THE ART OF LOGICAL THINKING/PART 13
CHAPTER XIII.
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."
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