OF LAWS OF NATURE.
§ 1. In the contemplation of that uniformity in the course of nature,
which is assumed in every inference from experience, one of the first
observations that present themselves is, that the uniformity in question
is not properly uniformity, but uniformities. The general regularity
results from the coexistence of partial regularities. The course of
nature in general is constant, because the course of each of the various
phenomena that compose it is so. A certain fact invariably occurs
whenever certain circumstances are present, and does not occur when they
are absent; the like is true of another fact; and so on. From these
separate threads of connexion between parts of the great whole which we
term nature, a general tissue of connexion unavoidably weaves itself, by
which the whole is held together. If A is always accompanied by D, B by
E, and C by F, it follows that A B is accompanied by D E, A C by D F, B
C by E F, and finally A B C by D E F; and thus the general character of
regularity is produced, which, along with and in the midst of infinite
diversity, pervades all nature.
The first point, therefore, to be noted in regard to what is called the
uniformity of the course of nature, is, that it is itself a complex
fact, compounded of all the separate uniformities which exist in respect
to single phenomena. These various uniformities, when ascertained by
what is regarded as a sufficient induction, we call in common parlance,
Laws of Nature. Scientifically speaking, that title is employed in a
more restricted sense, to designate the uniformities when reduced to
their most simple expression. Thus in the illustration already employed,
there were seven uniformities; all of which, if considered sufficiently
certain, would in the more lax application of the term, be called laws
of nature. But of the seven, three alone are properly distinct and
independent: these being presupposed, the others follow of course. The
three first, therefore, according to the stricter acceptation, are
called laws of nature; the remainder not; because they are in truth mere
_cases_ of the three first; virtually included in them; said, therefore,
to _result_ from them: whoever affirms those three has already affirmed
all the rest.
To substitute real examples for symbolical ones, the following are three
uniformities, or call them laws of nature: the law that air has weight,
the law that pressure on a fluid is propagated equally in all
directions, and the law that pressure in one direction, not opposed by
equal pressure in the contrary direction, produces motion, which does
not cease until equilibrium is restored. From these three uniformities
we should be able to predict another uniformity, namely, the rise of the
mercury in the Torricellian tube. This, in the stricter use of the
phrase, is not a law of nature. It is the result of laws of nature. It
is a _case_ of each and every one of the three laws: and is the only
occurrence by which they could all be fulfilled. If the mercury were not
sustained in the barometer, and sustained at such a height that the
column of mercury were equal in weight to a column of the atmosphere of
the same diameter; here would be a case, either of the air not pressing
upon the surface of the mercury with the force which is called its
weight, or of the downward pressure on the mercury not being propagated
equally in an upward direction, or of a body pressed in one direction
and not in the direction opposite, either not moving in the direction in
which it is pressed, or stopping before it had attained equilibrium. If
we knew, therefore, the three simple laws, but had never tried the
Torricellian experiment, we might _deduce_ its result from those laws.
The known weight of the air, combined with the position of the
apparatus, would bring the mercury within the first of the three
inductions; the first induction would bring it within the second, and
the second within the third, in the manner which we characterized in
treating of Ratiocination. We should thus come to know the more complex
uniformity, independently of specific experience, through our knowledge
of the simpler ones from which it results; though, for reasons which
will appear hereafter, _verification_ by specific experience would still
be desirable, and might possibly be indispensable.
Complex uniformities which, like this, are mere cases of simpler ones,
and have, therefore, been virtually affirmed in affirming those, may
with propriety be called _laws_, but can scarcely, in the strictness of
scientific speech, be termed Laws of Nature. It is the custom in
science, wherever regularity of any kind can be traced, to call the
general proposition which expresses the nature of that regularity, a
law; as when, in mathematics, we speak of the law of decrease of the
successive terms of a converging series. But the expression _law of
nature_ has generally been employed with a sort of tacit reference to
the original sense of the word law, namely, the expression of the will
of a superior. When, therefore, it appeared that any of the uniformities
which were observed in nature, would result spontaneously from certain
other uniformities, no separate act of creative will being supposed
necessary for the production of the derivative uniformities, these have
not usually been spoken of as laws of nature. According to one mode of
expression, the question, What are the laws of nature? may be stated
thus:--What are the fewest and simplest assumptions, which being
granted, the whole existing order of nature would result? Another mode
of stating it would be thus: What are the fewest general propositions
from which all the uniformities which exist in the universe might be
deductively inferred?
