INDUCTIVE METHOD
Sec. 1. It is necessary to describe briefly the process of investigating
laws of causation, not with the notion of teaching any one the Art of
Discovery, which each man pursues for himself according to his natural
gifts and his experience in the methods of his own science, but merely
to cast some light upon the contents of the next few chapters. Logic is
here treated as a process of proof; proof supposes that some general
proposition or hypothesis has been suggested as requiring proof; and the
search for such propositions may spring from scientific curiosity or
from practical interests.
We may, as Bain observes (_Logic_: B. iii. ch. 5), desire to detect a
process of causation either (1) amidst circumstances that have no
influence upon the process but only obscure it; as when, being pleased
with a certain scent in a garden, we wish to know from what flower it
rises; or, being attracted by the sound of some instrument in an
orchestra, we desire to know which it is: or (2) amidst circumstances
that alter the effect from what it would have been by the sole operation
of some cause; as when the air deflects a falling feather; or in some
more complex case, such as a rise or fall of prices that may extend over
many years.
To begin with, we must form definite ideas as to what the phenomenon is
that we are about to investigate; and in a case of any complexity this
is best done by writing a detailed description of it: e.g., to
investigate the cause of a recent fall of prices, we must describe
exactly the course of the phenomenon, dating the period over which it
extends, recording the successive fluctuations of prices, with their
maxima and minima, and noting the classes of goods or securities that
were more or less affected, etc.
Then the first step of elimination (as Bain further observes) is "to
analyse the situation mentally," in the light of analogies suggested by
our experience or previous knowledge. Dew, for example, is moisture
formed upon the surface of bodies from no apparent source. But two
possible sources are easily suggested by common experience: is it
deposited from the air, like the moisture upon a mirror when we breathe
upon it; or does it exude from the bodies themselves, like gum or
turpentine? Or, again, as to a fall of prices, a little experience in
business, or knowledge of Economics, readily suggests two possible
explanations: either cheaper production in making goods or carrying
them; or a scarcity of that in which the purchasing power of the chief
commercial nations is directly expressed, namely, gold.
Having thus analysed the situation and considered the possibility of
one, two, three, or more possible causes, we fix upon one of them for
further investigation; that is to say, we frame an hypothesis that this
is the cause. When an effect is given to find its cause, an inquirer
nearly always begins his investigations by thus framing an hypothesis as
to the cause.
The next step is to try to _verify_ this Hypothesis. This we may
sometimes do by _varying the circumstances_ of the phenomenon, according
to the Canons of direct Inductive Proof to be discussed in the next
chapter; that is to say, by _observing_ or _experimenting_ in such a way
as to get rid of or eliminate the obscuring or disturbing conditions.
Thus, to find out which flower in a garden gives a certain scent, it is
usually enough to rely on observation, going up to the likely flowers
one after the other and smelling them: at close quarters, the greater
relative intensity of the scent is sufficiently decisive. Or we may
resort to a sort of experiment, plucking a likely flower, as to which we
frame the hypothesis (this is the cause), and carrying it to some place
where the air is free from conflicting odours. Should observation or
experiment disprove our first hypothesis we try a second; and so on
until we succeed, or exhaust the known possibilities.
But if the phenomenon is so complex and extensive as a continuous fall
of prices, direct observation or experiment is a useless or impossible
method; and we must then resort to Deduction; that is, to indirect
Induction. If, for example, we take the hypothesis that the fall is due
to a scarcity of gold, we must show that there is a scarcity; what
effect such a scarcity may be expected to have upon prices from the
acknowledged laws of prices, and from the analogy of other cases of an
expanded or restricted currency; that this expectation agrees with the
statistics of recent commerce: and finally, that the alternative
hypothesis that the fall is due to cheaper production is not true;
either because there has not been a sufficient cheapening of general
production; or because, if there has been, the results to be rationally
expected from it are not such as to agree with the statistics of recent
commerce. (Ch. xviii.)
