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
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. 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 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 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, 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
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 connected with 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 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
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, &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 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 analysed, cannot 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 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
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.
The very promising generalization now commonly known as the Conservation
or Persistence of Force, bears a close resemblance to what the
conception of chemical composition would become, if divested of the one
circumstance which now distinguishes it from simple transformation. It
has long been known that heat is capable of producing electricity, and
electricity heat; that mechanical motion in numerous cases produces and
is produced by them both; and so of all other physical forces. It has of
late become the general belief of scientific inquirers that mechanical
force, electricity, magnetism, heat, light, and chemical action (to
which has subsequently been added vital action) are not so much causes
of one another as convertible into one another; and they are now
generally spoken of as forms of one and the same force, varying only in
its manifestations. This doctrine may be admitted, without by any means
implying that Force is a real entity, a Thing in itself, distinct from
all its phenomenal manifestations to our organs. Supposing the doctrine
true, the several kinds of phenomena which it identifies in respect of
their origin would nevertheless remain different facts; facts which
would be causes of one another--reciprocally causes and effects, which
is the first element in the form of causation properly called
transformation. What the doctrine contains more than this, is, that in
each of these cases of reciprocal causation, the causes are reproduced
without alteration in quantity. This is what takes place in the
transformations of matter: when water has been converted into hydrogen
and oxygen, these can be reconverted into precisely the same quantity of
water from which they were produced. To establish a corresponding law in
regard to Force, it has to be proved that heat is capable of being
converted into electricity, electricity into chemical action, chemical
action into mechanical force, and mechanical force back again into the
exact quantity of heat which was originally expended; and so through
all the interchanges. Were this proved, it would establish what
constitutes transformation, as distinguished from the simple fact of
reciprocal causation. The fact in issue is simply the quantitative
equivalence of all these natural agencies; whereby a given quantity of
any one is convertible into, and interchangeable with, a given, and
always the same, quantity of any other: this, no less, but also no more.
It cannot yet be said that the law has been fully proved of any case,
except that of interchange between heat and mechanical motion. It does
seem to be ascertained, not only that these two are convertible into
each other, but that after any number of conversions the original
quantities reappear without addition or diminution, like the original
quantities of hydrogen and oxygen after passing through the condition of
water. If the same thing comes to be proved true of all the other
forces, in relation to these two and to one another, the law of
Conservation will be established; and it will be a legitimate mode of
expressing the fact, to speak of Force, as we already speak of Matter,
as indestructible. But Force will not the less remain, to the
philosopher, a mere abstraction of the mind. All that will have been
proved is, that in the phenomena of Nature, nothing actually ceases
without generating a calculable, and always the same, quantity of some
other natural phenomenon, which again, when it ceases, will in its turn
either generate a calculable, and always the same, quantity of some
third phenomenon, or reproduce the original quantity of the first.
In these cases, where the heteropathic effect (as we called it in a
former chapter)[44] 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 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
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
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 (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 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[45] 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."[46]
§ 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 _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
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 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 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 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 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 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 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 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 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 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 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 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.
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 _à priori_ method. The more particular
consideration of this intellectual process requires a chapter to itself.