WEBVTT

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The next question has probably been
bothering you ever since very early on in

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the previous lecture. Namely, if valid
arguments can have false premises, then

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what good are they? Sure, there's this
technical logician's notion of a valid

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argument, but why should we care whether
arguments are valid if valid arguments can

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be really bad? Validity might be necessary
for an argument to be good or at least for

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a deductive argument to be good because
remember, there are also inductive

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arguments. But even though it's necessary,
it's not enough. You can have a horrible

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argument but still valid. Well, the great
thing about validity is that when you add

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true premises to a valid argument, then
you get something that really is valuable,

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which we're going to call a sound
argument. Because if you know that the

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premises are true and you also know that
it's not possible for the premises to be

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true and the conclusion, false, then, you
know, the conclusion must be true. So, in

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a sound argument, the conclusion has to be
true. And that is what makes it valuable

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cuz if we can get a deductive argument to
be sound, then you really got something.

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What you've got is a true conclusion.
Officially then, a sound argument is one

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where the premises are true and the
argument is valid. And we've got the same

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combinations of truth and falsity as
possibilities that we had in valid

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arguments. You can have both premises and
conclusion are true and then, if it's

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valid, the argument is sound and if it's
not valid, it's not. Or you can have the

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premises are true and the conclusions
false and then, it can't be valid. But if

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it's invalid, it's not sound. We can have
the premises are false and the conclusions

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true. And then if it's valid, it's not
sound and if it's invalid, it's not sound.

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Or we can have both the premises and the
conclusion are false, and then, it's not

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going to be sound whether it's valid or
not. So, the only combination, where it

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sound is when the premises are true and
the argument is valid and, in that case,

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you know that the conclusion is true. What
about lack of soundness? Well, there are

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two ways an argument yjay fail to be
sound, namely, either the argument can be

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invalid or one of its premises can be
false. So, it's a lot easier for an

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argument to be unsound. And we know that a
deductive argument tries to be valid and,

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of course, it wants its premises to be
true so a deductive argument is trying to

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be sound. And when it fails to be sound,
it's not going to be any good. And the

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next question is how can you know? If you
don't know whether the premises are true,

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you're not going to know whether the
arguments sound. Well, not quite, because

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if you, if the argument's valid and you
know it's valid, then you don't know

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whether it's sound unless you know the
premises are true. But if you that the

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argument is invalid, you already know it's
unsound, even if you don't know whether

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the premises are true. So, if you think
about it, that shows why you want to be

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able to test for validity. Because if you
can show the argument's invalid, then

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you're going to be able to, well, I know
it's unsound, regardless of what you think

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about whether the premises are true or
not. So, there's going to be some value to

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validity, namely, if you can show it's
invalid, you're going to show it's unsound

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and that means that the deductive argument
didn't get what it wanted. So, validity is

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going to be necessary for soundness and
soundness is going to be important because

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it guarantees the truth of the conclusion,
and then, validity derives its value from

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the fact that if it's not valid, it's not
sound. Okay. Now, there's a more to say

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about validity. And we'll say a lot more
about validity when we get to a formal

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logic in the second part of this course.
But for now, we're just going to stick

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with this pretty intuitive notion of
validity and see how we can use this

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notion of validity to reconstruct
arguments.