ASCERTAINMENT OF FACTS OF CAUSATION.
I.--_POST HOC ERGO PROPTER HOC_.
One of the chief contributions of the Old Logic to Inductive Method
was a name for a whole important class of misobservations. The fallacy
entitled _Post Hoc ergo Propter Hoc_--"After, therefore, Because
of"--consisted in alleging mere sequence as a proof of consequence or
causal sequence. The sophist appeals to experience, to observed facts:
the sequence which he alleges has been observed. But the appeal is
fallacious: the observation on which he relies amounts only to this,
that the one event has followed upon the other. This much must be
observable in all cases of causal sequence, but it is not enough for
proof. _Post hoc ergo propter hoc_ may be taken as a generic name for
imperfect proof of causation from observed facts of succession.
The standard example of the fallacy is the old Kentish peasant's
argument that Tenterden Steeple was the cause of Goodwin Sands. Sir
Thomas More (as Latimer tells the story in one of his Sermons to
ridicule incautious inference) had been sent down into Kent as a
commissioner to inquire into the cause of the silting up of Sandwich
Haven. Among those who came to his court was the oldest inhabitant,
and thinking that he from his great age must at least have seen more
than anybody else, More asked him what he had to say as to the cause
of the sands. "Forsooth, sir," was the greybeard's answer, "I am an
old man: I think that Tenterden Steeple is the cause of Goodwin Sands.
For I am an old man, and I may remember the building of Tenterden
Steeple, and I may remember when there was no steeple at all there.
And before that Tenterden Steeple was in building, there was no
manner of speaking of any flats or sands that stopped the haven;
and, therefore, I think that Tenterden Steeple is the cause of the
destroying and decaying of Sandwich Haven."
This must be taken as Latimer meant it to be, as a ridiculous example
of a purely imbecile argument from observation, but the appeal to
experience may have more show of reason and yet be equally fallacious.
The believers in Kenelm Digby's "Ointment of Honour" appealed to
experience in support of its efficacy. The treatment was to apply the
ointment, not to the wound, but to the sword that had inflicted it, to
dress this carefully at regular intervals, and, meantime, having bound
up the wound, to leave it alone for seven days. It was observed that
many cures followed upon this treatment. But those who inferred that
the cure was due to the bandaging of the sword, failed to observe
that there was another circumstance that might have been instrumental,
namely, the exclusion of the air and the leaving of the wound
undisturbed while the natural healing processes went on. And it
was found upon further observation that binding up the wound alone
answered the purpose equally well whether the sword was dressed or
not.
In cases where _post hoc_ is mistaken for _propter hoc_, simple
sequence for causal sequence, there is commonly some bias of prejudice
or custom which fixes observation on some one antecedent and diverts
attention from other circumstances and from what may be observed to
follow in other cases. In the minds of Digby and his followers there
was probably a veneration for the sword as the weapon of honour, and a
superstitious belief in some secret sympathy between the sword and its
owner. So when the practice of poisoning was common, and suspicion was
flurried by panic fear, observation was often at fault. Pope Clement
VIII. was said to have been killed by the fumes of a poisoned candle
which was placed in his bedroom. Undoubtedly candles were there, but
those who attributed the Pope's death to them took no notice of the
fact that a brazier of burning charcoal was at the same time in the
apartment with no sufficient outlet for its fumes. Prince Eugene
is said to have received a poisoned letter, which he suspected and
immediately threw from him. To ascertain whether his suspicions were
well founded the letter was administered to a dog, which, to make
assurance doubly sure, was fortified by an antidote. The dog died, but
no inquiry seems to have been made into the character of the antidote.
Hotspur's retort to Glendower showed a sound sense of the true value
to be attached to mere priority.
_Glendower_. At my nativity
The front of heaven was full of fiery shapes,
Of burning cressets: and at my birth
The frame and huge foundation of the earth
Shaked like a coward.
_Hotspur_. Why so it would have done at the same season, if
your mother's cat had but kittened, though yourself had never
been born.
1 Hen. IV., 3, 1, 13.
We all admit at once that the retort was just. What principle of sound
conclusion was involved in it? It is the business of Inductive Logic
to make such principles explicit.
