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.