8. SUMMARY.
(1) The elemental forms of evolved thought are the affirmative and negative judgments. This suggests two fundamental laws of thought, the law of identity and the law of contradiction. The former conditions the affirmative judgment, the latter the negative.
(2) The law of identity implies a permanency of being. “Everything remains identical with itself,” is a statement of identity.
Absolute identity may be divided into complete and incomplete identity.
In complete absolute identity the subject is the same as the predicate in both form and meaning. Truisms illustrate this.
In incomplete absolute identity the subject is identical with the predicate in meaning only. Illustrated by definitions.
In relative identity the whole of the subject may be affirmed of a part of the predicate or a part of the subject may be affirmed of a part of the predicate.
(3) “It is impossible for the same thing to be itself and its contradictory at the same time,” is a statement of the law of contradiction. Identity is constructive while contradiction is destructive in nature. To make the proposition negative the word not must be used with the copula. “Not” attached to the predicate with a hyphen makes the predicate negative, but not the proposition.
To use opposite terms in a contradictory sense leads to serious error.
The safest way of making a positive term a contradictory negative term is to prefix “not” with a hyphen or use “non.”
(4) The law of excluded middle is virtually a combination of identity and contradiction. It may be stated as follows: “A thing must either be itself or its contradictory.”
(5) “Every condition must have a sufficient reason for its existence,” is the law of sufficient reason. Its distinct province is physical science rather than logic.
(6) The laws may be expressed mathematically: excluded middle = identity + contradiction.
SCHEMATIC STATEMENT OF PRIMARY LAWS.
| Name | Stated | Symbolized | Illustrated |
|---|---|---|---|
| Absolute identity | Whatever is, is | A is A | Work is work |
| Relative identity | The whole is identical with a part or a part is identical with a part | All A is B Some A is B | Work is a blessing Some play is a blessing |
| Contradiction | Nothing can both be and not be at the same time | A is not not-A or A is not B or A is not not-B |
Work is not
not-work John is not honest Albert is not not-honest |
| Excluded middle | Everything must either be or not be | A is either A or not-A or A is either B or not-B |
Fair play is either fair play or
not-fair play This man is either educated or not-educated |