The method of scientific investigation is nothing but the expression of
the necessary mode of working of the human mind. It is simply the mode at
which all phenomena are reasoned about, rendered precise and exact. There
is no more difference, but there is just the same kind of difference,
between the mental operations of a man of science and those of an ordinary
person, as there is between the operations and methods of a baker or of a
butcher weighing out his goods in common scales, and the operations of a
chemist in performing a difficult and complex analysis by means of his
balance and finely graduated weights. It is not that the action of the
scales in the one case, and the balance in the other, differ in the
principles of their construction or manner of working; but the beam of one
is set on an infinitely finer axis than the other, and of course turns by
the addition of a much smaller weight.
You will understand this better, perhaps, if I give you some familiar
example. You have all heard it repeated, I dare say, that men of science
work by means of induction and deduction, and that by the help of these
operations, they, in a sort of sense, wring from Nature certain other
things, which are called natural laws, and causes, and that out of these,
by some cunning skill of their own, they build up hypotheses and theories.
And it is imagined by many, that the operations of the common mind can be
by no means compared with these processes, and that they have to be
acquired by a sort of special apprenticeship to the craft. To hear all
these large words, you would think that the mind of a man of science must
be constituted differently from that of his fellow men; but if you will
not be frightened by terms, you will discover that you are quite wrong,
and that all these terrible apparatus 87 are being
used by yourselves every day and every hour of your lives.
There is a well-known incident in one of Moliere's plays,88
where the author makes the hero express unbounded delight on being told
that he had been talking prose during the whole of his life. In the same
way, I trust, that you will take comfort, and be delighted with
yourselves, on the discovery that you have been acting on the principles
of inductive and deductive philosophy during the same period. Probably
there is not one here who has not in the course of the day had occasion to
set in motion a complex train of reasoning, of the very same kind, though
differing of course in degree, as that which a scientific man goes through
in tracing the causes of natural phenomena.
A very trivial circumstance will serve to exemplify this. Suppose you go
into a fruiterer's shop, wanting an apple,—you take up one, and, on
biting it, you find it is sour; you look at it, and see that it is hard
and green. You take up another one, and that too is hard, green, and sour.
The shopman offers you a third; but, before biting it, you examine it, and
find that it is hard and green, and you immediately say that you will not
have it, as it must be sour, like those that you have already tried.
Nothing can be more simple than that, you think; but if you will take the
trouble to analyse and trace out into its logical elements what has been
done by the mind, you will be greatly surprised. In the first place you
have performed the operation of induction. You found that, in two
experiences, hardness and greenness in apples went together with sourness.
It was so in the first case, and it was confirmed by the second. True, it
is a very small basis, but still it is enough to make an induction from;
you generalise the facts, and you expect to find sourness in apples where
you get hardness and greenness. You found upon that a general law that all
hard and green apples are sour; and that, so far as it goes, is a perfect
induction. Well, having got your natural law in this way, when you are
offered another apple which you find is hard and green, you say, "All hard
and green apples are sour; this apple is hard and green, therefore this
apple is sour." That train of reasoning is what logicians call a
syllogism, and has all its various parts and terms,—its major
premiss, its minor premiss and its conclusion. And, by the help of further
reasoning, which, if drawn out, would have to be exhibited in two or three
other syllogisms, you arrive at your final determination, "I will not have
that apple." So that, you see, you have, in the first place, established a
law by induction, and upon that you have founded a deduction, and reasoned
out the special particular case. Well now, suppose, having got your
conclusion of the law, that at some time afterwards, you are discussing
the qualities of apples with a friend: you will say to him, "It is a very
curious thing,—but I find that all hard and green apples are sour!"
Your friend says to you, "But how do you know that?" You at once reply,
"Oh, because I have tried them over and over again, and have always found
them to be so." Well, if we were talking science instead of common sense,
we should call that an experimental verification. And, if still opposed,
you go further, and say, "I have heard from the people in Somersetshire
and Devonshire, where a large number of apples are grown, that they have
observed the same thing. It is also found to be the case in Normandy, and
in North America. In short, I find it to be the universal experience of
mankind wherever attention has been directed to the subject." Whereupon,
your friend, unless he is a very unreasonable man, agrees with you, and is
convinced that you are quite right in the conclusion you have drawn. He
believes, although perhaps he does not know he believes it, that the more
extensive verifications are,—that the more frequently experiments
have been made, and results of the same kind arrived at,—that the
more varied the conditions under which the same results are attained, the
more certain is the ultimate conclusion, and he disputes the question no
further. He sees that the experiment has been tried under all sorts of
conditions, as to time, place, and people, with the same result; and he
says with you, therefore, that the law you have laid down must be a good
one, and he must believe it.
