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
This basic axiom of Induction rests upon the conviction that Nature's
laws and manifestations are regular, orderly and _uniform_. If we assume
that Nature does not manifest these qualities, then the axiom must fall,
and all inductive reason must be fallacious. As Brooks well says:
"Induction has been compared to a ladder upon which we ascend from facts
to laws. This ladder cannot stand unless it has something to rest upon;
and this something is our faith in the constancy of Nature's laws." Some
authorities have held that this perception of the uniformity of Nature's
laws is in the nature of an _intuitive_ truth, or an inherent law of our
intelligence. Others hold that it is in itself an _inductive_ truth,
arrived at by experience and observation at a very early age. We are
held to have noticed the uniformity in natural phenomena, and almost
instinctively infer that this uniformity is continuous and universal.
The authorities assume the existence of two kinds of Induction, namely:
(1) Perfect Induction; and (2) Imperfect Induction. Other, but similar,
terms are employed by different authorities to designate these two
classes.
_Perfect Induction_ necessitates a knowledge of _all_ the particulars
forming a class; that is, _all_ the individual objects, persons, things
or facts comprising a class must be known and enumerated in this form of
Induction. For instance, if we _knew positively_ all of Brown's
children, and that their names were John, Peter, Mark, Luke, Charles,
William, Mary and Susan, respectively; and that each and every one of
them were freckled and had red hair; then, in that case, instead of
simply _generalizing_ and stating that: "John, Peter, Mark, Luke,
Charles, William, Mary and Susan, who are _all_ of Brown's children, are
freckled and have red hair," we would save words, and state the
inductive conclusion: "All Brown's children are freckled and have red
hair." It will be noticed that in this case _we include in the process
only what is stated in the premise itself_, and we do not extend our
inductive process beyond the actual data upon which it is based. This
form of Induction is sometimes called "Logical Induction," because the
inference is a logical necessity, without the possibility of error or
exception. By some authorities it is held not to be Induction at all, in
the strict sense, but little more than a simplified form of enumeration.
In actual practice it is seldom available, for it is almost impossible
for us to know all the particulars in inferring a general law or truth.
In view of this difficulty, we fall back upon the more practical form of
induction known as:
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