§ 1. In the preceding exposition of the four methods of observation and
experiment, by which we contrive to distinguish among a mass of coexistent
phenomena the particular effect due to a given cause, or the particular
cause which gave birth to a given effect; it has been necessary to
suppose, in the first instance, for the sake of simplification, that this
analytical operation is encumbered by no other difficulties than what are
essentially inherent in its nature; and to represent to ourselves,
therefore, every effect, on the one hand as connected exclusively with a
single cause, and on the other hand as incapable of being mixed and
confounded with any other coexistent effect. We have regarded _a b c d e_,
the aggregate of the phenomena existing at any moment, as consisting of
dissimilar facts, _a_, _b_, _c_, _d_, and _e_, for each of which one, and
only one, cause needs be sought; the difficulty being only that of
singling out this one cause from the multitude of antecedent
circumstances, A, B, C, D, and E.
If such were the fact, it would be comparatively an easy task to
investigate the laws of nature. But the supposition does not hold, in
either of its parts. In the first place, it is not true that the same
phenomenon is always produced by the same cause: the effect _a_ may
sometimes arise from A, sometimes from B. And, secondly, the effects of
different causes are often not dissimilar, but homogeneous, and marked out
by no assignable boundaries from one another: A and B may produce not _a_
and _b_, but different portions of an effect _a_. The obscurity and
difficulty of the investigation of the laws of phenomena is singularly
increased by the necessity of adverting to these two circumstances;
Intermixture of Effects, and Plurality of Causes. To the latter, being the
simpler of the two considerations, we shall first direct our attention.
It is not true, then, that one effect must be connected with only one
cause, or assemblage of conditions; that each phenomenon can be produced
only in one way. There are often several independent modes in which the
same phenomenon could have originated. One fact may be the consequent in
several invariable sequences; it may follow, with equal uniformity, any
one of several antecedents, or collections of antecedents. Many causes may
produce motion: many causes may produce some kinds of sensation: many
causes may produce death. A given effect may really be produced by a
certain cause, and yet be perfectly capable of being produced without it.
§ 2. One of the principal consequences of this fact of Plurality of Causes
is, to render the first of the inductive methods, that of Agreement,
uncertain. To illustrate that method, we supposed two instances, A B C
followed by _a b c_, and A D E followed by _a d e_. From these instances
it might be concluded that A is an invariable antecedent of _a_, and even
that it is the unconditional invariable antecedent, or cause, if we could
be sure that there is no other antecedent common to the two cases. That
this difficulty may not stand in the way, let us suppose the two cases
positively ascertained to have no antecedent in common except A. The
moment, however, that we let in the possibility of a plurality of causes,
the conclusion fails. For it involves a tacit supposition, that _a_ must
have been produced in both instances by the same cause. If there can
possibly have been two causes, those two may, for example, be C and E: the
one may have been the cause of _a_ in the former of the instances, the
other in the latter, A having no influence in either case.
Suppose, for example, that two great artists, or great philosophers, that
two extremely selfish, or extremely generous characters, were compared
together as to the circumstances of their education and history, and the
two cases were found to agree only in one circumstance: would it follow
that this one circumstance was the cause of the quality which
characterized both those individuals? Not at all; for the causes which may
produce any type of character are innumerable; and the two persons might
equally have agreed in their character, though there had been no manner of
resemblance in their previous history.
This, therefore, is a characteristic imperfection of the Method of
Agreement; from which imperfection the Method of Difference is free. For
if we have two instances, A B C and B C, of which B C gives _b c_, and A
being added converts it into _a b c_, it is certain that in this instance
at least, A was either the cause of _a_, or an indispensable portion of
its cause, even though the cause which produces it in other instances may
be altogether different. Plurality of Causes, therefore, not only does not
diminish the reliance due to the Method of Difference, but does not even
render a greater number of observations or experiments necessary: two
instances, the one positive and the other negative, are still sufficient
for the most complete and rigorous induction. Not so, however, with the
Method of Agreement. The conclusions which that yields, when the number of
instances compared is small, are of no real value, except as, in the
character of suggestions, they may lead either to experiments bringing
them to the test of the Method of Difference, or to reasonings which may
explain and verify them deductively.
