0:00:00.070,0:00:03.910 [Music] 0:00:03.910,0:00:07.446 Scientists often gather data through 0:00:07.446,0:00:10.956 observation experiments, archival studies 0:00:10.956,0:00:14.306 and so on. But they are rarely satisfied 0:00:14.306,0:00:17.526 with data alone. Scientists want to draw 0:00:17.526,0:00:20.056 conclusions from those data. They want to 0:00:20.056,0:00:21.966 use the data to show that certain 0:00:21.966,0:00:24.586 theories are right and others are wrong. 0:00:25.296,0:00:27.856 To understand science, then, it will be 0:00:27.856,0:00:29.676 important to understand when it is 0:00:29.676,0:00:31.846 legitimate and when it is illegitimate 0:00:31.846,0:00:35.316 to draw a specific conclusion from what 0:00:35.316,0:00:37.386 we already know. We need to understand 0:00:37.386,0:00:42.660 arguments; and that is why, in this 0:00:37.386,0:00:40.026 the difference between good and bad 0:00:43.340,0:00:45.356 lecture, we will take a look at logic--the 0:00:45.356,0:00:49.446 study of argumentation. Let us first 0:00:49.446,0:00:53.296 introduce some terminology. An argument 0:00:53.296,0:00:56.146 consists of two parts: the premises and 0:00:56.146,0:00:59.386 the conclusion. The premises are the 0:00:59.386,0:01:02.176 things we presuppose and the conclusion 0:01:02.176,0:01:06.281 is what we conclude from those premises. 0:01:06.281,0:01:08.451 So let's look at an example: 0:01:08.451,0:01:12.221 No medieval King had absolute power over 0:01:12.221,0:01:15.991 his subjects. Louis 7 of France was a 0:01:15.991,0:01:20.661 medieval King. So Louis 7 of France did 0:01:20.661,0:01:23.071 not have absolute power over his 0:01:23.071,0:01:26.521 subjects. Here the first two lines are 0:01:26.521,0:01:29.551 the premises and a final line introduced 0:01:29.551,0:01:33.421 by the word "so" is the conclusion. In this 0:01:33.421,0:01:35.661 argument we assume that medieval kings 0:01:35.661,0:01:38.121 did not have absolute power and that 0:01:38.121,0:01:40.721 Louis 7 was a medieval King. And we 0:01:40.721,0:01:43.181 conclude that he did not have absolute 0:01:43.181,0:01:47.311 power. As a second piece of terminology 0:01:47.311,0:01:50.041 we will make a distinction between valid 0:01:50.041,0:01:53.511 and invalid arguments. A valid argument 0:01:53.511,0:01:55.610 is an argument in which the conclusion 0:01:55.610,0:01:58.448 really follows from the premises. 0:01:58.448,0:02:01.618 Our example about Louis 7 is an example 0:02:01.618,0:02:04.308 of a valid argument. The conclusion 0:02:04.308,0:02:07.338 really follows from the premises. It 0:02:07.338,0:02:10.377 makes sense to draw this conclusion from 0:02:10.377,0:02:12.718 these premises. 0:02:12.718,0:02:15.888 As an example of an invalid argument we 0:02:15.888,0:02:18.978 can take this: No medieval King had 0:02:18.978,0:02:22.387 absolute power over his subjects. Louis 0:02:22.387,0:02:25.080 seven of France was a great horseman. So 0:02:25.080,0:02:27.868 Louis seven of France did not have 0:02:27.868,0:02:31.898 absolute power over his subjects. We just 0:02:31.898,0:02:34.468 can't draw that conclusion from those 0:02:34.468,0:02:37.528 premises. So this argument is not valid. 0:02:37.528,0:02:41.198 It's invalid. Note that whether an 0:02:41.198,0:02:42.468 argument is valid or not 0:02:42.468,0:02:44.048 has nothing to do with whether the 0:02:44.048,0:02:46.678 premises or the conclusions are true. 0:02:46.678,0:02:49.678 Perhaps Louis 7 really was a great 0:02:49.678,0:02:52.168 horseman. Then all the premises and the 0:02:52.168,0:02:54.378 conclusion of that argument are true and 0:02:54.378,0:02:58.028 yet the argument is invalid because the 0:02:58.028,0:03:01.118 conclusion just doesn't follow from the 0:03:01.118,0:03:04.298 premises. On the other hand it's also 0:03:04.298,0:03:06.784 possible to have false premises and a 0:03:06.784,0:03:10.604 valid argument. For instance: No medieval 0:03:10.604,0:03:12.184 King had absolute power over his 0:03:12.184,0:03:14.724 subjects. Victor Gijsbers was a 0:03:14.724,0:03:17.834 medieval king. So Victor Gijsbers did not 0:03:17.834,0:03:20.374 have absolute power over his subjects. 