THE METHOD OF EXPLANATION.
Given perplexity as to the cause of any phenomenon, what is our
natural first step? We may describe it as searching for a clue: we
look carefully at the circumstances with a view to finding some
means of assimilating what perplexes us to what is already within our
knowledge. Our next step is to make a guess, or conjecture, or, in
scientific language, a hypothesis. We exercise our Reason or _Nous_,
or Imagination, or whatever we choose to call the faculty, and try to
conceive some cause that strikes us as sufficient to account for the
phenomenon. If it is not at once manifest that this cause has really
operated, our third step is to consider what appearances ought to
present themselves if it did operate. We then return to the facts in
question, and observe whether those appearances do present themselves.
If they do, and if there is no other way of accounting for the effect
in all its circumstances, we conclude that our guess is correct,
that our hypothesis is proved, that we have reached a satisfactory
explanation.
These four steps or stages may be distinguished in most protracted
inquiries into cause. They correspond to the four stages of what
Mr. Jevons calls the Inductive Method _par excellence_, Preliminary
Observation, Hypothesis, Deduction and Verification. Seeing that the
word Induction is already an overloaded drudge, perhaps it would be
better to call these four stages the Method of Explanation. The word
Induction, if we keep near its original and most established meaning,
would apply strictly only to the fourth stage, the Verification, the
bringing in of the facts to confirm our hypothesis. We might call the
method the Newtonian method, for all four stages are marked in the
prolonged process by which he made good his theory of Gravitation.
To give the name of Inductive Method simply to all the four stages
of an orderly procedure from doubt to a sufficient explanation is
to encourage a widespread misapprehension. There could be no greater
error than to suppose that only the senses are used in scientific
investigation. There is no error that men of science are so apt to
resent in the mouths of the non-scientific. Yet they have partly
brought it on themselves by their loose use of the word Induction,
which they follow Bacon in wresting from the traditional meaning of
Induction, using it to cover both Induction or the bringing in of
facts--an affair mainly of Observation--and Reasoning, the exercise of
Nous, the process of constructing satisfactory hypotheses. In reaction
against the popular misconception which Bacon encouraged, it is
fashionable now to speak of the use of Imagination in Science. This is
well enough polemically. Imagination as commonly understood is akin to
the constructive faculty in Science, and it is legitimate warfare to
employ the familiar word of high repute to force general recognition
of the truth. But in common usage Imagination is appropriated to
creative genius in the Fine Arts, and to speak of Imagination
in Science is to suggest that Science deals in fictions, and has
discarded Newton's declaration _Hypotheses non fingo_. In a fight for
popular respect, men of science may be right to claim for themselves
Imagination; but in the interests of clear understanding, the logician
must deplore that they should defend themselves from a charge due
to their abuse of one word by making an equally unwarrantable and
confusing extension of another.
Call it what we will, the faculty of likely guessing, of making
probable hypotheses, of conceiving in all its circumstances the past
situation or the latent and supramicroscopical situation out of
which a phenomenon has emerged, is one of the most important of
the scientific man's special gifts. It is by virtue of it that the
greatest advancements of knowledge have been achieved, the cardinal
discoveries in Molar and Molecular Physics, Biology, Geology, and
all departments of Science. We must not push the idea of stages in
explanatory method too far: the right explanation may be reached in
a flash. The idea of stages is really useful mainly in trying to make
clear the various difficulties in investigation, and the fact that
different men of genius may show different powers in overcoming them.
The right hypothesis may occur in a moment, as if by simple intuition,
but it may be tedious to prove, and the gifts that tell in proof,
such as Newton's immense mathematical power in calculating what
a hypothesis implies, Darwin's patience in verifying, Faraday's
ingenuity in devising experiments, are all great gifts, and may be
serviceable at different stages. But without originality and fertility
in probable hypothesis, nothing can be done.
