Lecture 3-2 - Soundness

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.