0:00:00.070,0:00:07.440 [Music] 0:00:04.009,0:00:11.010 Scientists often gather data through 0:00:07.440,0:00:14.340 observation experiments, archival studies 0:00:11.010,0:00:17.520 and so on. But they are rarely satisfied 0:00:14.340,0:00:20.070 with data alone. Scientists want to draw 0:00:17.520,0:00:21.960 conclusions from those data. They want to 0:00:20.070,0:00:24.590 use the data to show that certain 0:00:21.960,0:00:27.869 theories are right and others are wrong. 0:00:24.590,0:00:29.699 To understand science, then, it will be 0:00:27.869,0:00:31.830 important to understand when it is 0:00:29.699,0:00:35.340 legitimate and when it is illegitimate. 0:00:31.830,0:00:38.070 To draw a specific conclusion from what 0:00:35.340,0:00:40.040 we already know we need to understand 0:00:38.070,0:00:42.570 the difference between good and bad 0:00:40.040,0:00:45.210 arguments; and that is why, in this 0:00:42.570,0:00:49.469 lecture, we will take a look at logic--the 0:00:45.210,0:00:53.340 study of argumentation. Let us first 0:00:49.469,0:00:56.160 introduce some terminology. An argument 0:00:53.340,0:00:59.399 consists of two parts: the premises and 0:00:56.160,0:01:02.219 the conclusion. The premises are the 0:00:59.399,0:01:06.290 things we presuppose and the conclusion 0:01:02.219,0:01:08.479 is what we conclude from those premises. 0:01:06.290,0:01:12.240 So let's look at an example: 0:01:08.479,0:01:15.990 No medieval King had absolute power over 0:01:12.240,0:01:20.670 his subjects. Louis 7 of France was a 0:01:15.990,0:01:23.070 medieval King. So Louis 7 of France did 0:01:20.670,0:01:26.549 not have absolute power over his 0:01:23.070,0:01:29.579 subjects. Here the first two lines are 0:01:26.549,0:01:33.360 the premises and a final line introduced 0:01:29.579,0:01:35.670 by the word "so" is the conclusion. In this 0:01:33.360,0:01:38.159 argument we assume that medieval kings 0:01:35.670,0:01:40.740 did not have absolute power and that 0:01:38.159,0:01:43.200 Louis 7 was a medieval King. And we 0:01:40.740,0:01:47.329 conclude that he did not have absolute 0:01:43.200,0:01:50.070 power. As a second piece of terminology 0:01:47.329,0:01:53.549 we will make a distinction between valid 0:01:50.070,0:01:55.610 and invalid arguments. A valid argument 0:01:53.549,0:01:58.469 is an argument in which the conclusion 0:01:55.610,0:02:01.680 really follows from the premises. 0:01:58.469,0:02:04.320 Our example about Louis 7 is an example 0:02:01.680,0:02:07.380 of a valid argument. The conclusion 0:02:04.320,0:02:10.410 really follows from the premises. It 0:02:07.380,0:02:12.780 makes sense to draw this conclusion from 0:02:10.410,0:02:15.930 these premises. 0:02:12.780,0:02:19.020 As an example of an invalid argument we 0:02:15.930,0:02:22.140 can take this: No medieval King had 0:02:19.020,0:02:25.080 absolute power over his subjects. Louis 0:02:22.140,0:02:27.630 seven of France was a great horseman. So 0:02:25.080,0:02:31.950 Louis seven of France did not have 0:02:27.630,0:02:34.530 absolute power over his subjects. We just 0:02:31.950,0:02:37.550 can't draw that conclusion from those 0:02:34.530,0:02:41.220 premises. So this argument is not valid. 0:02:37.550,0:02:42.480 It's invalid. Note that whether an 0:02:41.220,0:02:44.100 argument is valid or not 0:02:42.480,0:02:46.700 has nothing to do with whether the 0:02:44.100,0:02:49.709 premises or the conclusions are true. 0:02:46.700,0:02:52.200 Perhaps Louis 7 really was a great 0:02:49.709,0:02:54.420 horseman. Then all the premises and the 0:02:52.200,0:02:58.019 conclusion of that argument are true and 0:02:54.420,0:03:01.170 yet the argument is invalid because the 0:02:58.019,0:03:04.350 conclusion just doesn't follow from the 0:03:01.170,0:03:06.840 premises. On the other hand it's also 0:03:04.350,0:03:10.620 possible to have false premises and a 0:03:06.840,0:03:12.180 valid argument. For instance: No medieval 0:03:10.620,0:03:14.760 King had absolute power over his 0:03:12.180,0:03:17.850 subjects. Victor Gijsbers was a 0:03:14.760,0:03:20.360 medieval king. So Victor Gijsbers did not 0:03:17.850,0:03:24.180 have absolute power over his subjects. 