Taking _Post Hoc ergo Propter Hoc_ as a generic name for fallacious
arguments of causation based on observed facts, for the fallacious
proof of causation from experience, the question for Logic is, What
more than mere _sequence_ is required to prove _consequence?_ When do
observations of _Post Hoc_ warrant the conclusion _Propter Hoc?_
II.--MEANING OF "CAUSE".--METHODS OF OBSERVATION--MILL'S EXPERIMENTAL
METHODS.
The methods formulated by Mill under the name of Experimental Methods
are methods actually practised by men of science with satisfactory
results, and are perfectly sound in principle. They were, indeed, in
substance, taken by him from the practice of the scientific laboratory
and study as generalised by Herschel. In effect what Mill did was to
restate them and fit them into a system. But the controversies into
which he was tempted in so doing have somewhat obscured their exact
function in scientific inquiry. Hostile critics, finding that they did
not serve the ends that he seemed to claim for them, have jumped to
the conclusion that they are altogether illusory and serve no purpose
at all.
First, we must dismiss the notion, encouraged by Mill's general theory
of Inference, that the Experimental Methods have anything special to
do with the observation and inferential extension of uniformities such
as that death is common to all organised beings. One of the Methods,
as we shall see, that named by Mill the Method of Agreement, does
incidentally and collaterally establish empirical laws in the course
of its observations, and this probably accounts for the prominence
given to it in Mill's system. But this is not its end and aim, and
the leading Method, that named by him the Method of Difference,
establishes as fact only a particular case of causal coincidence.
It is with the proof of theories of causation that the Experimental
Methods are concerned: they are methods of observing with a view to
such proof.[1]
The next point to be made clear is that the facts of causation with
which the Methods are concerned are observable facts, relations among
phenomena, but that the causal relations or conditions of which they
are the proof are not phenomena, in the meaning of being manifest
to the senses, but rather noumena, inasmuch as they are reached by
reasoning from what is manifest.
Take, for example, what is known as the _quaquaversus_ principle in
Hydrostatics, that pressure upon a liquid is propagated equally in
all directions. We cannot observe this extension of pressure among the
liquid particles directly. It cannot be traced among the particles
by any of our senses. But we can assume that it is so, consider what
ought to be visible if it is so, and then observe whether the visible
facts are in accordance with the hypothesis. A box can be made, filled
with water, and so fitted with pistons on top and bottom and on each
of its four sides that they will indicate the amount of pressure on
them from within. Let pressure then be applied through a hole in
the top, and the pistons show that it has been communicated to them
equally. The application of the pressure and the yielding of the
pistons are observable facts, facts in causal sequence: what happens
among the particles of the liquid is not observed but reasonably
conjectured, is not _phenomenal_ but _noumenal_.
This distinction, necessary to an understanding of the scope of the
Methods, was somewhat obscured by Mill in his preliminary
discussion of the meaning of "cause". Very rightly, though somewhat
inconsistently with his first theory of Induction, he insists that
"the notion of Cause being the root of the whole theory of Induction,
it is indispensable that this idea should at the very outset of our
inquiry be, with the utmost practicable degree of precision, fixed
and determined". But in this determination, not content with simply
recognising that it is with phenomena that the Experimental Methods
primarily deal, it being indeed only phenomena that can be the
subjects of experimental management and observation, he starts by
declaring that science has not to do with any causes except such as
are phenomenal--"when I speak of the cause of any phenomenon, I do not
mean a cause which is not itself a phenomenon"--and goes on to define
as the only correct meaning of cause "the sum total of conditions,"
including among them conditions which are not phenomenal, in the sense
of being directly open to observation.
When Mill protested that he had regard only to phenomenal causes, he
spoke as the partisan of a philosophical tradition. It would have been
well if he had acted upon his own remark that the proper understanding
of the scientific method of investigating cause is independent of
metaphysical analysis of what cause means. Curiously enough, this
remark is the preface to an analysis of cause which has but slight
relevance to science, and is really the continuation of a dispute
begun by Hume. This is the key to his use of the word phenomenon: it
must be interpreted with reference to this: when he spoke of causes
as phenomenal, he opposed the word to "occult" in some supposed
metaphysical sense.[2] And this irrelevant discussion, into the
vortex of which he allowed himself to be carried, obscured the fact,
elsewhere fully recognised by Mill himself, that science does attempt
to get beyond phenomena at ultimate laws which are not themselves
phenomena though they bind phenomena together. The "colligation"
of the facts, to use Whewell's phrase, is not a phenomenon, but a
noumenon.
