Principle of contradiction

Principle \Prin"ci*ple\, n. [F. principe, L. principium
   beginning, foundation, fr. princeps, -cipis. See {Prince}.]
   1. Beginning; commencement. [Obs.]
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            Doubting sad end of principle unsound. --Spenser.
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   2. A source, or origin; that from which anything proceeds;
      fundamental substance or energy; primordial substance;
      ultimate element, or cause.
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            The soul of man is an active principle. --Tillotson.
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   3. An original faculty or endowment.
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            Nature in your principles hath set [benignity].
                                                  --Chaucer.
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            Those active principles whose direct and ultimate
            object is the communication either of enjoyment or
            suffering.                            --Stewart.
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   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.
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            Therefore, leaving the principles of the doctrine of
            Christ, let us go on unto perfection. --Heb. vi. 1.
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            A good principle, not rightly understood, may prove
            as hurtful as a bad.                  --Milton.
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   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.
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            All kinds of dishonesty destroy our pretenses to an
            honest principle of mind.             --Law.
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   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.
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            Cathartine is the bitter, purgative principle of
            senna.                                --Gregory.
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   {Bitter principle}, {Principle of contradiction}, etc. See
      under {Bitter}, {Contradiction}, etc.
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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.
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            His fair demands
            Shall be accomplished without contradiction. --Shak.
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   2. Direct opposition or repugnancy; inconsistency;
      incongruity or contrariety; one who, or that which, is
      inconsistent.
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            can he make deathless death? That were to make
            Strange contradiction.                --Milton.
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            We state our experience and then we come to a manly
            resolution of acting in contradiction to it.
                                                  --Burke.
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            Both parts of a contradiction can not possibly be
            true.                                 --Hobbes.
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            Of contradictions infinite the slave. --Wordsworth.
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   {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."
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