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need not actually sce with our eyes two paper : your imagination fulfils tha 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 focws these two lines only to you can study geometrical properties i 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 pro Finally, 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 tele. facts 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 axi. heavy. 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 con mentally without the aid of experience; they cannot be so, because the nature
*“ For though, in order actually to see that and scope of their truths lie beyond the two given lines never meet, it would be neces
sary to follow them to infinity; yet without limits of experience. They have an doing so we may know that if they ever do other and a deeper sourie. They have meet, or if, after diverging from one another, a wider scopie, aid they come from they begin
again to approach, this must také
place not at an infinite, but at a finite distance. elsewhere.
Supposing, therefore, srch to be the case, we Not so, answers Mill. Here again can transport ourselves thither in imagination you reason like a schoolman ; you for and can frame a mental image of the appear. get the facts concealed behind your sent at that point, which we may rely on as
ance which one or both of the lines must pro conceptions; for examine your first being precisely similar to the reality. Now, argument. Doubtless you can discover, whether we fix our contemplation upon this without making use of your eyes, and imaginary picture, or call to mind the generale by purely mental contemplation, that former ocular observation, we learn by the evi
isations we have had occasion to make fron two straight lines cannot enclose adence of experience, that a line which, after space; but this contemplation is but a diverging from another straight line, begins to displaced experiment. Imaginary lines approach to it, produces the impression on our bere replace real lines: you construct bent line, not by the expression a straight
senses which we describe by the expression a the figure in your mind instead of on / lic Mill's Logic, i. 364.
traries of axioms are inconceivable, it is say, connects two general facts ordi nugatory, for this distinction does not narily successive, and asserts that the exist. Nothing prevents the contraries first is the Cause of the second. of certain propositions of experience This amounts to saying that the from being conceivable, and the con- course of nature is uniform. But induc. traries of others inconceivable. That tion does not set out from this axiom, depends on the constitution of our it leads up to it; we do not find it at minds. It may be that in some cases the beginning, but at the end of our re the mind may contradict its experience, searches.* Fundamentally, experience and in others not. It is possible that presupposes nothing beyond itself. No in certain cases our conceptions may à priori principle comes to authorize of differ from our perceptions, and some guide her. We observe that this stone times not. It may be that, in certain has fallen, that this hot coal has burnt cases, external sight is opposed to in- us, that this man has died, and we have ternal, and in certain others not. Now, no other means of induction except the we have already seen that in the case addition and comparison of these little of figures, the internal sight exactly re- isolated and transient facts. We learn produces the external. Therefore, in by simple practical experience that the axioms of figures, the mental sight can. sun gives light, that bodies fal., that not be opposed to the actual ; imagi- water quenches thirst, and we have no nation cannot contradict sensation. In other means of extending or criticizing other words, the contraries of such these inductions than by other like axioms will be inconceivable. Thus inductions. Every observation and axioms, although their contraries are every induction draws its value from inconceivable, are experiments of a itself, and from similar ones. It is a: certain class, and it is because they are ways experience which judges of ex. so that their contraries are incon-perience, and induction of induction ceivable. At every point there results The body of our truths has not, then, a this conclusion, which is the abstract of soul distinct from it, and vivifying it: the system: every instructive or fruit- it subsists by the harmony of all its ful proposition is derived from experi- parts taken as a whole, and by the vitalence, and is simply a connecting to ity of each part taken separately. gether of facts.
" Why is it that, with exactly the same
amount of evidence, both negative and posiVII.
tive, we did not reject the assertion that there Hence it follows that Induction is are black swans, while we should refuse cre the only key to nature. This theory is dence to any testimony which asserted that there
were men wearing their heads underneath their Mill's masterpiece. Only so thorough- shoulders? The first assertion was more credgoing a partisan of experience could ible than the latter. But why more credible? have constructed the theory of Induc- tually witnessed, what reason was there for
So long as neither phenomenon had been action.
finding the one harder to be believed than the What, then, is Induction ?
other Apparently because there is less con. Li Induction is that operation of the mind by stancy in the colours of animals, than in the which we infer that what we know to be true “We must first observe, that there is a in a particular case or cases, will be true in all principle implied in the very statement of what gases which resemble the former in certain as
Induction is; an assumption with regard to the signablo respects. In other words, Induction course of nature and the order of the universc: is the process by which we conclude that what namely, that there are such things in nature as is true of certain individuals of a class is true parallel cases; that what happens once, will of the whole class, or that what is true at cer- under a sufficient degree of similarity of cir. tain times will be true in similar circumstances cumstances, happen again, and not only again, at all tiines.”
