The Art of Logical Thinking; Or, The Laws of ReasoningAtkinson, William Walker
Philosophy
The Art of Logical Thinking; Or, The Laws of Reasoning
Atkinson, William Walker
Logic; 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:
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