THE ART OF LOGICAL THINKING/PART 14
CHAPTER XIV.
MAKING AND TESTING HYPOTHESES
The
older philosophers and logicians were often at a loss how to reasonably account
for the origin of hypotheses. It will be seen, after giving the matter a little
thought, that the actual formation of the hypothesis is more than a mere
grouping together or synthesis of facts or ideas—there is another mental
process which actually evolves the hypothesis or theory—which gives a
possible reason. What is this mental process? Let us consider the matter.
Brooks well says: "The hypotheses of science originate in what is called
anticipation. They are not the result of a mere synthesis of facts, for no
combination of facts can give the law or cause. We do not see the law; we see
the facts and the mind thinks the law. By the power of
anticipation, the mind often leaps from a few facts to the cause which produces
them or the law which governs them. Many hypotheses were but a happy
intuition of the mind. They were the result of what La Place calls 'a
great guess,' or what Plato so beautifully designates as 'a sacred suspicion of
truth.' The forming of hypotheses requires a suggestive mind, a lively fancy, a
philosophic imagination, that catches a glimpse of the idea through the form,
or sees the law standing behind the fact."
The
student of The New Psychology sees in the mental operation of the forming of
the hypothesis—"the mind thinking the law"—but an instance of the
operation of the activities of the Subconscious Mind, or even the
Superconscious Mind. (See the volume on the Subconscious Mind in this series.)
Not only does this hypothesis give the explanation which the old psychology has
failed to do, but it agrees with the ideas of others on the subject as stated
in the above quotation from Brooks; and moreover agrees with many recorded
instances of the formation of great hypotheses. Sir Wm. Hamilton discovered the
very important mathematical law of quaternions while walking one day in the
Dublin Observatory. He had pondered long on the subject, but without result.
But, finally, on that eventful day he suddenly "felt the galvanic circle
of thought" close, and the result was the realization of the fundamental
mathematical relations of the problem. Berthelot, the founder of Synthetic
Chemistry, has testified that the celebrated experiments which led to his
remarkable discoveries were seldom the result of carefully followed lines of conscious
thought or pure reasoning processes; but, instead, came to him "of their
own accord," so to speak, "as from a clear sky." In these and
many other similar instances, the mental operation was undoubtedly purely
subjective and subconscious. Dr. Hudson has claimed that the "Subjective
Mind" cannot reason inductively, and that its operations are purely and
distinctly deductive, but the testimony of many eminent scientists, inventors
and philosophers is directly to the contrary.
In
this connection the following quotation from Thomson is interesting: "The
system of anatomy which has immortalized the name of Oken is the consequence of
a flash of anticipation which glanced through his mind when he picked up in a
chance walk the skull of a deer, bleached and disintegrated by
the weather, and exclaimed after a glance, 'It is part of a vertebral
column!' When Newton saw the apple fall, the anticipatory question flashed
through his mind, 'Why do not the heavenly bodies fall like this apple?' In
neither case had accident any important share; Newton and Oken were prepared by
the deepest previous study to seize upon the unimportant fact offered to them,
and to show how important it might become; and if the apple and the deer-skull
had been wanting, some other falling body, or some other skull, would have
touched the string so ready to vibrate. But in each case there was a great step
of anticipation; Oken thought he saw a type of the whole skeleton in a single
vertebra, while Newton conceived at once that the whole universe was full of
bodies tending to fall.... The discovery of Goethe, which did for the vegetable
kingdom what Oken did for the animal, that the parts of a plant are to be
regarded as metamorphosed leaves, is an apparent exception to the necessity of
discipline for invention, since it was the discovery of a poet in a region to
which he seemed to have paid no especial or laborious attention. But
Goethe was himself most anxious to rest the basis of this discovery upon his
observation rather than his imagination, and doubtless with good reason.... As
with other great discoveries, hints had been given already, though not pursued,
both of Goethe's and Oken's principles. Goethe left his to be followed up by
others, and but for his great fame, perhaps his name would never have been
connected with it. Oken had amassed all the materials necessary for the
establishment of his theory; he was able at once to discover and conquer the
new territory."
It
must not be supposed, however, that all hypotheses flashing into the field of
consciousness from the Subconsciousness, are necessarily true or correct. On
the contrary many of them are incorrect, or at least only partially correct.
The Subconsciousness is not infallible or omniscient—it merely produces results
according to the material furnished it. But even these faulty hypotheses are
often of value in the later formation of a correct one. As Whewell says:
"To try wrong guesses is with most persons the only way to hit
upon right ones." Kepler is said to have erected at least twenty
hypotheses regarding the shape of the earth's orbit before he finally evolved
the correct one. As Brooks says: "Even incorrect hypotheses may be of use
in scientific research, since they may lead to more correct suppositions."
The supposition of the circular motions of the heavenly bodies around the earth as
a center, which lead to the conception of epicycles, etc., and at last to the
true theory is an illustration of this. So the 'theory of phlogiston' in
chemistry, made many facts intelligible, before the true one of 'oxidation'
superseded it. And so, as Thomson says, "with the theory that 'Nature
abhors a vacuum,' which served to bring together so many cognate facts not
previously considered as related. Even an incorrect conception of this kind has
its place in science, so long as it is applicable to the facts; when facts
occur which it cannot explain, we either correct it or replace it with a new
one. The pathway of science, some one remarks, is strewn with the remains of
discarded hypotheses."