In science we do the same thing;—the philosopher exercises precisely
the same faculties, though in a much more delicate manner. In scientific
inquiry it becomes a matter of duty to expose a supposed law to every
possible kind of verification, and to take care, moreover, that this is
done intentionally, and not left to a mere accident, as in the case of the
apples. And in science, as in common life, our confidence in a law is in
exact proportion to the absence of variation in the result of our
experimental verifications. For instance, if you let go your grasp of an
article you may have in your hand, it will immediately fall to the ground.
That is a very common verification of one of the best established laws of
nature—that of gravitation. The method by which men of science
establish the existence of that law is exactly the same as that by which
we have established the trivial proposition about the sourness of hard and
green apples. But we believe it in such an extensive, thorough, and
unhesitating manner because the universal experience of mankind verifies
it, and we can verify it ourselves at any time; and that is the strongest
possible foundation on which any natural law can rest.
So much, then, by way of proof that the method of establishing laws in
science is exactly the same as that pursued in common life. Let us now
turn to another matter (though really it is but another phase of the same
question), and that is, the method by which, from the relations of certain
phenomena, we prove that some stand in the position of causes towards the
others.
I want to put the case clearly before you, and I will therefore show you
what I mean by another familiar example. I will suppose that one of you,
on coming down in the morning to the parlor of your house, finds that a
tea-pot and some spoons which had been left in the room on the previous
evening are gone,—the window is open, and you observe the mark of a
dirty hand on the window-frame, and perhaps, in addition to that, you
notice the impress of a hob-nailed shoe on the gravel outside. All these
phenomena have struck your attention instantly, and before two seconds
have passed you say, "Oh, somebody has broken open the window, entered the
room, and run off with the spoons and the tea-pot!" That speech is out of
your mouth in a moment. And you will probably add, "I know there has; I am
quite sure of it!" You mean to say exactly what you know; but in reality
you are giving expression to what is, in all essential particulars, an
hypothesis. You do not KNOW it at all; it is nothing but an hypothesis
rapidly framed in your own mind. And it is an hypothesis founded on a long
train of inductions and deductions.
What are those inductions and deductions, and how have you got at this
hypothesis? You have observed in the first place, that the window is open;
but by a train of reasoning involving many inductions and deductions, you
have probably arrived long before at the general law—and a very good
one it is—that windows do not open of themselves; and you therefore
conclude that something has opened the window. A second general law that
you have arrived at in the same way is, that tea-pots and spoons do not go
out of a window spontaneously, and you are satisfied that, as they are not
now where you left them, they have been removed. In the third place, you
look at the marks on the windowsill, and the shoe-marks outside, and you
say that in all previous experience the former kind of mark has never been
produced by anything else but the hand of a human being; and the same
experience shows that no other animal but man at present wears shoes with
hob-nails in them such as would produce the marks in the gravel. I do not
know, even if we could discover any of those "missing links" that are
talked about, that they would help us to any other conclusion! At any rate
the law which states our present experience is strong enough for my
present purpose. You next reach the conclusion that, as these kind 89
of marks have not been left by any other animal than man, or are liable to
be formed in any other way than a man's hand and shoe, the marks in
question have been formed by a man in that way. You have, further, a
general law, founded on observation and experience, and that, too, is, I
am sorry to say, a very universal and unimpeachable one,—that some
men are thieves; and you assume at once from all these premisses—and
that is what constitutes your hypothesis—that the man who made the
marks outside and on the window-sill, opened the window, got into the
room, and stole your tea-pot and spoons. You have now arrived at a vera
causa;—you have assumed a cause which, it is plain, is competent to
produce all the phenomena you have observed. You can explain all these
phenomena only by the hypothesis of a thief. But that is a hypothetical
conclusion, of the justice of which you have no absolute proof at all; it
is only rendered highly probable by a series of inductive and deductive
reasonings.
