1 00:00:00,070 --> 00:00:07,440 [Music] 2 00:00:04,009 --> 00:00:11,010 Scientists often gather data through 3 00:00:07,440 --> 00:00:14,340 observation experiments, archival studies 4 00:00:11,010 --> 00:00:17,520 and so on. But they are rarely satisfied 5 00:00:14,340 --> 00:00:20,070 with data alone. Scientists want to draw 6 00:00:17,520 --> 00:00:21,960 conclusions from those data. They want to 7 00:00:20,070 --> 00:00:24,590 use the data to show that certain 8 00:00:21,960 --> 00:00:27,869 theories are right and others are wrong. 9 00:00:24,590 --> 00:00:29,699 To understand science, then, it will be 10 00:00:27,869 --> 00:00:31,830 important to understand when it is 11 00:00:29,699 --> 00:00:35,340 legitimate and when it is illegitimate. 12 00:00:31,830 --> 00:00:38,070 To draw a specific conclusion from what 13 00:00:35,340 --> 00:00:40,040 we already know we need to understand 14 00:00:38,070 --> 00:00:42,570 the difference between good and bad 15 00:00:40,040 --> 00:00:45,210 arguments; and that is why, in this 16 00:00:42,570 --> 00:00:49,469 lecture, we will take a look at logic--the 17 00:00:45,210 --> 00:00:53,340 study of argumentation. Let us first 18 00:00:49,469 --> 00:00:56,160 introduce some terminology. An argument 19 00:00:53,340 --> 00:00:59,399 consists of two parts: the premises and 20 00:00:56,160 --> 00:01:02,219 the conclusion. The premises are the 21 00:00:59,399 --> 00:01:06,290 things we presuppose and the conclusion 22 00:01:02,219 --> 00:01:08,479 is what we conclude from those premises. 23 00:01:06,290 --> 00:01:12,240 So let's look at an example: 24 00:01:08,479 --> 00:01:15,990 No medieval King had absolute power over 25 00:01:12,240 --> 00:01:20,670 his subjects. Louis 7 of France was a 26 00:01:15,990 --> 00:01:23,070 medieval King. So Louis 7 of France did 27 00:01:20,670 --> 00:01:26,549 not have absolute power over his 28 00:01:23,070 --> 00:01:29,579 subjects. Here the first two lines are 29 00:01:26,549 --> 00:01:33,360 the premises and a final line introduced 30 00:01:29,579 --> 00:01:35,670 by the word "so" is the conclusion. In this 31 00:01:33,360 --> 00:01:38,159 argument we assume that medieval kings 32 00:01:35,670 --> 00:01:40,740 did not have absolute power and that 33 00:01:38,159 --> 00:01:43,200 Louis 7 was a medieval King. And we 34 00:01:40,740 --> 00:01:47,329 conclude that he did not have absolute 35 00:01:43,200 --> 00:01:50,070 power. As a second piece of terminology 36 00:01:47,329 --> 00:01:53,549 we will make a distinction between valid 37 00:01:50,070 --> 00:01:55,610 and invalid arguments. A valid argument 38 00:01:53,549 --> 00:01:58,469 is an argument in which the conclusion 39 00:01:55,610 --> 00:02:01,680 really follows from the premises. 40 00:01:58,469 --> 00:02:04,320 Our example about Louis 7 is an example 41 00:02:01,680 --> 00:02:07,380 of a valid argument. The conclusion 42 00:02:04,320 --> 00:02:10,410 really follows from the premises. It 43 00:02:07,380 --> 00:02:12,780 makes sense to draw this conclusion from 44 00:02:10,410 --> 00:02:15,930 these premises. 