but as often as the same circumstances recur. This is the reasoning by which, having This, I say, is an assumption, involved in observed that Peter, John and a greater the actual course of nature, we find that the
every case of induction. And, if we consult or less number of men have died, we assumption is warranted. The universe, so conclude that all men will die. In far as known to us, is so constituted, that what. short, induction connects mortality
ever is true in any one case, is true in all cases with the quality of “ man ;
" that is to
of a certain description; the only difficulty is,
to find what description.' - Mill's Logic, i * Mill's Logic, i. 313.
general structure of their internal anatomy. that everywhere, always, the contact of But how do we know this? Doubtless from iron with the moist air will be followed experience. It appears, then, that we need experience to inform us in what degree, and in by the appearance of rust; the applica. what cases, or sorts of cases, experience is to tion of heat by the dilatation of bodies. be relied on. Experience must be consulted “The real cause is the whole of these in order to learn from it under what circum
antecedents." “ There is no scienstances arguments from it will be valid. We have no ulterior test to which we subject ex
tific foundation for distinguishing be. perience in general ; but we make experience tween the cause of a phenomenon and its own test. Experience testifies, that among the conditions of its happening ... The the uniformities which it exhibits, or seems to exhibit, some are more to be relied on than distinction drawn between the patient others; and uniformity, therefore, may be and he agent is purely verbal.” “ The presumed, from
any given number of instances, cause, then, philosophically speaking, with a greater degree of assurance, in propor- is the sum total of the conditions, posi. tion as the case belongs to a class in which the uniformities have hitherto been found more
tive and negative, taken together, the uniform." *
whole of the contingencies of every Experience is the only test, and it is to description, which being realized, the be found everywhere.
consequent invariably follows.” † Much Let us then consider how, without argument has been expended on the any help but that of experience, we can
word necessary : “ If there be any form general propositions, especially the term necessity, it is unconditional.
meaning which confessedly belongs to the most numerous and important of
That which is necessary, that all, those which connect two successive events, by saying that the first is the which must be, means that which will
be, whatever supposition we may make cause of the second. Cause is a great word ; let us ex
in regard to all other things." | This amine it. It carries in itself a whole is all we mean when we assert that the philosophy. From the idea we have of notion of cause includes the notion of Cause depend all our notions of nature. necessity. We mean that the antece.
dent is sufficient and complete, that To give a new idea of Causation is to transform human thought ; and we
there is no need to suppose any addi. shall see how Mill, like Hume and tional antecedent, that it contains all Comte, but better than they, has put requisite conditions, and that no other this idea into a new shape.
condition need exist. To follow unconWhat is a cause ? When Mill
ditionally, then, is the whole notion of
says Chat the contact of iron with moist air
cause and effect. We have none else. produces rust, or that heat dilates discover in our will a different type of
Philosophers are mistaken when they bodies, he does not speak of the mys. causation, and declare it an example of terious bond by which metaphysicians efficient cause in act and in exercise. connect cause and effect. He does not we see nothing of the kind, but there, busy himself with the intimate force and generative virtue which certain as elsewhere, we find only continuous philosophers insert between the thing successions. We do not see a fact producing and the product. Mill says:
engendering another fact, but a fact accompanying another.
« Our will,” The only notion of a cause, which the says Mill,“ produces our bodily actions theory of induction requires, is such a notion
as cold produces ice, or as a spark pro us can be gained from experience. The Law of Causation, the recognition of which is the duces an explosion of gunpowder." main pillar of inductive science, is but the There is here, as elsewhere, an antece familiar truth, that invariability of succession dent, the resolution or state of mind, s found by observation to obtain between anc a consequent, the effort or physi. every fact in nature and some other fact which has preceded it ; independently of all consid- cal sensation. Experience connects eration respecting the ulterior mode of produc-them, and enables us to foresee that tion of phenomena, and of every other ques. the effort will follow the resolution, as tion regarding the nature of 'Things in them- it enables us to foresee that the explom selves. " No other foundation underlies these taci f the spark. Let us then have
sion of gunpowder will follow the contwo expressions. Vie mean simply
* Ibid. i. 360.
