# contradictory statement

A contradictory statement is a statement (or form) which is false due to its logical form rather than because of the meaning of the terms employed.

In propositional logic^{}, a contradictory statement, a.k.a. contradiction^{}, is a statement which is false regardless of the truth values of the substatements which form it. According to G. Peano, one may generally denote a contradiction with the symbol $\u22cf$.

For a simple example, the statement $P\wedge \mathrm{\neg}P$ is a contradiction for any statement $P$.

The negation^{} $\mathrm{\neg}Q$ of every contradiction $Q$ is a tautology^{}, and vice versa:

$$\mathrm{\neg}\u22cf=\u22ce,\mathrm{\neg}\u22ce=\u22cf$$ |

To test a given statement or form to see if it is a contradiction, one may construct its truth table^{}. If it turns out that every value of the last column is “F”, then the statement is a contradiction.

Cf. the entry “contradiction (http://planetmath.org/Contradiction)”.

Title | contradictory statement |
---|---|

Canonical name | ContradictoryStatement |

Date of creation | 2013-03-22 16:27:07 |

Last modified on | 2013-03-22 16:27:07 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 9 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 03B05 |

Synonym | contradiction |

Related topic | Tautology |

Related topic | LogicalConnective |

Related topic | Contradiction |