On The Composition Of Causes.
§ 1. To complete the general notion of causation on which the rules of
experimental inquiry into the laws of nature must be founded, one
distinction still remains to be pointed out: a distinction so radical, and
of so much importance, as to require a chapter to itself.
The preceding discussions have rendered us familiar with the case in which
several agents, or causes, concur as conditions to the production of an
effect; a case, in truth, almost universal, there being very few effects
to the production of which no more than one agent contributes. Suppose,
then, that two different agents, operating jointly, are followed, under a
certain set of collateral conditions, by a given effect. If either of
these agents, instead of being joined with the other, had operated alone,
under the same set of conditions in all other respects, some effect would
probably have followed, which would have been different from the joint
effect of the two, and more or less dissimilar to it. Now, if we happen to
know what would be the effect of each cause when acting separately from
the other, we are often able to arrive deductively, or _a priori_, at a
correct prediction of what will arise from their conjunct agency. To
render this possible, it is only necessary that the same law which
expresses the effect of each cause acting by itself, shall also correctly
express the part due to that cause of the effect which follows from the
two together. This condition is realized in the extensive and important
class of phenomena commonly called mechanical, namely the phenomena of the
communication of motion (or of pressure, which is tendency to motion) from
one body to another. In this important class of cases of causation, one
cause never, properly speaking, defeats or frustrates another; both have
their full effect. If a body is propelled in two directions by two forces,
one tending to drive it to the north and the other to the east, it is
caused to move in a given time exactly as far in both directions as the
two forces would separately have carried it; and is left precisely where
it would have arrived if it had been acted upon first by one of the two
forces, and afterward by the other. This law of nature is called, in
dynamics, the principle of the Composition of Forces; and in imitation of
that well-chosen expression, I shall give the name of the Composition of
Causes to the principle which is exemplified in all cases in which the
joint effect of several causes is identical with the sum of their separate
effects.
This principle, however, by no means prevails in all departments of the
field of nature. The chemical combination of two substances produces, as
is well known, a third substance, with properties different from those of
either of the two substances separately, or of both of them taken
together. Not a trace of the properties of hydrogen or of oxygen is
observable in those of their compound, water. The taste of sugar of lead
is not the sum of the tastes of its component elements, acetic acid and
lead or its oxide; nor is the color of blue vitriol a mixture of the
colors of sulphuric acid and copper. This explains why mechanics is a
deductive or demonstrative science, and chemistry not. In the one, we can
compute the effects of combinations of causes, whether real or
hypothetical, from the laws which we know to govern those causes when
acting separately, because they continue to observe the same laws when in
combination which they observe when separate: whatever would have happened
in consequence of each cause taken by itself, happens when they are
together, and we have only to cast up the results. Not so in the phenomena
which are the peculiar subject of the science of chemistry. There most of
the uniformities to which the causes conform when separate, cease
altogether when they are conjoined; and we are not, at least in the
present state of our knowledge, able to foresee what result will follow
from any new combination until we have tried the specific experiment.
If this be true of chemical combinations, it is still more true of those
far more complex combinations of elements which constitute organized
bodies; and in which those extraordinary new uniformities arise which are
called the laws of life. All organized bodies are composed of parts
similar to those composing inorganic nature, and which have even
themselves existed in an inorganic state; but the phenomena of life, which
result from the juxtaposition of those parts in a certain manner, bear no
analogy to any of the effects which would be produced by the action of the
component substances considered as mere physical agents. To whatever
degree we might imagine our knowledge of the properties of the several
ingredients of a living body to be extended and perfected, it is certain
that no mere summing up of the separate actions of those elements will
ever amount to the action of the living body itself. The tongue, for
instance, is, like all other parts of the animal frame, composed of
gelatine, fibrine, and other products of the chemistry of digestion; but
from no knowledge of the properties of those substances could we ever
predict that it could taste, unless gelatine or fibrine could themselves
taste; for no elementary fact can be in the conclusion which was not in
the premises.
