Short note on valid arguments

On one characterization of deductive validity, a valid argument is any argument where it is "Logically impossible" for the set of premises to have only true members while the conclusion of the argument is false.

One consequence of this definition is that any argument with an inconsistent set of premises, or a contradictory premise will guarantee that an argument is valid. For example, consider the following argument:

1. P -> Q (Premise)
2. Q (Premise)
3. R & ~R (Premise)
4. P (Conclusion)

Ordinarily, this argument would appear to be affirming the consequent and is consequently invalid. However, since premise 3 is a contradiction it follows that it is not the case that every member of the set of premises can be true, so trivially the argument is valid.