Further, it is dangerous to regard words with the negative prefix as being contradictory of the affirmative form. For example: Valuable and invaluable are not contradictory. There is likewise some doubt as to the contradictory nature of such words as agreeable and disagreeable, though we are sure that agreeable and not-agreeable contradict each other. To use the “not” with a hyphen is safer than to depend upon some prefix which is supposed to mean “_not_.”
ILLUSTRATIONS OF CONTRADICTORY AND OPPOSITE TERMS.
_Opposite._ _Contradictory._ ──────────────── ─────────────────── bad good bad not-bad soft hard soft not-soft cold hot cold not-cold rough smooth rough not-rough good evil good not-good warm cool warm not-warm weak strong weak not-weak
The law of excluded middle may be considered as a combination of identity and contradiction. Identity gives the proposition, “John Doe is honest.” Contradiction, “John Doe is not honest.” Combine the two using _either_ and _or_ and we have the excluded middle proposition, “Either John Doe is honest or he is not honest.”
Excluded middle explains itself. Of the two contradictory notions it must be either the one or the other. There is no “go-between” notion.
The law may be stated in many ways, as will be seen by the following: (1) Everything must either be or not be. (2) Either a given judgment is true or its contradictory is true; there is no middle ground. (3) Of two contradictory judgments one must be true. (4) Every predicate may be affirmed or denied of every subject.
(1) A man is either mortal or he is not mortal. (2) John Doe is either honest or not-honest. (3) Either you are going or you are not going.
A is either A or not-A or A is either B or not-B.
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.=