Chapter XIII: Miscellaneous Examples of the Explanation of Laws of Nature (3)

79 This view of the necessary coexistence of opposite excitements
involves a great extension of the original doctrine of two
electricities. The early theorists assumed that, when amber was
rubbed, the amber was made positive and the rubber negative to the
same degree; but it never occurred to them to suppose that the
existence of the amber charge was dependent on an opposite charge in
the bodies with which the amber was contiguous, while the existence
of the negative charge on the rubber was equally dependent on a
contrary state of the surfaces that might accidentally be confronted
with it; that, in fact, in a case of electrical excitement by
friction, four charges were the minimum that could exist. But this
double electrical action is essentially implied in the explanation
now universally adopted in regard to the phenomena of the common
electric machine.

80 Pp. 159-162.

81 Infra, book iv., chap. ii. On Abstraction.

82 I must, however, remark, that this example, which seems to militate
against the assertion we made of the comparative inapplicability of
the Method of Difference to cases of pure observation, is really one
of those exceptions which, according to a proverbial expression,
prove the general rule. For this case, in which Nature, in her
experiment, seems to have imitated the type of the experiments made
by man, she has only succeeded in producing the likeness of man’s
most imperfect experiments; namely, those in which, though he
succeeds in producing the phenomenon, he does so by employing
complex means, which he is unable perfectly to analyse, and can form
therefore no sufficient judgment what portion of the effects may be
due, not to the supposed cause, but to some unknown agency of the
means by which that cause was produced. In the natural experiment
which we are speaking of, the means used was the clearing off a
canopy of clouds; and we certainly do not know sufficiently in what
this process consists, or on what it depends, to be certain _à
priori_ that it might not operate upon the deposition of dew
independently of any thermometric effect at the earth’s surface.
Even, therefore, in a case so favourable as this to Nature’s
experimental talents, her experiment is of little value except in
corroboration of a conclusion already attained through other means.

83 Discourse, pp. 156-8, and 171.

_ 84 Outlines of Astronomy_, p. 584.

85 Dr. Whewell, in his reply, expresses a very unfavourable opinion of
the utility of the Four Methods, as well as of the aptness of the
examples by which I have attempted to illustrate them. His words are
these (pp. 44-6):

“Upon these methods, the obvious thing to remark is, that they take
for granted the very thing which is most difficult to discover, the
reduction of the phenomena to formulæ such as are here presented to
us. When we have any set of complex facts offered to us; for
instance, those which were offered in the cases of discovery which I
have mentioned,—the facts of the planetary paths, of falling bodies,
of refracted rays, of cosmical motions, of chemical analysis; and
when, in any of these cases, we would discover the law of nature
which governs them, or, if any one chooses so to term it, the
feature in which all the cases agree, where are we to look for our
A, B, C, and _a, b, c_? Nature does not present to us the cases in
this form; and how are we to reduce them to this form? You say,
_when_ we find the combination of A B C with _a b c_ and A B D with
_a b d_, then we may draw our inference. Granted; but when and where
are we to find such combinations? Even now that the discoveries are
made, who will point out to us what are the A, B, C, and _a, b, c_
elements of the cases which have just been enumerated? Who will tell
us which of the methods of inquiry those historically real and
successful inquiries exemplify? Who will carry these formulæ through
the history of the sciences, as they have really grown up; and shew
us that these four methods have been operative in their formation;
or that any light is thrown upon the steps of their progress by
reference to these formulæ?”

He adds that, in this work, the methods have not been applied “to a
large body of conspicuous and undoubted examples of discovery,
extending along the whole history of science,” which ought to have
been done in order that the methods might be shown to possess the
“advantage” (which he claims as belonging to his own) of being those
“by which all great discoveries in science have really been
made.”—(p. 66.)