0:03:20.360,0:03:25.590 This argument is perfectly valid even 0:03:24.180,0:03:30.140 though the assumption that I am a 0:03:25.590,0:03:33.000 medieval King is, as far as I know, false. 0:03:30.140,0:03:35.610 We can now introduce our final piece of 0:03:33.000,0:03:38.820 terminology: The distinction between two 0:03:35.610,0:03:42.269 kinds of arguments. Deductive arguments 0:03:38.820,0:03:44.340 and inductive arguments. A deductive 0:03:42.269,0:03:46.310 argument is an argument in which the 0:03:44.340,0:03:49.350 truth of the premises 0:03:46.310,0:03:52.500 absolutely guarantee the truth of the 0:03:49.350,0:03:54.480 conclusion. It's just not possible for 0:03:52.500,0:03:56.870 the premises to be true and the 0:03:54.480,0:03:59.430 conclusion to be false. 0:03:56.870,0:04:01.799 Teturning to our original example, we can 0:03:59.430,0:04:03.150 see that this is a deductive argument. It 0:04:01.799,0:04:04.950 is true 0:04:03.150,0:04:07.530 the medieval Kings did not have absolute 0:04:04.950,0:04:10.620 power; and if it is true that Louis 7 was 0:04:07.530,0:04:13.200 a medieval King, then it must be true 0:04:10.620,0:04:15.600 that he did not have absolute power. 0:04:13.200,0:04:18.030 Or, in other words, if he did have 0:04:15.600,0:04:22.680 absolute power then one of those two 0:04:18.030,0:04:24.510 premises must be wrong. I'll come to the 0:04:22.680,0:04:27.090 definition of inductive arguments in a 0:04:24.510,0:04:28.980 moment, but first I want to point out two 0:04:27.090,0:04:33.120 interesting features of deductive 0:04:28.980,0:04:36.479 arguments: First if you use deductive 0:04:33.120,0:04:40.080 arguments you can't make any new 0:04:36.479,0:04:42.240 mistakes. The only way for the conclusion 0:04:40.080,0:04:45.780 of a deductive argument to be false is 0:04:42.240,0:04:47.970 if one of your assumptions is false, so 0:04:45.780,0:04:50.310 if you already believe something false 0:04:47.970,0:04:52.940 then your conclusion may end up being 0:04:50.310,0:04:56.610 false. But if your assumptions are true 0:04:52.940,0:04:57.570 your conclusions are guaranteed to be 0:04:56.610,0:05:00.930 true as well. 0:04:57.570,0:05:03.570 So deductive arguments never introduce 0:05:00.930,0:05:06.060 falsehoods if they weren't already there. 0:05:03.570,0:05:08.250 And that makes them very strong and good 0:05:06.060,0:05:13.320 arguments to use, because they're not 0:05:08.250,0:05:16.130 very risky. Second logicians found out 0:05:13.320,0:05:18.180 already more than 2,000 years ago--and 0:05:16.130,0:05:20.880 Aristotle played an important role here-- 0:05:18.180,0:05:23.820 that whether a deductive argument is 0:05:20.880,0:05:26.130 valid or not can be determined just by 0:05:23.820,0:05:29.460 looking at the form of the argument and 0:05:26.130,0:05:32.610 ignoring its content. Even if you know 0:05:29.460,0:05:35.430 nothing about medieval kings and Louis 7 0:05:32.610,0:05:39.389 you can still see that our example 0:05:35.430,0:05:44.550 argument is valid. How? Because there's 0:05:39.389,0:05:47.940 this form: No A is B. C is A. So C is not B. 0:05:44.550,0:05:51.599 Where A is "medieval King," B is "someone 0:05:47.940,0:05:53.669 with absolute power," and C is "Louis 7" But 0:05:51.599,0:05:55.470 we can put anything we like in the place 0:05:53.669,0:05:58.500 of those letters and the argument will 0:05:55.470,0:06:02.070 remain valid. For instance, let's choose A 0:05:58.500,0:06:05.190 "Is a Dutchman" B "is humble" and C "is Victor 0:06:02.070,0:06:07.260 or Gijsbers" Then we have: No Dutchman 0:06:05.190,0:06:10.050 is humble. Victor Gijsbers is a 0:06:07.260,0:06:12.840 Dutchman. So Victor Gijsbers is not 0:06:10.050,0:06:15.270 humble. Which is another valid argument. 