1 00:00:10,140 --> 00:00:16,420 So without further ado, let's go straight on to induction. 2 00:00:16,420 --> 00:00:26,620 You'll see that here there are a lot of things in common with the material we've just covered, so some of that I shall go over quite quickly. 3 00:00:26,620 --> 00:00:37,660 However, the handout seems to be relatively self-contained so that you can look at it separately. 4 00:00:37,660 --> 00:00:42,490 The people shown here, well, we've got David Hume on the left. 5 00:00:42,490 --> 00:00:48,040 Sir Peter Straughan, who was maudlin for many years and I think started out at University College. 6 00:00:48,040 --> 00:00:52,660 So he had very much in an Oxford man, Hugh Miller. 7 00:00:52,660 --> 00:01:04,650 Until recently, professor at Cambridge and Nelson Goodman, famous author of The Goodman Paradox. 8 00:01:04,650 --> 00:01:16,300 Now, the main historical reading that you will get on induction is David Hume's enquiry concerning human understanding Section four. 9 00:01:16,300 --> 00:01:20,340 And the discussion there starts with a vital distinction, a very, 10 00:01:20,340 --> 00:01:31,400 very important distinction and one that has remained of tremendous importance, though its exact formulation has changed over the years. 11 00:01:31,400 --> 00:01:36,890 Hume draws a distinction between relations of ideas and matters of fact. 12 00:01:36,890 --> 00:01:44,210 Well, what's the relation of ideas? Well, think, for example, of this proposition here. 13 00:01:44,210 --> 00:01:54,120 All bachelors are unmarried. OK, so we've got certain ideas like the idea of a bachelor, the idea of being unmarried. 14 00:01:54,120 --> 00:01:59,890 And we can see just by looking at the nature of those ideas, what we understand by them. 15 00:01:59,890 --> 00:02:01,930 What do we understand by a bachelor? 16 00:02:01,930 --> 00:02:13,930 Well, an unmarried man, if that is our idea of a bachelor, then we can see just by consulting our own ideas that all bachelors must be unmarried. 17 00:02:13,930 --> 00:02:19,100 Three times five equals half of 30. That's one of Hume's examples. 18 00:02:19,100 --> 00:02:28,910 Simply by examining our ideas of three and five and multiplication cetera, we can again see that that is true. 19 00:02:28,910 --> 00:02:32,660 More complicated example, Pythagoras's theorem. 20 00:02:32,660 --> 00:02:41,450 It seems that the proof of Pythagoras's theorem comes pretty much from just consulting the ideas of a Euclidian triangle. 21 00:02:41,450 --> 00:02:49,560 The axioms of Euclidean geometry and simply doing inferences from those. 22 00:02:49,560 --> 00:02:56,970 So these kinds of propositions offer Hume relations of ideas, the more modern term is analytic propositions, 23 00:02:56,970 --> 00:03:03,000 ones that can be known, if you like, purely by analysing the meaning of the terms. 24 00:03:03,000 --> 00:03:08,050 And she draws a distinction between relations of ideas and matters of fact now, 25 00:03:08,050 --> 00:03:15,520 matters of fact are things that we cannot know to be true or false simply by consulting our ideas. 26 00:03:15,520 --> 00:03:22,000 So he gives examples like The sun will rise tomorrow. The sun will not rise tomorrow. 27 00:03:22,000 --> 00:03:32,290 Those are things that we cannot know to be true, also be false just by thinking about her ideas of what the sun is. 28 00:03:32,290 --> 00:03:38,240 If we take a pen, hold it in the air and let go of it. 29 00:03:38,240 --> 00:03:45,200 Before it's fallen, the proposition that he will fall when released is a matter of fact. 30 00:03:45,200 --> 00:03:53,030 It doesn't follow from the idea of a pen from what we understand by a pen, from what we understand, by releasing it in air. 31 00:03:53,030 --> 00:03:57,950 It's not a matter of logic that the pen must fall. 32 00:03:57,950 --> 00:04:01,420 It's a matter of fact. 33 00:04:01,420 --> 00:04:11,880 So the modern term for that is a synthetic proposition, a proposition whose truth is determined by the facts of experience rather than what we mean. 34 00:04:11,880 --> 00:04:21,610 So this raises a natural question. Some matters of fact, we can know to be true or we think we can know to be true just by perceiving them. 35 00:04:21,610 --> 00:04:28,340 I can perceive that there's a lectern directly in front of me. So let's not worry about that. 36 00:04:28,340 --> 00:04:35,290 I can remember that it rained last week. I'm not going to worry about that. 37 00:04:35,290 --> 00:04:40,480 What about matters of fact that I don't directly perceive and that I don't remember? 