45 00:02:12,780 --> 00:02:19,020 As an example of an invalid argument we 46 00:02:15,930 --> 00:02:22,140 can take this: No medieval King had 47 00:02:19,020 --> 00:02:25,080 absolute power over his subjects. Louis 48 00:02:22,140 --> 00:02:27,630 seven of France was a great horseman. So 49 00:02:25,080 --> 00:02:31,950 Louis seven of France did not have 50 00:02:27,630 --> 00:02:34,530 absolute power over his subjects. We just 51 00:02:31,950 --> 00:02:37,550 can't draw that conclusion from those 52 00:02:34,530 --> 00:02:41,220 premises. So this argument is not valid. 53 00:02:37,550 --> 00:02:42,480 It's invalid. Note that whether an 54 00:02:41,220 --> 00:02:44,100 argument is valid or not 55 00:02:42,480 --> 00:02:46,700 has nothing to do with whether the 56 00:02:44,100 --> 00:02:49,709 premises or the conclusions are true. 57 00:02:46,700 --> 00:02:52,200 Perhaps Louis 7 really was a great 58 00:02:49,709 --> 00:02:54,420 horseman. Then all the premises and the 59 00:02:52,200 --> 00:02:58,019 conclusion of that argument are true and 60 00:02:54,420 --> 00:03:01,170 yet the argument is invalid because the 61 00:02:58,019 --> 00:03:04,350 conclusion just doesn't follow from the 62 00:03:01,170 --> 00:03:06,840 premises. On the other hand it's also 63 00:03:04,350 --> 00:03:10,620 possible to have false premises and a 64 00:03:06,840 --> 00:03:12,180 valid argument. For instance: No medieval 65 00:03:10,620 --> 00:03:14,760 King had absolute power over his 66 00:03:12,180 --> 00:03:17,850 subjects. Victor Gijsbers was a 67 00:03:14,760 --> 00:03:20,360 medieval king. So Victor Gijsbers did not 68 00:03:17,850 --> 00:03:24,180 have absolute power over his subjects. 69 00:03:20,360 --> 00:03:25,590 This argument is perfectly valid even 70 00:03:24,180 --> 00:03:30,140 though the assumption that I am a 71 00:03:25,590 --> 00:03:33,000 medieval King is, as far as I know, false. 72 00:03:30,140 --> 00:03:35,610 We can now introduce our final piece of 73 00:03:33,000 --> 00:03:38,820 terminology: The distinction between two 74 00:03:35,610 --> 00:03:42,269 kinds of arguments. Deductive arguments 75 00:03:38,820 --> 00:03:44,340 and inductive arguments. A deductive 76 00:03:42,269 --> 00:03:46,310 argument is an argument in which the 77 00:03:44,340 --> 00:03:49,350 truth of the premises 78 00:03:46,310 --> 00:03:52,500 absolutely guarantee the truth of the 79 00:03:49,350 --> 00:03:54,480 conclusion. It's just not possible for 80 00:03:52,500 --> 00:03:56,870 the premises to be true and the 81 00:03:54,480 --> 00:03:59,430 conclusion to be false. 82 00:03:56,870 --> 00:04:01,799 Teturning to our original example, we can 83 00:03:59,430 --> 00:04:03,150 see that this is a deductive argument. It 84 00:04:01,799 --> 00:04:04,950 is true 85 00:04:03,150 --> 00:04:07,530 the medieval Kings did not have absolute 86 00:04:04,950 --> 00:04:10,620 power; and if it is true that Louis 7 was 87 00:04:07,530 --> 00:04:13,200 a medieval King, then it must be true 88 00:04:10,620 --> 00:04:15,600 that he did not have absolute power. 