§ 1. The deductive operation by which we derive the law of an effect from
the laws of the causes, of which the concurrence gives rise to it, may be
undertaken either for the purpose of discovering the law, or of explaining
a law already discovered. The word _explanation_ occurs so continually and
holds so important a place in philosophy, that a little time spent in
fixing the meaning of it will be profitably employed.
An individual fact is said to be explained, by pointing out its cause,
that is, by stating the law or laws of causation, of which its production
is an instance. Thus, a conflagration is explained, when it is proved to
have arisen from a spark falling into the midst of a heap of combustibles.
And in a similar manner, a law or uniformity in nature is said to be
explained, when another law or laws are pointed out, of which that law
itself is but a case, and from which it could be deduced.
§ 2. There are three distinguishable sets of circumstances in which a law
of causation may be explained from, or, as it also is often expressed,
resolved into, other laws.
The first is the case already so fully considered; an intermixture of
laws, producing a joint effect equal to the sum of the effects of the
causes taken separately. The law of the complex effects is explained, by
being resolved into the separate laws of the causes which contribute to
it. Thus, the law of the motion of a planet is resolved into the law of
the tangential force, which tends to produce an uniform motion in the
tangent, and the law of the centripetal force, which tends to produce an
accelerating motion towards the sun; the real motion being a compound of
the two.
It is necessary here to remark, that in this resolution of the law of a
complex effect, the laws of which it is compounded are not the only
elements. It is resolved into the laws of the separate causes, together
with the fact of their co-existence. The one is as essential an ingredient
as the other; whether the object be to discover the law of the effect, or
only to explain it. To deduce the laws of the heavenly motions, we require
not only to know the law of a rectilineal and that of a gravitative force,
but the existence of both these forces in the celestial regions, and even
their relative amount. The complex laws of causation are thus resolved
into two distinct kinds of elements: the one, simpler laws of causation,
the other (in the aptly selected language of Dr. Chalmers) collocations;
the collocations consisting in the existence of certain agents or powers,
in certain circumstances of place and time. We shall hereafter have
occasion to return to this distinction, and to dwell on it at such a
length as dispenses with the necessity of further insisting on it here.
The first mode, then, of the explanation of Laws of Causation, is when the
law of an effect is resolved into the various tendencies of which it is
the result, and into the laws of those tendencies.
§ 3. A second case is when, between what seemed the cause and what was
supposed to be its effect, further observation detects an immediate link;
a fact caused by the antecedent, and in its turn causing the consequent;
so that the cause at first assigned is but the remote cause, operating
through the intermediate phenomenon. A seemed the cause of C, but it
subsequently appeared that A was only the cause of B, and that it is B
which was the cause of C. For example: mankind were aware that the act of
touching an outward object caused a sensation. It was, however, at last
discovered, that after we have touched the object, and before we
experience the sensation, some change takes place in a kind of thread
called a nerve, which extends from our outward organs to the brain.
Touching the object, therefore, is only the remote cause of our sensation;
that is, not the cause, properly speaking, but the cause of the cause;—the
real cause of the sensation is the change in the state of the nerve.
Future experience may not only give us more knowledge than we now have of
the particular nature of this change, but may also interpolate another
link: between the contact (for example) of the object with our outward
organs, and the production of the change of state in the nerve, there may
take place some electric phenomenon; or some phenomenon of a nature not
resembling the effects of any known agency. Hitherto, however, no such
intermediate link has been discovered; and the touch of the object must be
considered, provisionally at least, as the proximate cause of the
affection of the nerve. The sequence, therefore, of a sensation of touch
on contact with an object, is ascertained not to be an ultimate law; it is
resolved, as the phrase is, into two other laws,—the law, that contact
with an object produces an affection of the nerve; and the law, that an
affection of the nerve produces sensation.
To take another example: the more powerful acids corrode or blacken
organic compounds. This is a case of causation, but of remote causation;
and is said to be explained when it is shown that there is an intermediate
link, namely, the separation of some of the chemical elements of the
organic structure from the rest, and their entering into combination with
the acid. The acid causes this separation of the elements, and the
separation of the elements causes the disorganization, and often the
charring of the structure. So, again, chlorine extracts colouring matters,
(whence its efficacy in bleaching,) and purifies the air from infection.
