So without further ado, let's go straight on to induction. 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. However, the handout seems to be relatively self-contained so that you can look at it separately. The people shown here, well, we've got David Hume on the left. Sir Peter Straughan, who was maudlin for many years and I think started out at University College.
So he had very much in an Oxford man, Hugh Miller. Until recently, professor at Cambridge and Nelson Goodman, famous author of The Goodman Paradox. Now, the main historical reading that you will get on induction is David Hume's enquiry concerning human understanding Section four. And the discussion there starts with a vital distinction, a very, very important distinction and one that has remained of tremendous importance, though its exact formulation has changed over the years.
Hume draws a distinction between relations of ideas and matters of fact. Well, what's the relation of ideas? Well, think, for example, of this proposition here. All bachelors are unmarried. OK, so we've got certain ideas like the idea of a bachelor, the idea of being unmarried. And we can see just by looking at the nature of those ideas, what we understand by them. What do we understand by a bachelor?
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. Three times five equals half of 30. That's one of Hume's examples. Simply by examining our ideas of three and five and multiplication cetera, we can again see that that is true. More complicated example, Pythagoras's theorem. It seems that the proof of Pythagoras's theorem comes pretty much from just consulting the ideas of a Euclidian triangle.
The axioms of Euclidean geometry and simply doing inferences from those. So these kinds of propositions offer Hume relations of ideas, the more modern term is analytic propositions, ones that can be known, if you like, purely by analysing the meaning of the terms. And she draws a distinction between relations of ideas and matters of fact now, matters of fact are things that we cannot know to be true or false simply by consulting our ideas.
So he gives examples like The sun will rise tomorrow. The sun will not rise tomorrow. Those are things that we cannot know to be true, also be false just by thinking about her ideas of what the sun is. If we take a pen, hold it in the air and let go of it. Before it's fallen, the proposition that he will fall when released is a matter of fact. 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.
It's not a matter of logic that the pen must fall. It's a matter of fact. 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. 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. I can perceive that there's a lectern directly in front of me. So let's not worry about that.
I can remember that it rained last week. I'm not going to worry about that. What about matters of fact that I don't directly perceive and that I don't remember? How can I possibly know anything about those? And now we come to that example that's been mentioned before of the billiard balls. Paradigm example of a matter of fact. I see a yellow billiard ball moving towards a red one. I suppose that when they touch the red one will move.
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. It's a matter of fact. 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. So it's just an example of the kind of matter of fact that Hume is talking about. So why do I suppose that the red one will move when the yellow one hits it?
According to Hume, the only way we can ever draw any inference to a matter of fact, which we don't either see or remember, is by relying on causal relations. So then we get to this famous thought experiment. There's Adam as painted by Michelangelo. Adam's just been created by God. He sees one billiard ball moving towards another. Put yourself in his position. You have no experience at all to call on.
You've never seen anything like this. You are asked to predict what will happen when the first ball meets the second one. How could you possibly proceed? According to humans we've seen, you couldn't you would have no idea what was going to happen. Maybe when that ball hits that one, it will just stop. Maybe it will explode. Maybe it'll go right through it. Maybe it'll turn into a frog. Who knows? Without experience, you have no basis for any prediction.
So that means that any inference to a matter of fact, beyond what we perceive or remember. Seems if Hume's right to be based on assumptions of causality and all our knowledge of causal relations, such as with the billiard balls, comes from experience. Without experience, we can't make any predictions about what will cause what. And it seems clear that learning from experience takes for granted that observed phenomena, things that we've seen in the past.
Do provide a guide, a guide of at least some reliability to what's going to happen in the future. 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, extrapolation from our experience to the future, because experience is our only guide.
Well, here's a passage from a letter from a gentleman to his friend in Edinburgh that Hume wrote in seventeen forty five, the context of this was that Hume was applying for a chair in moral philosophy at Edinburgh and the clergy at Edinburgh were very much against him because they thought his treatise of human nature was atheistic. And so he wrote a letter trying to explain how the treatise wasn't nearly as bad as people thought it was.
It's not exactly clear how much of this letter we should take as entirely ingenuous. Some of it might possibly be suspected of somewhat glossing over the truth. But at any rate, in that letter he explained part of the background to his epistemological thinking. It is common for philosophers to distinguish the kinds of evidence into intuitive, demonstrative, sensible and moral.
When he talks about into charity of evidence, that is intuition like Locke, he means something that is immediately self evident. So, for example, that something is identical with itself. I am identical with me. Two is greater than one. These are things I can know to be true. Just self, evidently. By sensible evidence, you mean since Sawrey evidence the evidence of the senses? Demonstrative evidence. Well, that's demonstration. Logical argument.
And by moral evidence, humour means inductive reasoning, reasoning from experience. It's very important when you read the enquiry. Notice that when Hume uses the word moral, he does not mean ethical in the sense that you were I would mean by moral. So moral reasoning is reasoning about the world. So here Hume is drawing on lock. We've seen before how Locke draws this distinction between demonstrative and probable reasoning.
And we saw that for Locke, both types of reasoning involve a rational perception of the links. So Locke's view of demonstrative and probable reasoning or demonstrative moral reasoning is that in one case, 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. In or moral reasoning, when we reason from past experience, according to Locke, we see evidential connexions.
But they're only probable connexions, not demonstrative ones. OK, with that background, let's go back to Hume's question. We want to know why the second billiard ball will move when the first touches it. 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.
And we want to know what ground we have for extrapolating from past experience to the future, for expecting that the causal laws, if you like, that applied in the past, will apply in the future. What ground have we got? Well, is it self-evident? 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? No, you can't, because we can perfectly coherent B conceive of it not happening.
Do we have sensory knowledge? Can we see through our senses that what has happened in the past will happen in the future? Clearly not. What about factual inference, what about ordinary day to day inductive moral reasoning? No, because that is the very kind of reasoning that we're considering. We're asking ourselves whether it is possible to extrapolate from past to future, legitimately so relying on that kind of reasoning.
To justify our relying on that kind of reasoning would be going in a circle. So here I give a very brief review of the argument of the enquiry. I'm not going to go through this now in detail, but when you come to Hume's text, take a look at these slides and use them to inform your reading of these passages. That's a summary of the part. One argument where humour says that all factual inference is founded on experience.
It follows that all factual inference has to be based on an assumption of uniformity. The assumption that what has happened in the past is a guide to what will happen in the future. And then we get the proof that we have no ground for making that assumption.