tautología

A tautology is a statement that is true by necessity or by virtue of its logical form. It is a statement that is always true, regardless of the truth values of its component parts. In logic, a tautology is a formula that is true for all possible assignments of truth values to its propositional variables. For example, the statement "It is raining or it is not raining" is a tautology because it is true whether it is raining or not raining.

Tautologies are important in logic because they can be used to demonstrate the validity of arguments. An argument is valid if its conclusion necessarily follows from its premises. If an argument can be shown to be equivalent to a tautology, then it is a valid argument. Tautologies are also used in mathematics and computer science, where they can be used to simplify complex statements or to prove theorems.

In everyday language, the term tautology is often used to describe a statement that is unnecessarily repetitive or redundant. For example, the statement "a bachelor is an unmarried man" is a tautology in this sense, because the definition of a bachelor already includes the concept of being unmarried. While this use of the term is related to the logical definition, it is important to distinguish between the two. The logical definition of a tautology refers to a statement that is true by its logical structure, while the everyday use refers to a statement that repeats information already present.