It is only when the instances, being indefinitely multiplied and varied,
continue to suggest the same result, that this result acquires any high
degree of independent value. If there are but two instances, A B C and A D
E, although these instances have no antecedent in common except A, yet as
the effect may possibly have been produced in the two cases by different
causes, the result is at most only a slight probability in favour of A;
there may be causation, but it is almost equally probable that there was
only a coincidence. But the oftener we repeat the observation, varying the
circumstances, the more we advance towards a solution of this doubt. For
if we try A F G, A H K, &c., all unlike one another except in containing
the circumstance A, and if we find the effect _a_ entering into the result
in all these cases, we must suppose one of two things, either that it is
caused by A, or that it has as many different causes as there are
instances. With each addition, therefore, to the number of instances, the
presumption is strengthened in favour of A. The inquirer, of course, will
not neglect, if an opportunity present itself, to exclude A from some one
of these combinations, from A H K for instance, and by trying H K
separately, appeal to the Method of Difference in aid of the Method of
Agreement. By the Method of Difference alone can it be ascertained that A
is the cause of _a_; but that it is either the cause or another effect of
the same cause, may be placed beyond any reasonable doubt by the Method of
Agreement, provided the instances are very numerous, as well as
sufficiently various.
After how great a multiplication, then, of varied instances, all agreeing
in no other antecedent except A, is the supposition of a plurality of
causes sufficiently rebutted, and the conclusion that _a_ is the effect of
A divested of the characteristic imperfection and reduced to a virtual
certainty? This is a question which we cannot be exempted from answering;
but the consideration of it belongs to what is called the Theory of
Probability, which will form the subject of a chapter hereafter. It is
seen, however, at once, that the conclusion does amount to a practical
certainty after a sufficient number of instances, and that the method,
therefore, is not radically vitiated by the characteristic imperfection.
The result of these considerations is only, in the first place, to point
out a new source of inferiority in the Method of Agreement as compared
with other modes of investigation, and new reasons for never resting
contented with the results obtained by it, without attempting to confirm
them either by the Method of Difference, or by connecting them deductively
with some law or laws already ascertained by that superior method. And, in
the second place, we learn from this the true theory of the value of mere
_number_ of instances in inductive inquiry. The Plurality of Causes is the
only reason why mere number is of any importance. The tendency of
unscientific inquirers is to rely too much on number, without analysing
the instances; without looking closely enough into their nature, to
ascertain what circumstances are or are not eliminated by means of them.
Most people hold their conclusions with a degree of assurance proportioned
to the mere _mass_ of the experience on which they appear to rest; not
considering that by the addition of instances to instances, all of the
same kind, that is, differing from one another only in points already
recognised as immaterial, nothing whatever is added to the evidence of the
conclusion. A single instance eliminating some antecedent which existed in
all the other cases, is of more value than the greatest multitude of
instances which are reckoned by their number alone. It is necessary, no
doubt, to assure ourselves, by a repetition of the observation or
experiment, that no error has been committed concerning the individual
facts observed; and until we have assured ourselves of this, instead of
varying the circumstances, we cannot too scrupulously repeat the same
experiment or observation without any change. But when once this assurance
has been obtained, the multiplication of instances which do not exclude
any more circumstances would be entirely useless, were it not for the
Plurality of Causes.
It is of importance to remark, that the peculiar modification of the
Method of Agreement which, as partaking in some degree of the nature of
the Method of Difference, I have called the Joint Method of Agreement and
Difference, is not affected by the characteristic imperfection now pointed
out. For, in the joint method, it is supposed not only that the instances
in which _a_ is, agree only in containing A, but also that the instances
in which _a_ is not, agree only in not containing A. Now, if this be so, A
must be not only the cause of _a_, but the only possible cause: for if
there were another, as for example B, then in the instances in which _a_
is not, B must have been absent as well as A, and it would not be true
that these instances agree _only_ in not containing A. This, therefore,
constitutes an immense advantage of the joint method over the simple
Method of Agreement. It may seem, indeed, that the advantage does not
belong so much to the joint method, as to one of its two premisses, (if
they may be so called,) the negative premiss. The Method of Agreement,
when applied to negative instances, or those in which a phenomenon does
_not_ take place, is certainly free from the characteristic imperfection
which affects it in the affirmative case. The negative premiss, it might
therefore be supposed, could be worked as a simple case of the Method of
Agreement, without requiring an affirmative premiss to be joined with it.
But although this is true in principle, it is generally altogether
impossible to work the Method of Agreement by negative instances without
positive ones: it is so much more difficult to exhaust the field of
negation than that of affirmation. For instance, let the question be, what
is the cause of the transparency of bodies; with what prospect of success
could we set ourselves to inquire directly in what the multifarious
substances which are _not_ transparent, agree? But we might hope much
sooner to seize some point of resemblance among the comparatively few and
definite species of objects which _are_ transparent; and this being
attained, we should quite naturally be put upon examining whether the
_absence_ of this one circumstance be not precisely the point in which all
opaque substances will be found to resemble.
