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need not actually see with our eyes two | paper: your imagination fulfils the straight lines in order to know that they office of a diagram on paper: you trust cannot enclose a space; it is enough for to it as you trust to the diagram, and it us to refer to the inner mental concep- is as good as the other; for in regard tion which we have of them: the evi- to figures and lines the imagination exdence of our senses is not needed for actly reproduces the sensation. What this purpose; our belief arises wholly, you have seen with your eyes open, you with its full force, from the simple com- will see again exactly the same a minute parison of our ideas. Moreover, ex- afterwards with your eyes closed; and perience fo lows these two lines only to you can study geometrical properties limited distance, ten, a hundred, a transferred to the field of mental vision thousand feet; and the axiom is true as accurately as if they existed in the for a thousand, a hundred thousand, a field of actual sight. There are, there million miles, and for an unlimited dis- fore, experiments of the brain as there tance. Thus, beyond the point at which are ocular ones; and it is after just experience ceases, it is no longer experi- such an experiment that you deny to ence which establishes the axiom. two straight lines, indefinitely proFinally, the axiom is a necessary truth; longed, the property of enclosing a that is to say, the contrary is incon- space. You need not for this purpose ceivable. We cannot imagine a space pursue them to infinity, you need only enclosed by two straight lines: as soon transfer yourself in imagination to the as we imagine the space enclosed, the point where they converge, and there two lines cease to be straight; and as you have the impression of a bent line, soon as we imagine the two lines to be that is of one which ceases to be straight, the space ceases to be en- straight.* Your presence there in imclosed. In the assertion of axioms, the agination takes the place of an actual constituent ideas are irresistibly drawn presence; you can affirm by it what you together. In the negation of axioms, affirmed by your actual presence, and the constituent ideas inevitably repel as positively. The first is only the each other. Now this does not happen second in a more commodious form, with truths of experience: they state with greater flexibility and scope. It is an accidental relation, not a necessary like using a telescope instead of the connection; they lay down that two naked eye; the revelations of the telefacts are connected, and not that they scope are propositions of experience; must be connected; they show us that so are those of the imagination. As to bodies are heavy, not that they must be the argument which distinguishes axiheavy. Thus, axioms are not, and can- oms from propositions of experience unnot be the results of experience. They der the pretext that the contraries of the are not So, because we can form them latter are conceivable, while the conmentally 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.
*"For though, in order actually to see that
two given lines never meet, it would be necessary to follow them to infinity; yet without doing so we may know that if they ever do meet, or if, after diverging from one another, they begin again to approach, this must take place not at an infinite, but at a finite distance. Supposing, therefore, such to be the case, we can transport ourselves thither in imagination and can frame a mental image of the appear sent at that point, which we may rely on as ance which one or both of the lines must prebeing precisely similar to the reality. Now, whether we fix our contemplation upon this imaginary picture, or call to mind the general. isations we have had occasion to make from former ocular observation, we learn by the evi dence of experience, that a line which, after diverging from another straight line, begins to approach to it, produces the impression on our senses which we describe by the expression a bent line, not by the expression a straight MILL'S Logic, i. 364.
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 onlin
traries 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.
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." *
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 66 mortality with the quality of man ; that is to Mill's Logic, i. 315.
say, connects two general facts ordi narily 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 re searches. 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 fal, that water quenches thirst, and we have no other means of extending or criticizing these inductions than by other like inductions. Every observation and every induction draws its value from itself, and from similar ones. It is aways experience which judges of ex perience, 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.
66 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? tually witnessed, what reason was there for So long as neither phenomenon had been acfinding the one harder to be believed than the other? Apparently because there is less con. stancy in the colours of animals, than in the
"We must first observe, that there is a principle implied in the very statement of what Induction is; an assumption with regard to the course of nature and the order of the universe: namely, that there are such things in nature as parallel cases; that what happens once, will under a sufficient degree of similarity of cir. cumstances, happen again, and not only again, but as often as the same circumstances recur.
This, I say, is an assumption, involved in the actual course of nature, we find that the every case of induction. And, if we consult assumption is warranted. The universe, so far as known to us, is so constituted, that whatever is true in any one case, is true in all cases of a certain description; the only difficulty is, to find what description.' -MILL'S Logic, i 337.
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 aniformities have hitherto been found more uniform." *
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 s 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 s 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 quesregarding the nature of "Things in them
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." * "There is no scientific foundation for distinguishing be tween the cause of a phenomenon and the conditions of its happening... The distinction drawn between the patient and he 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."† 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." 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 addi tional antecedent, that it contains all condition need exist. To follow unconrequisite conditions, and that no other ditionally, then, is the whole notion of
cause and effect. We have none else.