38 00:04:40,480 --> 00:04:46,460 How can I possibly know anything about those? 39 00:04:46,460 --> 00:04:52,870 And now we come to that example that's been mentioned before of the billiard balls. 40 00:04:52,870 --> 00:05:01,810 Paradigm example of a matter of fact. I see a yellow billiard ball moving towards a red one. 41 00:05:01,810 --> 00:05:07,370 I suppose that when they touch the red one will move. 42 00:05:07,370 --> 00:05:15,520 But that it will move is not a relation of ideas. It cannot be known to be true just by consulting my ideas of billiard balls and movement. 43 00:05:15,520 --> 00:05:17,740 It's a matter of fact. 44 00:05:17,740 --> 00:05:25,690 And I can't see now that it's going to move and I clearly can't remember its movement because we're talking about something in the future. 45 00:05:25,690 --> 00:05:30,610 So it's just an example of the kind of matter of fact that Hume is talking about. 46 00:05:30,610 --> 00:05:37,360 So why do I suppose that the red one will move when the yellow one hits it? 47 00:05:37,360 --> 00:05:42,700 According to Hume, the only way we can ever draw any inference to a matter of fact, 48 00:05:42,700 --> 00:05:49,850 which we don't either see or remember, is by relying on causal relations. 49 00:05:49,850 --> 00:05:57,670 So then we get to this famous thought experiment. There's Adam as painted by Michelangelo. 50 00:05:57,670 --> 00:06:04,690 Adam's just been created by God. He sees one billiard ball moving towards another. 51 00:06:04,690 --> 00:06:10,870 Put yourself in his position. You have no experience at all to call on. 52 00:06:10,870 --> 00:06:21,900 You've never seen anything like this. You are asked to predict what will happen when the first ball meets the second one. 53 00:06:21,900 --> 00:06:31,300 How could you possibly proceed? According to humans we've seen, you couldn't you would have no idea what was going to happen. 54 00:06:31,300 --> 00:06:36,970 Maybe when that ball hits that one, it will just stop. Maybe it will explode. 55 00:06:36,970 --> 00:06:41,380 Maybe it'll go right through it. Maybe it'll turn into a frog. 56 00:06:41,380 --> 00:06:50,040 Who knows? Without experience, you have no basis for any prediction. 57 00:06:50,040 --> 00:06:57,380 So that means that any inference to a matter of fact, beyond what we perceive or remember. 58 00:06:57,380 --> 00:07:04,640 Seems if Hume's right to be based on assumptions of causality and all our knowledge of causal relations, 59 00:07:04,640 --> 00:07:17,080 such as with the billiard balls, comes from experience. Without experience, we can't make any predictions about what will cause what. 60 00:07:17,080 --> 00:07:24,680 And it seems clear that learning from experience takes for granted that observed phenomena, things that we've seen in the past. 61 00:07:24,680 --> 00:07:32,830 Do provide a guide, a guide of at least some reliability to what's going to happen in the future. 62 00:07:32,830 --> 00:07:42,910 So it seems that in order to make any prediction about the future, we have to take for granted or we have to have some basis for extrapolation, 63 00:07:42,910 --> 00:07:51,610 extrapolation from our experience to the future, because experience is our only guide. 64 00:07:51,610 --> 00:07:58,720 Well, here's a passage from a letter from a gentleman to his friend in Edinburgh that Hume wrote in seventeen forty five, 65 00:07:58,720 --> 00:08:06,820 the context of this was that Hume was applying for a chair in moral philosophy at Edinburgh and the clergy 66 00:08:06,820 --> 00:08:12,760 at Edinburgh were very much against him because they thought his treatise of human nature was atheistic. 67 00:08:12,760 --> 00:08:20,020 And so he wrote a letter trying to explain how the treatise wasn't nearly as bad as people thought it was. 68 00:08:20,020 --> 00:08:27,850 It's not exactly clear how much of this letter we should take as entirely ingenuous. 69 00:08:27,850 --> 00:08:34,420 Some of it might possibly be suspected of somewhat glossing over the truth. 70 00:08:34,420 --> 00:08:43,340 But at any rate, in that letter he explained part of the background to his epistemological thinking. 71 00:08:43,340 --> 00:08:54,040 It is common for philosophers to distinguish the kinds of evidence into intuitive, demonstrative, sensible and moral. 