There is a striking similarity between the objections here made
against Canons of Induction, and what was alleged, in the last
century, by as able men as Dr. Whewell, against the acknowledged
Canon of Ratiocination. Those who protested against the Aristotelian
Logic said of the Syllogism, what Dr. Whewell says of the Inductive
Methods, that it “takes for granted the very thing which is most
difficult to discover, the reduction of the argument to formulæ such
as are here presented to us.” The grand difficulty, they said, is to
obtain your syllogism, not to judge of its correctness when
obtained. On the matter of fact, both they and Dr. Whewell are
right. The greatest difficulty in both cases is first that of
obtaining the evidence, and next, of reducing it to the form which
tests its conclusiveness. But if we try so to reduce it without
knowing _to what_, we are not likely to make much progress. It is a
more difficult thing to solve a geometrical problem, than to judge
whether a proposed solution is correct: but if people were not able
to judge of the solution when found, they would have little chance
of finding it. And it cannot be pretended that to judge of an
induction when found, is perfectly easy, is a thing for which aids
and instruments are superfluous; for erroneous inductions, false
inferences from experience, are quite as common, on some subjects
much commoner, than true ones. The business of Inductive Logic is to
provide rules and models (such as the Syllogism and its rules are
for ratiocination) to which if inductive arguments conform, those
arguments are conclusive, and not otherwise. This is what the Four
Methods profess to be, and what I believe they are universally
considered to be by experimental philosophers, who had practised all
of them long before any one sought to reduce the practice to theory.

The assailants of the Syllogism had also anticipated Dr. Whewell in
the other branch of his argument. They said that no discoveries were
ever made by syllogism; and Dr. Whewell says, or seems to say, that
none were ever made by the four Methods of Induction. To the former
objectors, Archbishop Whately very pertinently answered, that their
argument, if good at all, was good against the reasoning process
altogether; for whatever cannot be reduced to syllogism, is not
reasoning. And Dr. Whewell’s argument, if good at all, is good
against all inferences from experience. In saying that no
discoveries were ever made by the four Methods, he affirms that none
were ever made by observation and experiment; for assuredly if any
were, it was by one or other of those methods.

This difference between us accounts for the dissatisfaction which my
examples give him; for I did not select them with a view to satisfy
any one who required to be convinced that observation and experiment
are modes of acquiring knowledge: I confess that in the choice of
them I thought only of illustration, and of facilitating the
_conception_ of the Methods by concrete instances. If it had been my
object to justify the processes themselves as means of
investigation, there would have been no need to look far off, or
make use of recondite or complicated instances. As a specimen of a
truth ascertained by the Method of Agreement, I might have chosen
the proposition, “Dogs bark.” This dog, and that dog, and the other
dog, answer to A B C, A D E, A F G. The circumstance of being a dog,
answers to A. Barking answers to _a_. As a truth made known by the
Method of Difference, “Fire burns” might have sufficed. Before I
touch the fire I am not burnt; this is B C; I touch it, and am
burnt; this is A B C, _a_ B C.

Such familiar experimental processes are not regarded as inductions
by Dr. Whewell; but they are perfectly homogeneous with those by
which, even on his own shewing, the pyramid of science is supplied
with its base. In vain he attempts to escape from this truth by
laying the most arbitrary restrictions on the choice of examples
admissible as instances of Induction: they must neither be such as
are still matter of discussion (p. 47), nor must any of them be
drawn from mental and social subjects (p. 53), nor from ordinary
observation and practical life (pp. 11-15). They must be taken
exclusively from the generalizations by which scientific thinkers
have ascended to great and comprehensive laws of natural phenomena.
Now it is seldom possible, in these complicated inquiries, to go
much beyond the initial steps, without calling in the instrument of
Deduction, and the temporary aid of hypotheses; as I myself, in
common with Dr. Whewell, have maintained against the purely
empirical school. Since therefore such cases could not conveniently
be selected to illustrate the principles of mere observation and
experiment, Dr. Whewell takes advantage of their absence to
represent the Experimental Methods as serving no purpose in
scientific investigation; forgetting that if those methods had not
supplied the first generalizations, there would have been no
materials for his own conception of Induction to work upon.

