Chapter 1.1: Introduction to logic

[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 know 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 high Spurs was a medieval king so Victor fiber's 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 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 fall suits 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 Dutchman B is humble and C is fixed or high Spurs then we have no Dutchman is humble Victor high stress is a Dutchman so Victor highest verse 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

Channel: Leiden University - Faculty of Humanities

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Keywords: Universiteit Leiden, Leiden University (College/University), Humanities (field of study), Geesteswetenschappen, Bachelor, Education, Arts, gijsbers, victor, logic, science, entertaining, philosophy, knowledge, introduction to science

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Length: 8min 56sec (536 seconds)

Published: Thu Sep 14 2017