The dispute between Mill and Whewell as to the place and value of
hypotheses in science was in the main a dispute about words. Mill
did not really undervalue hypothesis, and he gave a most luminous and
accurate account of the conditions of proof. But here and there he
incautiously spoke of the "hypothetical method" (by which he meant
what we have called the method of Explanation) as if it were a
defective kind of proof, a method resorted to by science when the
"experimental methods" could not be applied. Whether his language
fairly bore this construction is not worth arguing, but this was
manifestly the construction that Whewell had in his mind when he
retorted, as if in defence of hypotheses, that "the inductive process
consists in framing successive hypotheses, the comparison of these
with the ascertained facts of nature, and the introduction into them
of such modifications as the comparison may render necessary". This is
a very fair description of the whole method of explanation. There
is nothing really inconsistent with it in Mill's account of his
"hypothetical method"; only he erred himself or was the cause of error
in others in suggesting, intentionally or unintentionally, that
the Experimental Methods were different methods of proof. The
"hypothetical method," as he described it, consisting of Induction,
Ratiocination, and Verification, really comprehends the principles
of all modes of observation, whether naturally or artificially
experimental. We see this at once when we ask how the previous
knowledge is got in accordance with which hypotheses are framed. The
answer must be, by Observation. However profound the calculations,
it must be from observed laws, or supposed analogues of them, that
we start. And it is always by Observation that the results of these
calculations are verified.
Both Mill and Whewell, however, confined themselves too exclusively
to the great hypotheses of the Sciences, such as Gravitation and the
Undulatory Theory of Light. In the consideration of scientific method,
it is a mistake to confine our attention to these great questions,
which from the multitude of facts embraced can only be verified by
prolonged and intricate inquiry. Attempts at the explanation of the
smallest phenomena proceed on the same plan, and the verification
of conjectures about them is subject to the same conditions, and the
methods of investigation and the conditions of verification can be
studied most simply in the smaller cases. Further, I venture to think
it a mistake to confine ourselves to scientific inquiry in the narrow
sense, meaning thereby inquiry conducted within the pale of the
exact sciences. For not merely the exact sciences but all men in the
ordinary affairs of life must follow the same methods or at least
observe the same principles and conditions, in any satisfactory
attempt to explain.
Tares appear among the wheat. Good seed was sown: whence, then, come
the tares? "An enemy has done this." If an enemy has actually been
observed sowing the tares, his agency can be proved by descriptive
testimony. But if he has not been seen in the act, we must resort to
what is known in Courts of Law as circumstantial evidence. This is the
"hypothetical method" of science. That the tares are the work of an
enemy is a hypothesis: we examine all the circumstances of the case in
order to prove, by inference from our knowledge of similar cases,
that thus, and thus only, can those circumstances be accounted for.
Similarly, when a question is raised as to the authorship of an
anonymous book. We first search for a clue by carefully noting the
diction, the structure of the sentences, the character and sources of
the illustration, the special tracks of thought. We proceed upon the
knowledge that every author has characteristic turns of phrase and
imagery and favourite veins of thought, and we look out for such
internal evidence of authorship in the work before us. Special
knowledge and acumen may enable us to detect the authorship at once
from the general resemblance to known work. But if we would have clear
proof, we must show that the resemblance extends to all the details of
phrase, structure and imagery: we must show that our hypothesis of the
authorship of XYZ explains all the circumstances. And even this is
not sufficient, as many erroneous guesses from internal evidence
may convince us. We must establish further that there is no other
reasonable way of accounting for the matter and manner of the book;
for example, that it is not the work of an imitator. An imitator may
reproduce all the superficial peculiarities of an author with such
fidelity that the imitation can hardly be distinguished from the
original: thus few can distinguish between Fenton's work and Pope's
in the translation of the Odyssey. We must take such known facts into
account in deciding a hypothesis of authorship. Such hypotheses can
seldom be decided on internal evidence alone: other circumstantial
evidence--other circumstances that ought to be discoverable if the
hypothesis is correct--must be searched for.
The operation of causes that are manifest only in their effects must
be proved by the same method as the operation of past causes that
have left only their effects behind them. Whether light is caused by
a projection of particles from a luminous body or by an agitation
communicated through an intervening medium cannot be directly
observed. The only proof open is to calculate what should occur on
either hypothesis, and observe whether this does occur. In such a
case there is room for the utmost calculating power and experimental
ingenuity. The mere making of the general hypothesis or guess is
simple enough, both modes of transmitting influence, the projection
of moving matter and the travelling of an undulation or wave movement,
being familiar facts. But it is not so easy to calculate exactly how
a given impulse would travel, and what phenomena of ray and shadow,
of reflection, refraction and diffraction ought to be visible in
its progress. Still, no matter how intricate the calculation, its
correspondence with what can be observed is the only legitimate proof
of the hypothesis.
II.--OBSTACLES TO EXPLANATION.--PLURALITY OF CAUSES AND INTERMIXTURE
OF EFFECTS.