The Joint Method of Agreement and Difference, therefore, or, as I have
otherwise called it, the Indirect Method of Difference (because, like the
Method of Difference properly so called, it proceeds by ascertaining how
and in what the cases where the phenomenon is present, differ from those
in which it is absent) is, after the direct Method of Difference, the most
powerful of the remaining instruments of inductive investigation; and in
the sciences which depend on pure observation, with little or no aid from
experiment, this method, so well exemplified in the speculation on the
cause of dew, is the primary resource, so far as direct appeals to
experience are concerned.
§ 3. We have thus far treated Plurality of Causes only as a possible
supposition, which, until removed, renders our inductions uncertain, and
have only considered by what means, where the plurality does not really
exist, we may be enabled to disprove it. But we must also consider it as a
case actually occurring in nature, and which, as often as it does occur,
our methods of induction ought to be capable of ascertaining and
establishing. For this, however, there is required no peculiar method.
When an effect is really producible by two or more causes, the process for
detecting them is in no way different from that by which we discover
single causes. They may (first) be discovered as separate sequences, by
separate sets of instances. One set of observations or experiments shows
that the sun is a cause of heat, another that friction is a source of it,
another that percussion, another that electricity, another that chemical
action is such a source. Or (secondly) the plurality may come to light in
the course of collating a number of instances, when we attempt to find
some circumstance in which they all agree, and fail in doing so. We find
it impossible to trace, in all the cases in which the effect is met with,
any common circumstance. We find that we can eliminate _all_ the
antecedents; that no one of them is present in all the instances, no one
of them indispensable to the effect. On closer scrutiny, however, it
appears that though no one is always present, one or other of several
always is. If, on further analysis, we can detect in these any common
element, we may be able to ascend from them to some one cause which is the
really operative circumstance in them all. Thus it might, and perhaps
will, be discovered, that in the production of heat by friction,
percussion, chemical action, &c., the ultimate source is one and the same.
But if (as continually happens) we cannot take this ulterior step, the
different antecedents must be set down provisionally as distinct causes,
each sufficient of itself to produce the effect.
We here close our remarks on the Plurality of Causes, and proceed to the
still more peculiar and more complex case of the Intermixture of Effects,
and the interference of causes with one another: a case constituting the
principal part of the complication and difficulty of the study of nature;
and with which the four only possible methods of directly inductive
investigation by observation and experiment, are for the most part, as
will appear presently, quite unequal to cope. The instrument of Deduction
alone is adequate to unravel the complexities proceeding from this source;
and the four methods have little more in their power than to supply
premisses for, and a verification of, our deductions.
§ 4. A concurrence of two or more causes, not separately producing each
its own effect, but interfering with or modifying the effects of one
another, takes place, as has already been explained, in two different
ways. In the one, which is exemplified by the joint operation of different
forces in mechanics, the separate effects of all the causes continue to be
produced, but are compounded with one another, and disappear in one total.
In the other, illustrated by the case of chemical action, the separate
effects cease entirely, and are succeeded by phenomena altogether
different, and governed by different laws.
Of these cases the former is by far the more frequent, and this case it is
which, for the most part, eludes the grasp of our experimental methods.
The other and exceptional case is essentially amenable to them. When the
laws of the original agents cease entirely, and a phenomenon makes its
appearance, which, with reference to those laws, is quite heterogeneous;
when, for example, two gaseous substances, hydrogen and oxygen, on being
brought together, throw off their peculiar properties, and produce the
substance called water; in such cases the new fact may be subjected to
experimental inquiry, like any other phenomenon; and the elements which
are said to compose it may be considered as the mere agents of its
production; the conditions on which it depends, the facts which make up
its cause.
The _effects_ of the new phenomenon, the _properties_ of water, for
instance, are as easily found by experiment as the effects of any other
cause. But to discover the _cause_ of it, that is, the particular
conjunction of agents from which it results, is often difficult enough. In
the first place, the origin and actual production of the phenomenon are
most frequently inaccessible to our observation. If we could not have
learned the composition of water until we found instances in which it was
actually produced from oxygen and hydrogen, we should have been forced to
wait until the casual thought struck some one of passing an electric spark
through a mixture of the two gases, or inserting a lighted taper into it,
merely to try what would happen. Further, even if we could have
ascertained, by the Method of Agreement, that oxygen and hydrogen were
both present when water is produced, no experimentation on oxygen and
hydrogen separately, no knowledge of their laws, could have enabled us
deductively to infer that they would produce water. We require a specific
experiment on the two combined.
