Premise

A premise or premiss^[a] is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion.^[1] Arguments consist of a set of premises and a conclusion.

An argument is meaningful for its conclusion only when all of its premises are true. If one or more premises are false, the argument says nothing about whether the conclusion is true or false. For instance, a false premise on its own does not justify rejecting an argument's conclusion; to assume otherwise is a logical fallacy called denying the antecedent. One way to prove that a proposition is false is to formulate a sound argument with a conclusion that negates that proposition.

An argument is sound and its conclusion logically follows (it is true) if and only if the argument is valid and its premises are true.

An argument is valid if and only if it is the case that whenever the premises are all true, the conclusion must also be true. If there exists a logical interpretation where the premises are all true but the conclusion is false, the argument is invalid.

Key to evaluating the quality of an argument is determining if it is valid and sound. That is, whether its premises are true and whether their truth necessarily results in a true conclusion.

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