There are two main ways in which explanation may be baffled. There may
exist more than one cause singly capable of producing the effect in
question, and we may have no means of determining which of the equally
sufficient causes has actually been at work. For all that appears
the tares in our wheat may be the effect of accident or of malicious
design: an anonymous book may be the work of an original author or
of an imitator. Again, an effect may be the joint result of several
co-operating causes, and it may be impossible to determine their
several potencies. The bitter article in the _Quarterly_ may have
helped to kill John Keats, but it co-operated with an enfeebled
constitution and a naturally over-sensitive temperament, and we cannot
assign its exact weight to each of these coefficients. Death may be
the result of a combination of causes; organic disease co-operating
with exposure, over-fatigue co-operating with the enfeeblement of the
system by disease.
The technical names for these difficulties, Plurality of Causes and
Intermixture of Effects, are apt to confuse without some clearing up.
In both kinds of difficulty more causes than one are involved: but
in the one kind of case there is a plurality of possible or equally
probable causes, and we are at a loss to decide which: in the other
kind of case there is a plurality of co-operating causes; the effect
is the result or product of several causes working conjointly, and we
are unable to assign to each its due share.
It is with a view to overcoming these difficulties that Science
endeavours to isolate agencies and ascertain what each is capable of
singly. Mill and Bain treat Plurality of Causes and Intermixture of
Effects in connexion with the Experimental Methods. It is better,
perhaps, to regard them simply as obstacles to explanation, and the
Experimental Methods as methods of overcoming those obstacles. The
whole purpose of the Experimental Methods is to isolate agencies and
effects: unless they can be isolated, the Methods are inapplicable.
In situations where the effects observable may be referred with equal
probability to more than one cause, you cannot eliminate so as to
obtain a single agreement. The Method of Agreement is frustrated. And
an investigator can get no light from mixed effects, unless he
knows enough of the causes at work to be able to apply the Method
of Residues. If he does not, he must simply look out for or devise
instances where the agencies are at work separately, and apply the
principle of Single Difference.
Great, however, as the difficulties are, the theory of Plurality and
Intermixture baldly stated makes them appear greater than they are in
practice. There is a consideration that mitigates the complication,
and renders the task of unravelling it not altogether hopeless. This
is that different causes have distinctive ways of operating, and leave
behind them marks of their presence by which their agency in a given
case may be recognised.
An explosion, for example, occurs. There are several explosive
agencies, capable of causing as much destruction as meets the eye at
the first glance. The agent in the case before us may be gunpowder or
it may be dynamite. But the two agents are not so alike in their mode
of operation as to produce results identical in every circumstance.
The expert inquirer knows by previous observation that when gunpowder
acts the objects in the neighbourhood are blackened; and that an
explosion of dynamite tears and shatters in a way peculiar to
itself. He is thus able to interpret the traces, to make and prove a
hypothesis.
A man's body is found dead in water. It may be a question whether
death came by drowning or by previous violence. He may have been
suffocated and afterwards thrown into the water. But the circumstances
will tell the true story. Death by drowning has distinctive symptoms.
If drowning was the cause, water will be found in the stomach and
froth in the trachea.
Thus, though there may be a plurality of possible causes, the
causation in the given case may be brought home to one by distinctive
accompaniments, and it is the business of the scientific inquirer to
study these. What is known as the "ripple-mark" in sandstone surfaces
may be produced in various ways. The most familiar way is by the
action of the tides on the sand of the sea-shore, and the interpreter
who knows this way only would ascribe the marks at once to this
agency. But ripple-marks are produced also by the winds on drifting
sands, by currents of water where no tidal influence is felt, and
in fact by any body of water in a state of oscillation. Is it, then,
impossible to decide between these alternative possibilities of
causation? No: wind-ripples and current-ripples and tidal-ripples have
each their own special character and accompanying conditions, and the
hypothesis of one rather than another may be made good by means of
these. "In rock-formations," Mr. Page says,[1] "there are many things
which at first sight seem similar, and yet on more minute examination,
differences are detected and conditions discovered which render
it impossible that these appearances can have arisen from the same
causation."
The truth is that generally when we speak of plurality of causes, of
alternative possibilities of causation, we are not thinking of
the effect in its individual entirety, but only of some general or
abstract aspect of it. When we say, _e.g._, that death may be produced
by a great many different causes, poison, gunshot wounds, disease of
this or that organ, we are thinking of death in the abstract, not of
the particular case under consideration, which as an individual case,
has characters so distinctive that only one combination of causes is
possible.
The effort of science is to become less and less abstract in this
sense, by observing agencies or combinations of agencies apart and
studying the special characters of their effects. That knowledge
is then applied, on the assumption that where those characters are
present, the agent or combination of agencies has been at work. Given
an effect to be explained, it is brought home to one out of several
possible alternatives by _circumstantial evidence_.