This law is resolved into the two following laws. Chlorine has a powerful
affinity for bases of all kinds, particularly metallic bases and hydrogen.
Such bases are essential elements of colouring matters and contagious
compounds: which substances, therefore, are decomposed and destroyed by
chlorine.
§ 4. It is of importance to remark, that when a sequence of phenomena is
thus resolved into other laws, they are always laws more general than
itself. The law that A is followed by C, is less general than either of
the laws which connect B with C and A with B. This will appear from very
simple considerations.
All laws of causation are liable to be counteracted or frustrated, by the
non-fulfilment of some negative condition: the tendency, therefore, of B
to produce C may be defeated. Now the law that A produces B, is equally
fulfilled whether B is followed by C or not; but the law that A produces C
by means of B, is of course only fulfilled when B is really followed by C,
and is therefore less general than the law that A produces B. It is also
less general than the law that B produces C. For B may have other causes
besides A; and as A produces C only by means of B, while B produces C
whether it has itself been produced by A or by anything else, the second
law embraces a greater number of instances, covers as it were a greater
space of ground, than the first.
Thus, in our former example, the law that the contact of an object causes
a change in the state of the nerve, is more general than the law that
contact with an object causes sensation, since, for aught we know, the
change in the nerve may equally take place when, from a counteracting
cause, as for instance, strong mental excitement, the sensation does not
follow; as in a battle, where wounds are often received without any
consciousness of receiving them. And again, the law that change in the
state of a nerve produces sensation, is more general than the law that
contact with an object produces sensation; since the sensation equally
follows the change in the nerve when not produced by contact with an
object, but by some other cause; as in the well-known case, when a person
who has lost a limb feels the same sensation which he has been accustomed
to call a pain in the limb.
Not only are the laws of more immediate sequence into which the law of a
remote sequence is resolved, laws of greater generality than that law is,
but (as a consequence of, or rather as implied in, their greater
generality) they are more to be relied on; there are fewer chances of
their being ultimately found not to be universally true. From the moment
when the sequence of A and C is shown not to be immediate, but to depend
on an intervening phenomenon, then, however constant and invariable the
sequence of A and C has hitherto been found, possibilities arise of its
failure, exceeding those which can affect either of the more immediate
sequences, A, B, and B, C. The tendency of A to produce C may be defeated
by whatever is capable of defeating either the tendency of A to produce B,
or the tendency of B to produce C; it is therefore twice as liable to
failure as either of those more elementary tendencies; and the
generalization that A is always followed by C, is twice as likely to be
found erroneous. And so of the converse generalization, that C is always
preceded and caused by A; which will be erroneous not only if there should
happen to be a second immediate mode of production of C itself, but
moreover if there be a second mode of production of B, the immediate
antecedent of C in the sequence.
The resolution of the one generalization into the other two, not only
shows that there are possible limitations of the former, from which its
two elements are exempt, but shows also where these are to be looked for.
As soon as we know that B intervenes between A and C, we also know that if
there be cases in which the sequence of A and C does not hold, these are
most likely to be found by studying the effects or the conditions of the
phenomenon B.
It appears, then, that in the second of the three modes in which a law may
be resolved into other laws, the latter are more general, that is, extend
to more cases, and are also less likely to require limitation from
subsequent experience, than the law which they serve to explain. They are
more nearly unconditional; they are defeated by fewer contingencies; they
are a nearer approach to the universal truth of nature. The same
observations are still more evidently true with regard to the first of the
three modes of resolution. When the law of an effect of combined causes is
resolved into the separate laws of the causes, the nature of the case
implies that the law of the effect is less general than the law of any of
the causes, since it only holds when they are combined; while the law of
any one of the causes holds good both then, and also when that cause acts
apart from the rest. It is also manifest that the complex law is liable to
be oftener unfulfilled than any one of the simpler laws of which it is the
result, since every contingency which defeats any of the laws prevents so
much of the effect as depends on it, and thereby defeats the complex law.
The mere rusting, for example, of some small part of a great machine,
often suffices entirely to prevent the effect which ought to result from
the joint action of all the parts. The law of the effect of a combination
of causes is always subject to the whole of the negative conditions which
attach to the action of all the causes severally.
