WEBVTT 00:00:00.070 --> 00:00:07.440 [Music] 00:00:04.009 --> 00:00:11.010 Scientists often gather data through 00:00:07.440 --> 00:00:14.340 observation experiments, archival studies 00:00:11.010 --> 00:00:17.520 and so on. But they are rarely satisfied 00:00:14.340 --> 00:00:20.070 with data alone. Scientists want to draw 00:00:17.520 --> 00:00:21.960 conclusions from those data. They want to 00:00:20.070 --> 00:00:24.590 use the data to show that certain 00:00:21.960 --> 00:00:27.869 theories are right and others are wrong. 00:00:24.590 --> 00:00:29.699 To understand science, then, it will be 00:00:27.869 --> 00:00:31.830 important to understand when it is 00:00:29.699 --> 00:00:35.340 legitimate and when it is illegitimate. 00:00:31.830 --> 00:00:38.070 To draw a specific conclusion from what 00:00:35.340 --> 00:00:40.040 we already know we need to understand 00:00:38.070 --> 00:00:42.570 the difference between good and bad 00:00:40.040 --> 00:00:45.210 arguments; and that is why, in this 00:00:42.570 --> 00:00:49.469 lecture, we will take a look at logic--the 00:00:45.210 --> 00:00:53.340 study of argumentation. Let us first 00:00:49.469 --> 00:00:56.160 introduce some terminology. An argument 00:00:53.340 --> 00:00:59.399 consists of two parts: the premises and 00:00:56.160 --> 00:01:02.219 the conclusion. The premises are the 00:00:59.399 --> 00:01:06.290 things we presuppose and the conclusion 00:01:02.219 --> 00:01:08.479 is what we conclude from those premises. 00:01:06.290 --> 00:01:12.240 So let's look at an example: 00:01:08.479 --> 00:01:15.990 No medieval King had absolute power over 00:01:12.240 --> 00:01:20.670 his subjects. Louis 7 of France was a 00:01:15.990 --> 00:01:23.070 medieval King. So Louis 7 of France did 00:01:20.670 --> 00:01:26.549 not have absolute power over his 00:01:23.070 --> 00:01:29.579 subjects. Here the first two lines are 00:01:26.549 --> 00:01:33.360 the premises and a final line introduced 00:01:29.579 --> 00:01:35.670 by the word "so" is the conclusion. In this 00:01:33.360 --> 00:01:38.159 argument we assume that medieval kings 00:01:35.670 --> 00:01:40.740 did not have absolute power and that 00:01:38.159 --> 00:01:43.200 Louis 7 was a medieval King. And we 00:01:40.740 --> 00:01:47.329 conclude that he did not have absolute 00:01:43.200 --> 00:01:50.070 power. As a second piece of terminology 00:01:47.329 --> 00:01:53.549 we will make a distinction between valid 00:01:50.070 --> 00:01:55.610 and invalid arguments. A valid argument 00:01:53.549 --> 00:01:58.469 is an argument in which the conclusion 00:01:55.610 --> 00:02:01.680 really follows from the premises. 00:01:58.469 --> 00:02:04.320 Our example about Louis 7 is an example 00:02:01.680 --> 00:02:07.380 of a valid argument. The conclusion 00:02:04.320 --> 00:02:10.410 really follows from the premises. It 00:02:07.380 --> 00:02:12.780 makes sense to draw this conclusion from 00:02:10.410 --> 00:02:15.930 these premises. 00:02:12.780 --> 00:02:19.020 As an example of an invalid argument we 00:02:15.930 --> 00:02:22.140 can take this: No medieval King had 00:02:19.020 --> 00:02:25.080 absolute power over his subjects. Louis 00:02:22.140 --> 00:02:27.630 seven of France was a great horseman. So 00:02:25.080 --> 00:02:31.950 Louis seven of France did not have 00:02:27.630 --> 00:02:34.530 absolute power over his subjects. We just 00:02:31.950 --> 00:02:37.550 can't draw that conclusion from those 00:02:34.530 --> 00:02:41.220 premises. So this argument is not valid. 00:02:37.550 --> 00:02:42.480 It's invalid. Note that whether an 00:02:41.220 --> 00:02:44.100 argument is valid or not 00:02:42.480 --> 00:02:46.700 has nothing to do with whether the 00:02:44.100 --> 00:02:49.709 premises or the conclusions are true. 00:02:46.700 --> 00:02:52.200 Perhaps Louis 7 really was a great 00:02:49.709 --> 00:02:54.420 horseman. Then all the premises and the 00:02:52.200 --> 00:02:58.019 conclusion of that argument are true and 00:02:54.420 --> 00:03:01.170 yet the argument is invalid because the 00:02:58.019 --> 00:03:04.350 conclusion just doesn't follow from the 00:03:01.170 --> 00:03:06.840 premises. On the other hand it's also 00:03:04.350 --> 00:03:10.620 possible to have false premises and a 00:03:06.840 --> 00:03:12.180 valid argument. For instance: No medieval 00:03:10.620 --> 00:03:14.760 King had absolute power over his 00:03:12.180 --> 00:03:17.850 subjects. Victor Gijsbers was a 00:03:14.760 --> 00:03:20.360 medieval king. So Victor Gijsbers did not 00:03:17.850 --> 00:03:24.180 have absolute power over his subjects. 