WEBVTT 00:00:00.070 --> 00:00:03.910 line:1 [Music] 00:00:03.910 --> 00:00:07.446 line:1 Scientists often gather data through 00:00:07.446 --> 00:00:10.956 observation experiments, archival studies 00:00:10.956 --> 00:00:14.306 and so on. But they are rarely satisfied 00:00:14.306 --> 00:00:17.526 with data alone. Scientists want to draw 00:00:17.526 --> 00:00:20.056 conclusions from those data. They want to 00:00:20.056 --> 00:00:21.966 use the data to show that certain 00:00:21.966 --> 00:00:24.586 theories are right and others are wrong. 00:00:25.296 --> 00:00:27.856 To understand science, then, it will be 00:00:27.856 --> 00:00:29.676 important to understand when it is 00:00:29.676 --> 00:00:31.846 legitimate and when it is illegitimate 00:00:31.846 --> 00:00:35.316 to draw a specific conclusion from what 00:00:35.316 --> 00:00:37.386 we already know. We need to understand 00:00:37.386 --> 00:00:42.660 arguments; and that is why, in this 00:00:37.386 --> 00:00:40.026 the difference between good and bad 00:00:43.340 --> 00:00:45.356 lecture, we will take a look at logic--the 00:00:45.356 --> 00:00:49.446 study of argumentation. Let us first 00:00:49.446 --> 00:00:53.296 introduce some terminology. An argument 00:00:53.296 --> 00:00:56.146 consists of two parts: the premises and 00:00:56.146 --> 00:00:59.386 the conclusion. The premises are the 00:00:59.386 --> 00:01:02.176 things we presuppose and the conclusion 00:01:02.176 --> 00:01:06.281 is what we conclude from those premises. 00:01:06.281 --> 00:01:08.451 So let's look at an example: 00:01:08.451 --> 00:01:12.221 No medieval King had absolute power over 00:01:12.221 --> 00:01:15.991 his subjects. Louis 7 of France was a 00:01:15.991 --> 00:01:20.661 medieval King. So Louis 7 of France did 00:01:20.661 --> 00:01:23.071 not have absolute power over his 00:01:23.071 --> 00:01:26.521 subjects. Here the first two lines are 00:01:26.521 --> 00:01:29.551 the premises and a final line introduced 00:01:29.551 --> 00:01:33.421 by the word "so" is the conclusion. In this 00:01:33.421 --> 00:01:35.661 argument we assume that medieval kings 00:01:35.661 --> 00:01:38.121 did not have absolute power and that 00:01:38.121 --> 00:01:40.721 Louis 7 was a medieval King. And we 00:01:40.721 --> 00:01:43.181 conclude that he did not have absolute 00:01:43.181 --> 00:01:47.311 power. As a second piece of terminology 00:01:47.311 --> 00:01:50.041 we will make a distinction between valid 00:01:50.041 --> 00:01:53.511 and invalid arguments. A valid argument 00:01:53.511 --> 00:01:55.610 is an argument in which the conclusion 00:01:55.610 --> 00:01:58.448 really follows from the premises. 00:01:58.448 --> 00:02:01.618 Our example about Louis 7 is an example 00:02:01.618 --> 00:02:04.308 of a valid argument. The conclusion 00:02:04.308 --> 00:02:07.338 really follows from the premises. It 00:02:07.338 --> 00:02:10.377 makes sense to draw this conclusion from 00:02:10.377 --> 00:02:12.718 these premises. 00:02:12.718 --> 00:02:15.888 As an example of an invalid argument we 00:02:15.888 --> 00:02:18.978 can take this: No medieval King had 00:02:18.978 --> 00:02:22.387 absolute power over his subjects. Louis 00:02:22.387 --> 00:02:25.080 seven of France was a great horseman. So 00:02:25.080 --> 00:02:27.868 Louis seven of France did not have 00:02:27.868 --> 00:02:31.898 absolute power over his subjects. We just 00:02:31.898 --> 00:02:34.468 can't draw that conclusion from those 00:02:34.468 --> 00:02:37.528 premises. So this argument is not valid. 00:02:37.528 --> 00:02:41.198 It's invalid. Note that whether an 00:02:41.198 --> 00:02:42.468 argument is valid or not 00:02:42.468 --> 00:02:44.048 has nothing to do with whether the 00:02:44.048 --> 00:02:46.678 premises or the conclusions are true. 00:02:46.678 --> 00:02:49.678 Perhaps Louis 7 really was a great 00:02:49.678 --> 00:02:52.168 horseman. Then all the premises and the 00:02:52.168 --> 00:02:54.378 conclusion of that argument are true and 00:02:54.378 --> 00:02:58.028 yet the argument is invalid because the 00:02:58.028 --> 00:03:01.118 conclusion just doesn't follow from the 00:03:01.118 --> 00:03:04.298 premises. On the other hand it's also 00:03:04.298 --> 00:03:06.784 possible to have false premises and a 00:03:06.784 --> 00:03:10.604 valid argument. For instance: No medieval 00:03:10.604 --> 00:03:12.184 King had absolute power over his 00:03:12.184 --> 00:03:14.724 subjects. Victor Gijsbers was a 00:03:14.724 --> 00:03:17.834 medieval king. So Victor Gijsbers did not 00:03:17.834 --> 00:03:20.374 have absolute power over his subjects. 