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.
┌───────────┬───────────────────┬────────────────┬────────────────────┐ │ Name │ Stated │ Symbolized │ Illustrated │ ├───────────┼───────────────────┼────────────────┼────────────────────┤ │ Absolute │ Whatever is, is │ A is A │ Work is work │ │ identity │ │ │ │ ├───────────┼───────────────────┼────────────────┼────────────────────┤ │ Relative │ The whole is │ All A is B │ Work is a blessing │ │ identity │ identical with │ Some A is B │ Some play is a │ │ │ a part or a part │ │ blessing │ │ │ is identical │ │ │ │ │ with a part │ │ │ ├───────────┼───────────────────┼────────────────┼────────────────────┤ │ Contra- │ Nothing can both │ A is not not-A │ Work is not │ │ diction │ be and not be at │ or │ not-work │ │ │ the same time │ A is not B │ John is not honest │ │ │ │ or │ Albert is not │ │ │ │ A is not not-B │ not-honest │ ├───────────┼───────────────────┼────────────────┼────────────────────┤ │ Excluded │ Everything must │ A is either A │ Fair play is │ │ middle │ either be or not │ or not-A │ either fair play │ │ │ be │ or │ or not-fair play │ │ │ │ A is either B │ This man is either │ │ │ │ or not-B │ educated or │ │ │ │ │ not-educated │ └───────────┴───────────────────┴────────────────┴────────────────────┘
(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.