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.