THEORY AND HYPOTHESES
Following Jevons' classification, we find that the Second Step in
Inductive Reasoning is that called "The Making of Hypotheses."
A _Hypothesis_ is: "A supposition, proposition or principle _assumed or
taken for granted_ in order to draw a conclusion or inference in proof
of the point or question; a proposition assumed or taken for granted,
though not proved, for the purpose of deducing proof of a point in
question." It will be seen that a Hypothesis is merely held to be
_possibly or probably true_, and _not certainly true_; it is in the
nature of a _working assumption_, whose truth must be tested by observed
facts. The assumption may apply either to the _cause_ of things, or to
the _laws_ which govern things. Akin to a hypothesis, and by many people
confused in meaning with the latter, is what is called a Theory.
A _Theory_ is: "A verified hypothesis; a hypothesis which has been
established as, apparently, the true one." An authority says "_Theory_
is a stronger word than _hypothesis_. A _theory_ is founded on
principles which have been established on independent evidence. A
_hypothesis_ merely assumes the operation of a cause which would account
for the phenomena, but has not evidence that such cause was actually at
work. Metaphysically, a theory is nothing but a hypothesis supported by
a large amount of probable evidence." Brooks says: "When a hypothesis is
shown to explain all the facts that are known, these facts being varied
and extensive, it is said to be verified, and becomes a theory. Thus we
have the theory of universal gravitation, the Copernican theory of the
solar system, the undulatory theory of light, etc., all of which were
originally mere hypotheses. This is the manner in which the term is
usually employed in the inductive philosophy; though it must be admitted
that it is not always used in this strict sense. Discarded hypotheses
are often referred to as theories; and that which is actually a theory
is sometimes called a hypothesis."
The steps by which we build up a hypothesis are numerous and varied. In
the first place we may erect a hypothesis by the methods of what we have
described as Perfect Induction, or Logical Induction. In this case we
proceed by simple generalization or simple enumeration. The example of
the freckled, red-haired children of Brown, mentioned in a previous
chapter, explains this method. It requires the examination and knowledge
of every object or fact of which the statement or hypothesis is made.
Hamilton states that it is the only induction which is absolutely
necessitated by the laws of thought. It does not extend further than the
plane of experience. It is akin to mathematical reasoning.
Far more important is the process by which hypotheses are erected by
means of inferences from Imperfect Induction, by which we reason from
the known to the unknown, transcending experience, and making true
inductive inferences from the axiom of Inductive Reasoning. This process
involves the subject of Causes. Jevons says: "The cause of an event is
that antecedent, or set of antecedents, from which the event always
follows. People often make much difficulty about understanding what the
cause of an event means, but it really means nothing beyond _the things
that must exist before in order that the event shall happen afterward_."
Causes are often obscure and difficult to determine. The following five
difficulties are likely to arise: I. The cause may be out of our
experience, and is therefore not to be understood; II. Causes often act
conjointly, so that it is difficult to discover the one predominant
cause by reason of its associated causes; III. Often the presence of a
counteracting, or modifying cause may confuse us; IV. Often a certain
effect may be caused by either of several possible causes; V. That which
appears as a _cause_ of a certain effect may be but a co-effect of an
original cause.
Mill formulated several tests for ascertaining the causal agency in
particular cases, in view of the above-stated difficulties. These tests
are as follows: (1) The Method of Agreement; (2) The Method of
Difference; (3) The Method of Residues; and (4) The Method of
Concomitant Variations. The following definitions of these various tests
are given by Atwater as follows:
_Method of Agreement_: "If, whenever a given object or agency is present
without counteracting forces, a given effect is produced, there is a
strong evidence that the object or agency is the cause of the effect."
_Method of Difference_: "If, when the supposed cause is present the
effect is present, and when the supposed cause is absent the effect is
wanting, there being in neither case any other agents present to effect
the result, we may reasonably infer that the supposed cause is the real
one."
_Method of Residue_: "When in any phenomena we find a result remaining
after the effects of all known causes are estimated, we may attribute it
to a residual agent not yet reckoned."
_Method of Concomitant Variations_: "When a variation in a given
antecedent is accompanied by a variation of a given consequent, they are
in some manner related as cause and effect."
Atwater adds: "Whenever either of these criteria is found free from
conflicting evidence, and especially when several of them concur, the
evidence is clear that the cases observed are fair representatives of
the whole class, and warrant a valid inductive conclusion."
Jevons gives us the following valuable rules:
I. "Whenever we can alter the quantity of the things experimented on, we
can apply _a rule for discovering which are causes and which are
effects_, as follows: We must vary the quantity of one thing, making it
at one time greater and at another time less, and if we observe any
other thing which varies just at the same times, it will in all
probability be an _effect_."
II. "When things vary regularly and frequently, there is _a simple rule,
by following which we can judge whether changes are connected together
as causes and effects_, as follows: Those things which change in exactly
equal times are in all likelihood connected together."
III. "It is very difficult to explain how it is that we can ever reason
from one thing to a class of things by generalization, _when we cannot
be sure that the things resemble each other in the important points_....
Upon what grounds do we argue? We have to get a general law from
particular facts. This can only be done by going through all the steps
of inductive reasoning. Having made certain observations, we must frame
hypotheses as to the circumstances, or laws from which they proceed.
Then we must reason deductively; and after verifying the deductions in
as many cases as possible, we shall know how far we can trust similar
deductions concerning future events.... It is difficult to judge when we
may, and when we may not, safely infer from some things to others in
this simple way, without making a complete theory of the matter. _The
only rule_ that can be given to assist us is that _if things resemble
each other in a few properties only, we must observe many instances
before inferring that these properties will always be joined together in
other cases_."