0:06:12.840,0:06:18.720 Although of course the first premise is 0:06:15.270,0:06:20.610 false and so is the conclusion. So we can 0:06:18.720,0:06:22.800 see whether a deductive argument is 0:06:20.610,0:06:24.840 valid simply by looking at its form 0:06:22.800,0:06:27.810 without knowing anything about its 0:06:24.840,0:06:30.000 content. And that is really important 0:06:27.810,0:06:31.910 because that means that we can see 0:06:30.000,0:06:35.370 whether something is a good argument 0:06:31.910,0:06:38.150 without making any prior theoretical 0:06:35.370,0:06:40.860 assumptions about the content matter. If 0:06:38.150,0:06:42.870 we believe that scientists first 0:06:40.860,0:06:44.520 collect data and then come to a 0:06:42.870,0:06:47.310 conclusion about which theories are 0:06:44.520,0:06:50.610 right and wrong, this is exactly what we 0:06:47.310,0:06:53.340 would expect. We only need the data and 0:06:50.610,0:06:56.189 some valid arguments which can be shown 0:06:53.340,0:06:58.770 to be valid independent of any theories 0:06:56.189,0:07:02.610 or ideas, and then we draw our 0:06:58.770,0:07:08.069 conclusions. It would be great if science 0:07:02.610,0:07:09.560 worked like that. Unfortunately, and I bet 0:07:08.069,0:07:13.199 you saw that coming, 0:07:09.560,0:07:14.759 science doesn't work like that. And it 0:07:13.199,0:07:17.340 doesn't work like that because the most 0:07:14.759,0:07:21.960 important arguments in science are not 0:07:17.340,0:07:23.909 deductive. They are inductive. Remember 0:07:21.960,0:07:26.389 that a deductive argument is an argument 0:07:23.909,0:07:29.099 such that the truth of the premises 0:07:26.389,0:07:33.150 absolutely guarantees the truth of the 0:07:29.099,0:07:34.590 conclusion. An inductive argument is an 0:07:33.150,0:07:36.659 argument where the truth of the premises 0:07:34.590,0:07:39.719 gives good reason to believe the 0:07:36.659,0:07:43.560 conclusion but does not absolutely 0:07:39.719,0:07:44.300 guarantee its truth. Again let's look at 0:07:43.560,0:07:46.830 an example: 0:07:44.300,0:07:49.139 None of the medieval texts we have 0:07:46.830,0:07:52.770 studied argues against the existence of 0:07:49.139,0:07:55.610 God, so no scholar in the Middle Ages 0:07:52.770,0:07:58.770 argued against the existence of God. 0:07:55.610,0:08:00.629 That's a valid argument if it's true 0:07:58.770,0:08:03.120 that none of the texts we have makes 0:08:00.629,0:08:05.879 this argument, and we have a lot of texts, 0:08:03.120,0:08:08.210 and it's quite plausible that nobody in 0:08:05.879,0:08:12.389 that time actually made this argument. 0:08:08.210,0:08:14.580 But it's indeed only plausible. It could 0:08:12.389,0:08:18.449 be that the argument was made but 0:08:14.580,0:08:20.969 somehow it wasn't transmitted to us. So 0:08:18.449,0:08:23.089 in an inductive argument. The truth of 0:08:20.969,0:08:26.580 the premises makes the conclusion likely, 0:08:23.089,0:08:29.219 but it doesn't guarantee it. And that's 0:08:26.580,0:08:31.560 generally the case in science. We have 0:08:29.219,0:08:34.140 some limited data. We want to draw a 0:08:31.560,0:08:36.570 general conclusion from those, and our 0:08:34.140,0:08:39.419 data makes the conclusion likely but 0:08:36.570,0:08:41.789 they don't make it certain. So, in science, 0:08:39.419,0:08:44.760 we are continually making inductive 0:08:41.789,0:08:48.240 arguments. And, as we will see in the next 0:08:44.760,0:08:52.459 lecture, induction is a lot more 0:08:48.240,0:08:52.459 problematic than deduction.