(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.

NameStatedSymbolizedIllustrated
Absolute identityWhatever is, isA is AWork 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.