Part 4 (1/2)

CHAPTER X.

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 princ.i.p.al 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 quant.i.ty, 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 ill.u.s.trate the relations between the four cla.s.ses 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