Definition:Valid Argument

Definition

A valid argument is a logical argument in which the premises provide conclusive reasons for the conclusion.

When a proof is valid, we may say one of the following:

• The conclusion follows from the premises;
• The premises entail the conclusion;
• The conclusion is true on the strength of the premises;
• The conclusion is drawn from the premises;
• The conclusion is deduced from the premises;
• The conclusion is derived from the premises.

Proof

If all the premises of a valid argument are true, then the conclusion must also therefore be true.

It is not possible for the premises of a valid argument to be true, but for the conclusion to be false.

A proof is another name for a valid argument, but in this context the assumption is made that the premises are all true.

That is, a valid argument that has one or more false premises is not a proof.

Also known as

A valid argument is also known as a truth preserving argument.

Likewise, validity is also known as truth preservation.

Some authors use the term sound argument to mean the same thing that is defined here as a proof.

However, as some use sound argument to mean the same thing as a valid argument, it is recommended that this term not be used.

Linguistic Note

The word valid ultimately derives from the same root as the word value, and thus valid can be taken to mean having value.

Warning

In natural language, it is commonplace to discuss the nature of statements as being valid or invalid, when what is really meant is that a statement is either true or false.