0:03:20.374,0:03:24.154 This argument is perfectly valid even 0:03:24.154,0:03:25.584 though the assumption that I am a 0:03:25.614,0:03:28.434 medieval King is, as far as I know, false. 0:03:28.434,0:03:29.747 We can now introduce our final piece of 0:03:29.747,0:03:35.110 terminology: The distinction between two 0:03:35.610,0:03:38.744 kinds of arguments. Deductive arguments 0:03:38.744,0:03:42.204 and inductive arguments. A deductive 0:03:42.234,0:03:44.344 argument is an argument in which the 0:03:44.344,0:03:46.254 truth of the premises 0:03:46.274,0:03:49.264 absolutely guarantee the truth of the 0:03:49.264,0:03:52.484 conclusion. It's just not possible for 0:03:52.484,0:03:54.454 the premises to be true and the 0:03:54.454,0:03:56.854 conclusion to be false. 0:03:56.854,0:03:59.444 Returning to our original example, we can 0:03:59.444,0:04:01.784 see that this is a deductive argument. It 0:04:01.784,0:04:03.124 is true 0:04:03.124,0:04:04.944 the medieval Kings did not have absolute 0:04:04.944,0:04:07.514 power; and if it is true that Louis 7 was 0:04:07.514,0:04:10.584 a medieval King, then it must be true 0:04:10.584,0:04:13.194 that he did not have absolute power. 0:04:13.194,0:04:15.574 Or, in other words, if he did have 0:04:15.574,0:04:17.994 absolute power then one of those two 0:04:17.994,0:04:22.634 premises must be wrong. I'll come to the 0:04:22.634,0:04:24.474 definition of inductive arguments in a 0:04:24.474,0:04:27.054 moment, but first I want to point out two 0:04:27.054,0:04:28.964 interesting features of deductive 0:04:28.964,0:04:33.084 arguments: First, if you use deductive 0:04:33.084,0:04:36.474 arguments you can't make any new 0:04:36.474,0:04:40.070 mistakes. The only way for the conclusion 0:04:40.070,0:04:42.210 of a deductive argument to be false is 0:04:42.210,0:04:45.710 if one of your assumptions is false, so 0:04:45.710,0:04:47.940 if you already believe something false 0:04:47.940,0:04:50.280 then your conclusion may end up being 0:04:50.280,0:04:52.930 false. But if your assumptions are true 0:04:52.930,0:04:56.580 your conclusions are guaranteed to be 0:04:56.580,0:04:57.540 true as well. 0:04:57.540,0:05:00.870 So deductive arguments never introduce 0:05:00.870,0:05:03.570 falsehoods if they weren't already there. 0:05:03.570,0:05:06.050 And that makes them very strong and good 0:05:06.050,0:05:08.230 arguments to use, because they're not 0:05:08.230,0:05:13.290 very risky. Second, logicians found out 0:05:13.290,0:05:16.120 already more than 2,000 years ago--and 0:05:16.120,0:05:18.150 Aristotle played an important role here-- 0:05:18.150,0:05:20.850 that whether a deductive argument is 0:05:20.850,0:05:23.760 valid or not can be determined just by 0:05:23.760,0:05:26.080 looking at the form of the argument and 0:05:26.080,0:05:29.440 ignoring its content. Even if you know 0:05:29.440,0:05:32.580 nothing about medieval kings and Louis 7 0:05:32.580,0:05:35.410 you can still see that our example 0:05:35.410,0:05:39.310 argument is valid. How? Because there's 0:05:39.310,0:05:44.470 this form: No A is B. C is A. So C is not B. 0:05:44.470,0:05:47.890 Where A is "medieval King," B is "someone 0:05:47.890,0:05:51.490 with absolute power," and C is "Louis 7" But 0:05:51.490,0:05:53.660 we can put anything we like in the place 0:05:53.660,0:05:55.460 of those letters and the argument will 0:05:55.460,0:05:58.490 remain valid. For instance, let's choose A 0:05:58.490,0:06:02.040 "Is a Dutchman" B "is humble" and C "is Victor 0:06:02.040,0:06:05.180 or Gijsbers" Then we have: No Dutchman 0:06:05.180,0:06:07.240 is humble. Victor Gijsbers is a 0:06:07.240,0:06:10.010 Dutchman. So Victor Gijsbers is not 0:06:10.010,0:06:12.800 humble. Which is another valid argument. 