METHODS OF OBSERVATION.--ELIMINATION.--SINGLE AGREEMENT.
I.--THE PRINCIPLE OF ELIMINATION.
The essence of what Mill calls the Method of Agreement is really the
elimination[1] of accidental, casual, or fortuitous antecedents. It
is a method employed when we are given an effect and set to work to
discover the cause. It is from the effect that we start and work back.
We make a preliminary analysis of the antecedents; call the roll, as
it were, of all circumstances present before the effect appeared. Then
we proceed to examine other instances of the same effect, and other
instances of the occurrence of the various antecedents, and bring to
bear the principle that any antecedent in the absence of which the
effect has appeared or on the presence of which it has not appeared
may be set aside as fortuitous, as being not an indispensable
antecedent. This is really the guiding principle of the method as a
method of observation.
Let the inquiry, for example, be into the cause of Endemic Goitre.
Instances of the disease have been collected from the medical
observations of all countries over many years. Why is it endemic in
some localities and not in others? We proceed on the assumption that
the cause, whatever it is, must be some circumstance common to all
localities where it is endemic. If any such circumstance is obvious
at once, we may conclude on the mere principle of repeated coincidence
that there is causal connexion between it and the disease, and
continue our inquiry into the nature of the connexion. But if no such
circumstance is obvious, then in the course of our search for it we
eliminate, as fortuitous, conditions that are present in some cases
but absent in others. One of the earliest theories was that endemic
goitre was connected with the altitude and configuration of the
ground, some notorious centres of it being deeply cleft mountain
valleys, with little air and wind and damp marshy soil. But wider
observation found it in many valleys neither narrower nor deeper than
others that were exempt, and also in wide exposed valleys such as
the Aar. Was it due to the geological formation? This also had to
be abandoned, for the disease is often incident within very narrow
limits, occurring in some villages and sparing others though the
geological formation is absolutely the same. Was it due to the
character of the drinking-water? Especially to the presence of lime
or magnesia? This theory was held strongly, and certain springs
characterised as goitre-springs. But the springs in some goitre
centres show not a trace of magnesia. The comparative immunity of
coast regions suggested that it might be owing to a deficiency of
iodine in the drinking-water and the air, and many instances were
adduced in favour of this. But further inquiries made out the presence
of iodine in considerable quantities, in the air, the water, and the
vegetation of districts where goitre was widely prevalent; while in
Cuba it is said that not a trace of iodine is discoverable either in
the air or the water, and yet it is quite free from goitre. After
a huge multiplication of instances, resulting in the elimination of
every local condition that had been suggested as a possible cause,
Hirsch came to the conclusion that the true cause must be a morbid
poison, and that endemic goitre has to be reckoned among the
infectious diseases.[2]
On this negative principle, that if a circumstance comes and goes
without bringing the phenomenon in its train, the phenomenon
is causally independent of it, common-sense is always at work
disconnecting events that are occasionally coincident in time. A
bird sings at our window, for example, and the clock ticks on the
mantelpiece. But the clock does not begin to tick when the bird begins
to sing, nor cease to tick when the bird flies away. Accordingly, if
the clock should stop at any time, and we wished to inquire into the
cause, and anybody were to suggest that the stoppage of the clock was
caused by the stoppage of a bird's song outside, we should dismiss
the suggestion at once. We should eliminate this circumstance from our
inquiry, on the ground that from other observations we knew it to be
a casual or fortuitous concomitant. Hotspur's retort to Glendover
(p. 297) was based on this principle. When poetic sentiment or
superstition rejects a verdict of common-sense or science, it is
because it imagines a causal connexion to exist that is not open to
observation, as in the case of the grandfather's clock which stopped
short never to go again when the old man died.
II.--THE PRINCIPLE OF SINGLE AGREEMENT.
The procedure in Mill's "Method of Agreement" consists in thus
eliminating fortuitous antecedents or concomitants till only one
remains. We see the nature of the proof relied upon when we ask, How
far must elimination be carried in order to attain proof of causal
connexion? The answer is that we must go on till we have eliminated
all but one. We must multiply instances of the phenomenon, till we
have settled of each of the antecedents except one that it is not the
cause. We must have taken account of all the antecedents, and we
must have found in our observations that all but one have been only
occasionally present.
_When all the antecedents of an effect except one can be
absent without the disappearance of the effect, that one is
causally connected with the effect, due precautions being
taken that no other circumstances have been present besides
those taken account of._
Mill's Canon of the Method of Agreement is substantially identical
with this:--
When two or more instances of the phenomenon under
investigation have only one circumstance in common, the
circumstance in which alone all the instances agree is the
cause (or effect) of the given phenomenon.
