METHODS OF OBSERVATION.--SINGLE DIFFERENCE.
I.--THE PRINCIPLE OF SINGLE DIFFERENCE.--MILL'S "CANON".
On what principle do we decide, in watching a succession of phenomena,
that they are connected as cause and effect, that one happened
in consequence of the happening of another? It may be worded as
follows:--
_When the addition of an agent is followed by the appearance
or its subtraction by the disappearance of a certain effect,
no other influential circumstance having been added or
subtracted at the same time or in the meantime, and no change
having occurred among the original circumstances, that agent
is a cause of the effect._
On this principle we would justify our belief in the causal properties
of common things--that fire burns, that food appeases hunger, that
water quenches thirst, that a spark ignites gunpowder, that taking
off a tight shoe relieves a pinched foot. We have observed the
effect following when there was no other change in the antecedent
circumstances, when the circumstance to which we refer it was simply
added to or subtracted from the prior situation.
Suppose we doubt whether a given agent is or is not capable of
producing a certain effect in certain circumstances, how do we put it
to the proof? We add it singly or subtract it singly, taking care that
everything else remains as before, and watch the result. If we wish
to know whether a spoonful of sugar can sweeten a cup of tea, we taste
the tea without the sugar, then add the sugar, and taste again. The
isolated introduction of the agent is the proof, the experiment. If we
wish to know whether a pain in the foot is due to a tight lacing,
we relax the lacing and make no other change: if the pain then
disappears, we refer it to the lacing as the cause. The proof is the
disappearance of the pain on the subtraction of the single antecedent.
The principle on which we decide that there is causal connexion is
the same whether we make the experimental changes ourselves or merely
watch them as they occur--the only course open to us with the great
forces of nature which are beyond the power of human manipulation. In
any case we have proof of causation when we can make sure that there
was only one difference in the antecedent circumstances corresponding
to the difference of result.
Mill's statement of this principle, which he calls the Canon of the
Method of Difference, is somewhat more abstract, but the proof relied
upon is substantially the same.
_If an instance in which the phenomenon under investigation
occurs, and an instance in which it does not occur, have every
circumstance in common save one, that one occurring only in
the former, the circumstance in which alone the two instances
differ is [the effect, or][1] the cause, or an indispensable
part of the cause, of the phenomenon._
Mill's statement has the merit of exactness, but besides being too
abstract to be easy of application, the canon is apt to mislead in one
respect. The wording of it suggests that the two instances required
must be two separate sets of circumstances, such as may be put side
by side and compared, one exhibiting the phenomenon and the other
not. Now in practice it is commonly one set of circumstances that we
observe with a special circumstance introduced or withdrawn: the two
instances, the data of observation, are furnished by the scene before
and the scene after the experimental interference. In the case, for
example, of a man shot in the head and falling dead, death being the
phenomenon in question, the instance where it does not occur is the
man's condition before he received the wound, and the instance where
it does occur is his condition after, the single circumstance of
difference being the wound, a difference produced by the addition or
introduction of a new circumstance. Again, take the common coin and
feather experiment, contrived to show that the resistance of the air
is the cause of the feather's falling to the ground more slowly than
the coin. The phenomenon under investigation is the retardation of the
feather. When the two are dropped simultaneously in the receiver of
an air-pump, the air being left in, the feather flutters to the ground
after the coin. This is the instance where the phenomenon occurs. Then
the air is pumped out of the receiver, and the coin and the feather
being dropped at the same instant reach the ground together. This
is the instance where the phenomenon does not occur. The single
circumstances of difference is the presence of air in the former
instance, a difference produced by the subtraction of a circumstance.
Mill's Canon is framed so as to suit equally whether the significant
difference is produced by addition to or subtraction from an existing
sum of circumstances. But that is misleading in so far as it suggests
that the two instances must be separate sets of circumstances,
is shown by the fact that it misled himself when he spoke of the
application of the method in social investigations, such as the effect
of Protection on national wealth. "In order," he says, "to apply to
the case the most perfect of the methods of experimental inquiry, the
Method of Difference, we require to find two instances which tally in
every particular except the one which is the subject of inquiry.