Halleck
says regarding the danger of hasty inference: "Men must constantly
employ imperfect induction in order to advance; but great dangers attend
inductive inferences made from too narrow experience. A child has experience
with one or two dogs at his home. Because of their gentleness, he argues that
all dogs are gentle. He does not, perhaps, find out the contrary until he has
been severely bitten. His induction was too hasty. He had not tested a
sufficiently large number of dogs to form such a conclusion. From one or two
experiences with a large crop in a certain latitude, a farmer may argue that
the crop will generally be profitable, whereas it may not again prove so for
years. A man may have trusted a number of people and found them honest. He
concludes that people as a rule are honest, trusts a certain dishonest man, and
is ruined. The older people grow, the more cautious they generally become in
forming inductive conclusions. Many instances are noted and compared; but even
the wisest sometimes make mistakes. It once was a generally accepted fact that
all swans were white. Nobody had ever seen a dark swan, and the inference that
all swans were white was regarded as certainly true. Black swans were,
however, found in Australia."
Brooks
says regarding the probability of hypotheses: "The probability of a
hypothesis is in proportion to the number of facts and phenomena it will
explain. The larger the number of facts and phenomena that it will
satisfactorily account for, the greater our faith in the correctness of our
supposition.... If there is more than one hypothesis in respect to the facts
under consideration, that one which accounts for the greatest number of facts
is the most probable.... In order to verify a hypothesis it must be shown that
it will account for all the facts and phenomena. If these facts are numerous
and varied, and the subject is so thoroughly investigated that it is quite
certain that no important class of facts has been overlooked, the supposition
is regarded as true, and the hypothesis is said to be verified. Thus the
hypothesis of the 'daily rotation' of the earth on its axis to account for the
succession of day and night is accepted as absolutely true. This is the view
taken by Dr. Whewell and many other thinkers in respect to the verification
of a hypothesis. Some writers, however, as Mill and his school, maintain that
in order to verify a hypothesis, we must show not only that it explains all the
facts and phenomena, but that there is no other possible hypothesis which will
account for them.... The former view of verification is regarded as the correct
one. By the latter view, it is evident that a hypothesis could never be
verified."
Jevons
says: "In the fourth step (verification), we proceed to compare these
deductions with the facts already collected, or when necessary and practicable,
we make new observations and plan new experiments, so as to find out whether
the hypothesis agrees with nature. If we meet with several distinct
disagreements between our deductions and our observations, it will become
likely that the hypothesis is wrong, and we must then invent a new one. In
order to produce agreement it will sometimes be enough to change the hypothesis
in a small degree. When we get hold of a hypothesis which seems to give results
agreeing with a few facts, we must not at once assume that it is certainly
correct. We must go on making other deductions from it under various
circumstances, and, whenever it is possible, we ought to verify these results,
that is, compare them with facts observed through the senses. When a hypothesis
is shown in this way to be true in a great many of its results, especially when
it enables us to predict what we should never otherwise have believed or
discovered, it becomes certain that the hypothesis itself is a true one....
Sometimes it will happen that two or even three quite different hypotheses all
seem to agree with certain facts, so that we are puzzled which to select....
When there are thus two hypotheses, one as good as the other, we need to
discover some fact or thing which will agree with one hypothesis and not with
the other, because this immediately enables us to decide that the former
hypothesis is true and the latter false."
In
the above statements regarding the verification of hypotheses
we see references made to the testing of the latter upon the "facts"
of the case. These facts may be either the observed phenomena
or facts apparent to the perception, or else facts obtained by
deductive reasoning. The latter may be said to be facts which are held to be
true if the hypothesis be true. Thus if we erect the hypothesis that "All
men are mortal," we may reason deductively that it will follow that each
and every thing that is a man must die sooner or later. Then
we test our hypotheses upon each and every man whom we may
subject to observation and experiment. If we find a single man who does not
die, then the test disproves our hypotheses; if on the contrary all men (the
"facts" in the case) prove to be mortal, then is our hypotheses
proven or established. The deductive reasoning in this case is as follows:
"If so-and-so is true regarding such-and-such a class; and if
this particular thing belongs to that class; then it will follow that so-and-so
is true regarding this particular thing." This argument is expressed in
what is called a Hypothetical Proposition (see Chapter IX), the consideration
of which forms a part of the general subject of Deductive Reasoning. Therefore
as Jevons has said, "Deductive Reasoning is the Third Step in Inductive
Reasoning, and precedes Verification", which we have
already considered. Halleck says: "After Induction has classified
certain phenomena and thus given us a major premise, we may proceed deductively to
apply the inference to any new specimen that can be shown to belong to that
class. Induction hands over to deduction a ready-made major premise....
Deduction takes that as a fact, making no inquiry about its truth.... Only
after general laws have been laid down, after objects have been classified,
after major premises have been formed, can deduction be
employed."
In
view of the above facts, we shall now proceed to a consideration of that great
class of Reasoning known under the term—Deductive Reasoning.
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