Well welcome back. I've really missed you over the last
couple of weeks when you've have been off with wrong meta learning about
propopsitional logic and then categorical logic.
And, I hope that you enjoyed that. It's very important.
But in the next few weeks, we're going to turn to a different kind of argument.
Because that type of logic is appropriate for deductive arguments.
And what we're going to study instead is inductive arguments.
Now, deductive arguments are given quite often throughout life.
But inductive arguments are probably even more common.
Whenever you want to figure out who committed a crime, we're talking about an
inference of the best explanation. Then there are arguments from analogy,
which happen quite often. Just think of all the analogies that you
run into in life. And then we'll see statistical
generalizations. Well, just think about all the polls and
politics these days and statistical applications.
Whenever you want to know how those generalizations tell you something about
a particular person. And then we'll turn to causal reasoning.
Well, causes are crucial to everything, from science to figuring out what made
your car stop and decision-making and probability.
So we've got a lot of things to cover. And the first thing that we need to do is
to see the difference between inductive and deductive arguments.
Because you've been focused for a couple of weeks with wrong about deductive
arguments. And you need to understand what's the
difference between those arguments and the ones that we're going to study over
the next couple of weeks. In order to see that difference.
I'm going to show you a little video. It's a video I made a few years ago, so
you might notice that I was a little younger back then.
Okay fair enough, but. I think this video will help you see what
the difference is between inductive arguments and deductive arguments.
Rainy days and Mondays always get me down.
The sun will come out tomorrow. Let your bottom dollars out tomorrow.
There'll be sun tomorrow, tomorrow. Wait a minute.
How do you know that?
I heard a weather report. So what?
They get it wrong all the time. Well maybe the sun won't come out
tomorrow but at least it will come up tomorrow.
So you say, but is that really true? How many of you agree that the sun will
come up tomorrow morning? Of course.
Definitely. Absolutely yes.
Everybody knows that. Okay, so you all agree with her.
But, do you really know that it's true? How could you show that the sun will come
up tomorrow? I don't know.
I'm just a kid. Wait I, I didn't mean to get you all
upset. But there really is an issue here.
The question is, how can you prove that the sun will come up tomorrow morning?
Well here's one way that some people use, the conclusion is that the sun will come
up tomorrow. The premise is yesterday the sun came up.
The second premise the day before that the sun came up.
The third premise the day before that the sun came up, then the day before that,
then the day before that, and the day before that, and the day before that, and
the day before that, and the day before that.
Well that can get awfully long so we'll shorten the argument.
The conclusion is still that the sun will come up tomorrow but the premises are
just the sun came up yesterday and the sun came up everyday before that for an
awfully long time. Now, is the argument valid?
Yes or no? Right.
It's not valid. An argument is valid if and only if it's
not possible for the premises to be true and the conclusion false.
But it is possible for these premises to be true and this conclusion to be false.
Can you imagine how that would happen? One way would be if a meteor struck the
Earth in the middle of the night and stopped it from spinning.
Then the sun wouldn't rise tomorrow, . Now you're really freaking me out.
Don't worry, that's extremely unlikely. However, it's possible.
And that shows that the argument is not valid.
The next question is, is this argument any good.
An argument's good if it serves its purpose.
The purpose of this argument, and many other arguments, is to provide reasons
for its conclusion. So, do the premises in this argument
provide reasons for its conclusion? Yes.
Some philosophers deny this. But most people think that these premises
provide good reasons for its conclusion. So let's assume that for now.
What does that show? That shows that some arguments can be
good, even if they're not valid. But don't generalize too quickly.
There are other arguments that are no good, because they're invalid.
Take Bub for example. Is it true, that every sophomore is a
student? Yeah.
Are you a sophomore? No.
So you're not a student, right. Wrong, I, I am a student.
Well then what's wrong with the argument? Every sophomore's a student, you're not a
sophomore, so you're not a student. Well both the premises are true, but, the
conclusion's false so the argument must be invalid.
So you're telling me what makes that argument bad, is that it's invalid?
Yep. Good job.
Now we've got a puzzle. Some arguments are bad because they're
invalid, whereas other arguments are good even though they're invalid.
How can that be? Simple, there are two kinds of arguments,
deductive and inductive. Deductive arguments are bad when their
invalid. Inductive arguments can be good even
though their invalid. Why?
Because deductive arguments are intended to be valid, whereas inductive arguments
are not intended to be valid. The crucial point is that there are
different kinds of standards for evaluating arguments.
Deductive standards ask whether an argument is valid or invalid.
Inductive standards ask whether an argument is strong or weak.
There are several important differences between these standards.
First, deductive validity is all or nothing.
An argument is either valid or not. It can't be partly valid or a little
valid, anymore than a woman can be a little pregnant.
Inductive strength, in contrast, comes in degrees.
An argument is stronger when it gives more and better reasons for its
conclusion. So an arguement can be very weak, when
the reasons it gives for its conclussion are very weak, or can be moderately
strong when it gives moderately strong reasons for its conclussion, or it can be
very strong, when it gives very strong reasons for its conclussion.