0:06:12.800,0:06:15.210 Although of course the first premise is 0:06:15.210,0:06:18.670 false and so is the conclusion. So we can 0:06:18.670,0:06:20.560 see whether a deductive argument is 0:06:20.560,0:06:22.790 valid simply by looking at its form 0:06:22.790,0:06:24.850 without knowing anything about its 0:06:24.850,0:06:27.770 content. And that is really important 0:06:27.770,0:06:30.000 because that means that we can see 0:06:30.000,0:06:31.880 whether something is a good argument 0:06:31.880,0:06:35.340 without making any prior theoretical 0:06:35.340,0:06:38.130 assumptions about the content matter. If 0:06:38.130,0:06:40.860 we believe that scientists first 0:06:40.860,0:06:42.860 collect data and then come to a 0:06:42.860,0:06:44.550 conclusion about which theories are 0:06:44.550,0:06:47.260 right and wrong, this is exactly what we 0:06:47.260,0:06:50.530 would expect. We only need the data and 0:06:50.530,0:06:53.260 some valid arguments which can be shown 0:06:53.260,0:06:56.150 to be valid independent of any theories 0:06:56.150,0:06:58.750 or ideas, and then we draw our 0:06:58.750,0:07:02.580 conclusions. It would be great if science 0:07:02.580,0:07:08.020 worked like that. Unfortunately, and I bet 0:07:08.020,0:07:09.550 you saw that coming, 0:07:09.550,0:07:13.210 science doesn't work like that. And it 0:07:13.210,0:07:14.750 doesn't work like that because the most 0:07:14.750,0:07:17.290 important arguments in science are not 0:07:17.290,0:07:21.930 deductive. They are inductive. Remember 0:07:21.930,0:07:23.860 that a deductive argument is an argument 0:07:23.860,0:07:26.370 such that the truth of the premises 0:07:26.370,0:07:29.050 absolutely guarantees the truth of the 0:07:29.050,0:07:33.120 conclusion. An inductive argument is an 0:07:33.120,0:07:34.660 argument where the truth of the premises 0:07:34.660,0:07:36.626 gives good reason to believe the 0:07:36.626,0:07:39.686 conclusion but does not absolutely 0:07:39.686,0:07:43.556 guarantee its truth. Again let's look at 0:07:43.556,0:07:44.256 an example: 0:07:44.256,0:07:46.816 None of the medieval texts we have 0:07:46.816,0:07:49.126 studied argues against the existence of 0:07:49.126,0:07:52.746 God, so no scholar in the Middle Ages 0:07:52.746,0:07:55.596 argued against the existence of God. 0:07:55.596,0:07:58.746 That's a valid argument if it's true 0:07:58.746,0:08:00.596 that none of the texts we have makes 0:08:00.596,0:08:03.096 this argument, and we have a lot of texts, 0:08:03.096,0:08:05.876 and it's quite plausible that nobody in 0:08:05.876,0:08:08.196 that time actually made this argument. 0:08:08.196,0:08:12.366 But it's indeed only plausible. It could 0:08:12.366,0:08:14.576 be that the argument was made but 0:08:14.576,0:08:18.426 somehow it wasn't transmitted to us. So 0:08:18.426,0:08:20.936 in an inductive argument. The truth of 0:08:20.936,0:08:23.066 the premises makes the conclusion likely, 0:08:23.066,0:08:26.556 but it doesn't guarantee it. And that's 0:08:26.556,0:08:29.196 generally the case in science. We have 0:08:29.196,0:08:31.486 some limited data. We want to draw a 0:08:31.486,0:08:34.076 general conclusion from those, and our 0:08:34.076,0:08:36.416 data makes the conclusion likely but 0:08:36.416,0:08:41.789 they don't make it certain. So, in science, 0:08:36.448,0:08:41.789 we are continually making inductive 0:08:41.789,0:08:44.686 arguments. And, as we will see in the next 0:08:44.686,0:08:48.206 lecture, induction is a lot more 0:08:48.206,0:08:52.459 problematic than deduction.