Ibid. i 365 • Will's Lapric, i. 391.
| Ibid. i. 359
+ Ibid. &. 372.
done with all these foychological illu- Variations.* These are the only ways sions, and seek only, under the na:nes of by which we can penetrate into nature. cause and effect, for phenomena which | There are no other, and these are form pairs without exception or con- everywhere. And they all employ dition.
the same artifice, that is to say, Now, to establish these connections elimination ; for, in fact, induction is of phenomena, Mill discovers four nothing else. You have two groups, methods, and only four,-namely, the one of antecedents, the other of conMethods of Agreement,* of Difference,t sequents, each of them containing more of Residues, I and of Concomitant or fewer elements, ten, for example. # " If we take fifty crucibles of molten mat
To what antecedent is each consequent per and let the.n cool, and fifty solutions and joined? Is the first consequent joined let them evaporate, al will crystallize. Sul- to the first antecedent, or to the third, phar, sugar, alum, salt-substances, tempera- or sixth? The whole difficulty, and cures, circumstances--all are as different as they can be We find one, and only one, com
the only possible solution lie there. To mon fact-the change from the liquid to the resolve the difficulty, and to effect the solid state and conclude, therefore, that this solution, we must eliminate, that is, change is the invariable antecedent of crystal- exclude those antecedents which are lization. Here we have an example of the Method of Agreement. Its canon is :
not connected with the consequent we “1. If two or more instances of the phenomenon under investigation have only one antecedents but one to their respective consecircumstance in common, the circumstance in quents, and all the consequents but one to which alone all the instances agree, is the cause their respective antecedents, we conclude that (or effect) of the given phenomenon.'”- the remaining antecedent is connected to the Mill's Logic, i. 422. .
remaining consequent. For example, scientific "A bird in the air breathes ; plunged into men had calculated what ought to be the veloccarbonic acid gas, it ceases to breathe. In ity of sound according to the laws of the propaother words, in the second case, suffocation gation of sonorous waves, but found that a ensues. In other respects the two cases are as sound actually travelled quicker than their calsimilar as possible, since we have the same culations had indicated. This surplus or resibird in both, and they
take place in immediate due of speed was a consequent for which an succession. They differ only in the circum- antecedent had to be found. Laplace discov. Itance of immersion in carbonic acid gas being ered the antecedent in the heat developed by ubstituted for immersion in the atmosphere,
the condensation of each sonorous wave, and und we conclude that this circumstance is in- this new element, when introduced into the variably followed by suffocation. The Method calculation, rendered it perfectly accurate. of Difference is here employed. Its canon This is an example of the Method of Residues, 18:
the canon of which is as follows:16.11. If an instance in which the phenom- “IV. Subduct from any phenomenon such enon under investigation occurs, and an in- part as is known by previous inductions to be stance in which it does not occur have every the effect of certain antecedents, and the resie circumstance in common save one, that one due of the phenomenon is the effect of the reoccurring only in the former; the circum- maining antecedents.'"-Mill's Logic, i. 431, stance in which alone the two instances differ, "Let us take two facts-as the presence of is the effect, or the cause, or a necessary part the earth and the oscillation of the pendulum, of the cause, of the phenomenon.' "- Mill's or again the presence of the moon and the flow Logic, i. 423.
of the tide. To connect these phenomena 1. A combination of these methods is directly, we should have to suppress the first sometimes employed, and is termed the In- of them, and see if this suppression would ocdirect Method of Difference, or the Joint casion the stoppage of the second. Now, in Method of Agreement and Difference. It is, both instances, such suppression is impossible in fact, a double employment of the Method of So we employ an indirect means of corzecting Agreement, first applying that method to in- the phenomena. We observe that all the sances in which the phenomenon in question variations of the one correspond to certain OCCES, and then to instances in which it does variations of the other; that all the oscilla not occur. The fo'lowing is its canon :- tions of the pendulum correspond to certail
"• III. If two or more instances in which different positions of the earth that all states the phenomenon occurs have only one circum- of the tide correspond to positions of the moon stance ir common, while two or more instances From this we conclude that the second fact it in whick it does not occur have nothing in the antecedent of the first. These are ex common, save the absence of that circum- amples of the Method of Concomitant Varia. stance; the circumstance in which alone the tions. Its canon is :two sets of instances differ, is the effect, or “\V. Whatever phenomenon varies in any the cause, or a necessary part of the cause, of manner whenever another phenomenon varies the phenomenon.'")-Mill's Logic, i. 479. in some particular manner, is either a tause or
“If we take two groups--one of antecedents an effect of that phenomenon, or is connected word one of consequents--and can succeed in with it through some fact of causation namn manecting by previous investigations al the | Mill's Logic, i. 435.
are considering * But as we cannot | parison with the air in contact with it.' Bat exclude them effectually, and as in
there still remains the most important case a
all, that of nocturnal dew: does the same cirnature the pair of phenomena we are
cumstance exist in this case ? 'Is it a fact seeking is always surrounded with cir
that the object dewed is colder than the air? cumstances, we collect various cases, Certainly not, one would at first te inclined to which by their diversity enable the mind experiment is easy; we have only to lay 2
say; for what is to make it so?