We must have two nations alike in all natural advantages and
disadvantages; resembling each other in every quality physical and
moral; habits, usages, laws, and institutions, and differing only in
the circumstance that the one has a prohibitory tariff and the other
has not." It being impossible ever to find two such instances, he
concluded that the Method of Difference could not be applied in
social inquiries. But really it is not necessary in order to have two
instances that we should have two different nations: the same nation
before and after a new law or institution fulfils that requirement.
The real difficulty, as we shall see, is to satisfy the paramount
condition that the two instances shall differ in a single
circumstance. Every new enactment would be an experiment after the
Method of Difference, if all circumstances but it remained the same
till its results appeared. It is because this seldom or never occurs
that decisive observation is difficult or impossible, and the simple
method of difference has to be supplemented by other means.
To introduce or remove a circumstance singly is the typical
application of the principle; but it may be employed also to compare
the effects of different agents, each added alone to exactly similar
circumstances. A simple example is seen in Mr. Jamieson's agricultural
experiments to determine the effects of different manures, such as
coprolite and superphosphate, on the growth of crops. Care is taken
to have all the antecedent circumstances as exactly alike as possible,
except as regards the agency whose effects are to be observed. A field
is chosen of uniform soil and even exposure and divided into plots:
it is equally drained so as to have the same degree of moisture
throughout; the seed is carefully selected for the whole sowing.
Between the sowing and the maturing of the crop all parts of the
field are open to the same weather. Each plot may thus be regarded as
practically composing the same set of conditions, and any difference
in the product may with reasonable probability be ascribed to the
single difference in the antecedents, the manures which it is desired
to compare.
II.--APPLICATION OF THE PRINCIPLE.
The principle of referring a phenomenon to the only immediately
preceding change in antecedent circumstances that could possibly have
affected it, is so simple and so often employed by everybody every
day, that at first we do not see how there can be any difficulty
about it or any possibility of error. And once we understand how many
difficulties there are in reaching exact knowledge even on this simple
principle, and what care has to be taken, we are apt to overrate its
value, and to imagine that it carries us further than it really does.
The scientific expert must know how to apply this principle, and a
single application of it with the proper precautions may take him
days or weeks, and yet all that can be made good by it may carry but a
little way towards the knowledge of which he is in search.
When the circumstances are simple and the effect follows at once, as
when hot water scalds, or a blow with a stick breaks a pane of glass,
there can be no doubt of the causal connexion so far, though plenty
of room for further inquiry into the why. But the mere succession of
phenomena may be obscure. We may introduce more than one agent
without knowing it, and if some time elapses between the experimental
interference and the appearance of the effect, other agents may come
in without our knowledge.
We must know exactly what it is that we introduce and all the
circumstances into which we introduce it. We are apt to ignore the
presence of antecedents that are really influential in the result. A
man heated by work in the harvest field hastily swallows a glass of
water, and drops down dead. There is no doubt that the drinking of the
water was a causal antecedent, but the influential circumstance
may not have been the quantity or the quality of the liquid but its
temperature, and this was introduced into the situation as well as a
certain amount of the liquid components. In making tea we put in so
much tea and so much boiling water. But the temperature of the pot
is also an influential circumstance in the resulting infusion. So in
chemical experiments, where one might expect the result to depend only
upon the proportions of the ingredients, it is found that the quantity
is also influential, the degree of heat evolved entering as a
factor into the result. Before we can apply the principle of single
difference, we must make sure that there is really only a single
difference between the instances that we bring into comparison.
The air-pump was invented shortly before the foundation of the Royal
Society, and its members made many experiments with this new means
of isolating an agent and thus discovering its potentialities.
For example, live animals were put into the receiver, and the air
exhausted, with the result that they quickly died. The absence of the
air being the sole difference, it was thus proved to be indispensable
to life. But air is a composite agent, and when means were contrived
of separating its components, the effects of oxygen alone and of
carbonic acid alone were experimentally determined.
A good example of the difficulty of excluding agencies other than
those we are observing, of making sure that none such intrude,
is found in the experiments that have been made in connexion with
spontaneous generation. The question to be decided is whether life
ever comes into existence without the antecedent presence of living
germs. And the method of determining this is to exclude all germs
rigorously from a compound of inorganic matter, and observe whether
life ever appears. If we could make sure in any one case that no germs
were antecedently present, we should have proved that in that case at
least life was spontaneously generated.
