# Validity

<https://en.wikipedia.org/wiki/Validity_(logic>)

In logic, more precisely in deductive reasoning, an argument is **valid** iff it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion.

Valid arguments must be clearly expressed by means of sentences called *well-formed formulas*. The validity of an argument, its being valid, can be tested, proved or disproved, and depends on its logical form.

Satisfiability and validity are related to each other in a manner exactly analogous to the *square of opposition*.

A formula is:

* **satisfiable** if it is possible to find an interpretation that makes the formula true.
* **unsatisfiable** if none of the interpretations make the formula true.
* **valid** if it is true under every interpretation.
* **invalid** if some such interpretation makes the formula false.

A formula is satisfiable if it is true under at least one interpretation, thus a **tautology** is a formula whose **negation is unsatisfiable**. An unsatisfiable formula, both through negation and affirmation, is known formally as **contradiction**. A formula that is neither a tautology nor a contradiction is said to be **logically contingent**.

Deductive arguments are evaluated in terms of their validity and soundness. An argument is *valid* if it is impossible for its premises to be true while its conclusion is false. In other words, the conclusion must be true if the premises are true. An argument can be valid even if one or more of its premises are false. An argument is *sound* if it is valid and the premises are true.

**An argument form (schema) is valid** if every argument of that logical form is valid.

Arguments in which the truth of the premises guarantees the truth of the conclusion are *valid arguments*.

Arguments in which the truth of the premises makes the truth of the conclusion likely, but not certain, are called *inductively strong arguments*.

These two properties, validity and inductive strength, have given rise to deductive and inductive logic, respectively.

Arguments that are valid and have true premises are called **sound arguments**. Not all valid arguments are sound since some of their premises could be false, but **any sound argument is necessarily valid**.
