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 logicPlanetmathPlanetmath, a contradictory statement, a.k.a. contradictionMathworldPlanetmath, 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 .

For a simple example, the statement  P¬P  is a contradiction for any statement P.

The negationMathworldPlanetmath ¬Q of every contradiction Q is a tautologyMathworldPlanetmath, and vice versa:


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

Cf. the entry “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