Definition:Tautology

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

It is epitomised by the statement form:
 * $p \implies p$

that is:
 * if $p$ is true then $p$ is true.

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

The archetypal tautology is symbolised by $\top$, and referred to as Top.

Also known as
Tautologies are also referred to as logical truths.

Also defined as
Some sources define a tautology as a statement form which can be epitomised by:
 * $p \lor \lnot p$

which, while intuitively obvious, it not a universal definition as it does not apply in contexts in which Law of Excluded Middle does not necessarily hold.

Also see

 * Definition:Top (Logic), a symbol often used to represent tautologies in logical languages.
 * Definition:Contradiction
 * Definition:Contingent Statement


 * Definition:Validity