Under these difficulties, we should generally have been indebted for our
knowledge of the causes of this class of effects, not to any inquiry
directed specifically towards that end, but either to accident, or to the
gradual progress of experimentation on the different combinations of which
the producing agents are susceptible; if it were not for a peculiarity
belonging to effects of this description, that they often, under some
particular combination of circumstances, reproduce their causes. If water
results from the juxtaposition of hydrogen and oxygen whenever this can be
made sufficiently close and intimate, so, on the other hand, if water
itself be placed in certain situations, hydrogen and oxygen are reproduced
from it: an abrupt termination is put to the new laws, and the agents
reappear separately with their own properties as at first. What is called
chemical analysis is the process of searching for the causes of a
phenomenon among its effects, or rather among the effects produced by the
action of some other causes upon it.
Lavoisier, by heating mercury to a high temperature in a close vessel
containing air, found that the mercury increased in weight and became what
was then called red precipitate, while the air, on being examined after
the experiment, proved to have lost weight, and to have become incapable
of supporting life or combustion. When red precipitate was exposed to a
still greater heat, it became mercury again, and gave off a gas which did
support life and flame. Thus the agents which by their combination
produced red precipitate, namely the mercury and the gas, reappear as
effects resulting from that precipitate when acted upon by heat. So, if we
decompose water by means of iron filings, we produce two effects, rust and
hydrogen: now rust is already known by experiments upon the component
substances, to be an effect of the union of iron and oxygen: the iron we
ourselves supplied, but the oxygen must have been produced from the water.
The result therefore is that water has disappeared, and hydrogen and
oxygen have appeared in its stead: or in other words, the original laws of
these gaseous agents, which had been suspended by the superinduction of
the new laws called the properties of water, have again started into
existence, and the causes of water are found among its effects.
Where two phenomena, between the laws or properties of which considered in
themselves no connexion can be traced, are thus reciprocally cause and
effect, each capable in its turn of being produced from the other, and
each, when it produces the other, ceasing itself to exist (as water is
produced from oxygen and hydrogen, and oxygen and hydrogen are reproduced
from water); this causation of the two phenomena by one another, each
being generated by the other’s destruction, is properly transformation.
The idea of chemical composition is an idea of transformation, but of a
transformation which is incomplete; since we consider the oxygen and
hydrogen to be present in the water _as_ oxygen and hydrogen, and capable
of being discovered in it if our senses were sufficiently keen: a
supposition (for it is no more) grounded solely on the fact, that the
weight of the water is the sum of the separate weights of the two
ingredients. If there had not been this exception to the entire
disappearance, in the compound, of the laws of the separate ingredients;
if the combined agents had not, in this one particular of weight,
preserved their own laws, and produced a joint result equal to the sum of
their separate results; we should never, probably, have had the notion now
implied by the words chemical composition: and, in the fact of water
produced from hydrogen and oxygen and hydrogen and oxygen produced from
water, as the transformation would have been complete, we should have seen
only a transformation.
In these cases, then, when the heteropathic effect (as we called it in a
former chapter)(86) is but a transformation of its cause, or in other
words, when the effect and its cause are reciprocally such, and mutually
convertible into each other; the problem of finding the cause resolves
itself into the far easier one of finding an effect, which is the kind of
inquiry that admits of being prosecuted by direct experiment. But there
are other cases of heteropathic effects to which this mode of
investigation is not applicable. Take, for instance, the heteropathic laws
of mind; that portion of the phenomena of our mental nature which are
analogous to chemical rather than to dynamical phenomena; as when a
complex passion is formed by the coalition of several elementary impulses,
or a complex emotion by several simple pleasures or pains, of which it is
the result without being the aggregate, or in any respect homogeneous with
them. The product, in these cases, is generated by its various factors;
but the factors cannot be reproduced from the product: just as a youth can
grow into an old man, but an old man cannot grow into a youth. We cannot
ascertain from what simple feelings any of our complex states of mind are
generated, as we ascertain the ingredients of a chemical compound, by
making it, in its turn, generate them. We can only, therefore, discover
these laws by the slow process of studying the simple feelings themselves,
and ascertaining synthetically, by experimenting on the various
combinations of which they are susceptible, what they, by their mutual
action upon one another, are capable of generating.
§ 5. It might have been supposed that the other, and apparently simpler
variety of the mutual interference of causes, where each cause continues
to produce its own proper effect according to the same laws to which it
conforms in its separate state, would have presented fewer difficulties to
the inductive inquirer than that of which we have just finished the
consideration. It, presents, however, so far as direct induction apart
from deduction is concerned, infinitely greater difficulties. When a
concurrence of causes gives rise to a new effect, bearing no relation to
the separate effects of those causes, the resulting phenomenon stands
forth undisguised, inviting attention to its peculiarity, and presenting
no obstacle to our recognising its presence or absence among any number of
surrounding phenomena. It admits therefore of being easily brought under
the canons of induction, provided instances can be obtained such as those
canons require: and the non-occurrence of such instances, or the want of
means to produce them artificially, is the real and only difficulty in
such investigations; a difficulty not logical, but in some sort physical.
