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Buckle up for this one— validity is one of the toughest concepts
in logic. Validity is the technical term for good deductive reasoning. To say a
deductive argument is valid is to say that its reasoning is solid. An invalid
argument, on the other hand, is reasoning gone wrong.
So "valid" and "invalid" are terms we use to evaluate deductive arguments. They tag
the reasoning as success or failure. Only deductive reasoning is in play here. You
would never call an inductive argument valid or invalid. Of course, inductive
reasoning can be good or bad, too...but that's a different video. Here we're
focused like a laser beam on deductive arguments. So roughly, validity is just
good reasoning. We need a much more careful definition than that but we're
not quite ready yet. First we need to talk about truth. Truth is a good thing.
Validity is a good thing. But they are two different things! You can reason
badly with truths and you can reason perfectly with falsehoods. So learn to
keep validity and truth separate in your mind.
Validity applies to arguments. Truth applies to statements and these need to
be evaluated separately. There's no such thing as a false argument or a valid
statement. That's a mixing up of concepts. Here's an example. The Sun rises in the
morning. Therefore Bobcats have short, stubby
tails. Both of these statements are true, but the reasoning is so bad you can
barely call it reasoning. The premise does not support the conclusion. So the
argument is invalid— that's bad! But the statements are true— that's good! So keep
in mind: invalid does not mean false. Here's another example.
No Python will eat a bobcat. So pythons do not eat
cats in the Florida Everglades. The premise offers a rock-solid reason for
believing the conclusion. This is a valid argument—and that's good. But every
single statement here is false—that's bad.
So remember: valid does not mean true. Now we're ready for our definition. A
valid argument is built so that it is impossible for the premises to be true
and the conclusion false. It just can't happen. Because validity is
about structure—or as we say in logic— form. If we assume the premises are true,
the form of a valid argument forces the conclusion to be true. Let's play a shell
game. The ball is hidden under the top or bottom shell. It's not under the top
shell. So...? Now I ask you a question: Is it good reasoning to conclude the
ball is under the bottom shell? Don't overthink it—
don't tie your brain up in knots. This is easy! If it really is true that the ball
is hidden under the top or bottom shell, and if it really is true that it's not
under the top shell... well, then it's got to be here under the bottom shell. Your
brain recognizes the form of this argument. It's a structure that
guarantees the conclusion to be true, as long as the premises are true. It's valid.
Now there might be something bothering you about this. Maybe you've played the
shell game before—with a con artist— and you know that very often the other
shell comes up empty. Doesn't this show the reasoning of the argument to be bad?
No! A thousand times no! This is perfect reasoning, and just a moment ago your
brain recognized that. So where did things go wrong? The con artist was lying
to you. Maybe there never was a ball, or maybe it really was under the top shell,
just hidden, and we already know we got the conclusion wrong. But it's not the
reasoning that failed. It was the statements. That's why you
have to keep validity and truth separate in your mind.
Validity never promised that the conclusion will actually be true. And
here's proof: this is a valid argument with a false conclusion. But validity did
promise that you would never go wrong in the case where the premises are true.
When the premises are not actually true— well,
then you never know about the conclusion! But it's worth saying one more time: even
when the con artist is lying and the premises and conclusion are false, this
is valid reasoning. If the premises were actually true
we'd be entirely right in drawing the conclusion. So a valid argument has a
certain relationship between premises and conclusion, where if you take the
premises to be true, they guarantee the truth of the conclusion. But there's more
to an argument than just reasoning. There are also claims being made, and if any of
those claims are false, then watch out— the argument has a flaw. But it's not a
flaw in reasoning. It's a different kind of shortcoming... and the topic of a
different video.
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