OF THE DEDUCTIVE METHOD.
§ 1. The mode of investigation which, from the proved inapplicability of
direct methods of observation and experiment, remains to us as the main
source of the knowledge we possess or can acquire respecting the
conditions, and laws of recurrence, of the more complex phenomena, is
called, in its most general expression, the Deductive Method; and
consists of three operations: the first, one of direct induction; the
second, of ratiocination; the third, of verification.
I call the first step in the process an inductive operation, because
there must be a direct induction as the basis of the whole; though in
many particular investigations the place of the induction may be
supplied by a prior deduction; but the premises of this prior deduction
must have been derived from induction.
The problem of the Deductive Method is, to find the law of an effect,
from the laws of the different tendencies of which it is the joint
result. The first requisite, therefore, is to know the laws of those
tendencies; the law of each of the concurrent causes: and this supposes
a previous process of observation or experiment upon each cause
separately; or else a previous deduction, which also must depend for its
ultimate premises on observation or experiment. Thus, if the subject be
social or historical phenomena, the premises of the Deductive Method
must be the laws of the causes which determine that class of phenomena;
and those causes are human actions, together with the general outward
circumstances under the influence of which mankind are placed, and which
constitute man's position on the earth. The Deductive Method, applied to
social phenomena, must begin, therefore, by investigating, or must
suppose to have been already investigated, the laws of human action,
and those properties of outward things by which the actions of human
beings in society are determined. Some of these general truths will
naturally be obtained by observation and experiment, others by
deduction: the more complex laws of human action, for example, may be
deduced from the simpler ones; but the simple or elementary laws will
always, and necessarily, have been obtained by a directly inductive
process.
To ascertain, then, the laws of each separate cause which takes a share
in producing the effect, is the first desideratum of the Deductive
Method. To know what the causes are, which must be subjected to this
process of study, may or may not be difficult. In the case last
mentioned, this first condition is of easy fulfilment. That social
phenomena depend on the acts and mental impressions of human beings,
never could have been a matter of any doubt, however imperfectly it may
have been known either by what laws those impressions and actions are
governed, or to what social consequences their laws naturally lead.
Neither, again, after physical science had attained a certain
development, could there be any real doubt where to look for the laws on
which the phenomena of life depend, since they must be the mechanical
and chemical laws of the solid and fluid substances composing the
organized body and the medium in which it subsists, together with the
peculiar vital laws of the different tissues constituting the organic
structure. In other cases, really far more simple than these, it was
much less obvious in what quarter the causes were to be looked for: as
in the case of the celestial phenomena. Until, by combining the laws of
certain causes, it was found that those laws explained all the facts
which experience had proved concerning the heavenly motions, and led to
predictions which it always verified, mankind never knew that those
_were_ the causes. But whether we are able to put the question before,
or not until after, we have become capable of answering it, in either
case it must be answered; the laws of the different causes must be
ascertained, before we can proceed to deduce from them the conditions of
the effect.
The mode of ascertaining those laws neither is, nor can be, any other
than the fourfold method of experimental inquiry, already discussed. A
few remarks on the application of that method to cases of the
Composition of Causes, are all that is requisite.
It is obvious that we cannot expect to find the law of a tendency, by an
induction from cases in which the tendency is counteracted. The laws of
motion could never have been brought to light from the observation of
bodies kept at rest by the equilibrium of opposing forces. Even where
the tendency is not, in the ordinary sense of the word, counteracted,
but only modified, by having its effects compounded with the effects
arising from some other tendency or tendencies, we are still in an
unfavourable position for tracing, by means of such cases, the law of
the tendency itself. It would have been scarcely possible to discover
the law that every body in motion tends to continue moving in a straight
line, by an induction from instances in which the motion is deflected
into a curve, by being compounded with the effect of an accelerating
force. Notwithstanding the resources afforded in this description of
cases by the Method of Concomitant Variations, the principles of a
judicious experimentation prescribe that the law of each of the
tendencies should be studied, if possible, in cases in which that
tendency operates alone, or in combination with no agencies but those of
which the effect can, from previous knowledge, be calculated and allowed
for.
Accordingly, in the cases, unfortunately very numerous and important, in
which the causes do not suffer themselves to be separated and observed
apart, there is much difficulty in laying down with due certainty the
inductive foundation necessary to support the deductive method. This
difficulty is most of all conspicuous in the case of physiological
phenomena; it being seldom possible to separate the different agencies
which collectively compose an organized body, without destroying the
very phenomena which it is our object to investigate:
--following life, in creatures we dissect,
We lose it, in the moment we detect.
