IMMEDIATE REASONING
In the process of Judgment we must compare two concepts and ascertain
their agreement of disagreement. In the process of Reasoning we follow a
similar method and compare two judgments, the result of such comparison
being the deduction of a third judgment.
The simplest form of reasoning is that known as Immediate Reasoning, by
which is meant the deduction of one proposition from another which
_implies_ it. Some have defined it as: "_reasoning without a middle
term_." In this form of reasoning _only one proposition is required for
the premise_, and from that premise the conclusion is deduced directly
and without the necessity of comparison with any other term of
proposition.
The two principal methods employed in this form of Reasoning are; (1)
Opposition; (2) Conversion.
_Opposition_ exists between propositions having the same subject and
predicate, but differing in quality or quantity, or both. The Laws of
Opposition are as follows:
I. (1) If the universal is true, the particular is true. (2) If the
particular is false, the universal is false. (3) If the universal is
false, nothing follows. (4) If the particular is true, nothing follows.
II. (1) If one of two contraries is true, the other is false. (2) If one
of two contraries is false, nothing can be inferred. (3) Contraries are
never both true, but both may be false.
III. (1) If one of two sub-contraries is false, the other is true. (2)
If one of two sub-contraries is true, nothing can be inferred concerning
the other. (3) Sub-contraries can never be both false, but both may be
true.
IV. (1) If one of two contradictories is true, the other is false. (2)
If one of two contradictories is false, the other is true. (3)
Contradictories can never be both true or both false, but always one is
true and the other is false.
In order to comprehend the above laws, the student should familiarize
himself with the following arrangement, adopted by logicians as a
convenience:
{Universal {Affirmative (A)
{ {Negative (E)
Propositions {
{ {Affirmative (I)
{Particular {Negative (O)
Examples of the above: Universal Affirmative (A): "All men are mortal;"
Universal Negative (E): "No man is mortal;" Particular Affirmative (I):
"Some men are mortal;" Particular Negative (O): "Some men are not
mortal."
The following examples of abstract propositions are often used by
logicians as tending toward a clearer conception than examples such as
given above:
(A) "All A is B."
(I) "Some A is B."
(E) "No A is B."
(O) "Some A is not B."
These four forms of propositions bear certain logical relations to each
other, as follows:
A and E are styled _contraries_. I and O are _sub-contraries_; A and I
and also E and O are called _subalterns_; A and O and also I and E are
styled _contradictories_.
A close study of these relations, and the symbols expressing them, is
necessary for a clear comprehension of the Laws of Opposition stated a
little further back, as well as the principles of Conversion which we
shall mention a little further on. The following chart, called the
Square of Opposition, is also employed by logicians to illustrate the
relations between the four classes of propositions:
A CONTRARIES E
+------------------------+
|\ / |
| \ /S |
| C\ /E |
| O\ /I |
| N\ /R |
| T\ /O |
S| R\ /T |S
U| A\ /C |U
B| \ /I |B
A| \ /D |A
L| \ / |L
T| / \ |T
E| / D\ |E
R| / I\ |R
N| /A C\ |N
S| /R T\ |S
| /T O\ |
| /N R\ |
| /O I\ |
| /C E\ |
| / S\ |
|/ \ |
+------------------------+
I SUB-CONTRARIES O
_Conversion_ is the process of immediate reasoning by which we infer
from a given proposition another proposition having the predicate of
the original for its subject and the subject of the original for its
predicate; or stated in a few words: _Conversion is the transposition of
the subject and predicate of a proposition_. As Brooks states it:
"Propositions or judgments are _converted_ when the subject and
predicate change places in such a manner that the resulting judgment is
an inference from the given judgment." The new proposition, resulting
from the operation or Conversion, is called the Converse; the original
proposition is called the Convertend.
_The Law of Conversion_ is that: "No term must be distributed in the
Converse that is not distributed in the Convertend." This arises from
the obvious fact that nothing should be affirmed in the derived
proposition than there is in the original proposition.
There are three kinds of Conversion; _viz_: (1) Simple Conversion; (2)
Conversion by Limitation; (3) Conversion by Contraposition.
In _Simple Conversion_ there is no change in either quality or quantity.
In _Conversion by Limitation_ the quality is changed from universal to
particular. In Conversion by Negation the quality is changed but not
the quantity. Referring to the classification tables and symbols given
in the preceding pages of this chapter, we may now proceed to consider
the application of these methods of Conversion to each of the four kinds
of propositions; as follows:
_The Universal Affirmative_ (symbol A) proposition is converted by
Limitation, or by a change of quality from universal to particular. The
predicate not being "distributed" in the convertend, we must not
distribute it in the converse by saying "_all_." Thus in this case we
must convert the proposition, "all men are mortal" (A), into "some
mortals are men" (I).
_The Universal Negative_ (symbol E) is converted by Simple Conversion,
in which there is no change in either quality or quantity. For since
both terms of "E" are distributed, they may both be distributed in the
converse without violating the law of conversion. Thus "No man is
mortal" is converted into: "No mortals are men." "E" is converted into
"E."
_The Particular Affirmative_ (symbol I) is also converted by Simple
Conversion in which there is no change in either quality or quantity.
For since neither term is distributed in "I," neither term may be
distributed in the converse, and the latter must remain "I." For
instance; the proposition: "Some men are mortal" is converted into the
proposition, "Some mortals are men."
_The Particular Negative_ (symbol O) is converted by Conversion by
Negation, in which the quality is changed but not the quantity. Thus in
converting the proposition: "Some men are not mortal," we must _not_ say
"some mortals are not men," for in so doing we would distribute _men_ in
the predicate, where it is not distributed in the convertend. Avoiding
this, _we transfer the negative particle from the copula to the
predicate_ so that the convertend becomes "I" which is converted by
Simple Conversion. Thus we transfer "Some men are not mortal" into "Some
men are not-mortal" from which we easily convert (by simple Conversion)
the proposition: "Some not-mortals are men."
It will be well for students, at this point, to consider the three
following Fundamental Laws of Thought as laid down by the authorities,
which are as follows:
_The Law of Identity_, which states that: "The same quality or thing is
always the same quality or thing, no matter how different the conditions
in which it occurs."
_The Law of Contradiction_, which states that: "No thing can at the same
time and place both be and not be."
_The Law of Excluded Middle_, which states that: "Everything must either
be or not be; there is no other alternative or middle course."
Of these laws, Prof. Jevons, a noted authority, says: "Students are
seldom able to see at first their full meaning and importance. All
arguments may be explained when these self-evident laws are granted; and
it is not too much to say that the whole of logic will be plain to those
who will constantly use these laws as the key."