Now that we've seen which features distinguish inductive arguments from
deductive arguments, we want to look at the different kinds of inductive
arguments one by one. And the first two we're going to look at are moving up from
a sample to a generalization, and then moving back down from the generalization
to some kind of prediction in a particular case.
Generalizations are all around us. Almost all movies have credits.
Most popular bands have drummers. Many restaurants are closed on Mondays.
three quarters of police officers are very nice people.
Two thirds of books have chapters in them.
Half of the people I know like to play sports.
And my favorite of all, 87.2%.
The statistics are made up on the spot. It should come as no surprise at all that
there's so many generalizations filling our lives.
Because generalizations can be extremely useful, especially when you need to make
a decision. So, for example, if you're feeling a
little nauseous, that is a little sick at your stomach, then you need to know
whether most people who have symptoms of your sort have something serious enough
that they need to go to a doctor. And they also need to know whether
doctors can usually help people who have symptoms of that sort.
All of those generalizations are relevant to whether or not you want to go to the
doctor to see if you can get some help with your sick stomach.
But then the problem is, how can we decide which generalizations to believe?
Since there generalizations, and you pile all instances of certain sort, you can't
check them all out. You have to take a sample of some sort.
I mean, just imagine that your running a bakery.
And, your making jelly doughnuts and you want to know whether the jelly doughnuts
are filled with the right amount of jelly.
You can make hundreds of jelly donuts. You're not going to tear them all apart
and check every one for how much jelly they have in the middle, because then
you'd have no donuts left to sell to your customers.
Or imagine, that you want to buy a car. This time you're the customer.
You want to buy a car and you need to know how often these cars had problems in
the first year. Because if they have problems a lot
during the first year, you don't want to buy that kind of car.
But you don't want every car of that sort to been tested for the first year because
then you can't buy a new car, you're only going to have a used car because they've
all been used in the test. Or, imagine that you want to know what
types of trees grew during a certain period of history.
So, you look at the soil and you dig down, and you start looking for how many
pollen grains there are, and a certain level that indicates a certain age.
Well, you can't check every spot in the field because if you did that, you'd just
be destroying the entire field. So, in these cases and many other cases,
you just have to take samples. You can't test the whole class and then
you have to generalize from the sample to the larger class.
All of these generalizations from samples share a certain form.
First, we look at one instance of the sample.
We say that first F is G. That is the thing fats in the, fits in
the class F, and has the property G. And we check another.
The second F is also G, and the third F is also G.
And all the rest of the Fs in the sample are G.
So, we conclude that all Fs are G. Now notice that all in the conclusion
means everything in the class of Fs. It doesn't only mean the ones in our
sample. So we've started from premises that are
only about the sample, which is only a part of the general class.
And we've reached a conclusion about the whole class when we say that all Fs are
G. Now, other arguments of the same general
type are a little bit different. Because you don't always get complete
uniformity. You don't always get all Fs or G.
Sometimes you get the first F is G, and the second F is G, but the third F is not
G. And the fourth F is G, and the fifth F is
G, but the sixth F is not G. So you get, like, two-thirds of the Fs
are G. And then, you reach the conclusion that
two-thirds of all Fs are G. Again though, you've only looked at the
Fs in the sample. You've only observed a small part of that
total class of all Fs and you draw a conclusion that two-thirds of overall
class, the whole class of Fs has that property, G.
So, that's why you have a general, that's why it's called a generalization.
You start from a smaller sample, and reach a conclusion about a much larger
class. You generalize to the whole class.
The fact that the argument moves from a small part of the class to the whole
class shows that it's inductive. And what does that mean?
Well first, is the argument valid? Think back to one of the examples.
Almost all bands that I know of have drummers. Therefore, almost all bands
have drummers. Well, is it possible that the premises
are true and the conclusion false? Of course it is.
Because maybe I only listen to bands that have drummers, but there are a lot of
bands out there that don't have drummers, and I just didn't happen to listen to
them. That is, they weren't part of my sample,
okay? And is the argument defeasible?
That means, that you can add further information to the premises and it'll
make the argument much less strong. It might even undermine the argument
totally. And of course, it could because you could
give me all kinds of examples of bands that don't have drummers.
And then, I would have to change my conclusion that almost all bands have
drummers. So, this argument is defeasible.
Does that mean that it can't be strong? No.
It could still be strong. It could come in different types of
strength. How would you get a stronger argument or
a weaker argument in this case, while you can have a larger or smaller
sample. If I take a very large sample, the
argument's going to be stronger. If I take a very small sample, the
argument's going to be weaker. So it's not like validity, which is on or
off. It's either valid or not.
Instead, the strength of the argument comes in degrees depending on how big the
sample is. Now, does that mean that since it can't
be valid, it can only be strong to a certain degree that it's no good?
No. Because it's an inductive argument. Inductive arguments don't even try to be
valid, they don't even pretend to be valid.
That's not what they're supposed to be. And sob you can't criticize this argument
by saying it's not valid. It's doing everything that it's supposed
to do if it provides you with a strong reason,
and a strong enough reason for the conclusion.
That's what an inductive argument is supposed to do so if this argument does
it, [SOUND] it's a good argument. Then, even if inductive arguments,
including generalizations from samples, don't have to be valid. Tthey still do
need to be strong. And so, we need to figure out how to tell
when a generalization from a sample is a strong argument, when it provides a
strong reason for the conclusion. And to really answer that question, you
got to turn to statistics an area of mathematics.
And learn how to analyze the data much more carefully than we'll be able to do
here. But even mentioning the name statistics
raises fear in some people. Mark Twain is famous for having said,
there are three kinds of lies. There are lies, there are damn lies, and
there's statistics. He actually gives credit to Israeli for
having said it first. But the point is that statistics, are even worse than damn
lies, you can't trust them at all, or so Mark Twain says.
But on the other hand, some people say, statistics, that's math. It's all about
numbers, you can't question that. Here's one example of somebody who
suggests such a position. There's still one thing that's
irrefutable, and that is the numbers.
Numbers don't lie. You can't parse pull numbers.
They're infallible. Okay, fine.
He knows that statistics aren't infallible.
He's just being sarcastic. But there are many people who put a lot
of faith in the numbers and in statistics.
They seem to think that you always have to trust it when a statistician comes up
with an answer. And we're going to learn that neither of
these views is correct. It's not true that statistics are always
worse than damn lies, and it's also not true that the numbers are irrefutable.
The truth lies somewhere in the middle.