And for this reason I am inclined to the opinion, that physiology
(greatly and rapidly progressive as it now is) is embarrassed by
greater natural difficulties, and is probably susceptible of a less
degree of ultimate perfection, than even the social science; inasmuch as
it is possible to study the laws and operations of one human mind apart
from other minds, much less imperfectly than we can study the laws of
one organ or tissue of the human body apart from the other organs or
tissues.
It has been judiciously remarked that pathological facts, or, to speak
in common language, diseases in their different forms and degrees,
afford in the case of physiological investigation the most valuable
equivalent to experimentation properly so called; inasmuch as they often
exhibit to us a definite disturbance in some one organ or organic
function, the remaining organs and functions being, in the first
instance at least, unaffected. It is true that from the perpetual
actions and reactions which are going on among all parts of the organic
economy, there can be no prolonged disturbance in any one function
without ultimately involving many of the others; and when once it has
done so, the experiment for the most part loses its scientific value.
All depends on observing the early stages of the derangement; which,
unfortunately, are of necessity the least marked. If, however, the
organs and functions not disturbed in the first instance, become
affected in a fixed order of succession, some light is thereby thrown
upon the action which one organ exercises over another: and we
occasionally obtain a series of effects which we can refer with some
confidence to the original local derangement; but for this it is
necessary that we should know that the original derangement _was_ local.
If it was what is termed constitutional, that is, if we do not know in
what part of the animal economy it took its rise, or the precise nature
of the disturbance which took place in that part, we are unable to
determine which of the various derangements was cause and which effect;
which of them were produced by one another, and which by the direct,
though perhaps tardy, action of the original cause.
Besides natural pathological facts, we can produce pathological facts
artificially; we can try experiments, even in the popular sense of the
term, by subjecting the living being to some external agent, such as the
mercury of our former example, or the section of a nerve to ascertain
the functions of different parts of the nervous system. As this
experimentation is not intended to obtain a direct solution of any
practical question, but to discover general laws, from which afterwards
the conditions of any particular effect may be obtained by deduction;
the best cases to select are those of which the circumstances can be
best ascertained: and such are generally not those in which there is any
practical object in view. The experiments are best tried, not in a state
of disease, which is essentially a changeable state, but in the
condition of health, comparatively a fixed state. In the one, unusual
agencies are at work, the results of which we have no means of
predicting; in the other, the course of the accustomed physiological
phenomena would, it may generally be presumed, remain undisturbed, were
it not for the disturbing cause which we introduce.
Such, with the occasional aid of the Method of Concomitant Variations,
(the latter not less incumbered than the more elementary methods by the
peculiar difficulties of the subject,) are our inductive resources for
ascertaining the laws of the causes considered separately, when we have
it not in our power to make trial of them in a state of actual
separation. The insufficiency of these resources is so glaring, that no
one can be surprised at the backward state of the science of physiology;
in which indeed our knowledge of causes is so imperfect, that we can
neither explain, nor could without specific experience have predicted,
many of the facts which are certified to us by the most ordinary
observation. Fortunately, we are much better informed as to the
empirical laws of the phenomena, that is, the uniformities respecting
which we cannot yet decide whether they are cases of causation, or mere
results of it. Not only has the order in which the facts of organization
and life successively manifest themselves, from the first germ of
existence to death, been found to be uniform, and very accurately
ascertainable; but, by a great application of the Method of Concomitant
Variations to the entire facts of comparative anatomy and physiology,
the characteristic organic structure corresponding to each class of
functions has been determined with considerable precision. Whether these
organic conditions are the whole of the conditions, and in many cases
whether they are conditions at all, or mere collateral effects of some
common cause, we are quite ignorant: nor are we ever likely to know,
unless we could construct an organized body, and try whether it would
live.
Under such disadvantages do we, in cases of this description, attempt
the initial, or inductive step, in the application of the Deductive
Method to complex phenomena. But such, fortunately, is not the common
case. In general, the laws of the causes on which the effect depends may
be obtained by an induction from comparatively simple instances, or, at
the worst, by deduction from the laws of simpler causes, so obtained. By
simple instances are meant, of course, those in which the action of each
cause was not intermixed or interfered with, or not to any great extent,
by other causes whose laws were unknown. And only when the induction
which furnished the premises to the Deductive method rested on such
instances, has the application of such a method to the ascertainment of
the laws of a complex effect, been attended with brilliant results.