But now suppose that, a phenomenon having been suggested for
explanation, we are unable at the time to think of any cause--to frame
any hypothesis about it; we must then wait for the phenomenon to occur
again, and, once more observing its course and accompaniments and trying
to recall its antecedents, do our best to conceive an hypothesis, and
proceed as before. Thus, in the first great epidemic of influenza, some
doctors traced it to a deluge in China, others to a volcanic eruption
near Java; some thought it a mild form of Asiatic plague, and others
caught a specific microbe. As the disease often recurred, there were
fresh opportunities of framing hypotheses; and the microbe was
identified.
Again, the investigation may take a different form: given a supposed
Cause to find its Effect; e.g., a new chemical element, to find what
compounds it forms with other elements; or, the spots on the sun--have
they any influence upon our weather?
Here, if the given cause be under control, as a new element may be, it
is possible to try experiments with it according to the Canons of
Inductive Proof. The inquirer may form some hypothesis or expectation as
to the effects, to guide his observation of them, but will be careful
not to hold his expectation so confidently as to falsify his observation
of what actually happens.
But if the cause be, like the sun-spots, not under control, the inquirer
will watch on all sides what events follow their appearance and
development; he must watch for consequences of the new cause he is
studying in many different circumstances, that his observations may
satisfy the canons of proof. But he will also resort for guidance to
deduction; arguing from the nature of the cause, if anything is known of
its nature, what consequences may be expected, and comparing the results
of this deduction with any consequent which he suspects to be connected
with the cause. And if the results of deduction and observation agree,
he will still consider whether the facts observed may not be due to some
other cause.
A cause, however, may be under control and yet be too dangerous to
experiment with; such as the effects of a poison--though, if too
dangerous to experiment with upon man, it may be tried upon animals; or
such as a proposed change of the constitution by legislation; or even
some minor Act of Parliament, for altering the Poor Law, or regulating
the hours of labour. Here the first step must be deductive. We must ask
what consequences are to be expected from the nature of the change
(comparing it with similar changes), and from the laws of the special
circumstances in which it is to operate? And sometimes we may partially
verify our deduction by trying experiments upon a small scale or in a
mild form. There are conflicting deductions as to the probable effect of
giving Home Rule to Ireland; and experiments have been made in more or
less similar cases, as in the Colonies and in some foreign countries. As
to the proposal to make eight hours the legal limit of a day's labour in
all trades, we have all tried to forecast the consequences of this; and
by way of verification we might begin with nine hours; or we might
induce some other country to try the experiment first. Still, no
verification by experiments on a small scale, or in a mild form, or in
somewhat similar yet different circumstances, can be considered
logically conclusive. What proofs are conclusive we shall see in the
following chapters.
Sec. 2. To begin with the conditions of direct Induction.--An Induction is
an universal real proposition, based on observation, in reliance on the
uniformity of Nature: when well ascertained, it is called a Law. Thus,
that all life depends on the presence of oxygen is (1) an universal
proposition; (2) a real one, since the 'presence of oxygen' is not
connoted by 'life'; (3) it is based on observation; (4) it relies on the
uniformity of Nature, since all cases of life have not been examined.
Such a proposition is here called 'an induction,' when it is inductively
proved; that is, proved by facts, not merely deduced from more general
premises (except the premise of Nature's uniformity): and by the
'process of induction' is meant the method of inductive proof. The
phrase 'process of induction' is often used in another sense, namely for
the inference or judgment by which such propositions are arrived at. But
it is better to call this 'the process of hypothesis,' and to regard it
as a preliminary to the process of induction (that is, proof), as
furnishing the hypothesis which, if it can stand the proper tests,
becomes an induction or law.
Sec. 3. Inductive proofs are usually classed as Perfect and Imperfect.
They are said to be perfect when all the instances within the scope of
the given proposition have been severally examined, and the proposition
has been found true in each case. But we have seen (chap. xiii. Sec. 2)
that the instances included in universal propositions concerning Causes
and Kinds cannot be exhaustively examined: we do not know all planets,
all heat, all liquids, all life, etc.; and we never can, since a man's
life is never long enough. It is only where the conditions of time,
place, etc., are arbitrarily limited that examination can be exhaustive.