72 00:08:54,040 --> 00:09:02,330 When he talks about into charity of evidence, that is intuition like Locke, he means something that is immediately self evident. 73 00:09:02,330 --> 00:09:08,600 So, for example, that something is identical with itself. I am identical with me. 74 00:09:08,600 --> 00:09:12,380 Two is greater than one. These are things I can know to be true. 75 00:09:12,380 --> 00:09:23,710 Just self, evidently. By sensible evidence, you mean since Sawrey evidence the evidence of the senses? 76 00:09:23,710 --> 00:09:30,520 Demonstrative evidence. Well, that's demonstration. Logical argument. 77 00:09:30,520 --> 00:09:37,310 And by moral evidence, humour means inductive reasoning, reasoning from experience. 78 00:09:37,310 --> 00:09:40,250 It's very important when you read the enquiry. 79 00:09:40,250 --> 00:09:48,540 Notice that when Hume uses the word moral, he does not mean ethical in the sense that you were I would mean by moral. 80 00:09:48,540 --> 00:10:00,210 So moral reasoning is reasoning about the world. So here Hume is drawing on lock. 81 00:10:00,210 --> 00:10:07,380 We've seen before how Locke draws this distinction between demonstrative and probable reasoning. 82 00:10:07,380 --> 00:10:13,440 And we saw that for Locke, both types of reasoning involve a rational perception of the links. 83 00:10:13,440 --> 00:10:20,820 So Locke's view of demonstrative and probable reasoning or demonstrative moral reasoning is that in one case, 84 00:10:20,820 --> 00:10:31,380 when we reason from one step to another in our chain of reasoning, we see a clear, evident connexion from one step to the next. 85 00:10:31,380 --> 00:10:38,760 In or moral reasoning, when we reason from past experience, according to Locke, we see evidential connexions. 86 00:10:38,760 --> 00:10:45,010 But they're only probable connexions, not demonstrative ones. 87 00:10:45,010 --> 00:10:49,170 OK, with that background, let's go back to Hume's question. 88 00:10:49,170 --> 00:10:54,600 We want to know why the second billiard ball will move when the first touches it. 89 00:10:54,600 --> 00:11:04,570 We think that the only ground of such an inference is causation. We think that the only way we can learn about causation is from past experience. 90 00:11:04,570 --> 00:11:10,550 And we want to know what ground we have for extrapolating from past experience to the future, 91 00:11:10,550 --> 00:11:16,430 for expecting that the causal laws, if you like, that applied in the past, will apply in the future. 92 00:11:16,430 --> 00:11:20,450 What ground have we got? Well, is it self-evident? 93 00:11:20,450 --> 00:11:28,400 No, it isn't. Can it be demonstrated? Can you produce a logical proof that what's happened in the past will happen in the future? 94 00:11:28,400 --> 00:11:34,370 No, you can't, because we can perfectly coherent B conceive of it not happening. 95 00:11:34,370 --> 00:11:40,790 Do we have sensory knowledge? Can we see through our senses that what has happened in the past will happen in the future? 96 00:11:40,790 --> 00:11:48,220 Clearly not. What about factual inference, what about ordinary day to day inductive moral reasoning? 97 00:11:48,220 --> 00:11:52,480 No, because that is the very kind of reasoning that we're considering. 98 00:11:52,480 --> 00:12:01,590 We're asking ourselves whether it is possible to extrapolate from past to future, legitimately so relying on that kind of reasoning. 99 00:12:01,590 --> 00:12:08,560 To justify our relying on that kind of reasoning would be going in a circle. 100 00:12:08,560 --> 00:12:13,290 So here I give a very brief review of the argument of the enquiry. 101 00:12:13,290 --> 00:12:18,940 I'm not going to go through this now in detail, but when you come to Hume's text, 102 00:12:18,940 --> 00:12:26,440 take a look at these slides and use them to inform your reading of these passages. 103 00:12:26,440 --> 00:12:35,740 That's a summary of the part. One argument where humour says that all factual inference is founded on experience. 104 00:12:35,740 --> 00:12:40,570 It follows that all factual inference has to be based on an assumption of uniformity. 105 00:12:40,570 --> 00:12:46,180 The assumption that what has happened in the past is a guide to what will happen in the future. 106 00:12:46,180 --> 00:12:56,960 And then we get the proof that we have no ground for making that assumption.