00:03:20.374 --> 00:03:24.154 This argument is perfectly valid even 00:03:24.154 --> 00:03:25.614 though the assumption that I am a 00:03:25.614 --> 00:03:28.434 medieval King is, as far as I know, false. 00:03:28.434 --> 00:03:29.747 We can now introduce our final piece of 00:03:29.747 --> 00:03:35.110 terminology: The distinction between two 00:03:35.610 --> 00:03:38.744 kinds of arguments. Deductive arguments 00:03:38.744 --> 00:03:42.204 and inductive arguments. A deductive 00:03:42.234 --> 00:03:44.344 argument is an argument in which the 00:03:44.344 --> 00:03:46.254 truth of the premises 00:03:46.274 --> 00:03:49.264 absolutely guarantee the truth of the 00:03:49.264 --> 00:03:52.484 conclusion. It's just not possible for 00:03:52.484 --> 00:03:54.454 the premises to be true and the 00:03:54.454 --> 00:03:56.854 conclusion to be false. 00:03:56.854 --> 00:03:59.444 Returning to our original example, we can 00:03:59.444 --> 00:04:01.784 see that this is a deductive argument. It 00:04:01.784 --> 00:04:03.124 is true 00:04:03.124 --> 00:04:04.944 the medieval Kings did not have absolute 00:04:04.944 --> 00:04:07.514 power; and if it is true that Louis 7 was 00:04:07.514 --> 00:04:10.584 a medieval King, then it must be true 00:04:10.584 --> 00:04:13.194 that he did not have absolute power. 00:04:13.194 --> 00:04:15.574 Or, in other words, if he did have 00:04:15.574 --> 00:04:17.994 absolute power then one of those two 00:04:17.994 --> 00:04:22.634 premises must be wrong. I'll come to the 00:04:22.634 --> 00:04:24.474 definition of inductive arguments in a 00:04:24.474 --> 00:04:27.054 moment, but first I want to point out two 00:04:27.054 --> 00:04:28.964 interesting features of deductive 00:04:28.964 --> 00:04:33.084 arguments: First, if you use deductive 00:04:33.084 --> 00:04:36.474 arguments you can't make any new 00:04:36.474 --> 00:04:40.070 mistakes. The only way for the conclusion 00:04:40.070 --> 00:04:42.210 of a deductive argument to be false is 00:04:42.210 --> 00:04:45.710 if one of your assumptions is false, so 00:04:45.710 --> 00:04:47.940 if you already believe something false 00:04:47.940 --> 00:04:50.280 then your conclusion may end up being 00:04:50.280 --> 00:04:52.930 false. But if your assumptions are true 00:04:52.930 --> 00:04:56.580 your conclusions are guaranteed to be 00:04:56.580 --> 00:04:57.540 true as well. 00:04:57.540 --> 00:05:00.870 So deductive arguments never introduce 00:05:00.870 --> 00:05:03.570 falsehoods if they weren't already there. 00:05:03.570 --> 00:05:06.050 And that makes them very strong and good 00:05:06.050 --> 00:05:08.230 arguments to use, because they're not 00:05:08.230 --> 00:05:13.290 very risky. Second, logicians found out 00:05:13.290 --> 00:05:16.120 already more than 2,000 years ago--and 00:05:16.120 --> 00:05:18.150 Aristotle played an important role here-- 00:05:18.150 --> 00:05:20.850 that whether a deductive argument is 00:05:20.850 --> 00:05:23.760 valid or not can be determined just by 00:05:23.760 --> 00:05:26.080 looking at the form of the argument and 00:05:26.080 --> 00:05:29.440 ignoring its content. Even if you know 00:05:29.440 --> 00:05:32.580 nothing about medieval kings and Louis 7 00:05:32.580 --> 00:05:35.410 you can still see that our example 00:05:35.410 --> 00:05:39.310 argument is valid. How? Because there's 00:05:39.310 --> 00:05:44.470 this form: No A is B. C is A. So C is not B. 00:05:44.470 --> 00:05:47.890 Where A is "medieval King," B is "someone 00:05:47.890 --> 00:05:51.490 with absolute power," and C is "Louis 7" But 00:05:51.490 --> 00:05:53.660 we can put anything we like in the place 00:05:53.660 --> 00:05:55.460 of those letters and the argument will 00:05:55.460 --> 00:05:58.490 remain valid. For instance, let's choose A 00:05:58.490 --> 00:06:02.040 "Is a Dutchman" B "is humble" and C "is Victor 00:06:02.040 --> 00:06:05.180 or Gijsbers" Then we have: No Dutchman 00:06:05.180 --> 00:06:07.240 is humble. Victor Gijsbers is a 00:06:07.240 --> 00:06:10.010 Dutchman. So Victor Gijsbers is not 00:06:10.010 --> 00:06:12.800 humble. Which is another valid argument. 