Perfect induction might show (say) that every member of the present
House of Commons has two Christian names. Such an argument is sometimes
exhibited as a Syllogism in Darapti with a Minor premise in U., which
legitimates a Conclusion in A., thus:
A.B. to Z have two Christian names;
A.B. to Z are all the present M.P.'s:
.'. All the present M.P.'s have two Christian names.
But in such an investigation there is no need of logical method to find
the major premise; it is mere counting: and to carry out the syllogism
is a hollow formality. Accordingly, our definition of Induction excludes
the kind unfortunately called Perfect, by including in the notion of
Induction a reliance on the uniformity of Nature; for this would be
superfluous if every instance in question had been severally examined.
Imperfect Induction, then, is what we have to deal with: the method of
showing the credibility of an universal real proposition by an
examination of _some_ of the instances it includes, generally a small
fraction of them.
Sec. 4. Imperfect Induction is either Methodical or Immethodical. Now,
Method is procedure upon a principle; and if the method is to be precise
and conclusive, the principle must be clear and definite.
There is a Geometrical Method, because the axioms of Geometry are clear
and definite, and by their means, with the aid of definitions, laws are
deduced of the equality of lines and angles and other relations of
position and magnitude in space. The process of proof is purely
Deductive (the axioms and definitions being granted). Diagrams are used
not as facts for observation, but merely to fix our attention in
following the general argument; so that it matters little how badly they
are drawn, as long as their divergence from the conditions of the
proposition to be proved is not distracting. Even the appeal to
"superposition" to prove the equality of magnitudes (as in Euclid I. 4),
is not an appeal to observation, but to our judgment of what is implied
in the foregoing conditions. Hence no inference is required from the
special case to all similar ones; for they are all proved at once.
There is also, as we have seen, a method of Deductive Logic resting on
the Principles of Consistency and the _Dictum de omni et nullo_. And we
shall find that there is a method of Inductive Logic, resting on the
principle of Causation.
But there are a good many general propositions, more or less trustworthy
within a certain range of conditions, which cannot be methodically
proved for want of a precise principle by which they may be tested; and
they, therefore, depend upon Immethodical Induction, that is, upon the
examination of as many instances as can be found, relying for the rest
upon the undefinable principle of the Uniformity of Nature, since we are
not able to connect them with any of its definite modes enumerated in
chap. xiii. Sec. 7. To this subject we shall return in chap. xix., after
treating of Methodical Induction, or the means of determining that a
relation of events is of the nature of cause and effect, because the
relation can be shown to have the marks of causation, or some of them.
Sec. 5. Observations and Experiments are the _material_ grounds of
Induction. An experiment is an observation made under prepared, and
therefore known, conditions; and, when obtainable, it is much to be
preferred. Simple observation shows that the burning of the fire
depends, for one thing, on the supply of air; but it cannot show us that
it depends on oxygen. To prove this we must make experiments as by
obtaining pure oxygen and pure nitrogen (which, mixed in the proportion
of one to four, form the air) in separate vessels, and then plunging a
burning taper into the oxygen--when it will blaze fiercely; and again
plunging it into the nitrogen--when it will be extinguished. This shows
that the greater part of the air does nothing to keep the fire alight,
except by diminishing its intensity and so making it last longer.
Experiments are more perfect the more carefully they are prepared, and
the more completely the conditions are known under which the given
phenomenon is to be observed. Therefore, they become possible only when
some knowledge has already been gained by observation; for else the
preparation which they require could not be made.
Observation, then, was the first material ground of Induction, and in
some sciences it remains the chief ground. The heavenly bodies, the
winds and tides, the strata of the earth, and the movements of history,
are beyond our power to experiment with. Experiments upon the living
body or mind are indeed resorted to when practicable, even in the case
of man, as now in all departments of Psychology; but, if of a grave
nature, they are usually thought unjustifiable. And in political affairs
experiments are hindered by the reflection, that those whose interests
are affected must bear the consequences and may resent them. Hence, it
is in physical and chemical inquiries and in the physiology of plants
and animals (under certain conditions) that direct experiment is most
constantly practised.