Every great advance which marks an epoch in the progress of science, has
consisted in a step made towards the solution of this problem. Even a
simple colligation of inductions already made, without any fresh
extension of the inductive inference, is already an advance in that
direction. When Kepler expressed the regularity which exists in the
observed motions of the heavenly bodies, by the three general
propositions called his laws, he, in so doing, pointed out three simple
suppositions which, instead of a much greater number, would suffice to
construct the whole scheme of the heavenly motions, so far as it was
known up to that time. A similar and still greater step was made when
these laws, which at first did not seem to be included in any more
general truths, were discovered to be cases of the three laws of motion,
as obtaining among bodies which mutually tend towards one another with a
certain force, and have had a certain instantaneous impulse originally
impressed upon them. After this great discovery, Kepler's three
propositions, though still called laws, would hardly, by any person
accustomed to use language with precision, be termed laws of nature:
that phrase would be reserved for the simpler and more general laws into
which Newton is said to have resolved them.
According to this language, every well-grounded inductive generalization
is either a law of nature, or a result of laws of nature, capable, if
those laws are known, of being predicted from them. And the problem of
Inductive Logic may be summed up in two questions: how to ascertain the
laws of nature; and how, after having ascertained them, to follow them
into their results. On the other hand, we must not suffer ourselves to
imagine that this mode of statement amounts to a real analysis, or to
anything but a mere verbal transformation of the problem; for the
expression, Laws of Nature, _means_ nothing but the uniformities which
exist among natural phenomena (or, in other words, the results of
induction), when reduced to their simplest expression. It is, however,
something to have advanced so far, as to see that the study of nature is
the study of laws, not _a_ law; of uniformities, in the plural number:
that the different natural phenomena have their separate rules or modes
of taking place, which, though much intermixed and entangled with one
another, may, to a certain extent, be studied apart: that (to resume our
former metaphor) the regularity which exists in nature is a web composed
of distinct threads, and only to be understood by tracing each of the
threads separately; for which purpose it is often necessary to unravel
some portion of the web, and exhibit the fibres apart. The rules of
experimental inquiry are the contrivances for unravelling the web.
§ 2. In thus attempting to ascertain the general order of nature by
ascertaining the particular order of the occurrence of each one of the
phenomena of nature, the most scientific proceeding can be no more than
an improved form of that which was primitively pursued by the human
understanding, while undirected by science. When mankind first formed
the idea of studying phenomena according to a stricter and surer method
than that which they had in the first instance spontaneously adopted,
they did not, conformably to the well-meant but impracticable precept of
Descartes, set out from the supposition that nothing had been already
ascertained. Many of the uniformities existing among phenomena are so
constant, and so open to observation, as to force themselves upon
involuntary recognition. Some facts are so perpetually and familiarly
accompanied by certain others, that mankind learnt, as children learn,
to expect the one where they found the other, long before they knew how
to put their expectation into words by asserting, in a proposition, the
existence of a connexion between those phenomena. No science was needed
to teach that food nourishes, that water drowns, or quenches thirst,
that the sun gives light and heat, that bodies fall to the ground. The
first scientific inquirers assumed these and the like as known truths,
and set out from them to discover others which were unknown: nor were
they wrong in so doing, subject, however, as they afterwards began to
see, to an ulterior revision of these spontaneous generalizations
themselves, when the progress of knowledge pointed out limits to them,
or showed their truth to be contingent on some circumstance not
originally attended to. It will appear, I think, from the subsequent
part of our inquiry, that there is no logical fallacy in this mode of
proceeding; but we may see already that any other mode is rigorously
impracticable: since it is impossible to frame any scientific method of
induction, or test of the correctness of inductions, unless on the
hypothesis that some inductions deserving of reliance have been already
made.
Let us revert, for instance, to one of our former illustrations, and
consider why it is that, with exactly the same amount of evidence, both
negative and positive, we did not reject the assertion that there are
black swans, while we should refuse credence to any testimony which
asserted that there were men wearing their heads underneath their
shoulders. The first assertion was more credible than the latter. But
why more credible? So long as neither phenomenon had been actually
witnessed, what reason was there for finding the one harder to be
believed than the other? Apparently because there is less constancy in
the colours of animals, than in the general structure of their anatomy.