Bacon's phrase, _Instantia Crucis_,[2] or Finger-post Instance, might
be conveniently appropriated as a technical name for a circumstance
that is decisive between rival hypotheses. This was, in effect,
proposed by Sir John Herschel,[3] who drew attention to the importance
of these crucial instances, and gave the following example: "A curious
example is given by M. Fresnel, as decisive, in his mind, of the
question between the two great opinions on the nature of light, which,
since the time of Newton and Huyghens, have divided philosophers.
When two very clean glasses are laid one on the other, if they be
not perfectly flat, but one or both in an almost imperceptible degree
convex or prominent, beautiful and vivid colours will be seen between
them; and if these be viewed through a red glass, their appearance
will be that of alternate dark and bright stripes.... Now, the
coloured stripes thus produced are explicable on both theories, and
are appealed to by both as strong confirmatory facts; but there is a
difference in one circumstance according as one or the other theory is
employed to explain them. In the case of the Huyghenian doctrine,
the intervals between the bright stripes ought to appear _absolutely
black_; in the other, _half bright_, when viewed [in a particular
manner] through a prism. This curious case of difference was tried as
soon as the opposing consequences of the two theories were noted by M.
Fresnel, and the result is stated by him to be decisive in favour
of that theory which makes light to consist in the vibrations of an
elastic medium."
III.--THE PROOF OF A HYPOTHESIS.
The completest proof of a hypothesis is when that which has been
hypothetically assumed to exist as a means of accounting for certain
phenomena is afterwards actually observed to exist or is proved by
descriptive testimony to have existed. Our argument, for example, from
internal evidence that Mill in writing his Logic aimed at furnishing
a method for social investigations is confirmed by a letter to Miss
Caroline Fox, in which he distinctly avowed that object.
The most striking example of this crowning verification in Science
is the discovery of the planet Neptune, in which case an agent
hypothetically assumed was actually brought under the telescope as
calculated. Examples almost equally striking have occurred in the
history of the Evolution doctrine. Hypothetical ancestors with certain
peculiarities of structure have been assumed as links between living
species, and in some cases their fossils have actually been found in
the geological register.
Such triumphs of verification are necessarily rare. For the most part
the hypothetical method is applied to cases where proof by actual
observation is impossible, such as prehistoric conditions of the earth
or of life upon the earth, or conditions in the ultimate constitution
of matter that are beyond the reach of the strongest microscope.
Indeed, some would confine the word hypothesis to cases of this kind.
This, in fact, was done by Mill: hypothesis, as he defined it, was a
conjecture not completely proved, but with a large amount of evidence
in its favour. But seeing that the procedure of investigation is the
same, namely, conjecture, calculation and comparison of facts with the
calculated results, whether the agency assumed can be brought to the
test of direct observation or not, it seems better not to restrict the
word hypothesis to incompletely proved conjectures, but to apply it
simply to a conjecture made at a certain stage in whatever way it may
afterwards be verified.
In the absence of direct verification, the proof of a hypothesis is
exclusive sufficiency to explain the circumstances. The hypothesis
must account for all the circumstances, and there must be no other way
of accounting for them. Another requirement was mentioned by Newton
in a phrase about the exact meaning of which there has been some
contention. The first of his Regulae Philosophandi laid down that the
cause assumed must be a _vera causa_. "We are not," the Rule runs, "to
admit other causes of natural things than such as both are true, and
suffice for explaining their phenomena."[4]
It has been argued that the requirement of "verity" is superfluous;
that it is really included in the requirement of sufficiency; that if
a cause is sufficient to explain the phenomena it must _ipso facto_ be
the true cause. This may be technically arguable, given a sufficient
latitude to the word sufficiency: nevertheless, it is convenient
to distinguish between mere sufficiency to explain the phenomena
in question, and the proof otherwise that the cause assigned really
exists _in rerum natura_, or that it operated in the given case. The
frequency with which the expression _vera causa_ has been used since
Newton's time shows that a need is felt for it, though it may be hard
to define "verity" precisely as something apart from "sufficiency". If
we examine the common usage of the expression we shall probably find
that what is meant by insisting on a _vera causa_ is that we must
have some evidence for the cause assigned outside the phenomena in
question. In seeking for verification of a hypothesis we must extend
our range beyond the limited facts that have engaged our curiosity and
that demand explanation.
