SYMBOLIZATION OF EXCLUDED MIDDLE.
A is either A or not-A
or
A is either B or not-B.
5. THE LAW OF SUFFICIENT REASON.
The law may be stated in this wise. Every phenomenon, event or relation must have a sufficient reason for being what it is. To illustrate: (1) If Venus is the evening star, there must be a sufficient reason. (2) If the ground is wet, there must be a cause. Many logicians argue that this law has no place in logic, its field being that of the physical sciences. The laws of identity, contradiction and excluded middle are, however, universally regarded as the Primary Laws of thought.
6. UNITY OF PRIMARY LAWS OF THOUGHT ILLUSTRATED BY SYMBOLS.
| (1) Absolute Symbols | Relative Symbols. |
| Excluded middle. | |
| A is either A or not-A. | A is either B or not-B. |
| Contradiction. | |
| A is not not-A. | A is not B or A is not not-B. |
| Identity. | |
| A is A. | A is not-B or A is B. |
| (2) Propositions made to fit symbols. | |
| Excluded middle. | |
| A man is either a man or a not-man. | A man is either honest or not-honest. |
| Contradiction. | |
| A man is not a not-man. | A man is not honest, or a man is not not-honest. |
| Identity. | |
| A man is a man. | A man is not-honest, or a man is honest. |
The “excluded middle” propositions of the foregoing express alternatives which are mutually contradictory. There is no middle ground. The “contradictory propositions” contradict the identity of the subject with one alternative, while the “identity” propositions affirm the identity of the subject with the other alternative. This is made possible because of the principle, “Of two mutually contradictory terms, if one is true the other must be false.” The foregoing scheme shows how closely “contradictory” and “identity” propositions are related to “excluded middle” propositions. Expressed mathematically: excluded middle = contradiction + identity.
7. OUTLINE.
PRIMARY LAWS OF THOUGHT.
(1) Two fundamental laws.