 Mae bwysig, yn holliaeth ac mae'r cyfarfodyddar yn those ystod o'u drwpwn yn ein cyfarfodyddar. Mae'n uchwanigiaid iawn i'r carfodyddar nifer yn cael ei ffyrw. Yn y gwrs hyn, mae'r hyn yn cymryd yn ochr yn gymweithio ar gyfer cyffredinol ac cynnwysol. Felly, na fydd y ffordd y tro i'r ll wyfan, vaod i'r Percol 1, pwysig y Rydydd, of relations. And you might well wonder what on earth is going on there. We've seen that Hume starts off talking about association and how that gives rise to complex ideas, and then he sets out to give this taxonomy of the complex ideas. And then in the very next section he says, well let's start with relations, here are the different kinds of relations. And you might wonder is this just boring taxonomy or is there something else going on? Well as I'll explain to you now, there's quite a lot more going on. To understand this let's go back to John Locke. John Locke, as so often, is the source of things that feed into Hume's philosophy. So recall what John Locke was trying to do was explain how all our ideas could be explained as arriving from experience. And one of the things he wanted to do, particularly in book two of his essay concerning human understanding, was to go through all the various ideas showing how they could arise from experience. So Locke was very much in the business of taxonomising, listing all the various ideas we have showing how they can all be explained as arising from experience. So if you look through Locke you'll see that he draws a distinction between different categories of relation. What he's trying to do is look at all the various types of relation that there are. Well there's cause and effect relations, relations of time, relations of place and extension, identity and diversity, what he calls proportional relations. Proportional relations by the way include both what Hume calls degrees in quality and proportions in quantity or number. So it's kind of mathematical relations broadly speaking. He then says that there are lots of other types of relation. Indeed infinite other relations. For example there are natural relations such as father and son, brothers, countrymen. Just noticed by the way for future reference when Hume talks about a natural relation he doesn't mean what Locke means. When Hume talks about a natural relation he just means an associative relation. When we think of one thing as related to another it's because the idea of one of them naturally leads our thought to the idea of the other because they resemble each other, because they're close by, they're contiguous or because one cause is the other or is the cause of it. That's what Hume means by a natural relation, what Locke means by a natural relation is more or less a blood relation. And then there are instituted or voluntary relations, general, citizen, patron and client, constable, dictator. These are instituted relations, relations that come from social relations or politics etc. And then there are various moral relations. Okay, now let's think about Hume's taxonomy of relations in relation to Locke's. Well, Hume has a relation called contrariety where Locke has diversity. That seems to be something like a way of bringing negation into the whole picture. Locke talks about agreement or disagreement of ideas. Hume talks about resemblance. And we'll see that he thinks that resemblance enters into every relation. He doesn't actually explain why and it's somewhat mysterious to be frank. So when you read treatise 115 and you see this thing about resemblance coming into every relation and you might think that's rather strange. How's that? Well, it's not well explained and it's not clear what role Hume takes it to play. But it is quite intriguing that Locke talks about agreement and disagreement of ideas in very much the same way. Locke's agreement seems to be a general sort of logical glue rather than anything more specific. So there's quite a similarity between what Hume says about resemblance and what Locke says about agreement. Locke doesn't treat resemblance as a single type. He recognises all sorts of different kinds of resemblance and talks about them as different relations. So countrymen, those who were born in the same country, that's a kind of resemblance. And there are myriad resemblances. Whereas Hume wants to reduce them all to one general relation of resemblance. Now look at these two passages. Now these are quite well-known passages in Hume scholarship for the following reason. Norman Kemp Smith, very famous Hume scholar, wrote a major book in 1941, one of the few early 20th century works that's still worth reading on Hume. Kemp Smith famously made a speculation about Hume's philosophy. Kemp Smith wanted to say that Hume's philosophy is driven primarily by the moral theory. He saw Hume as influenced by Hutchison. Hutchison wanted to say that morality is ultimately derived from feeling, from sympathy, from our fellow feeling towards other people. That's where it comes from. And Kemp Smith wanted to say that Hume took over that insight and wanted to apply it to his philosophy generally. So when we make an inductive inference, for example, Hume says things that imply that that's somewhat similar to feeling. We see an A followed by a B again and again and again, C A again, we feel that a B is going to follow. So there's actually quite a big structural similarity between what Hume says about induction and what he says about morality. Kemp Smith speculated that it was actually the theory of morality that was driving the philosophy and that Hume had worked on book three of the treatise on morals before he wrote book one. Now, as evidence for that, Kemp Smith gave these examples. He said, notice, when Hume wants to give examples of causal relations, he gives relations that are morally pertinent. There we are. That gives evidence that what's really driving Hume's philosophy is the moral theory. Well, it's an interesting speculation. It's not particularly popular these days because for all sorts of reasons it just doesn't seem to hold up as a theory of the order in which things were done. But what I want to suggest is that there's a more interesting explanation. I mean, it is an intriguing fact that when Hume wants to give examples of causal relations, he doesn't give billiard balls, he gives moral relations. But suppose you look at these in the light of Locke's taxonomy. Remember, Locke had this proliferation of relations, including a whole load of what he called natural relations, blood relations, and instituted relations. And here is Hume saying all the relations of blood depend upon cause and effect. Right, so all blood relations are