§ 2. When the laws of the causes have been ascertained, and the first
stage of the great logical operation now under discussion satisfactorily
accomplished, the second part follows; that of determining from the laws
of the causes, what effect any given combination of those causes will
produce. This is a process of calculation, in the wider sense of the
term; and very often involves processes of calculation in the narrowest
sense. It is a ratiocination; and when our knowledge of the causes is so
perfect, as to extend to the exact numerical laws which they observe in
producing their effects, the ratiocination may reckon among its premises
the theorems of the science of number, in the whole immense extent of
that science. Not only are the most advanced truths of mathematics often
required to enable us to compute an effect, the numerical law of which
we already know; but, even by the aid of those most advanced truths, we
can go but a little way. In so simple a case as the common problem of
three bodies gravitating towards one another, with a force directly as
their mass and inversely as the square of the distance, all the
resources of the calculus have not hitherto sufficed to obtain any
general solution but an approximate one. In a case a little more
complex, but still one of the simplest which arise in practice, that of
the motion of a projectile, the causes which affect the velocity and
range (for example) of a cannon-ball may be all known and estimated; the
force of the gunpowder, the angle of elevation, the density of the air,
the strength and direction of the wind; but it is one of the most
difficult of mathematical problems to combine all these, so as to
determine the effect resulting from their collective action.
Besides the theorems of number, those of geometry also come in as
premises, where the effects take place in space, and involve motion and
extension, as in mechanics, optics, acoustics, astronomy. But when the
complication increases, and the effects are under the influence of so
many and such shifting causes as to give no room either for fixed
numbers, or for straight lines and regular curves, (as in the case of
physiological, to say nothing of mental and social phenomena,) the laws
of number and extension are applicable, if at all, only on that large
scale on which precision of details becomes unimportant. Although these
laws play a conspicuous part in the most striking examples of the
investigation of nature by the Deductive Method, as for example in the
Newtonian theory of the celestial motions, they are by no means an
indispensable part of every such process. All that is essential in it is
reasoning from a general law to a particular case, that is, determining
by means of the particular circumstances of that case, what result is
required in that instance to fulfil the law. Thus in the Torricellian
experiment, if the fact that air has weight had been previously known,
it would have been easy, without any numerical data, to deduce from the
general law of equilibrium, that the mercury would stand in the tube at
such a height that the column of mercury would exactly balance a column
of the atmosphere of equal diameter; because, otherwise, equilibrium
would not exist.
By such ratiocinations from the separate laws of the causes, we may, to
a certain extent, succeed in answering either of the following
questions: Given a certain combination of causes, what effect will
follow? and, What combination of causes, if it existed, would produce a
given effect? In the one case, we determine the effect to be expected in
any complex circumstances of which the different elements are known: in
the other case we learn, according to what law--under what antecedent
conditions--a given complex effect will occur.
§ 3. But (it may here be asked) are not the same arguments by which the
methods of direct observation and experiment were set aside as illusory
when applied to the laws of complex phenomena, applicable with equal
force against the Method of Deduction? When in every single instance a
multitude, often an unknown multitude, of agencies, are clashing and
combining, what security have we that in our computation _à priori_ we
have taken all these into our reckoning? How many must we not generally
be ignorant of? Among those which we know, how probable that some have
been overlooked; and, even were all included, how vain the pretence of
summing up the effects of many causes, unless we know accurately the
numerical law of each,--a condition in most cases not to be fulfilled;
and even when fulfilled, to make the calculation transcends, in any but
very simple cases, the utmost power of mathematical science with all its
most modern improvements.
These objections have real weight, and would be altogether unanswerable,
if there were no test by which, when we employ the Deductive Method, we
might judge whether an error of any of the above descriptions had been
committed or not. Such a test however there is: and its application
forms, under the name of Verification, the third essential component
part of the Deductive Method; without which all the results it can give
have little other value than that of conjecture. To warrant reliance on
the general conclusions arrived at by deduction, these conclusions must
be found, on careful comparison, to accord with the results of direct
observation wherever it can be had. If, when we have experience to
compare with them, this experience confirms them, we may safely trust to
them in other cases of which our specific experience is yet to come. But
if our deductions have led to the conclusion that from a particular
combination of causes a given effect would result, then in all known
cases where that combination can be shown to have existed, and where the
effect has not followed, we must be able to show (or at least to make a
probable surmise) what frustrated it: if we cannot, the theory is
imperfect, and not yet to be relied upon. Nor is the verification
complete, unless some of the cases in which the theory is borne out by
the observed result, are of at least equal complexity with any other
cases in which its application could be called for.