The difficulty here arises from the subtlety of the agent under
observation. The notion that maggots are spontaneously generated in
putrid meat, was comparatively easy to explode. It was found that when
flies were excluded by fine wire-gauze, the maggots did not appear.
But in the case of microscopic organisms proof is not so easy. The
germs are invisible, and it is difficult to make certain of their
exclusion. A French experimenter, Pouchet, thought he had obtained
indubitable cases of spontaneous generation. He took infusions of
vegetable matter, boiled them to a pitch sufficient to destroy all
germs of life, and hermetically sealed up the liquid in glass
flasks. After an interval, micro-organisms appeared. Doubts as to the
conclusion that they had been spontaneously generated turned upon two
questions: whether all germs in the liquid had been destroyed by the
preliminary boiling, and whether germs could have found access in the
course of the interval before life appeared. At a certain stage in
Pouchet's process he had occasion to dip the mouths of the flasks
in mercury. It occurred to Pasteur in repeating the experiments that
germs might have found their way in from the atmospheric dust on the
surface of this mercury. That this was so was rendered probable by his
finding that when he carefully cleansed the surface of the mercury no
life appeared afterwards in his flasks.
The application of the principle in human affairs is rendered
uncertain by the immense complication of the phenomena, the difficulty
of experiment, and the special liability of our judgments to
prejudice. That men and communities of men are influenced by
circumstances is not to be denied, and the influence of circumstances,
if it is to be traced at all, must be traced through observed facts.
Observation of the succession of phenomena must be part at least of
any method of tracing cause and effect. We must watch what follows
upon the addition of new agencies to a previously existing sum. But
we can seldom or never get a decisive observation from one pair of
instances, a clear case of difference of result preceded by a single
difference in the antecedents. The simple Method of Experimental
Addition or Subtraction is practically inapplicable. We can do nothing
with a man analogous to putting him into a hermetically sealed retort.
Any man or any community that is the subject of our observations
must be under manifold influences. Each of them probably works some
fraction of the total change observable, but how are they to be
disentangled? Consider, for example, how impossible it would be
to prove in an individual case, on the strict principle of Single
Difference, that Evil communications corrupt good manners. Moral
deterioration may be observed following upon the introduction of
an evil companion, but how can we make sure that no other degrading
influence has operated, and that no original depravity has developed
itself in the interval? Yet such propositions of moral causation can
be proved from experience with reasonable probability. Only it must
be by more extended observations than the strict Method of Difference
takes into account. The method is to observe repeated coincidences
between evil companionship and moral deterioration, and to account for
this in accordance with still wider observations of the interaction of
human personalities.
For equally obvious reasons the simple Method of Difference is
inapplicable to tracing cause and effect in communities. Every new law
or repeal of an old law is the introduction of a new agency, but the
effects of it are intermixed with the effects of other agencies that
operate at the same time. Thus Professor Cairnes remarks, concerning
the introduction of a high Protective Tariff into the United States
in 1861, that before its results could appear in the trade and
manufacture of the States, there occurred (1) The great Civil War,
attended with enormous destruction of capital; (2) Consequent upon
this the creation of a huge national debt, and a great increase of
taxation; (3) The issue of an inconvertible paper currency, deranging
prices and wages; (4) The discovery of great mineral resources and
oil-springs; (5) A great extension of railway enterprise. Obviously in
such circumstances other methods than the Method of Difference must
be brought into play before there can be any satisfactory reasoning on
the facts observed. Still what investigators aim at is the isolation
of the results of single agencies.
[Footnote 1: Prof. Bain, who adopts Mill's Canon, silently
drops the words within brackets. They seem to be an
inadvertence. The "circumstance," in all the examples
that Mill gives, is an antecedent circumstance. Herschel's
statement, of which Mill's is an adaptation, runs as follows:
"If we can either find produced by nature, or produce
designedly for ourselves, two instances which agree exactly in
all but one particular and differ in that one, its influence
in producing the phenomenon, if it have any, must thereby be
rendered apparent".]