The next question has probably been bothering you ever since very early on in
the previous lecture. Namely, if valid arguments can have false premises, then
what good are they? Sure, there's this technical logician's notion of a valid
argument, but why should we care whether arguments are valid if valid arguments can
be really bad? Validity might be necessary for an argument to be good or at least for
a deductive argument to be good because remember, there are also inductive
arguments. But even though it's necessary, it's not enough. You can have a horrible
argument but still valid. Well, the great thing about validity is that when you add
true premises to a valid argument, then you get something that really is valuable,
which we're going to call a sound argument. Because if you know that the
premises are true and you also know that it's not possible for the premises to be
true and the conclusion, false, then, you know, the conclusion must be true. So, in
a sound argument, the conclusion has to be true. And that is what makes it valuable
cuz if we can get a deductive argument to be sound, then you really got something.
What you've got is a true conclusion. Officially then, a sound argument is one
where the premises are true and the argument is valid. And we've got the same
combinations of truth and falsity as possibilities that we had in valid
arguments. You can have both premises and conclusion are true and then, if it's
valid, the argument is sound and if it's not valid, it's not. Or you can have the
premises are true and the conclusions false and then, it can't be valid. But if
it's invalid, it's not sound. We can have the premises are false and the conclusions
true. And then if it's valid, it's not sound and if it's invalid, it's not sound.
Or we can have both the premises and the conclusion are false, and then, it's not
going to be sound whether it's valid or not. So, the only combination, where it
sound is when the premises are true and the argument is valid and, in that case,
you know that the conclusion is true. What about lack of soundness? Well, there are
two ways an argument yjay fail to be sound, namely, either the argument can be
invalid or one of its premises can be false. So, it's a lot easier for an
argument to be unsound. And we know that a deductive argument tries to be valid and,
of course, it wants its premises to be true so a deductive argument is trying to
be sound. And when it fails to be sound, it's not going to be any good. And the
next question is how can you know? If you don't know whether the premises are true,
you're not going to know whether the arguments sound. Well, not quite, because
if you, if the argument's valid and you know it's valid, then you don't know
whether it's sound unless you know the premises are true. But if you that the
argument is invalid, you already know it's unsound, even if you don't know whether
the premises are true. So, if you think about it, that shows why you want to be
able to test for validity. Because if you can show the argument's invalid, then
you're going to be able to, well, I know it's unsound, regardless of what you think
about whether the premises are true or not. So, there's going to be some value to
validity, namely, if you can show it's invalid, you're going to show it's unsound
and that means that the deductive argument didn't get what it wanted. So, validity is
going to be necessary for soundness and soundness is going to be important because
it guarantees the truth of the conclusion, and then, validity derives its value from
the fact that if it's not valid, it's not sound. Okay. Now, there's a more to say
about validity. And we'll say a lot more about validity when we get to a formal
logic in the second part of this course. But for now, we're just going to stick
with this pretty intuitive notion of validity and see how we can use this
notion of validity to reconstruct arguments.