There is another and a still stronger reason why the law of a complex
effect must be less general than the laws of the causes which conspire to
produce it. The same causes, acting according to the same laws, and
differing only in the proportions in which they are combined, often
produce effects which differ not merely in quantity, but in kind. The
combination of a centripetal with a projectile force, in the proportions
which obtain in all the planets and satellites of our solar system, gives
rise to an elliptical motion; but if the ratio of the two forces to each
other were slightly altered, it is demonstrable that the motion produced
would be in a circle, or a parabola, or an hyperbola: and it has been
surmised that in the case of some comets one of these is really the fact.
Yet the law of the parabolic motion would be resolvable into the very same
simple laws into which that of the elliptical motion is revolved, namely,
the law of the permanence of rectilineal motion, and the law of
gravitation. If, therefore, in the course of ages, some circumstance were
to manifest itself which, without defeating the law of either of those
forces, should merely alter their proportion to one another, (such as the
shock of a comet, or even the accumulating effect of the resistance of the
medium in which astronomers have been led to surmise that the motions of
the heavenly bodies take place;) the elliptical motion might be changed
into a motion in some other conic section; and the complex law, that the
heavenly motions take place in ellipses, would be deprived of its
universality, though the discovery would not at all detract from the
universality of the simpler laws into which that complex law is resolved.
The law, in short, of each of the concurrent causes remains the same,
however their collocations may vary; but the law of their joint effect
varies with every difference in the collocations. There needs no more to
show how much more general the elementary laws must be, than any of the
complex laws which are derived from them.
§ 5. Besides the two modes which have been treated of, there is a third
mode in which laws are resolved into one another; and in this it is
self-evident that they are resolved into laws more general than
themselves. This third mode is the _subsumption_ (as it has been called)
of one law under another: or (what comes to the same thing) the gathering
up of several laws into one more general law which includes them all. The
most splendid example of this operation was when terrestrial gravity and
the central force of the solar system were brought together under the
general law of gravitation. It had been proved antecedently that the earth
and the other planets tend to the sun; and it had been known from the
earliest times that terrestrial bodies tend towards the earth. These were
similar phenomena; and to enable them both to be subsumed under one law,
it was only necessary to prove that, as the effects were similar in
quality, so also they, as to quantity, conform to the same rules. This was
first shown to be true of the moon, which agreed with terrestrial objects
not only in tending to a centre, but in the fact that this centre was the
earth. The tendency of the moon towards the earth being ascertained to
vary as the inverse square of the distance, it was deduced from this, by
direct calculation, that if the moon were as near to the earth as
terrestrial objects are, and the tangential force were suspended, the moon
would fall towards the earth through exactly as many feet in a second as
those objects do by virtue of their weight. Hence the inference was
irresistible, that the moon also tends to the earth by virtue of its
weight: and that the two phenomena, the tendency of the moon to the earth
and the tendency of terrestrial objects to the earth, being not only
similar in quality, but, when in the same circumstances, identical in
quantity, are cases of one and the same law of causation. But the tendency
of the moon to the earth and the tendency of the earth and planets to the
sun, were already known to be cases of the same law of causation: and thus
the law of all these tendencies, and the law of terrestrial gravity, were
recognized as identical, or in other words, were subsumed under one
general law, that of gravitation.
In a similar manner, the laws of magnetic phenomena have recently been
subsumed under known laws of electricity. It is thus that the most general
laws of nature are usually arrived at: we mount to them by successive
steps. For, to arrive by correct induction at laws which hold under such
an immense variety of circumstances, laws so general as to be independent
of any varieties of space or time which we are able to observe, requires
for the most part many distinct sets of experiments or observations,
conducted at different times and by different people. One part of the law
is first ascertained, afterwards another part: one set of observations
teaches us that the law holds good under some conditions, another that it
holds good under other conditions, by combining which observations we find
that it holds good under conditions much more general, or even
universally. The general law, in this case, is literally the sum of all
the partial ones; it is the recognition of the same sequence in different
sets of instances; and may, in fact, be regarded as merely one step in the
process of elimination. That tendency of bodies towards one another, which
we now call gravity, had at first been observed only on the earth’s
surface, where it manifested itself only as a tendency of all bodies
towards the earth, and might, therefore, be ascribed to a peculiar
property of the earth itself: one of the circumstances, namely, the
proximity of the earth, had not been eliminated. To eliminate this
circumstance required a fresh set of instances in other parts of the
universe: these we could not ourselves create; and though nature had
created them for us, we were placed in very unfavourable circumstances for
observing them. To make these observations, fell naturally to the lot of a
different set of persons from those who studied terrestrial phenomena, and
had, indeed, been a matter of great interest at a time when the idea of
explaining celestial facts by terrestrial laws was looked upon as the
confounding of an indefeasible distinction. When, however, the celestial
motions were accurately ascertained, and the deductive processes performed
from which it appeared that their laws and those of terrestrial gravity
corresponded, those celestial observations became a set of instances which
exactly eliminated the circumstance of proximity to the earth; and proved
that in the original case, that of terrestrial objects, it was not the
earth, as such, that caused the motion or the pressure, but the
circumstance common to that case with the celestial instances, namely, the
presence of some great body within certain limits of distance.
