Logic vs Evidence

[genkaus]

Of course it can. If the premises are false then the conclusion is false, but can be bother logically sound. It is important to remember that in logic, 'sound' only means that the conclusion does not contradict the premises - 'sound' isn't the same as 'true'. This is the classic example:

P1. Socrates was a mammal.
P2. All mammals are cats.
C. Socrates was a cat.

Here, the problem is with P2. Thus the conclusion ('Socrates was a cat') is sound, as it follows necessarily from the premises. However, since premise 2 is demonstrable false (not all mammals are cats), the conclusion cannot be true.

Boru

You are confusing soundness and validity

An argument is sound if and only if

The argument is valid.
All of its premises are true.

Here, P2 is false which makes the argument valid but unsound.

Edit: I see Cato beat me to it.