An argument is valid if and only if the truth of premises entails the truth of conclusion. 1

Relationship with NTP

Another concept, necessarily truth-preserving (NTP), closely resembles validity, but validity demands more. An argument is valid solely due to its structure. 1 While this distinction is non-exist in formal logic language, it arise in natural languages. Consider the following argument:

The above argument is NTP only because we have the knowledge that water is . Thus, this is not a valid argument.

Validity Test

There are various way to test the validity of an argument such as:

Also, if we can get a counterexample where premises are true but the conclusion is false, we can immediately prove that an argument is invalid.

Relationship with Soundness

Note that validity doesn’t mean truth. If a promise is false, then even a valid argument can’t guarantee conclusion. On the other hand, even when the conclusion is true, we can’t guarantee that the promise is true. If a valid argument is also true, we say that it is sound.

Footnotes

  1. Smith, Nicholas J.J.. Logic : The Laws of Truth, Princeton University Press, 2012. Chapter 1 2