There can be little doubt that Newton himself aimed his rule at the
Cartesian hypothesis of Vortices. This was an attempt to explain the
solar system on the hypothesis that cosmic space is filled with a
fluid in which the planets are carried round as chips of wood in a
whirlpool, or leaves or dust in a whirlwind. Now this is so far a
_vera causa_ that the action of fluid vortices is a familiar one: we
have only to stir a cup of tea with a bit of stalk in it to get an
instance. The agency supposed is sufficient also to account for the
revolution of a planet round the sun, given sufficient strength in the
fluid to buoy up the planet. But if there were such a fluid in space
there would be other phenomena: and in the absence of these other
phenomena the hypothesis must be dismissed as imaginary. The fact that
comets pass into and out of spaces where the vortices must be assumed
to be in action without exhibiting any perturbation is an _instantia
crucis_ against the hypothesis.
If by the requirement of a _vera causa_ were meant that the cause
assigned must be one directly open to observation, this would
undoubtedly be too narrow a limit. It would exclude such causes as the
ether which is assumed to fill interstellar space as a medium for
the propagation of light. The only evidence for such a medium and
its various properties is sufficiency to explain the phenomena. Like
suppositions as to the ultimate constitution of bodies, it is of the
nature of what Professor Bain calls a "Representative Fiction": the
only condition is that it must explain all the phenomena, and that
there must be no other way of explaining all. When it is proved
that light travels with a finite velocity, we are confined to two
alternative ways of conceiving its transmission, a projection of
matter from the luminous body and the transference of vibrations
through an intervening medium. Either hypothesis would explain many of
the facts: our choice must rest with that which best explains all.
But supposing that all the phenomena of light were explained by
attributing certain properties to this intervening medium, it would
probably be held that the hypothesis of an ether had not been fully
verified till other phenomena than those of light had been shown to
be incapable of explanation on any other hypothesis. If the properties
ascribed to it to explain the phenomena of light sufficed at the same
time to explain otherwise inexplicable phenomena connected with Heat,
Electricity, or Gravity, the evidence of its reality would be greatly
strengthened.
Not only must the circumstances in hand be explained, but other
circumstances must be found to be such as we should expect if the
cause assigned really operated. Take, for example, the case of Erratic
blocks or boulders, huge fragments of rock found at a distance from
their parent strata. The lowlands of England, Scotland, and Ireland,
and the great central plain of Northern Europe contain many such
fragments. Their composition shows indubitably that they once formed
part of hills to the northward of their present site. They must
somehow have been detached and transported to where we now find them.
How? One old explanation is that they were carried by witches, or
that they were themselves witches accidentally dropped and turned
into stone. Any such explanation by supernatural means can neither
be proved nor disproved. Some logicians would exclude such hypotheses
altogether on the ground that they cannot be rendered either more
or less probable by subsequent examination.[5] The proper scientific
limit, however, is not to the making of hypotheses, but to the proof
of them. The more hypotheses the merrier: only if such an agency as
witchcraft is suggested, we should expect to find other evidence
of its existence in other phenomena that could not otherwise be
explained. Again, it has been suggested that the erratic boulders may
have been transported by water. Water is so far a _vera causa_ that
currents are known to be capable of washing huge blocks to a great
distance. But blocks transported in this way have the edges worn off
by the friction of their passage: and, besides, currents strong enough
to dislodge and force along for miles blocks as big as cottages must
have left other marks of their presence. The explanation now received
is that glaciers and icebergs were the means of transport. But this
explanation was not accepted till multitudes of circumstances were
examined all tending to show that glaciers had once been present in
the regions where the erratic blocks are found. The minute habits of
glaciers have been studied where they still exist: how they slowly
move down carrying fragments of rock; how icebergs break off when they
reach water, float off with their load, and drop it when they melt;
how they grind and smooth the surfaces of rocks over which they pass
or that are frozen into them: how they undercut and mark the faces
of precipices past which they move; how moraines are formed at the
melting ends of them, and so forth. When a district exhibits all the
circumstances that are now observed to attend the action of glaciers
the proof of the hypothesis that glaciers were once there is complete.
[Footnote 1: Page's _Philosophy of Geology_, p. 38.]
[Footnote 2: Crux in this phrase means a cross erected at the
parting of ways, with arms to tell whither each way leads.]
[Footnote 3: _Discourse_, Sec. 218.]
[Footnote 4: Causas rerum naturalium non plures admitti
debere quam quae et veriae sint et carum phenomenis explicandis
sufficiant.]
[Footnote 5: See Prof. Fowler on the Conditions of Hypotheses,
_Inductive Logic_, pp. 100-115.]