I suppose your first action, assuming that you are a man of ordinary
common sense, and that you have established this hypothesis to your own
satisfaction, will very likely be to go off for the police, and set them
on the track of the burglar, with the view to the recovery of your
property. But just as you are starting with this object, some person comes
in, and on learning what you are about, says, "My good friend, you are
going on a great deal too fast. How do you know that the man who really
made the marks took the spoons? It might have been a monkey that took
them, and the man may have merely looked in afterwards." You would
probably reply, "Well, that is all very well, but you see it is contrary
to all experience of the way tea-pots and spoons are abstracted; so that,
at any rate, your hypothesis is less probable than mine." While you are
talking the thing over in this way, another friend arrives, one of the
good kind of people that I was talking of a little while ago. And he might
say, "Oh, my dear sir, you are certainly going on a great deal too fast.
You are most presumptuous. You admit that all these occurrences took place
when you were fast asleep, at a time when you could not possibly have
known anything about what was taking place. How do you know that the laws
of Nature are not suspended during the night? It may be that there has
been some kind of supernatural interference in this case." In point of
fact, he declares that your hypothesis is one of which you cannot at all
demonstrate the truth, and that you are by no means sure that the laws of
Nature are the same when you are asleep as when you are awake.
Well, now, you cannot at the moment answer that kind of reasoning. You
feel that your worthy friend has you somewhat at a disadvantage. You will
feel perfectly convinced in your own mind, however, that you are quite
right, and you say to him, "My good friend, I can only be guided by the
natural probabilities of the case, and if you will be kind enough to stand
aside and permit me to pass, I will go and fetch the police." Well, we
will suppose that your journey is successful, and that by good luck you
meet with a policeman; that eventually the burglar is found with your
property on his person, and the marks correspond to his hand and to his
boots. Probably any jury would consider those facts a very good
experimental verification of your hypothesis, touching the cause of the
abnormal phenomena observed in your parlor, and would act accordingly.
Now, in this supposititious case, I have taken phenomena of a very common
kind, in order that you might see what are the different steps in an
ordinary process of reasoning, if you will only take the trouble to
analyse it carefully. All the operations I have described, you will see,
are involved in the mind of any man of sense in leading him to a
conclusion as to the course he should take in order to make good a robbery
and punish the offender. I say that you are led, in that case, to your
conclusion by exactly the same train of reasoning as that which a man of
science pursues when he is endeavouring to discover the origin and laws of
the most occult phenomena. The process is, and always must be, the same;
and precisely the same mode of reasoning was employed by Newton 90
and Laplace 91 in their endeavours to discover
and define the causes of the movements of the heavenly bodies, as you,
with your own common sense, would employ to detect a burglar. The only
difference is, that the nature of the inquiry being more abstruse, every
step has to be most carefully watched, so that there may not be a single
crack or flaw in your hypothesis. A flaw or crack in many of the
hypotheses of daily life may be of little or no moment as affecting the
general correctness of the conclusions at which we may arrive; but, in a
scientific inquiry, a fallacy, great or small, is always of importance,
and is sure to be in the long run constantly productive of mischievous if
not fatal results.
Do not allow yourselves to be misled by the common notion that an
hypothesis is untrustworthy simply because it is an hypothesis. It is
often urged, in respect to some scientific conclusion, that, after all, it
is only an hypothesis. But what more have we to guide us in nine-tenths of
the most important affairs of daily life than hypotheses, and often very
ill-based ones? So that in science, where the evidence of an hypothesis is
subjected to the most rigid examination, we may rightly pursue the same
course. You may have hypotheses, and hypotheses. A man may say, if he
likes, that the moon is made of green cheese: that is an hypothesis. But
another man, who has devoted a great deal of time and attention to the
subject, and availed himself of the most powerful telescopes and the
results of the observations of others, declares that in his opinion it is
probably composed of materials very similar to those of which our own
earth is made up: and that is also only an hypothesis. But I need not tell
you that there is an enormous difference in the value of the two
hypotheses. That one which is based on sound scientific knowledge is sure
to have a corresponding value; and that which is a mere hasty random guess
is likely to have but little value. Every great step in our progress in
discovering causes has been made in exactly the same way as that which I
have detailed to you. A person observing the occurrence of certain facts
and phenomena asks, naturally enough, what process, what kind of operation
known to occur in Nature applied to the particular case, will unravel and
explain the mystery? Hence you have the scientific hypothesis; and its
value will be proportionate to the care and completeness with which its
basis had been tested and verified. It is in these matters as in the
commonest affairs of practical life: the guess of the fool will be folly,
while the guess of the wise man will contain wisdom. In all cases, you see
that the value of the result depends on the patience and faithfulness with
which the investigator applies to his hypothesis every possible kind of
verification.
