by antecedent; and which consists in affirming that every assertion which is not merely verbal forms in effect a couple, that is to say, joins together two facts which were separate by their nature.