It is otherwise with cases of what, in a preceding chapter, has been
denominated the Composition of Causes. There, the effects of the separate
causes do not terminate and give place to others, thereby ceasing to form
any part of the phenomenon to be investigated; on the contrary, they still
take place, but are intermingled with, and disguised by, the homogeneous
and closely allied effects of other causes. They are no longer _a_, _b_,
_c_, _d_, _e_, existing side by side, and continuing to be separately
discernible; they are + _a_, - _a_, 1/2 _b_, - _b_, 2 _b_, &c., some of
which cancel one another, while many others do not appear distinguishably,
but merge in one sum: forming altogether a result, between which and the
causes whereby it was produced there is often an insurmountable difficulty
in tracing by observation any fixed relation whatever.
The general idea of the Composition of Causes has been seen to be, that
although two or more laws interfere with one another, and apparently
frustrate or modify one another’s operation, yet in reality all are
fulfilled, the collective effect being the exact sum of the effects of the
causes taken separately. A familiar instance is that of a body kept in
equilibrium by two equal and contrary forces. One of the forces if acting
alone would carry it in a given time a certain distance to the west, the
other if acting alone would carry it exactly as far towards the east; and
the result is the same as if it had been first carried to the west as far
as the one force would carry it, and then back towards the east as far as
the other would carry it, that is, precisely the same distance; being
ultimately left where it was found at first.
All laws of causation are liable to be in this manner counteracted, and
seemingly frustrated, by coming into conflict with other laws, the
separate result of which is opposite to theirs, or more or less
inconsistent with it. And hence, with almost every law, many instances in
which it really is entirely fulfilled, do not, at first sight, appear to
be cases of its operation at all. It is so in the example just adduced: a
force, in mechanics, means neither more nor less than a cause of motion,
yet the sum of the effects of two causes of motion may be rest. Again, a
body solicited by two forces in directions making an angle with one
another, moves in the diagonal; and it seems a paradox to say that motion
in the diagonal is the sum of two motions in two other lines. Motion,
however, is but change of place, and at every instant the body is in the
exact place it would have been in if the forces had acted during alternate
instants instead of acting in the same instant; (saving that if we suppose
two forces to act successively which are in truth simultaneous, we must of
course allow them double the time.) It is evident, therefore, that each
force has had, during each instant, all the effect which belonged to it;
and that the modifying influence which one of two concurrent causes is
said to exercise with respect to the other, may be considered as exerted
not over the action of the cause itself, but over the effect after it is
completed. For all purposes of predicting, calculating, or explaining
their joint result, causes which compound their effects may be treated as
if they produced simultaneously each of them its own effect, and all these
effects coexisted visibly.
Since the laws of causes are as really fulfilled when the causes are said
to be counteracted by opposing causes, as when they are left to their own
undisturbed action, we must be cautious not to express the laws in such
terms as would render the assertion of their being fulfilled in those
cases a contradiction. If, for instance, it were stated as a law of nature
that a body to which a force is applied moves in the direction of the
force, with a velocity proportioned to the force directly, and to its own
mass inversely; when in point of fact some bodies to which a force is
applied do not move at all, and those which do move are, from the very
first, retarded by the action of gravity and other resisting forces, and
at last stopped altogether; it is clear that the general proposition,
though it would be true under a certain hypothesis, would not express the
facts as they actually occur. To accommodate the expression of the law to
the real phenomena, we must say, not that the object moves, but that it
_tends_ to move, in the direction and with the velocity specified. We
might, indeed, guard our expression in a different mode, by saying that
the body moves in that manner unless prevented, or except in so far as
prevented, by some counteracting cause. But the body does not only move in
that manner unless counteracted; it _tends_ to move in that manner even
when counteracted; it still exerts, in the original direction, the same
energy of movement as if its first impulse had been undisturbed, and
produces, by that energy, an exactly equivalent quantity of effect. This
is true even when the force leaves the body as it found it, in a state of
absolute rest; as when we attempt to raise a body of three tons weight
with a force equal to one ton. For if, while we are applying this force,
wind or water or any other agent supplies an additional force just
exceeding two tons, the body will be raised; thus proving that the force
we applied exerted its full effect, by neutralizing an equivalent portion
of the weight which it was insufficient altogether to overcome. And if,
while we are exerting this force of one ton upon the object in a direction
contrary to that of gravity, it be put into a scale and weighed, it will
be found to have lost a ton of its weight, or in other words, to press
downwards with a force only equal to the difference of the two forces.