There are thus two different modes of the conjunct action of causes; from
which arise two modes of conflict, or mutual interference, between laws of
nature. Suppose, at a given point of time and space, two or more causes,
which, if they acted separately, would produce effects contrary, or at
least conflicting with each other; one of them tending to undo, wholly or
partially, what the other tends to do. Thus the expansive force of the
gases generated by the ignition of gunpowder tends to project a bullet
toward the sky, while its gravity tends to make it fall to the ground. A
stream running into a reservoir at one end tends to fill it higher and
higher, while a drain at the other extremity tends to empty it. Now, in
such cases as these, even if the two causes which are in joint action
exactly annul one another, still the laws of both are fulfilled; the
effect is the same as if the drain had been open for half an hour
first,(132) and the stream had flowed in for as long afterward. Each agent
produces the same amount of effect as if it had acted separately, though
the contrary effect which was taking place during the same time
obliterated it as fast as it was produced. Here, then, are two causes,
producing by their joint operations an effect which at first seems quite
dissimilar to those which they produce separately, but which on
examination proves to be really the sum of those separate effects. It will
be noticed that we here enlarge the idea of the sum of two effects, so as
to include what is commonly called their difference, but which is in
reality the result of the addition of opposites; a conception to which
mankind are indebted for that admirable extension of the algebraical
calculus, which has so vastly increased its powers as an instrument of
discovery, by introducing into its reasonings (with the sign of
subtraction prefixed, and under the name of Negative Quantities) every
description whatever of positive phenomena, provided they are of such a
quality in reference to those previously introduced, that to add the one
is equivalent to subtracting an equal quantity of the other.
There is, then, one mode of the mutual interference of laws of nature, in
which, even when the concurrent causes annihilate each other’s effects,
each exerts its full efficacy according to its own law—its law as a
separate agent. But in the other description of cases, the agencies which
are brought together cease entirely, and a totally different set of
phenomena arise: as in the experiment of two liquids which, when mixed in
certain proportions, instantly become, not a larger amount of liquid, but
a solid mass.
§ 2. This difference between the case in which the joint effect of causes
is the sum of their separate effects, and the case in which it is
heterogeneous to them—between laws which work together without alteration,
and laws which, when called upon to work together, cease and give place to
others—is one of the fundamental distinctions in nature. The former case,
that of the Composition of Causes, is the general one; the other is always
special and exceptional. There are no objects which do not, as to some of
their phenomena, obey the principle of the Composition of Causes; none
that have not some laws which are rigidly fulfilled in every combination
into which the objects enter. The weight of a body, for instance, is a
property which it retains in all the combinations in which it is placed.
The weight of a chemical compound, or of an organized body, is equal to
the sum of the weights of the elements which compose it. The weight either
of the elements or of the compound will vary, if they be carried farther
from their centre of attraction, or brought nearer to it; but whatever
effects the one effects the other. They always remain precisely equal. So,
again, the component parts of a vegetable or animal substance do not lose
their mechanical and chemical properties as separate agents, when, by a
peculiar mode of juxtaposition, they, as an aggregate whole, acquire
physiological or vital properties in addition. Those bodies continue, as
before, to obey mechanical and chemical laws, in so far as the operation
of those laws is not counteracted by the new laws which govern them as
organized beings; when, in short, a concurrence of causes takes place
which calls into action new laws bearing no analogy to any that we can
trace in the separate operation of the causes, the new laws, while they
supersede one portion of the previous laws, may co-exist with another
portion, and may even compound the effect of those previous laws with
their own.
Again, laws which were themselves generated in the second mode, may
generate others in the first. Though there are laws which, like those of
chemistry and physiology, owe their existence to a breach of the principle
of Composition of Causes, it does not follow that these peculiar, or, as
they might be termed, _heteropathic_ laws, are not capable of composition
with one another. The causes which by one combination have had their laws
altered, may carry their new laws with them unaltered into their ulterior
combinations. And hence there is no reason to despair of ultimately
raising chemistry and physiology to the condition of deductive sciences;
for though it is impossible to deduce all chemical and physiological
truths from the laws or properties of simple substances or elementary
agents, they may possibly be deducible from laws which commence when these
elementary agents are brought together into some moderate number of not
very complex combinations. The Laws of Life will never be deducible from
the mere laws of the ingredients, but the prodigiously complex Facts of
Life may all be deducible from comparatively simple laws of life; which
laws (depending indeed on combinations, but on comparatively simple
combinations, of antecedents) may, in more complex circumstances, be
strictly compounded with one another, and with the physical and chemical
laws of the ingredients. The details of the vital phenomena, even now,
afford innumerable exemplifications of the Composition of Causes; and in
proportion as these phenomena are more accurately studied, there appears
more reason to believe that the same laws which operate in the simpler
combinations of circumstances do, in fact, continue to be observed in the
more complex. This will be found equally true in the phenomena of mind;
and even in social and political phenomena, the results of the laws of
mind. It is in the case of chemical phenomena that the least progress has
yet been made in bringing the special laws under general ones from which
they may be deduced; but there are even in chemistry many circumstances to
encourage the hope that such general laws will hereafter be discovered.