00:03:20.360 --> 00:03:25.590 This argument is perfectly valid even 00:03:24.180 --> 00:03:30.140 though the assumption that I am a 00:03:25.590 --> 00:03:33.000 medieval King is, as far as I know, false. 00:03:30.140 --> 00:03:35.610 We can now introduce our final piece of 00:03:33.000 --> 00:03:38.820 terminology: The distinction between two 00:03:35.610 --> 00:03:42.269 kinds of arguments. Deductive arguments 00:03:38.820 --> 00:03:44.340 and inductive arguments. A deductive 00:03:42.269 --> 00:03:46.310 argument is an argument in which the 00:03:44.340 --> 00:03:49.350 truth of the premises 00:03:46.310 --> 00:03:52.500 absolutely guarantee the truth of the 00:03:49.350 --> 00:03:54.480 conclusion. It's just not possible for 00:03:52.500 --> 00:03:56.870 the premises to be true and the 00:03:54.480 --> 00:03:59.430 conclusion to be false. 00:03:56.870 --> 00:04:01.799 Teturning to our original example, we can 00:03:59.430 --> 00:04:03.150 see that this is a deductive argument. It 00:04:01.799 --> 00:04:04.950 is true 00:04:03.150 --> 00:04:07.530 the medieval Kings did not have absolute 00:04:04.950 --> 00:04:10.620 power; and if it is true that Louis 7 was 00:04:07.530 --> 00:04:13.200 a medieval King, then it must be true 00:04:10.620 --> 00:04:15.600 that he did not have absolute power. 00:04:13.200 --> 00:04:18.030 Or, in other words, if he did have 00:04:15.600 --> 00:04:22.680 absolute power then one of those two 00:04:18.030 --> 00:04:24.510 premises must be wrong. I'll come to the 00:04:22.680 --> 00:04:27.090 definition of inductive arguments in a 00:04:24.510 --> 00:04:28.980 moment, but first I want to point out two 00:04:27.090 --> 00:04:33.120 interesting features of deductive 00:04:28.980 --> 00:04:36.479 arguments: First if you use deductive 00:04:33.120 --> 00:04:40.080 arguments you can't make any new 00:04:36.479 --> 00:04:42.240 mistakes. The only way for the conclusion 00:04:40.080 --> 00:04:45.780 of a deductive argument to be false is 00:04:42.240 --> 00:04:47.970 if one of your assumptions is false, so 00:04:45.780 --> 00:04:50.310 if you already believe something false 00:04:47.970 --> 00:04:52.940 then your conclusion may end up being 00:04:50.310 --> 00:04:56.610 false. But if your assumptions are true 00:04:52.940 --> 00:04:57.570 your conclusions are guaranteed to be 00:04:56.610 --> 00:05:00.930 true as well. 00:04:57.570 --> 00:05:03.570 So deductive arguments never introduce 00:05:00.930 --> 00:05:06.060 falsehoods if they weren't already there. 00:05:03.570 --> 00:05:08.250 And that makes them very strong and good 00:05:06.060 --> 00:05:13.320 arguments to use, because they're not 00:05:08.250 --> 00:05:16.130 very risky. Second logicians found out 00:05:13.320 --> 00:05:18.180 already more than 2,000 years ago--and 00:05:16.130 --> 00:05:20.880 Aristotle played an important role here-- 00:05:18.180 --> 00:05:23.820 that whether a deductive argument is 00:05:20.880 --> 00:05:26.130 valid or not can be determined just by 00:05:23.820 --> 00:05:29.460 looking at the form of the argument and 00:05:26.130 --> 00:05:32.610 ignoring its content. Even if you know 00:05:29.460 --> 00:05:35.430 nothing about medieval kings and Louis 7 00:05:32.610 --> 00:05:39.389 you can still see that our example 00:05:35.430 --> 00:05:44.550 argument is valid. How? Because there's 00:05:39.389 --> 00:05:47.940 this form: No A is B. C is A. So C is not B. 00:05:44.550 --> 00:05:51.599 Where A is "medieval King," B is "someone 00:05:47.940 --> 00:05:53.669 with absolute power," and C is "Louis 7" But 00:05:51.599 --> 00:05:55.470 we can put anything we like in the place 00:05:53.669 --> 00:05:58.500 of those letters and the argument will 00:05:55.470 --> 00:06:02.070 remain valid. For instance, let's choose A 00:05:58.500 --> 00:06:05.190 "Is a Dutchman" B "is humble" and C "is Victor 00:06:02.070 --> 00:06:07.260 or Gijsbers" Then we have: No Dutchman 00:06:05.190 --> 00:06:10.050 is humble. Victor Gijsbers is a 00:06:07.260 --> 00:06:12.840 Dutchman. So Victor Gijsbers is not 00:06:10.050 --> 00:06:15.270 humble. Which is another valid argument. 