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 VII of France was a medieval king. So, Louis VII of France did not have absolute power over his subjects.
Here the first two lines are the premises, and the 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 VII 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 VII 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 VII of France was a great horseman.
So, Louis VII 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 VII 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 guarantees the truth of the conclusion. It's just not possible for the premises to be true and the conclusion to be false. Returning to our original example, we can see that this is a deductive argument. It is true that medieval kings did not have absolute power. And if it is true that Louis VII 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 2000 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 VII, you can still see that our example argument is valid. How? Because it has 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 VII. 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 Dutchman, B is humble, and C is Victor 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, then 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.