These facts are correctly indicated by the expression _tendency_. All laws
of causation, in consequence of their liability to be counteracted,
require to be stated in words affirmative of tendencies only, and not of
actual results. In those sciences of causation which have an accurate
nomenclature, there are special words which signify a tendency to the
particular effect with which the science is conversant; thus _pressure_,
in mechanics, is synonymous with tendency to motion, and forces are not
reasoned on as causing actual motion, but as exerting pressure. A similar
improvement in terminology would be very salutary in many other branches
of science.
The habit of neglecting this necessary element in the precise expression
of the laws of nature, has given birth to the popular prejudice that all
general truths have exceptions; and much unmerited distrust has thence
accrued to the conclusions of science, when they have been submitted to
the judgment of minds insufficiently disciplined and cultivated. The rough
generalizations suggested by common observation usually have exceptions;
but principles of science, or in other words, laws of causation, have not.
“What is thought to be an exception to a principle,” (to quote words used
on a different occasion,) “is always some other and distinct principle
cutting into the former; some other force which impinges(87) against the
first force, and deflects it from its direction. There are not a law and
an exception to that law, the law acting in ninety-nine cases and the
exception in one. There are two laws, each possibly acting in the whole
hundred cases, and bringing about a common effect by their conjunct
operation. If the force which, being the less conspicuous of the two, is
called the _disturbing_ force, prevails sufficiently over the other force
in some one case, to constitute that case what is commonly called an
exception, the same disturbing force probably acts as a modifying cause in
many other cases which no one will call exceptions.
“Thus if it were stated to be a law of nature that all heavy bodies fall
to the ground, it would probably be said that the resistance of the
atmosphere, which prevents a balloon from falling, constitutes the balloon
an exception to that pretended law of nature. But the real law is, that
all heavy bodies _tend_ to fall; and to this there is no exception, not
even the sun and moon; for even they, as every astronomer knows, tend
towards the earth, with a force exactly equal to that with which the earth
tends towards them. The resistance of the atmosphere might, in the
particular case of the balloon, from a misapprehension of what the law of
gravitation is, be said to _prevail over_ the law; but its disturbing
effect is quite as real in every other case, since though it does not
prevent, it retards the fall of all bodies whatever. The rule, and the
so-called exception, do not divide the cases between them; each of them is
a comprehensive rule extending to all cases. To call one of these
concurrent principles an exception to the other, is superficial, and
contrary to the correct principles of nomenclature and arrangement. An
effect of precisely the same kind, and arising from the same cause, ought
not to be placed in two different categories, merely as there does or does
not exist another cause preponderating over it.”(88)
§ 6. We have now to consider according to what method these complex
effects, compounded of the effects of many causes, are to be studied; how
we are enabled to trace each effect to the concurrence of causes in which
it originated, and ascertain the conditions of its recurrence, the
circumstances in which it maybe expected again to occur. The conditions of
a phenomenon which arises from a composition of causes, may be
investigated either deductively or experimentally.
The case, it is evident, is naturally susceptible of the deductive mode of
investigation. The law of an effect of this description is a result of the
laws of the separate causes on the combination of which it depends, and is
therefore in itself capable of being deduced from these laws. This is
called the method _à priori_. The other, or _à posteriori_ method,
professes to proceed according to the canons of experimental inquiry.
Considering the whole assemblage of concurrent causes which produced the
phenomenon, as one single cause, it attempts to ascertain that cause in
the ordinary manner, by a comparison of instances. This second method
subdivides itself into two different varieties. If it merely collates
instances of the effect, it is a method of pure observation. If it
operates upon the causes, and tries different combinations of them, in
hopes of ultimately hitting the precise combination which will produce the
given total effect, it is a method of experiment.
In order more completely to clear up the nature of each of these three
methods, and determine which of them deserves the preference, it will be
expedient (conformably to a favourite maxim of Lord Chancellor Eldon, to
which, though it has often incurred philosophical ridicule, a deeper
philosophy will not refuse its sanction) to “clothe them in
circumstances.” We shall select for this purpose a case which as yet
furnishes no very brilliant example of the success of any of the three
methods, but which is all the more suited to illustrate the difficulties
inherent in them. Let the subject of inquiry be, the conditions of health
and disease in the human body; or (for greater simplicity) the conditions
of recovery from a given disease; and in order to narrow the question
still more, let it be limited, in the first instance, to this one inquiry:
Is, or is not some particular medicament (mercury, for instance) a remedy
for that disease.
Now, the deductive method would set out from known properties of mercury,
and known laws of the human body, and by reasoning from these, would
attempt to discover whether mercury will act upon the body when in the
morbid condition supposed, in such a manner as to restore health. The
experimental method would simply administer mercury in as many cases as
possible, noting the age, sex, temperament, and other peculiarities of
bodily constitution, the particular form or variety of the disease, the
particular stage of its progress, &c., remarking in which of these cases
it produced a salutary effect, and with what circumstances it was on those
occasions combined. The method of simple observation would compare
instances of recovery, to find whether they agreed in having been preceded
by the administration of mercury; or would compare instances of recovery
with instances of failure, to find cases which, agreeing in all other
respects, differed only in the fact that mercury had been administered, or
that it had not.