00:06:12.800 --> 00:06:15.210 Although of course the first premise is 00:06:15.210 --> 00:06:18.670 false and so is the conclusion. So we can 00:06:18.670 --> 00:06:20.560 see whether a deductive argument is 00:06:20.560 --> 00:06:22.790 valid simply by looking at its form 00:06:22.790 --> 00:06:24.850 without knowing anything about its 00:06:24.850 --> 00:06:27.770 content. And that is really important 00:06:27.770 --> 00:06:30.000 because that means that we can see 00:06:30.000 --> 00:06:31.880 whether something is a good argument 00:06:31.880 --> 00:06:35.340 without making any prior theoretical 00:06:35.340 --> 00:06:38.130 assumptions about the content matter. If 00:06:38.130 --> 00:06:40.860 we believe that scientists first 00:06:40.860 --> 00:06:42.860 collect data and then come to a 00:06:42.860 --> 00:06:44.550 conclusion about which theories are 00:06:44.550 --> 00:06:47.260 right and wrong, this is exactly what we 00:06:47.260 --> 00:06:50.530 would expect. We only need the data and 00:06:50.530 --> 00:06:53.260 some valid arguments which can be shown 00:06:53.260 --> 00:06:56.150 to be valid independent of any theories 00:06:56.150 --> 00:06:58.750 or ideas, and then we draw our 00:06:58.750 --> 00:07:02.580 conclusions. It would be great if science 00:07:02.580 --> 00:07:08.020 worked like that. Unfortunately, and I bet 00:07:08.020 --> 00:07:09.550 you saw that coming, 00:07:09.550 --> 00:07:13.210 science doesn't work like that. And it 00:07:13.210 --> 00:07:14.750 doesn't work like that because the most 00:07:14.750 --> 00:07:17.290 important arguments in science are not 00:07:17.290 --> 00:07:21.930 deductive. They are inductive. Remember 00:07:21.930 --> 00:07:23.860 that a deductive argument is an argument 00:07:23.860 --> 00:07:26.370 such that the truth of the premises 00:07:26.370 --> 00:07:29.050 absolutely guarantees the truth of the 00:07:29.050 --> 00:07:33.120 conclusion. An inductive argument is an 00:07:33.120 --> 00:07:34.660 argument where the truth of the premises 00:07:34.660 --> 00:07:36.626 gives good reason to believe the 00:07:36.626 --> 00:07:39.686 conclusion but does not absolutely 00:07:39.686 --> 00:07:43.556 guarantee its truth. Again let's look at 00:07:43.556 --> 00:07:44.256 an example: 00:07:44.256 --> 00:07:46.816 None of the medieval texts we have 00:07:46.816 --> 00:07:49.126 studied argues against the existence of 00:07:49.126 --> 00:07:52.746 God, so no scholar in the Middle Ages 00:07:52.746 --> 00:07:55.596 argued against the existence of God. 00:07:55.596 --> 00:07:58.746 That's a valid argument if it's true 00:07:58.746 --> 00:08:00.596 that none of the texts we have makes 00:08:00.596 --> 00:08:03.096 this argument, and we have a lot of texts, 00:08:03.096 --> 00:08:05.876 and it's quite plausible that nobody in 00:08:05.876 --> 00:08:08.196 that time actually made this argument. 00:08:08.196 --> 00:08:12.366 But it's indeed only plausible. It could 00:08:12.366 --> 00:08:14.576 be that the argument was made but 00:08:14.576 --> 00:08:18.426 somehow it wasn't transmitted to us. So 00:08:18.426 --> 00:08:20.936 in an inductive argument. The truth of 00:08:20.936 --> 00:08:23.066 the premises makes the conclusion likely, 00:08:23.066 --> 00:08:26.556 but it doesn't guarantee it. And that's 00:08:26.556 --> 00:08:29.196 generally the case in science. We have 00:08:29.196 --> 00:08:31.486 some limited data. We want to draw a 00:08:31.486 --> 00:08:34.076 general conclusion from those, and our 00:08:34.076 --> 00:08:36.416 data makes the conclusion likely but 00:08:36.416 --> 00:08:41.789 they don't make it certain. So, in science, 00:08:36.448 --> 00:08:41.789 we are continually making inductive 00:08:41.789 --> 00:08:44.686 arguments. And, as we will see in the next 00:08:44.686 --> 00:08:48.206 lecture, induction is a lot more 00:08:48.206 --> 00:08:52.459 problematic than deduction.