If direct observation and collation of instances have furnished us with
any empirical laws of the effect (whether true in all observed cases, or
only true for the most part), the most effectual verification of which
the theory could be susceptible would be, that it led deductively to
those empirical laws; that the uniformities, whether complete or
incomplete, which were observed to exist among the phenomena, were
accounted for by the laws of the causes--were such as could not but
exist if those be really the causes by which the phenomena are produced.
Thus it was very reasonably deemed an essential requisite of any true
theory of the causes of the celestial motions, that it should lead by
deduction to Kepler's laws: which, accordingly, the Newtonian theory
did.
In order, therefore, to facilitate the verification of theories obtained
by deduction, it is important that as many as possible of the empirical
laws of the phenomena should be ascertained, by a comparison of
instances, conformably to the Method of Agreement: as well as (it must
be added) that the phenomena themselves should be described, in the most
comprehensive as well as accurate manner possible; by collecting from
the observation of parts, the simplest possible correct expressions for
the corresponding wholes: as when the series of the observed places of a
planet was first expressed by a circle, then by a system of epicycles,
and subsequently by an ellipse.
It is worth remarking, that complex instances which would have been of
no use for the discovery of the simple laws into which we ultimately
analyse their phenomena, nevertheless, when they have served to verify
the analysis, become additional evidence of the laws themselves.
Although we could not have got at the law from complex cases, still when
the law, got at otherwise, is found to be in accordance with the result
of a complex case, that case becomes a new experiment on the law, and
helps to confirm what it did not assist to discover. It is a new trial
of the principle in a different set of circumstances; and occasionally
serves to eliminate some circumstance not previously excluded, and the
exclusion of which might require an experiment impossible to be
executed. This was strikingly conspicuous in the example formerly
quoted, in which the difference between the observed and the calculated
velocity of sound was ascertained to result from the heat extricated by
the condensation which takes place in each sonorous vibration. This was
a trial, in new circumstances, of the law of the development of heat by
compression; and it added materially to the proof of the universality of
that law. Accordingly any law of nature is deemed to have gained in
point of certainty, by being found to explain some complex case which
had not previously been thought of in connexion with it; and this indeed
is a consideration to which it is the habit of scientific inquirers to
attach rather too much value than too little.
To the Deductive Method, thus characterized in its three constituent
parts, Induction, Ratiocination, and Verification, the human mind is
indebted for its most conspicuous triumphs in the investigation of
nature. To it we owe all the theories by which vast and complicated
phenomena are embraced under a few simple laws, which, considered as the
laws of those great phenomena, could never have been detected by their
direct study. We may form some conception of what the method has done
for us, from the case of the celestial motions; one of the simplest
among the greater instances of the Composition of Causes, since (except
in a few cases not of primary importance) each of the heavenly bodies
may be considered, without material inaccuracy, to be never at one time
influenced by the attraction of more than two bodies, the sun and one
other planet or satellite; making, with the reaction of the body itself,
and the force generated by the body's own motion and acting in the
direction of the tangent, only four different agents on the concurrence
of which the motions of that body depend; a much smaller number, no
doubt, than that by which any other of the great phenomena of nature is
determined or modified. Yet how could we ever have ascertained the
combination of forces on which the motions of the earth and planets are
dependent, by merely comparing the orbits or velocities of different
planets, or the different velocities or positions of the same planet?
Notwithstanding the regularity which manifests itself in those motions,
in a degree so rare among the effects of a concurrence of causes; and
although the periodical recurrence of exactly the same effect, affords
positive proof that all the combinations of causes which occur at all,
recur periodically; we should not have known what the causes were, if
the existence of agencies precisely similar on our own earth had not,
fortunately, brought the causes themselves within the reach of
experimentation under simple circumstances. As we shall have occasion to
analyse, further on, this great example of the Method of Deduction, we
shall not occupy any time with it here, but shall proceed to that
secondary application of the Deductive Method, the result of which is
not to prove laws of phenomena, but to explain them.