(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 |
9. ILLUSTRATIVE EXERCISES.
(1a) Each of the following propositions is made possible because of the existence of which law of thought?
In answering this question I summarize in my mind the meaning of each law of thought. Viz.:
(1) In complete absolute identity the subject and predicate are the same in form and meaning.
(2) In incomplete absolute identity the subject and predicate are the same in meaning, but not in form.