OF EMPIRICAL LAWS.
§ 1. Scientific inquirers give the name of Empirical Laws to those
uniformities which observation or experiment has shown to exist, but on
which they hesitate to rely in cases varying much from those which have
been actually observed, for want of seeing any reason _why_ such a law
should exist. It is implied, therefore, in the notion of an empirical
law, that it is not an ultimate law; that if true at all, its truth is
capable of being, and requires to be, accounted for. It is a derivative
law, the derivation of which is not yet known. To state the explanation,
the _why_, of the empirical law, would be to state the laws from which
it is derived; the ultimate causes on which it is contingent. And if we
knew these, we should also know what are its limits; under what
conditions it would cease to be fulfilled.
The periodical return of eclipses, as originally ascertained by the
persevering observation of the early eastern astronomers, was an
empirical law, until the general laws of the celestial motions had
accounted for it. The following are empirical laws still waiting to be
resolved into the simpler laws from which they are derived. The local
laws of the flux and reflux of the tides in different places: the
succession of certain kinds of weather to certain appearances of sky:
the apparent exceptions to the almost universal truth that bodies expand
by increase of temperature: the law that breeds, both animal and
vegetable, are improved by crossing: that gases have a strong tendency
to permeate animal membranes: that substances containing a very high
proportion of nitrogen (such as hydrocyanic acid and morphia) are
powerful poisons: that when different metals are fused together, the
alloy is harder than the various elements: that the number of atoms of
acid required to neutralize one atom of any base, is equal to the number
of atoms of oxygen in the base: that the solubility of substances in one
another, depends[12] (at least in some degree) on the similarity of
their elements.
An empirical law, then, is an observed uniformity, presumed to be
resolvable into simpler laws, but not yet resolved into them. The
ascertainment of the empirical laws of phenomena often precedes by a
long interval the explanation of those laws by the Deductive Method; and
the verification of a deduction usually consists in the comparison of
its results with empirical laws previously ascertained.
§ 2. From a limited number of ultimate laws of causation, there are
necessarily generated a vast number of derivative uniformities, both of
succession and of coexistence. Some are laws of succession or of
coexistence between different effects of the same cause: of these we had
examples in the last chapter. Some are laws of succession between
effects and their remote causes; resolvable into the laws which connect
each with the intermediate link. Thirdly, when causes act together and
compound their effects, the laws of those causes generate the
fundamental law of the effect, namely, that it depends on the
coexistence of those causes. And, finally, the order of succession or of
coexistence which obtains among effects, necessarily depends on their
causes. If they are effects of the same cause, it depends on the laws of
that cause; if on different causes, it depends on the laws of those
causes severally, and on the circumstances which determine their
coexistence. If we inquire further when and how the causes will
coexist, that, again, depends on _their_ causes: and we may thus trace
back the phenomena higher and higher, until the different series of
effects meet in a point, and the whole is shown to have depended
ultimately on some common cause; or until, instead of converging to one
point, they terminate in different points, and the order of the effects
is proved to have arisen from the collocation of some of the primeval
causes, or natural agents. For example, the order of succession and of
coexistence among the heavenly motions, which is expressed by Kepler's
laws, is derived from the coexistence of two primeval causes, the sun,
and the original impulse or projectile force belonging to each
planet.[13] Kepler's laws are resolved into the laws of these causes and
the fact of their coexistence.
Derivative laws, therefore, do not depend solely on the ultimate laws
into which they are resolvable: they mostly depend on those ultimate
laws, and an ultimate fact; namely, the mode of coexistence of some of
the component elements of the universe. The ultimate laws of causation
might be the same as at present, and yet the derivative laws completely
different, if the causes coexisted in different proportions, or with any
difference in those of their relations by which the effects are
influenced. If, for example, the sun's attraction, and the original
projectile force, had existed in some other ratio to one another than
they did (and we know of no reason why this should not have been the
case), the derivative laws of the heavenly motions might have been quite
different from what they are. The proportions which exist happen to be
such as to produce regular elliptical motions; any other proportions
would have produced different ellipses, or circular, or parabolic, or
hyperbolic motions, but still regular ones; because the effects of each
of the agents accumulate according to an uniform law; and two regular
series of quantities, when their corresponding terms are added, must
produce a regular series of some sort, whatever the quantities
themselves are.