Herschel's statement, on which this canon is founded, runs as follows:
"Any circumstance in which all the facts without exception agree, may
be the cause in question, or if not, at least a collateral effect
of the same cause: if there be but one such point of agreement, the
possibility becomes a certainty".
All the instances examined must agree in one circumstance--hence the
title Method of Agreement. But it is not in the agreement merely that
the proof consists, but the agreement in one circumstance combined
with difference in all the other circumstances, when we are certain
that every circumstance has come within our observation. It is the
singleness of the agreement that constitutes the proof just as it is
the singleness of the difference in the Method of Difference.[3]
It has been said that Mill's Method of Agreement amounts after all
only to an uncontradicted _Inductio per enumerationem simplicem_,
which he himself stigmatised as Induction improperly so called. But
this is not strictly correct. It is a misunderstanding probably caused
by calling the method that of agreement simply, instead of calling it
the Method of Single Agreement, so as to lay stress upon the process
of elimination by which the singleness is established. It is true that
in the course of our observations we do perform an induction by simple
enumeration. In eliminating, we at the same time generalise. That is
to say, in multiplying instances for the elimination of non-causes, we
necessarily at the same time multiply instances where the true causal
antecedent, if there is only one possible, is present. An antecedent
containing the true cause must always be there when the phenomenon
appears, and thus we may establish by our eliminating observations a
uniformity of connexion between two facts.
Take, for example, Roger Bacon's inquiry into the cause of the colours
of the rainbow. His first notion seems to have been to connect the
phenomenon with the substance crystal, probably from his thinking of
the crystal firmament then supposed to encircle the universe. He found
the rainbow colours produced by the passage of light through hexagonal
crystals. But on extending his observations, he found that the passage
of light through other transparent mediums was also attended by the
phenomenon. He found it in dewdrops, in the spray of waterfalls, in
drops shaken from the oar in rowing. He thus eliminated the substance
crystal, and at the same time established the empirical law that
the passage of light through transparent mediums of a globular or
prismatic shape was a causal antecedent of the rainbow colours.[4]
Ascertainment of invariable antecedents may thus proceed side by side
with that of variable antecedents, the use of the elimination being
simply to narrow the scope of the inquiry. But the proof set forth in
Mill's Canon does not depend merely on one antecedent or concomitant
being invariably present, but also on the assumption that all the
influential circumstances have been within our observation. Then only
can we be sure that the instances have _only one_ circumstance in
common.
The truth is that owing to the difficulty of fulfilling this
condition, proof of causation in accordance with Mill's Canon is
practically all but impossible. It is not attained in any of the
examples commonly given. The want of conclusiveness is disguised
by the fact that both elimination and positive observation of mere
agreement or uniform concomitance are useful and suggestive in the
search for causes, though they do not amount to complete proof such as
the Canon describes. Thus in the inquiry into the cause of goitre, the
elimination serves some purpose though the result is purely negative.
When the inquirer is satisfied that goitre is not originated by any
directly observable local conditions, altitude, temperature, climate,
soil, water, social circumstances, habits of exertion, his search
is profitably limited. And mere frequency, much more constancy of
concomitance, raises a presumption of causal connexion, and looking
out for it is valuable as a mode of reconnoitring. The first thing
that an inquirer naturally asks when confronted by numerous instances
of a phenomenon is, What have they in common? And if he finds that
they have some one circumstance invariably or even frequently present,
although he cannot prove that they have no other circumstance in
common as the Cannon of Single Agreement requires, the presumption of
causal connexion is strong enough to furnish good ground for further
inquiry. If an inquirer finds an illness with marked symptoms in a
number of different households, and finds also that all the households
get their milk supply from the same source, this is not conclusive
proof of causation, but it is a sufficient presumption to warrant him
in examining whether there is any virulent ingredient in the milk.
Thus varying the circumstances so as to bring out a common antecedent,
though it does not end in exact proof, may indicate causal connexion
though it does not prove what the nature of the connexion is. Roger
Bacon's observations indicated that the production of rainbow colours
was connected with the passage of light through a transparent globe or
prism. It was reserved for Newton to prove by other methods that
white light was composed of rays, and that those rays were differently
refracted in passing through the transparent medium. We have
another example of how far mere agreement, revealed by varying the
circumstances, carries us towards discovery of the cause, in Wells's
investigation of the cause of dew. Comparing the numerous instances of
dew appearing without visible fall of moisture, Wells found that they
all agreed in the comparative coldness of the surface dewed. This was
all the agreement that he established by observation; he did not carry
observation to the point of determining that there was absolutely
no other common circumstance: when he had simply discovered dewed
surfaces, he tried next to show by reasoning from other knows facts
how the coldness of the surface affected the aqueous vapour of the
neighbouring air. He did not establish his Theory of Dew by the Method
of Agreement: but the observation of an agreement or common feature in
a number of instances was a stage in the process by which he reached
his theory.
