Can an argument be valid even though one of its premises is false?

Question

Is it possible for an argument to be valid by virtue of its logical form, but contain a false premise? In other words, can a premise be false even though the argument itself is logically valid?

Answer 1

Yes, an argument can be valid even though a premise is false.

Arguments are valid (or invalid) and sound (or unsound). A properly formed argument is said to be valid, which means that it is structured in such a way that if all of its premises are true, and all terms are used clearly and without equivocation, then the conclusion is true.

A sound argument is one that is valid and all of its premises are true and all of its terms are clear and consistent. Such an argument has demonstrated the truth of the conclusion.

Consider the simple categorical argument:

All M are P.

All S are M.

Therefore, all S are P.

This is a structurally-valid argument. Let us substitute some terms for S, M and P.

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

This example is sound. The argument is valid, the premises are true and the terms are being used in a clear, consistent way. But consider the same structure with different terms.

All hamsters are blue.

All prickly things are hamsters.

Therefore, all prickly things are blue.

This argument is valid, but not sound. It is properly structured, but has one or more false premises, and so fails to demonstrate the truth of the conclusion.