89 00:04:13,200 --> 00:04:18,030 Or, in other words, if he did have 90 00:04:15,600 --> 00:04:22,680 absolute power then one of those two 91 00:04:18,030 --> 00:04:24,510 premises must be wrong. I'll come to the 92 00:04:22,680 --> 00:04:27,090 definition of inductive arguments in a 93 00:04:24,510 --> 00:04:28,980 moment, but first I want to point out two 94 00:04:27,090 --> 00:04:33,120 interesting features of deductive 95 00:04:28,980 --> 00:04:36,479 arguments: First if you use deductive 96 00:04:33,120 --> 00:04:40,080 arguments you can't make any new 97 00:04:36,479 --> 00:04:42,240 mistakes. The only way for the conclusion 98 00:04:40,080 --> 00:04:45,780 of a deductive argument to be false is 99 00:04:42,240 --> 00:04:47,970 if one of your assumptions is false, so 100 00:04:45,780 --> 00:04:50,310 if you already believe something false 101 00:04:47,970 --> 00:04:52,940 then your conclusion may end up being 102 00:04:50,310 --> 00:04:56,610 false. But if your assumptions are true 103 00:04:52,940 --> 00:04:57,570 your conclusions are guaranteed to be 104 00:04:56,610 --> 00:05:00,930 true as well. 105 00:04:57,570 --> 00:05:03,570 So deductive arguments never introduce 106 00:05:00,930 --> 00:05:06,060 falsehoods if they weren't already there. 107 00:05:03,570 --> 00:05:08,250 And that makes them very strong and good 108 00:05:06,060 --> 00:05:13,320 arguments to use, because they're not 109 00:05:08,250 --> 00:05:16,130 very risky. Second logicians found out 110 00:05:13,320 --> 00:05:18,180 already more than 2,000 years ago--and 111 00:05:16,130 --> 00:05:20,880 Aristotle played an important role here-- 112 00:05:18,180 --> 00:05:23,820 that whether a deductive argument is 113 00:05:20,880 --> 00:05:26,130 valid or not can be determined just by 114 00:05:23,820 --> 00:05:29,460 looking at the form of the argument and 115 00:05:26,130 --> 00:05:32,610 ignoring its content. Even if you know 116 00:05:29,460 --> 00:05:35,430 nothing about medieval kings and Louis 7 117 00:05:32,610 --> 00:05:39,389 you can still see that our example 118 00:05:35,430 --> 00:05:44,550 argument is valid. How? Because there's 119 00:05:39,389 --> 00:05:47,940 this form: No A is B. C is A. So C is not B. 120 00:05:44,550 --> 00:05:51,599 Where A is "medieval King," B is "someone 121 00:05:47,940 --> 00:05:53,669 with absolute power," and C is "Louis 7" But 122 00:05:51,599 --> 00:05:55,470 we can put anything we like in the place 123 00:05:53,669 --> 00:05:58,500 of those letters and the argument will 124 00:05:55,470 --> 00:06:02,070 remain valid. For instance, let's choose A 125 00:05:58,500 --> 00:06:05,190 "Is a Dutchman" B "is humble" and C "is Victor 126 00:06:02,070 --> 00:06:07,260 or Gijsbers" Then we have: No Dutchman 127 00:06:05,190 --> 00:06:10,050 is humble. Victor Gijsbers is a 128 00:06:07,260 --> 00:06:12,840 Dutchman. So Victor Gijsbers is not 129 00:06:10,050 --> 00:06:15,270 humble. Which is another valid argument. 130 00:06:12,840 --> 00:06:18,720 Although of course the first premise is 131 00:06:15,270 --> 00:06:20,610 false and so is the conclusion. So we can 132 00:06:18,720 --> 00:06:22,800 see whether a deductive argument is 133 00:06:20,610 --> 00:06:24,840 valid simply by looking at its form 134 00:06:22,800 --> 00:06:27,810 without knowing anything about its 135 00:06:24,840 --> 00:06:30,000 content. And that is really important 136 00:06:27,810 --> 00:06:31,910 because that means that we can see 137 00:06:30,000 --> 00:06:35,370 whether something is a good argument 138 00:06:31,910 --> 00:06:38,150 without making any prior theoretical 139 00:06:35,370 --> 00:06:40,860 assumptions about the content matter. If 140 00:06:38,150 --> 00:06:42,870 we believe that scientists first 141 00:06:40,860 --> 00:06:44,520 