00:06:12.840 --> 00:06:18.720 Although of course the first premise is 00:06:15.270 --> 00:06:20.610 false and so is the conclusion. So we can 00:06:18.720 --> 00:06:22.800 see whether a deductive argument is 00:06:20.610 --> 00:06:24.840 valid simply by looking at its form 00:06:22.800 --> 00:06:27.810 without knowing anything about its 00:06:24.840 --> 00:06:30.000 content. And that is really important 00:06:27.810 --> 00:06:31.910 because that means that we can see 00:06:30.000 --> 00:06:35.370 whether something is a good argument 00:06:31.910 --> 00:06:38.150 without making any prior theoretical 00:06:35.370 --> 00:06:40.860 assumptions about the content matter. If 00:06:38.150 --> 00:06:42.870 we believe that scientists first 00:06:40.860 --> 00:06:44.520 collect data and then come to a 00:06:42.870 --> 00:06:47.310 conclusion about which theories are 00:06:44.520 --> 00:06:50.610 right and wrong, this is exactly what we 00:06:47.310 --> 00:06:53.340 would expect. We only need the data and 00:06:50.610 --> 00:06:56.189 some valid arguments which can be shown 00:06:53.340 --> 00:06:58.770 to be valid independent of any theories 00:06:56.189 --> 00:07:02.610 or ideas, and then we draw our 00:06:58.770 --> 00:07:08.069 conclusions. It would be great if science 00:07:02.610 --> 00:07:09.560 worked like that. Unfortunately, and I bet 00:07:08.069 --> 00:07:13.199 you saw that coming, 00:07:09.560 --> 00:07:14.759 science doesn't work like that. And it 00:07:13.199 --> 00:07:17.340 doesn't work like that because the most 00:07:14.759 --> 00:07:21.960 important arguments in science are not 00:07:17.340 --> 00:07:23.909 deductive. They are inductive. Remember 00:07:21.960 --> 00:07:26.389 that a deductive argument is an argument 00:07:23.909 --> 00:07:29.099 such that the truth of the premises 00:07:26.389 --> 00:07:33.150 absolutely guarantees the truth of the 00:07:29.099 --> 00:07:34.590 conclusion. An inductive argument is an 00:07:33.150 --> 00:07:36.659 argument where the truth of the premises 00:07:34.590 --> 00:07:39.719 gives good reason to believe the 00:07:36.659 --> 00:07:43.560 conclusion but does not absolutely 00:07:39.719 --> 00:07:44.300 guarantee its truth. Again let's look at 00:07:43.560 --> 00:07:46.830 an example: 00:07:44.300 --> 00:07:49.139 None of the medieval texts we have 00:07:46.830 --> 00:07:52.770 studied argues against the existence of 00:07:49.139 --> 00:07:55.610 God, so no scholar in the Middle Ages 00:07:52.770 --> 00:07:58.770 argued against the existence of God. 00:07:55.610 --> 00:08:00.629 That's a valid argument if it's true 00:07:58.770 --> 00:08:03.120 that none of the texts we have makes 00:08:00.629 --> 00:08:05.879 this argument, and we have a lot of texts, 00:08:03.120 --> 00:08:08.210 and it's quite plausible that nobody in 00:08:05.879 --> 00:08:12.389 that time actually made this argument. 00:08:08.210 --> 00:08:14.580 But it's indeed only plausible. It could 00:08:12.389 --> 00:08:18.449 be that the argument was made but 00:08:14.580 --> 00:08:20.969 somehow it wasn't transmitted to us. So 00:08:18.449 --> 00:08:23.089 in an inductive argument. The truth of 00:08:20.969 --> 00:08:26.580 the premises makes the conclusion likely, 00:08:23.089 --> 00:08:29.219 but it doesn't guarantee it. And that's 00:08:26.580 --> 00:08:31.560 generally the case in science. We have 00:08:29.219 --> 00:08:34.140 some limited data. We want to draw a 00:08:31.560 --> 00:08:36.570 general conclusion from those, and our 00:08:34.140 --> 00:08:39.419 data makes the conclusion likely but 00:08:36.570 --> 00:08:41.789 they don't make it certain. So, in science, 00:08:39.419 --> 00:08:44.760 we are continually making inductive 00:08:41.789 --> 00:08:48.240 arguments. And, as we will see in the next 00:08:44.760 --> 00:08:52.459 lecture, induction is a lot more 00:08:48.240 --> 00:08:52.459 problematic than deduction.