# Tautology

 “”The First Rule of Tautology Club is the first rule of Tautology Club. —Tautology Club

 Part of the series on Key articles General logic Bad logic v - t - e

A tautology is a tautological statement.

## But seriously

A tautology is a statement that, by virtue of logic and nothing more, is true. Because of this, such statements contain no useful information: "The red bicycle is red". Sometimes this can extend beyond simple logic to obvious definitional facts: "The red bicycle has two wheels".

Sometimes tautologies are hard to extricate and identify when they are buried in masses of argumentative prose. In other situations, it may be obscured by experimental design.[1]

One particular kind of tautology is "assuming the antecedent", also known as "circular logic". This is often engaged in by bible thumpers, who will justify their argument with biblical citations and take the Bible's own assertions as proof of its being true. This can be stated as:

## Formal definition

"given A (and whatever puffery is there to hide the fallacy), then (eventually) A".

Reduced to the statement "A implies A", this is actually the simplest form of tautology.

## Legitimate uses

Technically speaking, every mathematical statement is a tautology. Tautologies can be useful for emphasizing important facts, or putting them in more useful forms. And naturally, any assumption that disagrees with a tautology is false.