§ 7. That the last of these three modes of investigation is applicable to
the case, no one has ever seriously contended. No conclusions of value, on
a subject of such intricacy, ever were obtained in that way. The utmost
that could result would be a vague general impression for or against the
efficacy of mercury, of no avail for guidance unless confirmed by one of
the other two methods. Not that the results, which this method strives to
obtain, would not be of the utmost possible value if they could be
obtained. If all the cases of recovery which presented themselves, in an
examination extending to a great number of instances, were cases in which
mercury had been administered, we might generalize with confidence from
this experience, and should have obtained a conclusion of real value. But
no such basis for generalization can we, in a case of this description,
hope to obtain. The reason is that which we have so often spoken of as
constituting the characteristic imperfection of the Method of Agreement;
Plurality of Causes. Supposing even that mercury does tend to cure the
disease, so many other causes, both natural and artificial, also tend to
cure it, that there are sure to be abundant instances of recovery, in
which mercury has not been administered: unless, indeed, the practice be
to administer it in all cases; on which supposition it will equally be
found in the cases of failure.
When an effect results from the union of many causes, the share which each
has in the determination of the effect cannot in general be great: and the
effect is not likely, even in its presence or absence, still less in its
variations, to follow, even approximatively, any one of the causes.
Recovery from a disease is an event to which, in every case, many
influences must concur. Mercury may be one such influence; but from the
very fact that there are many other such, it will necessarily happen that
although mercury is administered, the patient, for want of other
concurring influences, will often not recover, and that he often will
recover when it is not administered, the other favourable influences being
sufficiently powerful without it. Neither, therefore, will the instances
of recovery agree in the administration of mercury, nor will the instances
of failure agree in its non-administration. It is much if, by multiplied
and accurate returns from hospitals and the like, we can collect that
there are rather more recoveries and rather fewer failures when mercury is
administered than when it is not; a result of very secondary value even as
a guide to practice, and almost worthless as a contribution to the theory
of the subject.
§ 8. The inapplicability of the method of simple observation to ascertain
the conditions of effects dependent on many concurring causes, being thus
recognised; we shall next inquire whether any greater benefit can be
expected from the other branch of the _à posteriori_ method, that which
proceeds by directly trying different combinations of causes, either
artificially produced or found in nature, and taking notice what is their
effect: as, for example, by actually trying the effect of mercury, in as
many different circumstances as possible. This method differs from the one
which we have just examined, in turning our attention directly to the
causes or agents, instead of turning it to the effect, recovery from the
disease. And since, as a general rule, the effects of causes are far more
accessible to our study than the causes of effects, it is natural to think
that this method has a much better chance of proving successful than the
former.
The method now under consideration is called the Empirical Method; and in
order to estimate it fairly, we must suppose it to be completely, not
incompletely, empirical. We must exclude from it everything which partakes
of the nature not of an experimental but of a deductive operation. If for
instance we try experiments with mercury upon a person in health, in order
to ascertain the general laws of its action upon the human body, and then
reason from these laws to determine how it will act upon persons affected
with a particular disease, this may be a really effectual method, but this
is deduction. The experimental method does not derive the law of a complex
case from the simpler laws which conspire to produce it, but makes its
experiments directly upon the complex case. We must make entire
abstraction of all knowledge of the simpler tendencies, the _modi
operandi_ of mercury in detail. Our experimentation must aim at obtaining
a direct answer to the specific question, Does or does not mercury tend to
cure the particular disease?
Let us see, therefore, how far the case admits of the observance of those
rules of experimentation, which it is found necessary to observe in other
cases. When we devise an experiment to ascertain the effect of a given
agent, there are certain precautions which we never, if we can help it,
omit. In the first place, we introduce the agent into the midst of a set
of circumstances which we have exactly ascertained. It needs hardly be
remarked how far this condition is from being realized in any case
connected with the phenomena of life; how far we are from knowing what are
all the circumstances which pre-exist in any instance in which mercury is
administered to a living being. This difficulty, however, though
insuperable in most cases, may not be so in all; there are sometimes
(though I should think never in physiology) concurrences of many causes,
in which we yet know accurately what the causes are. But when we have got
clear of this obstacle we encounter another still more serious. In other
cases, when we intend to try an experiment, we do not reckon it enough
that there be no circumstance in the case, the presence of which is
unknown to us. We require also that none of the circumstances which we do
know, shall have effects susceptible of being confounded with those of the
agent whose properties we wish to study. We take the utmost pains to
exclude all causes capable of composition with the given cause; or if
forced to let in any such causes, we take care to make them such, that we
can compute and allow for their influence, so that the effect of the given
cause may, after the subduction of those other effects, be apparent as a
residual phenomenon.