Since inductive strength comes in degrees, we can't simply ask, whether an
arguement is strong, we need to ask whether it's strong enough, that depends
on the context and the values at stake. Psyched about your cooking lesson?
Yeah! One of the most important things in
cooking, is to make sure that whatever it is you're cooking is done.
When people cook cakes, the way they normally test it for being done, is they
take a straw or a piece of bamboo and they stick it in the middle of the cake.
If it comes up with raw dough it's not done.
If it comes up clean, like this, that means it's done.
Well, at least in that spot. If you want to make sure that it's done,
throughout the whole cake, then you have to test other spots as well.
Whoa, what are you doing? So much for that.
Now, when you're cooking turkey, you could use the same method.
You could stick in a straw or a piece of bamboo and see whether any pink juice
comes out. If it comes out pink, then it's not done.
But, if it comes out clean, then the turkeys done.
See any pink juice? No.
Then it must be done. Let's try a piece.
There. .
But you wouldn't want to do that with turkey because you can get very sick from
uncooked turkey. That's why most of the time they build a
pop up meat thermometer right into the turkey to make sure that nobody eats
uncooked turkey [SOUND] But this is not a cooking class.
The point here is simply that whether an argument is strong enough depends on
what's at stake. When there's a lot to loose we demand
better reasons and stronger arguments. Context is also important in another way.
Additional information from the context can weaken an inductive argument.
That is, it can change it from strong to weak.
In technical language, the inductive standard of strength is called
defeasible, or non-monotonic. In contrast, the deductive standard of
validity is indefeasible, or monotonic. That means that, no matter what premises
you add to a valid argument, it will still be valid.
Go ahead, try. Here's an example.
If Joe is a sophomore then Joe is a student.
Joe is not a student, so Joe is not a sophomore.
Add any premise you want to that argument, and it will still be valid.
Which shows that the deductive standard of validity is indefeasible.
In contrast, the inductive standard of strength is defeasible.
If you add additional premises or additional information, it can make a
strong argument weak. Consider a courtroom.
I'm sure it was him. He was only ten feet away from me, I saw
him do it. I'm sure it was him, I saw him with my
own eyes. I'd like to cross examine this witness.
Are you positive that it was the defendant sitting right there?
Or, could it have been his identical twin brother?
Who is entering the courtroom right now. It could have been.
I can't tell them apart. Now I would like to recall the first
witness. Let me remind you that you're still under
oath. Can you tell the difference between those
two gentlemen? No.
They look like the same person to me. Now, there's at least a reasonable doubt,
isn't there? What was very strong evidence becomes
much weaker when we add the new evidence about the identical twin.
That is an example of the defeasibility of inductive standards.
Although tricky, it's important to classify arguments as inductive or
deductive. Because it affects whether they're good
or bad. An inductive argument might not be valid
but it can still be good. For example, the sun came up yesterday,
it came up every day for thousands of years therefore, it will come up
tomorrow. That's a good argument even though it's
invalid because it's not intended to be valid.
This is just one instance of a general rule that you shouldn't criticize
something for not being what it's not supposed to be.
This book can be a good book even though, , it's no good as a Frisbee.
Similarly an argument can be a good argument.
Even it it's not valid. It's not intended to be valid.
That is, if it's an inductive argument. This point undermines many common
mistakes, about inductive arguments, many people think that inductive arguments are
somehow inferior to deductive arguments, because they're not valid, but that can't
be right. Because it's easy to take any inductive
argument and turn it into a deductive argument.
For example, most of Joe's friends are seniors, So, Joe must be a senior too.
Well, we can make that argument valid simply by adding a conditional premise.
If most of Joe's friends are seniors, then Joe is a senior too.
But that just shifts all the doubts about the inductive argument into doubts about
the conditional premise. So, it hasn't really made us more sure of
whether Joe is a senior. Our definition of induction also
undermines the second common mistake. Many people believe that induction always
takes us from the particular to the general.
But no matter how many people say that, it's just plain wrong.
Inductive generalization is one kind of inductive argument, but it's not the only
kind. In fact, we're going to study five
different types of inductive arguments. To see the differences between these
arguments, let's do a simple experiment. .
Excuse me we're testing a new type of lemonade here could you help us out?
Sure thank you. First could you try one from that cup?
That's pretty good. Great, glad to hear it.
Now could you try the second cup please? Oh that's terrible!
Your reaction suggests that you don't like that.
Well obviously, you put dish washing liquid in there.
How do you know that? Well it tastes like soap.
Is that why you spit it out. Well, I didn't spit out the first one,
did I? You might be interested to know that you
agreed with over 90% of the people we've tested so far.
They all liked our lemonade better than dishwashing liquid.
That's great. And if you take it back to your dorm, and
try this test on your friends, I bet they'll like our lemonade too.
Well, of course they would. Listen, this is stupid.
I'm out of here. This experiment would be stupid, if it
were intended to show something about lemonade.
But all it's supposed to show is the differences among the different kinds of
inductive arguments. Our next step will be to look at each of
these times of induction in more detail.