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 _à priori_, at a correct prediction of what will
arise from their conjunct agency. To enable us to do this, 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
afterwards 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 entirely different from
those of either of the two substances separately, or 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 colour of blue vitriol a mixture of the
colours 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 all 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 observed 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 conformed 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, fibrin, 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 fibrin
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 towards 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,[31] and the stream had flowed in for as long
afterwards. Each agent produced 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 operation 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 affects the one
affects 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 coexist 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 analysed 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.
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 incumbered 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 cannot 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.
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 coexistence, 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.