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[Music]

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Scientists often gather data through

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observation experiments, archival studies

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and so on. But they are rarely satisfied

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with data alone. Scientists want to draw

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conclusions from those data. They want to

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use the data to show that certain

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theories are right and others are wrong.

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To understand science, then, it will be

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important to understand when it is

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legitimate and when it is illegitimate.

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To draw a specific conclusion from what

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we already know we need to understand

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the difference between good and bad

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arguments; and that is why, in this

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

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study of argumentation. Let us first

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introduce some terminology. An argument

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consists of two parts: the premises and

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the conclusion. The premises are the

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things we presuppose and the conclusion

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is what we conclude from those premises.

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So let's look at an example:

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No medieval King had absolute power over

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his subjects. Louis 7 of France was a

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medieval King. So Louis 7 of France did

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not have absolute power over his

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subjects. Here the first two lines are

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the premises and a final line introduced

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

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argument we assume that medieval kings

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did not have absolute power and that

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Louis 7 was a medieval King. And we

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conclude that he did not have absolute

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power. As a second piece of terminology

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we will make a distinction between valid

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and invalid arguments. A valid argument

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is an argument in which the conclusion

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really follows from the premises.

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Our example about Louis 7 is an example

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of a valid argument. The conclusion

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really follows from the premises. It

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makes sense to draw this conclusion from

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these premises.

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As an example of an invalid argument we

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can take this: No medieval King had

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absolute power over his subjects. Louis

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seven of France was a great horseman. So

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Louis seven of France did not have

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absolute power over his subjects. We just

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can't draw that conclusion from those

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premises. So this argument is not valid.

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It's invalid. Note that whether an

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argument is valid or not

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has nothing to do with whether the

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premises or the conclusions are true.

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Perhaps Louis 7 really was a great

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horseman. Then all the premises and the

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conclusion of that argument are true and

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yet the argument is invalid because the

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conclusion just doesn't follow from the

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premises. On the other hand it's also

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possible to have false premises and a

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valid argument. For instance: No medieval

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King had absolute power over his

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subjects. Victor Gijsbers was a

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medieval king. So Victor Gijsbers did not

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have absolute power over his subjects.

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This argument is perfectly valid even

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though the assumption that I am a

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

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We can now introduce our final piece of

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terminology: The distinction between two

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kinds of arguments. Deductive arguments

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and inductive arguments. A deductive

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argument is an argument in which the

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truth of the premises

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absolutely guarantee the truth of the

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conclusion. It's just not possible for

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the premises to be true and the

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conclusion to be false.

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Teturning to our original example, we can

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see that this is a deductive argument. It

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is true

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the medieval Kings did not have absolute

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power; and if it is true that Louis 7 was

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a medieval King, then it must be true

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that he did not have absolute power.

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Or, in other words, if he did have

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absolute power then one of those two

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premises must be wrong. I'll come to the

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definition of inductive arguments in a

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moment, but first I want to point out two

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interesting features of deductive

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arguments: First if you use deductive

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arguments you can't make any new

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mistakes. The only way for the conclusion

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of a deductive argument to be false is

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if one of your assumptions is false, so

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if you already believe something false

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then your conclusion may end up being

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false. But if your assumptions are true

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your conclusions are guaranteed to be

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true as well.

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So deductive arguments never introduce

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falsehoods if they weren't already there.

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And that makes them very strong and good

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arguments to use, because they're not

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very risky. Second logicians found out

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already more than 2,000 years ago--and

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Aristotle played an important role here--

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that whether a deductive argument is

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valid or not can be determined just by

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looking at the form of the argument and

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ignoring its content. Even if you know

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nothing about medieval kings and Louis 7

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you can still see that our example

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argument is valid. How? Because there's

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

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

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

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we can put anything we like in the place

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of those letters and the argument will

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remain valid. For instance, let's choose A

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

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or Gijsbers" Then we have: No Dutchman

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is humble. Victor Gijsbers is a

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Dutchman. So Victor Gijsbers is not

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humble. Which is another valid argument.

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Although of course the first premise is

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false and so is the conclusion. So we can

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see whether a deductive argument is

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valid simply by looking at its form

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without knowing anything about its

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content. And that is really important

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because that means that we can see

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whether something is a good argument

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without making any prior theoretical

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assumptions about the content matter. If

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we believe that scientists first

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collect data and then come to a

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conclusion about which theories are

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right and wrong, this is exactly what we

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would expect. We only need the data and

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some valid arguments which can be shown

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to be valid independent of any theories

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or ideas, and then we draw our

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conclusions. It would be great if science

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worked like that. Unfortunately, and I bet

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you saw that coming,

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science doesn't work like that. And it

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doesn't work like that because the most

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important arguments in science are not

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deductive. They are inductive. Remember

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that a deductive argument is an argument

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such that the truth of the premises

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absolutely guarantees the truth of the

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conclusion. An inductive argument is an

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argument where the truth of the premises

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gives good reason to believe the

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conclusion but does not absolutely

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guarantee its truth. Again let's look at

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an example:

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None of the medieval texts we have

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studied argues against the existence of

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God, so no scholar in the Middle Ages

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argued against the existence of God.

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That's a valid argument if it's true

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that none of the texts we have makes

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this argument, and we have a lot of texts,

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and it's quite plausible that nobody in

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that time actually made this argument.

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But it's indeed only plausible. It could

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be that the argument was made but

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somehow it wasn't transmitted to us. So

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in an inductive argument. The truth of

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the premises makes the conclusion likely,

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

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generally the case in science. We have

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some limited data. We want to draw a

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general conclusion from those, and our

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data makes the conclusion likely but

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

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we are continually making inductive

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arguments. And, as we will see in the next

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lecture, induction is a lot more

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problematic than deduction.