§ 3. Now this last-mentioned element in the resolution of a derivative
law, the element which is not a law of causation, but a collocation of
causes, cannot itself be reduced to any law. There is (as formerly
remarked[14]) no uniformity, no _norma_, principle, or rule, perceivable
in the distribution of the primeval natural agents through the universe.
The different substances composing the earth, the powers that pervade
the universe, stand in no constant relation to one another. One
substance is more abundant than others, one power acts through a larger
extent of space than others, without any pervading analogy that we can
discover. We not only do not know of any reason why the sun's attraction
and the force in the direction of the tangent coexist in the exact
proportion they do, but we can trace no coincidence between it and the
proportions in which any other elementary powers in the universe are
intermingled. The utmost disorder is apparent in the combination of the
causes; which is consistent with the most regular order in their
effects; for when each agent carries on its own operations according to
an uniform law, even the most capricious combination of agencies will
generate a regularity of some sort; as we see in the kaleidoscope, where
any casual arrangement of coloured bits of glass produces by the laws of
reflection a beautiful regularity in the effect.
§ 4. In the above considerations lies the justification of the limited
degree of reliance which scientific inquirers are accustomed to place in
empirical laws.
A derivative law which results wholly from the operation of some one
cause, will be as universally true as the laws of the cause itself; that
is, it will always be true except where some one of those effects of the
cause, on which the derivative law depends, is defeated by a
counteracting cause. But when the derivative law results not from
different effects of one cause, but from effects of several causes, we
cannot be certain that it will be true under any variation in the mode
of coexistence of those causes, or of the primitive natural agents on
which the causes ultimately depend. The proposition that coal beds rest
on certain descriptions of strata exclusively, though true on the earth
so far as our observation has reached, cannot be extended to the moon or
the other planets, supposing coal to exist there; because we cannot be
assured that the original constitution of any other planet was such as
to produce the different depositions in the same order as in our globe.
The derivative law in this case depends not solely on laws, but on a
collocation; and collocations cannot be reduced to any law.
Now it is the very nature of a derivative law which has not yet been
resolved into its elements, in other words, an empirical law, that we do
not know whether it results from the different effects of one cause, or
from effects of different causes. We cannot tell whether it depends
wholly on laws, or partly on laws and partly on a collocation. If it
depends on a collocation, it will be true in all the cases in which that
particular collocation exists. But, since we are entirely ignorant, in
case of its depending on a collocation, what the collocation is, we are
not safe in extending the law beyond the limits of time and place in
which we have actual experience of its truth. Since within those limits
the law has always been found true, we have evidence that the
collocations, whatever they are, on which it depends, do really exist
within those limits. But, knowing of no rule or principle to which the
collocations themselves conform, we cannot conclude that because a
collocation is proved to exist within certain limits of place or time,
it will exist beyond those limits. Empirical laws, therefore, can only
be received as true within the limits of time and place in which they
have been found true by observation: and not merely the limits of time
and place, but of time, place, and circumstance: for since it is the
very meaning of an empirical law that we do not know the ultimate laws
of causation on which it is dependent, we cannot foresee, without actual
trial, in what manner or to what extent the introduction of any new
circumstance may affect it.
§ 5. But how are we to know that an uniformity, ascertained by
experience, is only an empirical law? Since, by the supposition, we have
not been able to resolve it into any other laws, how do we know that it
is not an ultimate law of causation?
I answer, that no generalization amounts to more than an empirical law
when the only proof on which it rests is that of the Method of
Agreement. For it has been seen that by that method alone we never can
arrive at causes. The utmost that the Method of Agreement can do is, to
ascertain the whole of the circumstances common to all cases in which a
phenomenon is produced: and this aggregate includes not only the cause
of the phenomenon, but all phenomena with which it is connected by any
derivative uniformity, whether as being collateral effects of the same
cause, or effects of any other cause which, in all the instances we have
been able to observe, coexisted with it. The method affords no means of
determining which of these uniformities are laws of causation, and which
are merely derivative laws, resulting from those laws of causation and
from the collocation of the causes. None of them, therefore, can be
received in any other character than that of derivative laws, the
derivation of which has not been traced; in other words, empirical laws:
in which light, all results obtained by the Method of Agreement (and
therefore almost all truths obtained by simple observation without
experiment) must be considered, until either confirmed by the Method of
Difference, or explained deductively, in other words accounted for _à
priori_.