Where direct experiment is possible, however, it has many advantages
over unaided observation. If one experiment does not enable us to
observe the phenomenon satisfactorily, we may try again and again;
whereas the mere observer, who wishes to study the bright spots on Mars,
or a commercial crisis, must wait for a favourable opportunity. Again,
in making experiments we can vary the conditions of the phenomenon, so
as to observe its different behaviour in each case; whereas he who
depends solely on observation must trust the bounty of nature to supply
him with a suitable diversity of instances. It is a particular advantage
of experiment that a phenomenon may sometimes be 'isolated,' that is,
removed from the influence of all agents except that whose operation we
desire to observe, or except those whose operation is already known:
whereas a simple observer, who has no control over the conditions of the
subject he studies, can never be quite sure that its movements or
changes are not due to causes that have never been conspicuous enough to
draw his attention. Finally, experiment enables us to observe coolly and
circumspectly and to be precise as to what happens, the time of its
occurrence, the order of successive events, their duration, intensity
and extent.
But whether we proceed by observation or experiment, the utmost
attainable exactness of measurements and calculation is requisite; and
these presuppose some Unit, in multiples or divisions of which the
result may be expressed. This unit cannot be an abstract number as in
Arithmetic, but must be one something--an hour, or a yard, or a
pound--according to the nature of the phenomenon to be measured. But
what is an hour, or a yard or a pound? There must in each case be some
constant Standard of reference to give assurance that the unit may
always have the same value. "The English pound is defined by a certain
lump of platinum preserved at Westminster." The unit may be identical
with the standard or some division or multiple of it; and, in measuring
the same kind of phenomena, different units may be used for different
purposes as long as each bears a constant relation to the standard.
Thus, taking the rotation of the earth as the standard of Time, the
convenient unit for long periods is a year (which is a multiple); for
shorter periods, a day (which is identical); for shorter still, an hour
(which is a division), or a second, or a thousandth of a second. (See
Jevons' _Principles of Science_, ch. 14.)
Sec. 6. The principle of Causation is the _formal_ ground of Induction; and
the Inductive Canons derived from it are means of testing the formal
sufficiency of observations to justify the statement of a Law. If we can
observe the process of cause and effect in nature we may generalise our
observation into a law, because that process is invariable. First, then,
can we observe the course of cause and effect? Our power to do so is
limited by the refinement of our senses aided by instruments, such as
lenses, thermometers, balances, etc. If the causal process is
essentially molecular change, as in the maintenance of combustion by
oxygen, we cannot directly observe it; if the process is partly cerebral
or mental, as in social movements which depend on feeling and opinion,
it can but remotely be inferred; even if the process is a collision of
moving masses (billiard-balls), we cannot really observe what happens,
the elastic yielding, and recoil and the internal changes that result;
though no doubt photography will throw some light upon this, as it has
done upon the galloping of horses and the impact of projectiles. Direct
observation is limited to the effect which any change in a phenomenon
(or its index) produces upon our senses; and what we believe to be the
causal process is a matter of inference and calculation. The meagre and
abstract outlines of Inductive Logic are apt to foster the notion, that
the evidence on which Science rests is simple; but it is amazingly
intricate and cumulative.
Secondly, so far as we can observe the process of nature, how shall we
judge whether a true causal instance, a relation of cause and effect,
is before us? By looking for the five marks of Causation. Thus, in the
experiment above described, showing that oxygen supports combustion, we
find--(1) that the taper which only glowed before being plunged into the
oxygen, bursts into flame when there--Sequence; (2) that this begins to
happen at once without perceptible interval--Immediacy; (3) that no
other agent or disturbing circumstance was present (the preparation of
the experiment having excluded any such thing)--Unconditionalness; (4)
the experiment may be repeated as often as we like with the same
result--Invariableness. Invariableness, indeed, I do not regard as
formally necessary to be shown, supposing the other marks to be clear;
for it can only be proved within our experience; and the very object of
Induction is to find grounds of belief beyond actual experience.
However, for material assurance, to guard against his own liability to
error, the inquirer will of course repeat his experiments.
The above four are the qualitative marks of Causation: the fifth and
quantitative mark is the Equality of Cause and Effect; and this, in the
above example, the Chemist determines by showing that, instead of the
oxygen and wax that have disappeared during combustion, an equivalent
weight of carbon dioxide, water, etc., has been formed.