These precautions are inapplicable to such cases as we are now
considering. The mercury of our experiment being tried with an unknown
multitude (or even let it be a known multitude) of other influencing
circumstances, the mere fact of their being influencing circumstances
implies that they disguise the effect of the mercury, and preclude us from
knowing whether it has any effect or no. Unless we already knew what and
how much is owing to every other circumstance, (that is, unless we suppose
the very problem solved which we are considering the means of solving,) we
cannot tell that those other circumstances may not have produced the whole
of the effect, independently or even in spite of the mercury. The Method
of Difference, in the ordinary mode of its use, namely by comparing the
state of things following the experiment with the state which preceded it,
is thus, in the case of intermixture of effects, entirely unavailing;
because other causes than that whose effect we are seeking to determine,
have been operating during the transition. As for the other mode of
employing the Method of Difference, namely by comparing, not the same case
at two different periods, but different cases, this in the present
instance is quite chimerical. In phenomena so complicated it is
questionable if two cases similar in all respects but one ever occurred;
and were they to occur, we could not possibly know that they were so
exactly similar.
Anything like a scientific use of the method of experiment, in these
complicated cases, is therefore out of the question. We can in the most
favourable cases only discover, by a succession of trials, that a certain
cause is _very often_ followed by a certain effect. For, in one of these
conjunct effects, the portion which is determined by any one of the
influencing agents, is generally, as we before remarked, but small; and it
must be a more potent cause than most, if even the tendency which it
really exerts is not thwarted by other tendencies in nearly as many cases
as it is fulfilled.
If so little can be done by the experimental method to determine the
conditions of an effect of many combined causes, in the case of medical
science, still less is this method applicable to a class of phenomena,
more complicated than even those of physiology, the phenomena of politics
and history. There, Plurality of Causes exists in almost boundless excess,
and the effects are, for the most part, inextricably interwoven with one
another. To add to the embarrassment, most of the inquiries in political
science relate to the production of effects of a most comprehensive
description, such as the public wealth, public security, public morality,
and the like: results liable to be affected directly or indirectly either
in _plus_ or in _minus_ by nearly every fact which exists, or event which
occurs, in human society. The vulgar notion, that the safe methods on
political subjects are those of Baconian induction, that the true guide is
not general reasoning, but specific experience, will one day be quoted as
among the most unequivocal marks of a low state of the speculative
faculties in any age in which it is accredited. Nothing can be more
ludicrous than the sort of parodies on experimental reasoning which one is
accustomed to meet with, not in popular discussion only, but in grave
treatises, when the affairs of nations are the theme. “How,” it is asked,
“can an institution be bad, when the country has prospered under it?” “How
can such or such causes have contributed to the prosperity of one country,
when another has prospered without them?” Whoever makes use of an argument
of this kind, not intending to deceive, should be sent back to learn the
elements of some one of the more easy physical sciences. Such reasoners
ignore the fact of Plurality of Causes in the very case which affords the
most signal example of it. So little could be concluded, in such a case,
from any possible collation of individual instances, that even the
impossibility, in social phenomena, of making artificial experiments, a
circumstance otherwise so prejudicial to directly inductive inquiry,
hardly affords, in this case, additional reason of regret. For even if we
could try experiments upon a nation or upon the human race, with as little
scruple as M. Majendie tries them upon dogs or rabbits, we should never
succeed in making two instances identical in every respect except the
presence or absence of some one indefinite circumstance. The nearest
approach to an experiment in the philosophical sense, which takes place in
politics, is the introduction of a new operative element into national
affairs by some special and assignable measure of government, such as the
enactment or repeal of a particular law. But where there are so many
influences at work, it requires some time for the influence of any new
cause upon national phenomena to become apparent; and as the causes
operating in so extensive a sphere are not only infinitely numerous, but
in a state of perpetual alteration, it is always certain that before the
effect of the new cause becomes conspicuous enough to be a subject of
induction, so many of the other influencing circumstances will have
changed as to vitiate the experiment.
Two, therefore, of the three possible methods for the study of phenomena
resulting from the composition of many causes, being, from the very nature
of the case, inefficient and illusory; there remains only the third,—that
which considers the causes separately, and computes the effect from the
balance of the different tendencies which produce it: in short, the
deductive, or _à priori_ method. The more particular consideration of this
intellectual process requires a chapter to itself.