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[Music]

Scientists often gather data through

observation experiments, archival studies

and so on. But they are rarely satisfied

with data alone. Scientists want to draw

conclusions from those data. They want to

use the data to show that certain

theories are right and others are wrong.

To understand science, then, it will be

important to understand when it is

legitimate and when it is illegitimate.

To draw a specific conclusion from what

we already know we need to understand

the difference between good and bad

arguments; and that is why, in this

lecture, we will take a look at logic--the

study of argumentation. Let us first

introduce some terminology. An argument

consists of two parts: the premises and

the conclusion. The premises are the

things we presuppose and the conclusion

is what we conclude from those premises.

So let's look at an example:

No medieval King had absolute power over

his subjects. Louis 7 of France was a

medieval King. So Louis 7 of France did

not have absolute power over his

subjects. Here the first two lines are

the premises and a final line introduced

by the word "so" is the conclusion. In this

argument we assume that medieval kings

did not have absolute power and that

Louis 7 was a medieval King. And we

conclude that he did not have absolute

power. As a second piece of terminology

we will make a distinction between valid

and invalid arguments. A valid argument

is an argument in which the conclusion

really follows from the premises.

Our example about Louis 7 is an example

of a valid argument. The conclusion

really follows from the premises. It

makes sense to draw this conclusion from

these premises.

As an example of an invalid argument we

can take this: No medieval King had

absolute power over his subjects. Louis

seven of France was a great horseman. So

Louis seven of France did not have

absolute power over his subjects. We just

can't draw that conclusion from those

premises. So this argument is not valid.

It's invalid. Note that whether an

argument is valid or not

has nothing to do with whether the

premises or the conclusions are true.

Perhaps Louis 7 really was a great

horseman. Then all the premises and the

conclusion of that argument are true and

yet the argument is invalid because the

conclusion just doesn't follow from the

premises. On the other hand it's also

possible to have false premises and a

valid argument. For instance: No medieval

King had absolute power over his

subjects. Victor Gijsbers was a

medieval king. So Victor Gijsbers did not

have absolute power over his subjects.

This argument is perfectly valid even

though the assumption that I am a

medieval King is, as far as I know, false.

We can now introduce our final piece of

terminology: The distinction between two

kinds of arguments. Deductive arguments

and inductive arguments. A deductive

argument is an argument in which the

truth of the premises

absolutely guarantee the truth of the

conclusion. It's just not possible for

the premises to be true and the

conclusion to be false.

Teturning to our original example, we can

see that this is a deductive argument. It

is true

the medieval Kings did not have absolute

power; and if it is true that Louis 7 was

a medieval King, then it must be true

that he did not have absolute power.

Or, in other words, if he did have

absolute power then one of those two

premises must be wrong. I'll come to the

definition of inductive arguments in a

moment, but first I want to point out two

interesting features of deductive

arguments: First if you use deductive

arguments you can't make any new

mistakes. The only way for the conclusion

of a deductive argument to be false is

if one of your assumptions is false, so

if you already believe something false

then your conclusion may end up being

false. But if your assumptions are true

your conclusions are guaranteed to be

true as well.

So deductive arguments never introduce

falsehoods if they weren't already there.

And that makes them very strong and good

arguments to use, because they're not

very risky. Second logicians found out

already more than 2,000 years ago--and

Aristotle played an important role here--

that whether a deductive argument is

valid or not can be determined just by

looking at the form of the argument and

ignoring its content. Even if you know

nothing about medieval kings and Louis 7

you can still see that our example

argument is valid. How? Because there's

this form: No A is B. C is A. So C is not B.

Where A is "medieval King," B is "someone

with absolute power," and C is "Louis 7" But

we can put anything we like in the place

of those letters and the argument will

remain valid. For instance, let's choose A

"Is a Dutchman" B "is humble" and C "is Victor

or Gijsbers" Then we have: No Dutchman

is humble. Victor Gijsbers is a

Dutchman. So Victor Gijsbers is not

humble. Which is another valid argument.

Although of course the first premise is

false and so is the conclusion. So we can

see whether a deductive argument is

valid simply by looking at its form

without knowing anything about its

content. And that is really important

because that means that we can see

whether something is a good argument

without making any prior theoretical

assumptions about the content matter. If

we believe that scientists first

collect data and then come to a

conclusion about which theories are

right and wrong, this is exactly what we

would expect. We only need the data and

some valid arguments which can be shown

to be valid independent of any theories

or ideas, and then we draw our

conclusions. It would be great if science

worked like that. Unfortunately, and I bet

you saw that coming,

science doesn't work like that. And it

doesn't work like that because the most

important arguments in science are not

deductive. They are inductive. Remember

that a deductive argument is an argument

such that the truth of the premises

absolutely guarantees the truth of the

conclusion. An inductive argument is an

argument where the truth of the premises

gives good reason to believe the

conclusion but does not absolutely

guarantee its truth. Again let's look at

an example:

None of the medieval texts we have

studied argues against the existence of

God, so no scholar in the Middle Ages

argued against the existence of God.

That's a valid argument if it's true

that none of the texts we have makes

this argument, and we have a lot of texts,

and it's quite plausible that nobody in

that time actually made this argument.

But it's indeed only plausible. It could

be that the argument was made but

somehow it wasn't transmitted to us. So

in an inductive argument. The truth of

the premises makes the conclusion likely,

but it doesn't guarantee it. And that's

generally the case in science. We have

some limited data. We want to draw a

general conclusion from those, and our

data makes the conclusion likely but

they don't make it certain. So, in science,

we are continually making inductive

arguments. And, as we will see in the next

lecture, induction is a lot more

problematic than deduction.