Here, then, we have all the marks of causation; but in the ordinary
judgments of life, in history, politics, criticism, business, we must
not expect such clear and direct proofs; in subsequent chapters it will
appear how different kinds of evidence are combined in different
departments of investigation.
Sec. 7. The Inductive Canons, to be explained in the next chapter, describe
the character of observations and experiments that justify us in drawing
conclusions about causation; and, as we have mentioned, they are derived
from the principle of Causation itself. According to that principle,
cause and effect are invariably, immediately and unconditionally
antecedent and consequent, and are equal as to the matter and energy
embodied.
Invariability can only be observed, in any of the methods of induction,
by collecting more and more instances, or repeating experiments. Of
course it can never be exhaustively observed.
Immediacy, too, in direct Induction, is a matter for observation the
most exact that is possible.
Succession, or the relation itself of antecedent and consequent, must
either be directly observed (or some index of it); or else ascertained
by showing that energy gained by one phenomenon has been lost by
another, for this implies succession.
But to determine the unconditionality of causation, or the
indispensability of some condition, is the great object of the methods,
and for that purpose the meaning of unconditionality may be further
explicated by the following rules for the determination of a Cause.
A. QUALITATIVE DETERMINATION
_I.--For Positive Instances._
To prove a supposed Cause: (a) Any agent whose introduction among
certain conditions (without further change) is followed by a given
phenomenon; or, (b) whose removal is followed by the cessation (or
modification) of that phenomenon, is (so far) the cause or an
indispensable condition of it.
To find the Effect: (c) Any event that follows a given phenomenon, when
there is no further change; or, (d) that does not occur when the
conditions of a former occurrence are exactly the same, except for the
absence of that phenomenon, is the effect of it (or is dependent on
it).
_II.--For Negative Instances._
To exclude a supposed Cause: (a) Any agent that can be introduced among
certain conditions without being followed by a given phenomenon (or that
is found without that phenomenon); or (b) that can be removed when that
phenomenon is present without impairing it (or that is absent when that
phenomenon is present), is not the cause, or does not complete the
cause, of that phenomenon in those circumstances.
To exclude a supposed Effect: (c) Any event that occurs without the
introduction (or presence) of a given phenomenon; or (d) that does not
occur when that phenomenon is introduced (or is present), is not the
effect of that phenomenon.
* * * * *
Subject to the conditions thus stated, the rules may be briefly put as
follows:
I. (a) That which (without further change) is followed by a given event
is its cause.
II. (a) That which is not so followed is not the cause.
I. (b) That which cannot be left out without impairing a phenomenon is a
condition of it.
II. (b) That which can be left out is not a condition of it.
B. QUANTITATIVE DETERMINATION
The Equality of Cause and Effect may be further explained by these
rules:
III. (a) When a cause (or effect) increases or decreases, so does its
effect (or cause).
III. (b) If two phenomena, having the other marks of cause and effect,
seem unequal, the less contains an unexplored factor.
III. (c) If an antecedent and consequent do not increase or decrease
correspondingly, they are not cause and effect, so far as they vary.
It will next be shown that these propositions are variously combined in
Mill's five Canons of Induction: Agreement, the Joint Method,
Difference, Variations, Residues. The first three are sometimes called
Qualitative Methods, and the two last Quantitative; and although this
grouping is not quite accurate, seeing that Difference is often used
quantitatively, yet it draws attention to an important distinction
between a mere description of conditions and determination by exact
measurement.
To avoid certain misunderstandings, some slight alterations have been
made in the wording of the Canons. It may seem questionable whether the
Canons add anything to the above propositions: I think they do. They are
not discussed in the ensuing chapter merely out of reverence for Mill,
or regard for a nascent tradition; but because, as describing the
character of observations and experiments that justify us in drawing
conclusions about causation, they are guides to the analysis of
observations and to the preparation of experiments. To many eminent
investigators the Canons (as such) have been unknown; but they prepared
their work effectively so far only as they had definite ideas to the
same purport. A definite conception of the conditions of proof is the
necessary antecedent of whatever preparations may be made for proving
anything.