But how do we know this? Doubtless, from experience. It appears, then,
that we need experience to inform us, in what degree, and in what cases,
or sort of cases, experience is to be relied on. Experience must be
consulted in order to learn from it under what circumstances arguments
from it will be valid. We have no ulterior test to which we subject
experience in general; but we make experience its own test. Experience
testifies, that among the uniformities which it exhibits or seems to
exhibit, some are more to be relied on than others; and uniformity,
therefore, may be presumed, from any given number of instances, with a
greater degree of assurance, in proportion as the case belongs to a
class in which the uniformities have hitherto been found more uniform.
This mode of correcting one generalization by means of another, a
narrower generalization by a wider, which common sense suggests and
adopts in practice, is the real type of scientific Induction. All that
art can do is but to give accuracy and precision to this process, and
adapt it to all varieties of cases, without any essential alteration in
its principle.
There are of course no means of applying such a test as that above
described, unless we already possess a general knowledge of the
prevalent character of the uniformities existing throughout nature. The
indispensable foundation, therefore, of a scientific formula of
induction, must be a survey of the inductions to which mankind have been
conducted in unscientific practice; with the special purpose of
ascertaining what kinds of uniformities have been found perfectly
invariable, pervading all nature, and what are those which have been
found to vary with difference of time, place, or other changeable
circumstances.
§ 3. The necessity of such a survey is confirmed by the consideration,
that the stronger inductions are the touchstone to which we always
endeavour to bring the weaker. If we find any means of deducing one of
the less strong inductions from stronger ones, it acquires, at once, all
the strength of those from which it is deduced; and even adds to that
strength; since the independent experience on which the weaker induction
previously rested, becomes additional evidence of the truth of the
better established law in which it is now found to be included. We may
have inferred, from historical evidence, that the uncontrolled power of
a monarch, of an aristocracy, or of the majority, will often be abused:
but we are entitled to rely on this generalization with much greater
assurance when it is shown to be a corollary from still better
established facts; the very low degree of elevation of character ever
yet attained by the average of mankind, and the little efficacy, for the
most part, of the modes of education hitherto practised, in maintaining
the predominance of reason and conscience over the selfish propensities.
It is at the same time obvious that even these more general facts derive
an accession of evidence from the testimony which history bears to the
effects of despotism. The strong induction becomes still stronger when a
weaker one has been bound up with it.
On the other hand, if an induction conflicts with stronger inductions,
or with conclusions capable of being correctly deduced from them, then,
unless on reconsideration it should appear that some of the stronger
inductions have been expressed with greater universality than their
evidence warrants, the weaker one must give way. The opinion so long
prevalent that a comet, or any other unusual appearance in the heavenly
regions, was the precursor of calamities to mankind, or to those at
least who witnessed it; the belief in the veracity of the oracles
of Delphi or Dodona; the reliance on astrology, or on the
weather-prophecies in almanacs, were doubtless inductions supposed to be
grounded on experience:[13] and faith in such delusions seems quite
capable of holding out against a great multitude of failures, provided
it be nourished by a reasonable number of casual coincidences between
the prediction and the event. What has really put an end to these
insufficient inductions, is their inconsistency with the stronger
inductions subsequently obtained by scientific inquiry, respecting the
causes on which terrestrial events really depend; and where those
scientific truths have not yet penetrated, the same or similar delusions
still prevail.
It may be affirmed as a general principle, that all inductions, whether
strong or weak, which can be connected by ratiocination, are
confirmatory of one another; while any which lead deductively to
consequences that are incompatible, become mutually each other's test,
showing that one or other must be given up, or at least more guardedly
expressed. In the case of inductions which confirm each other, the one
which becomes a conclusion from ratiocination rises to at least the
level of certainty of the weakest of those from which it is deduced;
while in general all are more or less increased in certainty. Thus the
Torricellian experiment, though a mere case of three more general laws,
not only strengthened greatly the evidence on which those laws rested,
but converted one of them (the weight of the atmosphere) from a doubtful
generalization into a completely established doctrine.
If, then, a survey of the uniformities which have been ascertained to
exist in nature, should point out some which, as far as any human
purpose requires certainty, may be considered quite certain and quite
universal; then by means of these uniformities we may be able to raise
multitudes of other inductions to the same point in the scale. For if we
can show, with respect to any inductive inference, that either it must
be true, or one of these certain and universal inductions must admit of
an exception; the former generalization will attain the same certainty,
and indefeasibleness within the bounds assigned to it, which are the
attributes of the latter. It will be proved to be a law; and if not a
result of other and simpler laws, it will be a law of nature.
There are such certain and universal inductions; and it is because there
are such, that a Logic of Induction is possible.