The different actions of a chemical compound will never, undoubtedly, be
found to be the sums of the actions of its separate elements; but there
may exist, between the properties of the compound and those of its
elements, some constant relation, which, if discoverable by a sufficient
induction, would enable us to foresee the sort of compound which will
result from a new combination before we have actually tried it, and to
judge of what sort of elements some new substance is compounded before we
have analyzed it. The law of definite proportions, first discovered in its
full generality by Dalton, is a complete solution of this problem in one,
though but a secondary aspect, that of quantity; and in respect to
quality, we have already some partial generalizations, sufficient to
indicate the possibility of ultimately proceeding farther. We can
predicate some common properties of the kind of compounds which result
from the combination, in each of the small number of possible proportions,
of any acid whatever with any base. We have also the curious law,
discovered by Berthollet, that two soluble salts mutually decompose one
another whenever the new combinations which result produce an insoluble
compound, or one less soluble than the two former. Another uniformity is
that called the law of isomorphism; the identity of the crystalline forms
of substances which possess in common certain peculiarities of chemical
composition.(133) Thus it appears that even heteropathic laws, such laws
of combined agency as are not compounded of the laws of the separate
agencies, are yet, at least in some cases, derived from them according to
a fixed principle. There may, therefore, be laws of the generation of laws
from others dissimilar to them; and in chemistry, these undiscovered laws
of the dependence of the properties of the compound on the properties of
its elements, may, together with the laws of the elements themselves,
furnish the premises by which the science is perhaps destined one day to
be rendered deductive.
It would seem, therefore, that there is no class of phenomena in which the
Composition of Causes does not obtain: that as a general rule, causes in
combination produce exactly the same effects as when acting singly: but
that this rule, though general, is not universal: that in some instances,
at some particular points in the transition from separate to united
action, the laws change, and an entirely new set of effects are either
added to, or take the place of, those which arise from the separate agency
of the same causes: the laws of these new effects being again susceptible
of composition, to an indefinite extent, like the laws which they
superseded.
§ 3. That effects are proportional to their causes is laid down by some
writers as an axiom in the theory of causation; and great use is sometimes
made of this principle in reasonings respecting the laws of nature, though
it is encumbered with many difficulties and apparent exceptions, which
much ingenuity has been expended in showing not to be real ones. This
proposition, in so far as it is true, enters as a particular case into the
general principle of the Composition of Causes; the causes compounded
being, in this instance, homogeneous; in which case, if in any, their
joint effect might be expected to be identical with the sum of their
separate effects. If a force equal to one hundred weight will raise a
certain body along an inclined plane, a force equal to two hundred weight
will raise two bodies exactly similar, and thus the effect is proportional
to the cause. But does not a force equal to two hundred weight actually
contain in itself two forces each equal to one hundred weight, which, if
employed apart, would separately raise the two bodies in question? The
fact, therefore, that when exerted jointly they raise both bodies at once,
results from the Composition of Causes, and is a mere instance of the
general fact that mechanical forces are subject to the law of Composition.
And so in every other case which can be supposed. For the doctrine of the
proportionality of effects to their causes can not of course be applicable
to cases in which the augmentation of the cause alters the kind of effect;
that is, in which the surplus quantity superadded to the cause does not
become compounded with it, but the two together generate an altogether new
phenomenon. Suppose that the application of a certain quantity of heat to
a body merely increases its bulk, that a double quantity melts it, and a
triple quantity decomposes it: these three effects being heterogeneous, no
ratio, whether corresponding or not to that of the quantities of heat
applied, can be established between them. Thus the supposed axiom of the
proportionality of effects to their causes fails at the precise point
where the principle of the Composition of Causes also fails; viz., where
the concurrence of causes is such as to determine a change in the
properties of the body generally, and render it subject to new laws, more
or less dissimilar to those to which it conformed in its previous state.
The recognition, therefore, of any such law of proportionality is
superseded by the more comprehensive principle, in which as much of it as
is true is implicitly asserted.(134)
The general remarks on causation, which seemed necessary as an
introduction to the theory of the inductive process, may here terminate.
That process is essentially an inquiry into cases of causation. All the
uniformities which exist in the succession of phenomena, and most of the
uniformities in their co-existence, are either, as we have seen,
themselves laws of causation, or consequences resulting from, and
corollaries capable of being deduced from, such laws. If we could
determine what causes are correctly assigned to what effects, and what
effects to what causes, we should be virtually acquainted with the whole
course of nature. All those uniformities which are mere results of
causation might then be explained and accounted for; and every individual
fact or event might be predicted, provided we had the requisite data, that
is, the requisite knowledge of the circumstances which, in the particular
instance, preceded it.
To ascertain, therefore, what are the laws of causation which exist in
nature; to determine the effect of every cause, and the causes of all
effects, is the main business of Induction; and to point out how this is
done is the chief object of Inductive Logic.