The truth is that a very simple analysis of "cause" is sufficient for
the purposes of scientific inquiry. It is enough to make sure that
causal sequence or consequence shall not be confounded with simple
sequence. Causal sequence is simple sequence and something more, that
something more being expressed by calling it causal. What we call a
cause is not merely antecedent or prior in time to what we call its
effect: it is so related to the effect that if it or an equivalent
event had not happened the effect would not have happened. Anything
in the absence of which a phenomenon would not have come to pass as it
did come to pass is a cause in the ordinary sense. We may describe it
as an indispensable antecedent, with this reservation (which will
be more fully understood afterwards), that if we speak of a
general effect, such as death, the antecedents must be taken with
corresponding generality.
It is misleading to suggest, as Mill does, by defining cause as "the
sum total of conditions"--a definition given to back up his conception
of cause as phenomenal--that science uses the word cause in a
different meaning from that of ordinary speech. It is quite true
that "the cause, philosophically speaking, is the sum total of the
conditions, positive and negative, taken together: the whole of
the contingencies of every description, which being realised,
the consequent invariably follows". But this does not imply any
discrepancy between the scientific or philosophical meaning and the
ordinary meaning. It is only another way of saying that the business
of science or philosophy is to furnish a complete explanation of an
event, an account of all its indispensable antecedents. The plain
man would not refuse the name of cause to anything that science or
philosophy could prove to be an indispensable antecedent, but his
interest in explanation is more limited. It is confined to what he
wants to know for the purpose he has in hand. Nor could the man of
science consistently refuse the name of cause to what the plain man
applies it to, if it really was something in consequence of which the
event took place. Only his interest in explanation is different. The
indispensable antecedents that he wants to know may not be the same.
Science or philosophy applies itself to the satisfaction of a wider
curiosity: it wants to know all the causes, the whole why, the sum
total of conditions. To that end the various departments of science
interest themselves in various species of conditions. But all
understand the word cause in the ordinary sense.
We must not conclude from accidental differences in explanation or
statement of cause, dependent on the purpose in view, that the word
Cause is used in different senses. In answering a question as to
the cause of anything, we limit ourselves to what we suppose our
interrogator to be ignorant of and desirous of knowing. If asked why
the bells are ringing, we mention a royal marriage, or a victory, or a
church meeting, or a factory dinner hour, or whatever the occasion
may be. We do not consider it necessary to mention that the bells
are struck by a clapper. Our hearer understands this without our
mentioning it. Nor do we consider it necessary to mention the acoustic
condition, that the vibration of the bells is communicated to our ears
through the air, or the physiological condition, that the vibrations
in the drums of our ears are conveyed by a certain mechanism of bone
and tissue to the nerves. Our hearer may not care to know this,
though quite prepared to admit that these conditions are indispensable
antecedents. Similarly, a physiographer, in stating the cause of the
periodical inundation of the Nile, would consider it enough to mention
the melting of snow on the mountains in the interior of Africa,
without saying anything of such conditions as the laws of gravity
or the laws of liquefaction by heat, though he knows that these
conditions are also indispensable. Death is explained by the doctor
when referred to a gunshot wound, or a poison, or a virulent disease.
The Pathologist may inquire further, and the Moral Philosopher further
still. But all inquiries into indispensable conditions are inquiries
into cause. And all alike have to be on their guard against mistaking
simple sequence for consequence.
To speak of the sum total of conditions, as the Cause in a
distinctively scientific sense, is misleading in another direction. It
rather encourages the idea that science investigates conditions in
the lump, merely observing the visible relations between sets of
antecedents and their consequents. Now this is the very thing
that science must avoid in order to make progress. It analyses the
antecedent situation, tries to separate the various coefficients, and
finds out what they are capable of singly. It must recognise that
some of the antecedents of which it is in search are not open to
observation. It is these, indeed, for the most part that constitute
the special subject-matter of the sciences in Molar as well as in
Molecular Physics. For practical every-day purposes, it is chiefly
the visible succession of phenomena that concerns us, and we are
interested in the latent conditions only in as far as they provide
safer ground for inference regarding such visible succession. But to
reach the latent conditions is the main work of science.