. the to lop off these circumstances, and to thermometer in contact with the dewed subdiscover the pair of phenomena distinct stance, and hang one at a little distance above ly. In short, we can only perform it, out of reach of its influence. The experi induction by discovering pairs of phe has been asked, and the answer has been in
ment has been therefore made ; the question nomena : we form these only by isola- variably in the affirmative. Whenever an ob sion; we isolate only by means of com- ject contracts dew, it is colder than the air.' parisons.
“Here then is a complete application of the
Method of Agreement, establishing the fact of VIII.
an invariable connection between the deposi.
tion of dew on a surface, and the coldness of These are the rules; an example that surface compared with the external air will make them clearer. We will show
But which of these is cause, and which effect?
or are they both effects of something else? On you the methods in exercise ; here is
this subject the Method of Agreement can afan example which combines nearly the ford us no light: we must call in a more potent whole of them, namely, Dr. Well's
method. We must collect more facts, or, theory of dew. I will give it to you in
which comes to the same thing, vary the cir.
cumstances ; since every instance in which the Mill's own words, which are so clear circumstances differ is a fresh fact: and especthat you must have the pleasure of ially, we must note the contrary or negative pondering over them :
To We must
cases, i.e. where no dew is produced: 'for a separate dew from rain and the moist
comparison between instances of dew and in
stances of no dew, is the condition necessary to ure of fogs, and limit the application bring the Method of Difference into play. of the term to what is really meant, “Now, first, no dew is produced on the which is, the spontaneous appearance
surface of polished metals, but it is very coof moisture on substances exposed in
piously on glass, both exposed with their faces
upwards, and in some cases the under side of a the open air when no rain or visible wet
horizontal plate of glass is also dewed.' Here is falling." | What is the cause of is an instance in which the effect is produced,
and another instance in which it is not prothe phenomena we have thus defined,
duced ; but we cannot yet pronounce, as the and how was that cause discovered ?
canon of the Method of Difference requires, "Now, here we have analogous pheno
that the latter instance agrees with the former mena in the moisture which bedews a cold
in all its circumstances except one: for the
difference between glass and polished metals metal or stone when we breathe upon it, that
are manifold, and the only thing we can as yet which appears on a glass of water fresh from the well in hot weather; that which appears on
be sure of is, that the cause of dew will be the inside of windows when sudden rain or hail
found among the circumstances by which the chills the external air ; that which runs down
former substance is distinguished from the
latter." cur walls when, after a long frost, a warm moist thaw comes on.' Comparing these cases, we find that they all contain the phenomenon
To detect this particular circumstance which was proposed as the subject of investiga
of difference, we have but one practica. tion. Now all these instances agree in one ble method, that of Concomitant Variapoint, the coldness of the object dewed in com
*“The Method of Agreement,” says Mill “In the cases of polished metal and pol. (Logic, i. 424), “ stands on the ground that ished glass, the contrast shows evidently that whatever can be eliminated, is not connected the substance has much to do with the phe with the phenomenon by any law. The Method nomenon ; therefore let the substance alone be of Difference has for its foundation, that what- diversified as much as possible, bv exposing ever can not be eliminated, is connected with polished surfaces of various kinds. This done, the phenomenon by a law." The Method of
a scale of intensity becomes obvious. Those Residues is a case of the Method of Differ- polished substances are found to be most ences. The Method of Concomitant Varia- strongly dewed which conduct heat worsi tions is another case of the same method ; with while those which conduct well resist dew most this distinction, that it is applied, not to the effectually.' paenomena, but to their variations.
“ The conclusion obtained is, that cæteris + This quotation, and all the others in this paribus the deposition of dew is in some proparagraph, are taken from Mill's Logic, i. portion to the power which the body possesses 451-9. Mr. Mill quotes from Sir John Her- of resisting the passage of heat; and that this, schel's Discourse on the Study of Natural therefore (or something connected with this), Philosoplay.
must be at least one of the causes which assis