What is "principle of contradiction"

Principle \Prin"ci*ple\, n. [F. principe, L. principium beginning, foundation, fr. princeps, -cipis. See Prince.]

1. Beginning; commencement. [Obs.]

   Doubting sad end of principle unsound.
   --Spenser.

2. A source, or origin; that from which anything proceeds; fundamental substance or energy; primordial substance; ultimate element, or cause.

   The soul of man is an active principle.
   --Tillotson.

3. An original faculty or endowment.

   Nature in your principles hath set [benignity].
   --Chaucer.

   Those active principles whose direct and ultimate object is the communication either of enjoyment or suffering.
   --Stewart.

4. A fundamental truth; a comprehensive law or doctrine, from which others are derived, or on which others are founded; a general truth; an elementary proposition; a maxim; an axiom; a postulate.

   Therefore, leaving the principles of the doctrine of Christ, let us go on unto perfection.
   --Heb. vi. 1.

   A good principle, not rightly understood, may prove as hurtful as a bad.
   --Milton.

5. A settled rule of action; a governing law of conduct; an opinion or belief which exercises a directing influence on the life and behavior; a rule (usually, a right rule) of conduct consistently directing one's actions; as, a person of no principle.

   All kinds of dishonesty destroy our pretenses to an honest principle of mind.
   --Law.

6. (Chem.) Any original inherent constituent which characterizes a substance, or gives it its essential properties, and which can usually be separated by analysis; -- applied especially to drugs, plant extracts, etc.

   Cathartine is the bitter, purgative principle of senna.
   --Gregory.

   Bitter principle, Principle of contradiction, etc. See under Bitter, Contradiction, etc.

Contradiction \Con`tra*dic"tion\, n. [L. contradictio answer, objection: cf. F. contradiction.]

1. An assertion of the contrary to what has been said or affirmed; denial of the truth of a statement or assertion; contrary declaration; gainsaying.

   His fair demands Shall be accomplished without contradiction.
   --Shak.

2. Direct opposition or repugnancy; inconsistency; incongruity or contrariety; one who, or that which, is inconsistent.

   can he make deathless death? That were to make Strange contradiction.
   --Milton.

   We state our experience and then we come to a manly resolution of acting in contradiction to it.
   --Burke.

   Both parts of a contradiction can not possibly be true.
   --Hobbes.

   Of contradictions infinite the slave.
   --Wordsworth.

   Principle of contradiction (Logic), the axiom or law of thought that a thing cannot be and not be at the same time, or a thing must either be or not be, or the same attribute can not at the same time be affirmed and and denied of the same subject; also called the law of the excluded middle.

   Note: It develops itself in three specific forms which have been called the ``Three Logical Axioms.'' First, ``A is A.'' Second, ``A is not Not-A'' Third, ``Everything is either A or Not-A.''