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 because 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.