His challenge, however, to point out which of the four methods are
exemplified in certain important cases of scientific inquiry, is
easily answered. “The planetary paths,” as far as they are a case of
induction at all, (see, on this point, the second chapter of the
present Book) fall under the Method of Agreement. The law of
“falling bodies,” namely that they describe spaces proportional to
the squares of the times, was historically a deduction from the
first law of motion; but the experiments by which it was verified,
and by which it might have been discovered, were examples of the
Method of Agreement; and the apparent variation from the true law,
caused by the resistance of the air, was cleared up by experiments
_in vacuo_, constituting an application of the Method of Difference.
The law of “refracted rays,” (the constancy of the ratio between the
sines of incidence and of refraction for each refracting substance)
was ascertained by direct measurement, and therefore by the Method
of Agreement. The “cosmical motions” were determined by highly
complex processes of thought, in which Deduction was predominant,
but the Methods of Agreement and of Concomitant Variations had a
large part in establishing the empirical laws. Every case without
exception of “chemical analysis” constitutes a well marked example
of the Method of Difference. To any one acquainted with the
subjects—to Dr. Whewell himself, there would not be the smallest
difficulty in setting out “the A B C and _a b c_ elements” of these
cases.

If discoveries are ever made by observation and experiment without
Deduction, the four methods are methods of discovery: but even if
they were not methods of discovery, it would not be the less true
that they are the sole methods of Proof; and in that character, even
the results of Deduction are amenable to them. The great
generalizations which begin as Hypotheses must end by being proved,
and are in reality (as will be shown hereafter) proved by the Four
Methods. Now it is with Proof, as such, that Logic is principally
concerned. This distinction has indeed no chance of finding favour
with Dr. Whewell; for it is the peculiarity of his system not to
recognise, in cases of Induction, any necessity for proof. If, after
assuming an hypothesis and carefully collating it with facts,
nothing is brought to light inconsistent with it, that is, if
experience does not _dis_prove it, he is content: at least until a
simpler hypothesis, equally consistent with experience, presents
itself. If this be Induction, doubtless there is no necessity for
the four methods. But to suppose that it is so, appears to me a
radical misconception of the nature of the evidence of physical
truths.

_ 86 Ante_, p. 378.

87 It seems hardly necessary to say that the word _impinges_, as a
general term to express collision of forces, was here used by a
figure of speech, and not as expressive of any theory respecting the
nature of force.

_ 88 Essays on some Unsettled Questions of Political Economy_, Essay V.

89 There is no danger of confounding this acceptation of the term with
the peculiar employment of the phrase “tangential force” in the
theory of the planetary perturbations.

90 Suprà, p. 420.

91 As corroborating the opinion that the protoxide of iron in the
venous blood is only partially carbonated, the fact has been
suggested, that the system shows great readiness to absorb an extra
quantity of carbonic acid, as furnished in effervescing drinks. In
such cases the acid must combine with something, and that something
is not improbably the free protoxide. It would be worth ascertaining
whether the protoxide itself or its carbonate has the greatest
facility in absorbing oxygen and turning itself into hydrated
peroxide in the lungs. If the carbonate, then the beneficial effect,
on the animal economy, of drinks which give an artificial supply of
carbonic acid to the system, would be, to that extent, deductively
established.

92 It was an old generalization in surgery, that tight bandaging had a
tendency to prevent or dissipate local inflammation. This sequence,
being, in the progress of physiological knowledge, resolved into
more general laws, led to the important surgical invention made by
Dr. Arnott, the treatment of local inflammation and tumours by means
of an equable pressure, produced by a bladder partially filled with
air. The pressure, by keeping back the blood from the part, prevents
the inflammation, or the tumour, from being nourished; in the case
of inflammation, it removes the stimulus, which the organ is unfit
to receive: in the case of tumours, by keeping back the nutritive
fluid it causes the absorption of matter to exceed the supply, and
the diseased mass is gradually absorbed and disappears.