Philosophers are mistaken when they causation, and declare it an example of discover in our will a different type of efficient cause in act and in exercise. We see 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 pro duces an explosion of gunpowder." There is here, as elsewhere, an antecedent, the resolution or state of mind, and a consequent, the effort or physi cal sensation. Experience connects them, and enables us to foresee that the effort will follow the resolution, as it enables us to foresee that the explo sion of gunpowder will follow the contact of the spark. Let us then have ↑ Ibid. ir 365.
* Ibid. i. 360. ↑ Ibid. 1. 373.
done with all these psychological illu- | sions, 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,* of Difference,t of Residues, and of Concomitant
"If we take fifty crucibles of molten matter and let then cool, and fifty solutions and let them evaporate, al will crystallize. Sulphur, sugar, alum, salt-substances, temperatures, circumstances-all are as different as they can be. We find one, and only one, common fact-the change from the liquid to the solid state and conclude, therefore, that this change is the invariable antecedent of crystallization. Here we have an example of the Method of Agreement. Its canon is :
"1. If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon." MILL'S Logic, i. 422.
"A bird in the air breathes; plunged into carbonic acid gas, it ceases to breathe. In other words, in the second case, suffocation ensues. In other respects the two cases are as similar as possible, since we have the same bird in both, and they take place in immediate succession. They differ only in the circumItance of immersion in carbonic acid gas being ubstituted for immersion in the atmosphere, and we conclude that this circumstance is invariably followed by suffocation. The Method of Difference is here employed. Its canon
"II. If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or a necessary part of the cause, of the phenomenon.' ”— MILL'S Logic, i. 423.
["A combination of these methods is sometimes employed, and is termed the Indirect Method of Difference, or the Joint Method of Agreement and Difference. It is, in fact, a double employment of the Method of Agreement, first applying that method to instances in which the phenomenon in question DCCES, and then to instances in which it does not occur. The following is its canon :
"III. If two or more instances in which the phenomenon occurs have only one circumstance ir common, while two or more instances in which it does not occur have nothing in common, save the absence of that circumstance; the circumstance in which alone the two sets of instances differ, is the effect, or the cause, or a necessary part of the cause, of the phenomenon.'"]-MILL'S Logic, i. 429.
"If we take two groups-one of antecedents and one of consequents-and can succeed in onnecting by previous investigations al the
Variations.* 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
antecedents but one to their respective consequents, and all the consequents but one to their respective antecedents, we conclude that the remaining antecedent is connected to the remaining consequent. For example, scientific men had calculated what ought to be the velocity of sound according to the laws of the propagation of sonorous waves, but found that a sound actually travelled quicker than their calculations had indicated. This surplus or residue of speed was a consequent for which an antecedent had to be found. Laplace discovered the antecedent in the heat developed by the condensation of each sonorous wave, and this new element, when introduced into the calculation, rendered it perfectly accurate. This is an example of the Method of Residues, the canon of which is as follows:
"IV. Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the resi due of the phenomenon is the effect of the remaining antecedents.'"-MILL's Logic, i. 431.
"Tet us take two facts-as the presence of the earth and the oscillation of the pendulum, or again the presence of the moon and the flow of the tide. To connect these phenomena directly, we should have to suppress the first of them, and see if this suppression would oc casion the stoppage of the second. Now, in both instances, such suppression is impossible So we employ an indirect means of connecting the phenomena. We observe that all the variations of the one correspond to certai variations of the other; that all the oscilla tions of the pendulum correspond to certain different positions of the earth that all states of the tide correspond to positions of the moon From this we conclude that the second fact it the antecedent of the first. These are ex amples of the Method of Concomitant Variations. Its canon is :
"V. Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a tause of an effect of that phenomenon, or is connected with it through some fact of causation"". MILL'S Logic, i. 435.
are considering * 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 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.
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." t What is the cause of the phenomena we have thus defined,
and how was that cause discovered?
666 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 com
"The Method of Agreement," says Mill (Logic, i. 424), "stands on the ground that whatever can be eliminated, is not connected with the phenomenon by any law. The Method of Difference has for its foundation, that whatever can not be eliminated, is connected with the phenomenon by a law." The Method of Residues is a case of the Method of Differences. The Method of Concomitant Variations is another case of the same method; with this distinction, that it is applied, not to the paenomena, but to their variations.
+ This quotation, and all the others in this paragraph, are taken from Mill's Logic, i. 451-9. Mr. Mill quotes from Sir John Herschel's Discourse on the Study of Natural Philosophy.
parison with the air in contact with it.' But there still remains the most important case of all, that of nocturnal dew: does the same cir. cumstance 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 experi has been asked, and the answer has been inment has been therefore made; the question variably in the affirmative. Whenever an ob ject 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 deposi tion 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 cir cumstances; 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, duced; but we cannot yet pronounce, as the and another instance in which it is not procanon of the Method of Difference requires, that the latter instance agrees with the former in all its circumstances except one: for the difference 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 practica. ble method, that of Concomitant Variations:
"In the cases of polished metal and pol ished 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 wors while those which conduct well resist dew most effectually.'
"The conclusion obtained is, that cæteris 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 assis