III.--MILL'S "JOINT METHOD OF AGREEMENT AND DIFFERENCE".
After examining a variety of instances in which an effect appears,
and finding that they all agree in the antecedent presence of some one
circumstance, we may proceed to examine instances otherwise similar
(_in pari materia_, as Prof. Fowler puts it) where the effect does not
appear. If these all agree in the absence of the circumstance that is
uniformly present with the effect, we have corroborative evidence that
there is causal connexion between this circumstance and the effect.
The principle of this method seems to have been suggested to Mill by
Wells's investigations into Dew. Wells exposed a number of polished
surfaces of various substances, and compared those in which there was
a copious deposit of dew with those in which there was little or
none. If he could have got two surfaces, one dewed and the other
not, identical in every concomitant but one, he would have attained
complete proof on the principle of Single Difference. But this being
impracticable, he followed a course which approximated to the method
of eliminating every circumstance but one from instances of dew, and
every circumstance but one in the instances of no-dew. Mill sums up as
follows the results of his experiments: "It appears that the instances
in which much dew is deposited, which are very various, agree in
this, and, _so far as we are able to observe, in this only_, that they
either radiate heat rapidly or conduct it slowly: qualities between
which there is no other circumstance of agreement than that by virtue
of either, the body tends to lose heat from the surface more rapidly
than it can be restored from within. The instances, on the contrary,
in which no dew, or but a small quantity of it, is formed, and which
are also extremely various, agree (_as far as we can observe_) _in
nothing except_ in _not_ having this same property. We seem therefore
to have detected the characteristic difference between the substances
on which the dew is produced, and those on which it is not produced.
And thus have been realised the requisitions of what we have termed
the Indirect Method of Difference, or the Joint Method of Agreement
and Difference." The Canon of this Method is accordingly stated by
Mill as follows:--
If two or more instances in which the phenomenon occurs have
only one circumstance in common, while two or more instances
in which it does not occur have nothing in common save the
absence of that circumstance; the circumstance in which alone
the two sets of instances differ, is the effect, or the cause,
or an indispensable part of the cause, of the phenomenon.
In practice, however, this theoretical standard of proof is never
attained. What investigators really proceed upon is the presumption
afforded, to use Prof. Bain's terms, by Agreement in Presence combined
with Agreement in Absence. When it is found that all substances which
have a strong smell agree in being readily oxidisable, and that the
marsh gas or carbonetted hydrogen which has no smell is not oxidisable
at common temperatures, the presumption that oxidation is one of the
causal circumstances in smell is strengthened, even though we have not
succeeded in eliminating every circumstance but this one from either
the positive or the negative instances. So in the following examples
given by Prof. Fowler there is not really a compliance with the
theoretical requirements of Mill's Method: there is only an increased
presumption from the double agreement. "The Joint Method of Agreement
and Difference (or the Indirect Method of Difference, or, as I
should prefer to call it, the Double Method of Agreement) is being
continually employed by us in the ordinary affairs of life. If when I
take a particular kind of food, I find that I invariably suffer from
some particular form of illness, whereas, when I leave it off, I cease
to suffer, I entertain a double assurance that the food is the cause
of my illness. I have observed that a certain plant is invariably
plentiful on a particular soil; if, with a wide experience, I fail to
find it growing on any other soil, I feel confirmed in my belief that
there is in this particular soil some chemical constituent, or
some peculiar combination of chemical constituents, which is highly
favourable, if not essential, to the growth of the plant."
[Footnote 1: Elimination, or setting aside as being of no
concern, must not be confounded with the exclusion of agents
practised in applying the Method of Difference. We use the
word in its ordinary sense of putting outside the sphere of
an argument. By a curious slip, Professor Bain follows Mill in
applying the word sometimes to the process of singling out or
disentangling a causal circumstance. This is an inadvertent
departure from the ordinary usage, according to which
elimination means discarding from consideration as being
non-essential.]
[Footnote 2: Hirsch's _Geographical and Historical Pathology_,
Creighton's translation, vol. ii. pp. 121-202.]
[Footnote 3: The bare titles Difference and Agreement, though
they have the advantage of simplicity, are apt to puzzle
beginners inasmuch as in the Method of Difference the
agreement among the instances is at a maximum, and the
difference at a minimum, and _vice versa_ in the Method of
Agreement. In both Methods it is really the isolation of the
connexion between antecedent and sequent that constitutes the
proof.]
[Footnote 4: That rainbows in the sky are produced by the
passage of light through minute drops in the clouds was an
inference from this observed uniformity.]