Of Plurality Of Causes, And Of The Intermixture Of Effects.
§ 1. In the preceding exposition of the four methods of observation and
experiment, by which we contrive to distinguish among a mass of
co-existent 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 co-existent 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. The cause indeed may not be simple; it
may consist of an assemblage of conditions; but we have supposed that
there was only one possible assemblage of conditions from which the given
effect could result.
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 mechanical 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 apparently 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 very numerous; 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, though 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 favor 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 toward a solution of this doubt. For if
we try A F G, A H K, etc., 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 favor 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 connected
with A divested of the characteristic imperfection, and reduced to a
virtual certainty? This is a question which we can not 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 analyzing 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 recognized 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
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 can
not 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 is entirely
useless, provided there have been already enough to exclude the
supposition of 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 premises (if they
may be so called), the negative premise. 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 premise, it might
therefore be supposed, could be worked as a simple case of the Method of
Agreement, without requiring an affirmative premise to be joined with it.
But though 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 is now thought that in
the production of heat by friction, percussion, chemical action, etc., the
ultimate source is one and the same. But if (as continually happens) we
can not 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
premises 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. Besides, many substances, though they can
be analyzed, can not by any known artificial means be recompounded.
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 toward 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
re-appear 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 connection 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 facts 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, where the heteropathic effect (as we called it in a former
chapter)(147) is but a transformation of its cause, or in other words,
where 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 can not be reproduced from the product; just as a youth
can grow into an old man, but an old man can not grow into a youth. We can
not 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 recognizing 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_, ½_b_, _–b_, 2_b_, etc.; 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
though 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 the body in a given time a certain distance to the west,
the other if acting alone would carry it exactly as far toward 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 toward 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 co-existed 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 (at least in the
region of our earth) 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 downward 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(148)
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
toward the earth, with a force exactly equal to that with which the earth
tends toward 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.”(149)
§ 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 may be 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 _a priori_. The other, or _a 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 the 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 favorite 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 the given 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 would tend 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, etc., remarking in
which of these cases it was attended with 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 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 can not in general be great, and
the effect is not likely, even in its presence or absence, still less in
its variations, to follow, even approximately, 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 favorable 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.(150)
§ 8. The inapplicability of the method of simple observation to ascertain
the conditions of effects dependent on many concurring causes, being thus
recognized, we shall next inquire whether any greater benefit can be
expected from the other branch of the _a 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 every thing 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
concurrences of many causes, in which we yet know accurately what the
causes are. Moreover, the difficulty may be attenuated by sufficient
multiplication of experiments, in circumstances rendering it improbable
that any of the unknown causes should exist in them all. 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 agents 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 not. 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
can not 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.
Any thing like a scientific use of the method of experiment, in these
complicated cases, is therefore out of the question. We can generally,
even in the most favorable 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 usually, 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. Some causes indeed there are which are more
potent than any counteracting causes to which they are commonly exposed;
and accordingly there are some truths in medicine which are sufficiently
proved by direct experiment. Of these the most familiar are those that
relate to the efficacy of the substances known as Specifics for particular
diseases, “quinine, colchicum, lime-juice, cod-liver oil,”(151) and a few
others. Even these are not invariably followed by success; but they
succeed in so large a proportion of cases, and against such powerful
obstacles, that their _tendency_ to restore health in the disorders for
which they are prescribed may be regarded as an experimental truth.(152)
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
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. Magendie tried them on dogs and rabbits, we should never succeed in
making two instances identical in every respect except the presence or
absence of some one definite 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.(153)
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 infers the effect from the
balance of the different tendencies which produce it: in short, the
deductive, or _a priori_ method. The more particular consideration of this
intellectual process requires a chapter to itself.