THE ART OF LOGICAL THINKING/ PART 2
CHAPTER II.
THE PROCESS OF REASONING
The
processes of Reasoning may be said to comprise four general stages or steps, as
follows:
I. Abstraction,
by which is meant the process of drawing off and setting
aside from an object, person or thing, a quality or attribute,
and making of it a distinct object of thought. For instance, if I perceive in
a lion the quality of strength, and am able to
think of this quality abstractly and independently of the animal—if the
term strength has an actual mental meaning to me, independent
of the lion—then I have abstracted that quality; the thinking
thereof is an act of abstraction; and the thought-idea itself is
an abstract idea. Some writers hold that these abstract ideas are
realities, and "not mere figments of fancy." As Brooks says:
"The rose dies, but my idea of its color and fragrance remains."
Other authorities regard Abstraction as but an act of attention concentrated
upon but the particular quality to the exclusion of others, and that the
abstract idea has no existence apart from the general idea of the object in which
it is included. Sir William Hamilton says: "We can rivet our attention on
some particular mode of a thing, as its smell, its color, its figure, its size,
etc., and abstract it from the others. This may be called Modal Abstraction.
The abstraction we have now been considering is performed on individual
objects, and is consequently particular. There is nothing necessarily connected
with generalization in abstraction; generalization is indeed dependent on
abstraction, which it supposes; but abstraction does not involve
generalization."
II. Generalization,
by which is meant the process of forming Concepts or General Ideas. It acts in
the direction of apprehending the common qualities of objects, persons and
things, and combining and uniting them into a single notion or conception which
will comprehend and include them all. A General Idea or Concept differs from a
particular idea in that it includes within itself the qualities of the
particular and other particulars, and accordingly may be applied to any one of
these particulars as well as to the general class. For
instance, one may have a particular idea of some particular horse,
which applies only to that particular horse. He may also have a General Idea
of horse, in the generic or class sense, which
idea applies not only to the general class of horse but also
to each and every horse which is included in that class. The
expression of Generalization or Conception is called a Concept.
III. Judgment,
by which is meant the process of comparing two objects, persons or things, one
with another, and thus perceiving their agreement or disagreement. Thus we may
compare the two concepts horse and animal, and
perceiving a certain agreement between them we form the judgment that:
"A horse is an animal;" or
comparing horse and cow, and perceiving their
disagreement, we form the judgment: "A horse is not
a cow." The expression of a judgment is called a
Proposition.
IV. Reasoning,
by which is meant the process of comparing two objects, persons or things,
through their relation to a third object, person or thing. Thus we may reason
(a) that all mammals are animals; (b) that a horse is a mammal; (c)
that, therefore, a horse is an animal; the result of the reasoning
being the statement that: "A horse is an animal." The most
fundamental principle of reasoning, therefore, consists in the comparing of two
objects of thought through and by means of their relation to a third
object. The natural form of expression of this process of Reasoning is
called a Syllogism.
It
will be seen that these four processes of reasoning necessitate the employment
of the processes of Analysis and Synthesis, respectively. Analysis means a
separating of an object of thought into its constituent parts, qualities or
relations. Synthesis means the combining of the qualities, parts or relations
of an object of thought into a composite whole. These two processes are found
in all processes of Reasoning. Abstraction is principally analytic;
Generalization or Conception chiefly synthetic; Judgment is either or both
analytic or synthetic; Reasoning is either a synthesis of particulars in
Induction, or an evolution of the particular from the general in Deduction.
There
are two great classes of Reasoning; viz., (1) Inductive Reasoning,
or the inference of general truths from particular truths; and (2) Deductive
Reasoning, or the inference of particular truths from general truths.
Inductive
Reasoning proceeds by discovering a general truth from particular
truths. For instance, from the particular truths that individual men die we
discover the general truth that "All men must die;" or from observing
that in all observed instances ice melts at a certain temperature, we may infer
that "All ice melts at a certain temperature." Inductive Reasoning
proceeds from the known to the unknown. It is essentially a
synthetic process. It seeks to discover general laws from particular facts.
Deductive
Reasoning proceeds by discovering particular truths from general
truths. Thus we reason that as all men die, John Smith, being a man, must die;
or, that as all ice melts at a certain temperature, it follows that the
particular piece of ice under consideration will melt at that certain
temperature. Deductive Reasoning is therefore seen to be essentially an
analytical process.
Mills
says of Inductive Reasoning: "The inductive method of the ancients
consisted in ascribing the character of general truths to all propositions
which are true in all the instances of which we have knowledge. Bacon exposed
the insufficiency of this method, and physical investigation has now far
outgrown the Baconian conception.... Induction, then, is that operation by
which we infer that what we know to be true in a particular case or cases, will
be true in all cases which resemble the former in certain assignable respects.
In other words, induction is the process by which we conclude that what is true
of certain individuals of a class is true of the whole class, or that what is
true at certain times will be true in similar circumstances at all times."
Regarding
Deductive Reasoning, a writer says: "Deductive Reasoning is that process
of reasoning by which we arrive at the necessary consequences, starting
from admitted or established premises." Brooks says: "The general
truths from which we reason to particulars are derived from several distinct
sources. Some are intuitive, as the axioms of mathematics or logic. Some of
them are derived from induction.... Some of them are merely hypothetical,
as in the investigation of the physical sciences. Many of the hypotheses and
theories of the physical sciences are used as general truth for deductive
reasoning; as the theory of gravitation, the theory of light; etc. Reasoning
from the theory of universal gravitation, Leverrier discovered the position of
a new planet in the heavens before it had been discovered by human eyes."
Halleck
points out the interdependence of Inductive and Deductive Reasoning in the
following words: "Man has to find out through his own experience, or that
of others, the major premises from which he argues or draws
his conclusions. By induction we examine what seems to us a sufficient number
of individual cases. We then conclude that the rest of these cases, which we
have not examined, will obey the same general laws.... The premise,
'All cows chew the cud,' was laid down after a certain number of cows had been
examined. If we were to see a cow twenty years hence, we should expect that she
chewed her cud.... After Induction has classified certain phenomena and thus
given us a major premise, we proceed deductively to apply the inference to
any new specimen that can be shown to belong to that class."
The
several steps of Deductive Reasoning shall now be considered in turn as we
proceed.
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