It is, however, only through observation of what is open to the senses
that science can reach the underlying conditions, and, therefore,
to understand its methods we must consider generally what is open to
observation in causal succession. What can be observed when phenomena
follow one another as cause and effect, that is, when the one happens
in consequence of the happening of the other? In Hume's theory,
which Mill formally adopted with a modification,[3] there is nothing
observable but the constancy or invariability of the connexion. When
we say that Fire burns, there is nothing to be observed except that a
certain sensation invariably follows upon close proximity to fire. But
this holds good only if our observation is arbitrarily limited to the
facts enounced in the expression. If this theory were sound, science
would be confined to the observation of empirical laws. But that there
is something wrong with it becomes apparent when we reflect that it
has been ascertained beyond doubt that in many observed changes, and
presumably in all, there is a transference of energy from one form to
another. The paralogism really lies in the assumption from which
Hume deduced his theory, namely, that every idea is a copy of some
impression. As a matter of fact, we have ideas that are not copies
of any one impression, but a binding together, colligation, or
intellection of several impressions. Psychological analysis shows us
that even when we say that things exist with certain qualities, we are
expressing not single impressions or mental phenomena, but supposed
causes and conditions of such, _noumena_ in short, which connect our
recollections of many separate impressions and expectations of more.
The Experimental Methods proceed on the assumption that there is other
outward and visible evidence of causal connexion than invariability of
sequence. In the leading Method it is assumed that when events may be
observed to follow one another in a certain way, they are in causal
sequence. If we can make sure that an antecedent change is the only
change that has occurred in an antecedent situation, we have proof
positive that any immediately subsequent change in the situation is a
consequent, that the successive changes are in causal sequence. Thus
when Pascal's barometer was carried to the top of Puy le Dome, and
the mercury in it fell, the experimenters argued that the fall of the
mercury was causally connected with the change of elevation, all the
other circumstances remaining the same. This is the foundation of the
so-called Method of Difference. To determine that the latent condition
was a difference in the weight of the atmosphere, needed other
observations, calculations and inferences; but if it could be shown
that the elevation was the only antecedent changed in a single
instance, causal connexion was established between this and the
phenomenon of the fall of the barometer.
It is obvious that in coming to this conclusion we assume what cannot
be demonstrated but must simply be taken as a working principle to be
confirmed by its accordance with experience, that nothing comes into
being without some change in the antecedent circumstances. This is the
assumption known as the Law of Causation--_ex nihilo nihil fit_.
Again, certain observable facts are taken as evidence that there is
no causal connexion. On the assumption that any antecedent in whose
absence a phenomenon takes place is not causally connected with it,
we set aside or eliminate various antecedents as fortuitous or
non-causal. This negative principle, as we shall see, is the
foundation of what Mill called the Method of Agreement.
Be it remarked, once for all, that before coming to a conclusion on
the Positive Method or Method of Difference, we may often have to make
many observations on the Negative Method. Thus Pascal's experimenters,
before concluding that the change of altitude was the only influential
change, tried the barometer in exposed positions and in sheltered,
when the wind blew and when it was calm, in rain and in fog, in order
to prove that these circumstances were indifferent. We must expound
and illustrate the methods separately, but every method known to
science may have in practice to be employed in arriving at a single
conclusion.
[Footnote 1: This is implied, as I have already remarked, in
the word Experimental. An experiment is a proof or trial: of
what? Of a theory, a conjecture.]
[Footnote 2: If we remember, as becomes apparent on exact
psychological analysis, that things and their qualities are as
much _noumena_ and not, strictly speaking, _phenomena_ as the
attraction of gravity or the quaquaversus principle in liquid
pressure, the prejudice against occultism is mitigated.]
[Footnote 3: The modification was that causation is not only
"invariable" but also "unconditional" sequence. This addition
of unconditionality as part of the meaning of cause, after
defining cause as the sum total of the conditions, is very
much like arguing in a circle. After all, the only point
recognised in the theory as observable is the invariability of
the sequence. But this is less important than the fact that
in his canons of the Experimental Methods Mill recognised that
more is observable.]