Definition

1. Noun:
   • (Logic) A proposition that is true if and only if another proposition is false: In formal logic, a "negation" is a statement that directly contradicts another statement, creating an opposite truth value.
   • The speech act of negating: The action of denying, refusing, or contradicting something through language.
   • A negative statement; a statement that is a refusal or denial of some other statement: An utterance or declaration that expresses contradiction, denial, or opposition to a previous claim or idea.

Usage Examples

• Noun (Logical Proposition):

  • The negation of the statement "It is raining" is "It is not raining."
  • In the truth table, the negation column shows the opposite values.

• Noun (Speech Act):

  • Her sharp negation of the accusation ended the debate.
  • The act of negation is fundamental to critical argument.

• Noun (Negative Statement):

  • His answer was a simple negation: "No, I did not."
  • The document contained a formal negation of the earlier claims.

Advanced Usage

• "Double Negation": In logic and some languages, using two negatives which can result in an affirmative or emphasize the negative.

  • In standard English, "I don't know nothing" is often considered a non-standard double negation meaning "I don't know anything."

• "Negation as Failure": A concept in logic programming where something is assumed false if it cannot be proven true.

  • The system uses negation as failure to conclude an event did not occur.

Variants and Related Words

• Negate (verb): To nullify, deny, or make ineffective.

  • The new evidence may negate the previous theory.

• Negative (adjective): Expressing denial, refusal, or absence; characterized by a lack of positive qualities.

  • She received a negative response to her request.

• Negativity (noun): The expression of criticism or pessimism; the character of being negative.

  • Try to avoid negativity in the workplace.

Synonyms

• Denial: A statement that something is not true or does not exist.
• Contradiction: A combination of statements, ideas, or features that are opposed to one another.
• Refusal: An act of expressing unwillingness to do something.
• Rejection: The dismissing or refusing of a proposal, idea, etc.

Antonyms

• Affirmation: A declaration that something is true; a positive assertion.
• Confirmation: The action of confirming something; establishing the truth or validity.
• Assertion: A confident and forceful statement of fact or belief.

Related Phrases and Concepts

• Logical Negation (Symbol: ¬, ~): The operation in logic that takes a proposition to another proposition "not P".

  • The symbol ¬P represents the logical negation of proposition P.

• Negation of a Quantifier: In predicate logic, the rules for negating statements with "for all" (∀) and "there exists" (∃).

  • The negation of "All cats are black" is "There exists a cat that is not black."

Noun

1. (logic) a proposition that is true if and only if another proposition is false
2. the speech act of negating
3. a negative statement; a statement that is a refusal or denial of some other statement