collect data and then come to a 142 00:06:42,870 --> 00:06:47,310 conclusion about which theories are 143 00:06:44,520 --> 00:06:50,610 right and wrong, this is exactly what we 144 00:06:47,310 --> 00:06:53,340 would expect. We only need the data and 145 00:06:50,610 --> 00:06:56,189 some valid arguments which can be shown 146 00:06:53,340 --> 00:06:58,770 to be valid independent of any theories 147 00:06:56,189 --> 00:07:02,610 or ideas, and then we draw our 148 00:06:58,770 --> 00:07:08,069 conclusions. It would be great if science 149 00:07:02,610 --> 00:07:09,560 worked like that. Unfortunately, and I bet 150 00:07:08,069 --> 00:07:13,199 you saw that coming, 151 00:07:09,560 --> 00:07:14,759 science doesn't work like that. And it 152 00:07:13,199 --> 00:07:17,340 doesn't work like that because the most 153 00:07:14,759 --> 00:07:21,960 important arguments in science are not 154 00:07:17,340 --> 00:07:23,909 deductive. They are inductive. Remember 155 00:07:21,960 --> 00:07:26,389 that a deductive argument is an argument 156 00:07:23,909 --> 00:07:29,099 such that the truth of the premises 157 00:07:26,389 --> 00:07:33,150 absolutely guarantees the truth of the 158 00:07:29,099 --> 00:07:34,590 conclusion. An inductive argument is an 159 00:07:33,150 --> 00:07:36,659 argument where the truth of the premises 160 00:07:34,590 --> 00:07:39,719 gives good reason to believe the 161 00:07:36,659 --> 00:07:43,560 conclusion but does not absolutely 162 00:07:39,719 --> 00:07:44,300 guarantee its truth. Again let's look at 163 00:07:43,560 --> 00:07:46,830 an example: 164 00:07:44,300 --> 00:07:49,139 None of the medieval texts we have 165 00:07:46,830 --> 00:07:52,770 studied argues against the existence of 166 00:07:49,139 --> 00:07:55,610 God, so no scholar in the Middle Ages 167 00:07:52,770 --> 00:07:58,770 argued against the existence of God. 168 00:07:55,610 --> 00:08:00,629 That's a valid argument if it's true 169 00:07:58,770 --> 00:08:03,120 that none of the texts we have makes 170 00:08:00,629 --> 00:08:05,879 this argument, and we have a lot of texts, 171 00:08:03,120 --> 00:08:08,210 and it's quite plausible that nobody in 172 00:08:05,879 --> 00:08:12,389 that time actually made this argument. 173 00:08:08,210 --> 00:08:14,580 But it's indeed only plausible. It could 174 00:08:12,389 --> 00:08:18,449 be that the argument was made but 175 00:08:14,580 --> 00:08:20,969 somehow it wasn't transmitted to us. So 176 00:08:18,449 --> 00:08:23,089 in an inductive argument. The truth of 177 00:08:20,969 --> 00:08:26,580 the premises makes the conclusion likely, 178 00:08:23,089 --> 00:08:29,219 but it doesn't guarantee it. And that's 179 00:08:26,580 --> 00:08:31,560 generally the case in science. We have 180 00:08:29,219 --> 00:08:34,140 some limited data. We want to draw a 181 00:08:31,560 --> 00:08:36,570 general conclusion from those, and our 182 00:08:34,140 --> 00:08:39,419 data makes the conclusion likely but 183 00:08:36,570 --> 00:08:41,789 they don't make it certain. So, in science, 184 00:08:39,419 --> 00:08:44,760 we are continually making inductive 185 00:08:41,789 --> 00:08:48,240 arguments. And, as we will see in the next 186 00:08:44,760 --> 00:08:52,459 lecture, induction is a lot more 187 00:08:48,240 --> 00:08:52,459 problematic than deduction.