Definition:Contradiction

Definition
A contradiction is a statement which is always false, independently of any relevant circumstances that could theoretically influence its truth value.

This has the form:
 * $p \land \neg p$

or, equivalently:
 * $\neg p \land p$

that is:
 * $p$ is true and, at the same time, $p$ is not true.

An example of a "relevant circumstance" here is the truth value of $p$.

The archetypal contradiction can be symbolised by $\bot$, and referred to as bottom.

Also known as
This is also known as a logical falsehood or logical falsity.

Some sources use the terms inconsistency or unsatisfiable formula.

On, these terms are reserved for the analogous concepts for proof systems and formal semantics respectively.

Also see

 * Definition:Bottom (Logic)


 * Principle of Non-Contradiction


 * Definition:Tautology
 * Definition:Contingent Statement