§ 6. There are, then, three modes of explaining laws of causation, or,
which is the same thing, resolving them into other laws. First, when the
law of an effect of combined causes is resolved into the separate laws of
the causes, together with the fact of their combination. Secondly, when
the law which connects any two links, not proximate, in a chain of
causation, is resolved into the laws which connect each with the
intermediate links. Both of these are cases of resolving one law into two
or more; in the third, two or more are resolved into one: when, after the
law has been shown to hold good in several different classes of cases, we
decide that what is true in each of these classes of cases, is true under
some more general supposition, consisting of what all those classes of
cases have in common. We may here remark that this last operation involves
none of the uncertainties attendant on induction by the Method of
Agreement, since we need not suppose the result to be extended by way of
inference to any new class of cases, different from those by the
comparison of which it was engendered.
In all these three processes, laws are, as we have seen, resolved into
laws more general than themselves; laws extending to all the cases which
the former extend to, and others besides. In the first two modes they are
also resolved into laws more certain, in other words, more universally
true than themselves; they are, in fact, proved not to be themselves laws
of nature, the character of which is to be universally true, but _results_
of laws of nature, which may be only true conditionally, and for the most
part. No difference of this sort exists in the third case; since here the
partial laws are, in fact, the very same law as the general one, and any
exception to them would be an exception to it too.
By all the three processes, the range of deductive science is extended;
since the laws, thus resolved, may be thenceforth deduced demonstratively
from the laws into which they are resolved. As already remarked, the same
deductive process which proves a law or fact of causation if unknown,
serves to explain it when known.
The word explanation is here used in its philosophical sense. What is
called explaining one law of nature by another, is but substituting one
mystery for another; and does nothing to render the general course of
nature other than mysterious: we can no more assign a _why_ for the more
extensive laws than for the partial ones. The explanation may substitute a
mystery which has become familiar, and has grown to _seem_ not mysterious,
for one which is still strange. And this is the meaning of explanation, in
common parlance. But the process with which we are here concerned often
does the very contrary: it resolves a phenomenon with which we are
familiar, into one of which we previously knew little or nothing; as when
the common fact of the fall of heavy bodies is resolved into a tendency of
all particles of matter towards one another. It must be kept constantly in
view, therefore, that in science, those who speak of explaining any
phenomenon mean (or should mean) pointing out not some more familiar, but
merely some more general, phenomenon, of which it is a partial
exemplification; or some laws of causation which produce it by their joint
or successive action, and from which, therefore, its conditions may be
determined deductively. Every such operation brings us a step nearer
towards answering the question which was stated in a previous chapter as
comprehending the whole problem of the investigation of nature, viz. What
are the fewest assumptions, which being granted, the order of nature as it
exists would be the result? What are the fewest general propositions from
which all the uniformities existing in nature could be deduced?
The laws, thus explained or resolved, are sometimes said to be _accounted
for_; but the expression is incorrect, if taken to mean anything more than
what has been already stated. In minds not habituated to accurate
thinking, there is often a confused notion that the general laws are the
_causes_ of the partial ones; that the law of general gravitation, for
example, causes the phenomenon of the fall of bodies to the earth. But to
assert this, would be a misuse of the word cause: terrestrial gravity is
not an effect of general gravitation, but a _case_ of it; that is, one
kind of the particular instances in which that general law obtains. To
account for a law of nature means, and can mean, nothing more than to
assign other laws more general, together with collocations, which laws and
collocations being supposed, the partial law follows without any
additional supposition.