These empirical laws may be of greater or less authority, according as
there is reason to presume that they are resolvable into laws only, or
into laws and collocations together. The sequences which we observe in
the production and subsequent life of an animal or a vegetable, resting
on the Method of Agreement only, are mere empirical laws; but though the
antecedents in those sequences may not be the causes of the consequents,
both the one and the other are doubtless, in the main, successive stages
of a progressive effect originating in a common cause, and therefore
independent of collocations. The uniformities, on the other hand, in the
order of superposition of strata on the earth, are empirical laws of a
much weaker kind, since they not only are not laws of causation, but
there is no reason to believe that they depend on any common cause: all
appearances are in favour of their depending on the particular
collocation of natural agents which at some time or other existed on our
globe, and from which no inference can be drawn as to the collocation
which exists or has existed in any other portion of the universe.
§ 6. Our definition of an empirical law including not only those
uniformities which are not known to be laws of causation, but also those
which are, provided there be reason to presume that they are not
ultimate laws; this is the proper place to consider by what signs we may
judge that even if an observed uniformity be a law of causation, it is
not an ultimate but a derivative law.
The first sign is, if between the antecedent _a_ and the consequent _b_
there be evidence of some intermediate link; some phenomenon of which we
can surmise the existence, though from the imperfection of our senses or
of our instruments we are unable to ascertain its precise nature and
laws. If there be such a phenomenon (which may be denoted by the letter
_x_), it follows that even if _a_ be the cause of _b_, it is but the
remote cause, and that the law, _a_ causes _b_, is resolvable into at
least two laws, _a_ causes _x_, and _x_ causes _b_. This is a very
frequent case, since the operations of nature mostly take place on so
minute a scale, that many of the successive steps are either
imperceptible, or very indistinctly perceived.
Take, for example, the laws of the chemical composition of substances;
as that hydrogen and oxygen being combined, water is produced. All we
see of the process is, that the two gases being mixed in certain
proportions, and heat or electricity being applied, an explosion takes
place, the gases disappear, and water remains. There is no doubt about
the law, or about its being a law of causation. But between the
antecedent (the gases in a state of mechanical mixture, heated or
electrified), and the consequent (the production of water), there must
be an intermediate process which we do not see. For if we take any
portion whatever of the water, and subject it to analysis, we find that
it always contains hydrogen and oxygen; nay, the very same proportions
of them, namely, two thirds, in volume, of hydrogen, and one third
oxygen. This is true of a single drop; it is true of the minutest
portion which our instruments are capable of appreciating. Since, then,
the smallest perceptible portion of the water contains both those
substances, portions of hydrogen and oxygen smaller than the smallest
perceptible must have come together in every such minute portion of
space; must have come closer together than when the gases were in a
state of mechanical mixture, since (to mention no other reasons) the
water occupies far less space than the gases. Now, as we cannot see this
contact or close approach of the minute particles, we cannot observe
with what circumstances it is attended, or according to what laws it
produces its effects. The production of water, that is, of the sensible
phenomena which characterize the compound, may be a very remote effect
of those laws. There may be innumerable intervening links; and we are
sure that there must be some. Having full proof that corpuscular action
of some kind takes place previous to any of the great transformations in
the sensible properties of substances, we can have no doubt that the
laws of chemical action, as at present known, are not ultimate but
derivative laws; however ignorant we may be, and even though we should
for ever remain ignorant, of the nature of the laws of corpuscular
action from which they are derived.
In like manner, all the processes of vegetative life, whether in the
vegetable properly so called or in the animal body, are corpuscular
processes. Nutrition is the addition of particles to one another,
sometimes merely replacing other particles separated and excreted,
sometimes occasioning an increase of bulk or weight, so gradual, that
only after a long continuance does it become perceptible. Various
organs, by means of peculiar vessels, secrete from the blood, fluids,
the component particles of which must have been in the blood, but which
differ from it most widely both in mechanical properties and in chemical
composition. Here, then, are abundance of unknown links to be filled up;
and there can be no doubt that the laws of the phenomena of vegetative
or organic life are derivative laws, dependent on properties of the
corpuscles, and of those elementary tissues which are comparatively
simple combinations of corpuscles.
