OF THE EXPLANATION OF LAWS OF NATURE.
§ 1. The deductive operation by which we derive the law of an effect
from the laws of the causes, the concurrence of which 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 effect 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 acquired 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 coexistence. 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
expression 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 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, together
with 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 intermediate
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
subsequently 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, 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 sometimes
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 an equally strong 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 demonstrated that the motion
produced would be in a circle, or a parabola, or an hyperbola: and it is
thought that in the case of some comets one of these is probably 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
resolved, 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 some solid body, 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 planetary 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 acquired force in the direction of the tangent 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 recognised as identical, and were subsumed
under one general law, that of gravitation.
In a similar manner, the laws of magnetic phenomena have more 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 extended 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 was
resolved into the 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.