§ 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 co-existence 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 pre-supposed, 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 a 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; although, 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 another 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 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 other 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 internal 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 sorts
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 re-consideration 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:(64) 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 a 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 one of the best-established doctrines in the range of
physical science.
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 as 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 induction, 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.