The first sign, then, from which a law of causation, though hitherto
unresolved, may be inferred to be a derivative law, is any indication of
the existence of an intermediate link or links between the antecedent
and the consequent. The second is, when the antecedent is an extremely
complex phenomenon, and its effects therefore, probably, in part at
least, compounded of the effects of its different elements; since we
know that the case in which the effect of the whole is not made up of
the effects of its parts, is exceptional, the Composition of Causes
being by far the more ordinary case.
We will illustrate this by two examples, in one of which the antecedent
is the sum of many homogeneous, in the other of heterogeneous, parts.
The weight of a body is made up of the weights of its minute particles:
a truth which astronomers express in its most general terms, when they
say that bodies, at equal distances, gravitate to one another in
proportion to their quantity of matter. All true propositions,
therefore, which can be made concerning gravity, are derivative laws;
the ultimate law into which they are all resolvable being, that every
particle of matter attracts every other. As our second example, we may
take any of the sequences observed in meteorology: for instance, a
diminution of the pressure of the atmosphere (indicated by a fall of the
barometer) is followed by rain. The antecedent is here a complex
phenomenon, made up of heterogeneous elements; the column of the
atmosphere over any particular place consisting of two parts, a column
of air, and a column of aqueous vapour mixed with it; and the change in
the two together manifested by a fall of the barometer, and followed by
rain, must be either a change in one of these, or in the other, or in
both. We might, then, even in the absence of any other evidence, form a
reasonable presumption, from the invariable presence of both these
elements in the antecedent, that the sequence is probably not an
ultimate law, but a result of the laws of the two different agents; a
presumption only to be destroyed when we had made ourselves so well
acquainted with the laws of both, as to be able to affirm that those
laws could not by themselves produce the observed result.
There are but few known cases of succession from very complex
antecedents, which have not either been actually accounted for from
simpler laws, or inferred with great probability (from the ascertained
existence of intermediate links of causation not yet understood) to be
capable of being so accounted for. It is, therefore, highly probable
that all sequences from complex antecedents are thus resolvable, and
that ultimate laws are in all cases comparatively simple. If there were
not the other reasons already mentioned for believing that the laws of
organized nature are resolvable into simpler laws, it would be almost a
sufficient reason that the antecedents in most of the sequences are so
very complex.
§ 7. In the preceding discussion we have recognised two kinds of
empirical laws: those known to be laws of causation, but presumed to be
resolvable into simpler laws; and those not known to be laws of
causation at all. Both these kinds of laws agree in the demand which
they make for being explained by deduction, and agree in being the
appropriate means of verifying such deduction, since they represent the
experience with which the result of the deduction must be compared. They
agree, further, in this, that until explained, and connected with the
ultimate laws from which they result, they have not attained the highest
degree of certainty of which laws are susceptible. It has been shown on
a former occasion that laws of causation which are derivative, and
compounded of simpler laws, are not only, as the nature of the case
implies, less general, but even less certain, than the simpler laws
from which they result; not in the same degree to be relied on as
universally true. The inferiority of evidence, however, which attaches
to this class of laws, is trifling, compared with that which is inherent
in uniformities not known to be laws of causation at all. So long as
these are unresolved, we cannot tell on how many collocations, as well
as laws, their truth may be dependent; we can never, therefore, extend
them with any confidence to cases in which we have not assured
ourselves, by trial, that the necessary collocation of causes, whatever
it may be, exists. It is to this class of laws alone that the property,
which philosophers usually consider as characteristic of empirical laws,
belongs in all its strictness; the property of being unfit to be relied
on beyond the limits of time, place, and circumstance, in which the
observations have been made. These are empirical laws in a more emphatic
sense; and when I employ that term (except where the context manifestly
indicates the reverse) I shall generally mean to designate those
uniformities only, whether of succession or of coexistence, which are
not known to be laws of causation.