actually causal relations. The relation of cause and effect, we may observe to be the source of all the relations of interest and duty by which men influence each other in society and are placed in the ties of government and subordination. Okay, so all Locke's instituted relations are causal relations too. So what I'm suggesting is this. Hume got hold of Locke's taxonomy of relations, where Locke had a proliferation of relations of similarity, Hume puts them all under heading of resemblance, where Locke had blood relations and instituted relations, Locke puts them all under the heading of causation. And as a result, he's able to reduce all of Locke's proliferation of relations to seven categories. And there in Treaties 115, he spells out these categories. So he says all the types of relation there are, what he calls philosophical relations, that is relations as considered by philosophers, are resemblance, cause and effect, space and time, identity, contrariety, proportions in quantity, degrees in quality. Okay, so far what I've argued is that what Hume is doing here is taking Locke's taxonomy and shrinking it, reducing it to seven categories of relation. Why? What's going on here? Well, his motivation doesn't become clear until book one part three. Book one part three, right at the beginning, he draws a distinction between two different categories of relation. These are commonly called constant relations and inconstant. That's a term he does talk, use once, apparently referring to this distinction, so it's worth using that term. On the one hand, you've got relations that depend entirely on the ideas which we compare together. So resemblance, contrariety, degrees in quality, proportions in quantity or number. So the claim there is that if you take two things and compare them together, these relations between them, their resemblance or their contrariety or degrees in quality or proportions in quantity or number, those will depend purely on the things you're comparing together. On the other hand, there are three inconstant relations. Identity, relations of time and place, cause and effect. Now, the last two of those are fairly straightforward, right? Time and place, yes, of course, take one thing, take another thing, they could remain the same things and yet be in different relations of time and place. Causation, cause and effect. Well, we can think of anything causing anything. So whatever A and B might be, take those ideas, you could have those very same ideas and have one thing causing another or not causing. It wouldn't change their identity. But what about the notion of identity? That's a bit of a strange one to put here, you might think. How is it supposed that that relation can be changed without any change in the ideas? Well, Hume is here talking about identity over time. So think of coming across something today and then coming across something next week and wondering whether they're the same thing. The thought would be that you can perceive the thing now and have your idea of that thing. Next week you can perceive the other thing and have your idea of that and you can speculate whether they are or are not the same thing without actually changing those ideas. Okay. So you've got three, four constant relations, three inconstant relations. Here is the payoff. Hume wants to argue later in the treatise that certain things cannot be demonstrated, cannot be demonstratively proved, proved with certainty going purely from our ideas. One of them is the causal maxim, that every beginning of existence must have a cause. So that's in treatise 1-3-3. And he argues, well, since that doesn't include, isn't based on inconstant relations, it cannot be demonstrated. Only things that are based on constant relations can be demonstrated. Again, in book 3 of the treatise, the first section of that when he's talking about morality, as we've seen, he's going to argue that morality is not founded on reason. And as part of that he wants to say that moral distinctions cannot be demonstrated. So again he says they can't be demonstrated because they involve inconstant relations. They're not based purely on constant relations. Now he doesn't actually enunciate this principle as such but his use of it in those two passages seems pretty clearly to indicate that this is the thought that's driving him. We've got these seven relations, seven types of relation. We divide them between those that depend only on the ideas called those constant relations and those which depend on something else, you know, situation in time and place or whatever it might be. Well, only things that depend on the constant relations can possibly be demonstrated because they're the only things that depend only on the ideas, right? Seems plausible. And Hume uses it, as I say, to argue that the causal maxim can't be shown to be intuitively true. Therefore, incidentally it can't be demonstrated. And that moral relations cannot be demonstrated. Now sadly that's complete nonsense. It's a great shame but it just doesn't work. So let's look at some examples. Every mother is a parent. That's intuitively true, isn't it? Every mother is a parent. And yet, on Hume's conception, mother is a causal relation. Indeed, that seems plausible. It's a causal relation. Parent is a causal relation. So here we have a proposition that involves two causal relations. It doesn't mean it can't be demonstrated. Or anyone who's paternal grandparents have two sons has an uncle. Agreed? If your paternal grandparents have two sons, well, one of them must be your father. The other one's an uncle. So again, we've got a relation, we've got a proposition that can be demonstrated even though it involves causal relations. And then we've got one, I've put one at the top involving identity. If A equals B and B equals C, then A equals C. And transitivity of identity. Intuitively true. Anything that lies inside a small building lies inside a building. It involves the relation of contiguity. But nevertheless it can be demonstrated. So Hume's principle in the abstract sounds quite plausible, right? You think, well, the only way you can demonstrate something, a priori, is if it involves relations that are constant. That seems about right. But then when you start looking at examples, it falls apart. What's gone wrong? Well, I only know of one person in the literature who's actually discussed this in ways that I think are really illuminating. And that's Jonathan Bennett. Two works there. Incidentally, the website will contain links to all these various things. So if you want to chase them up, you're very welcome to do so. What Bennett suggests is that Hume is essentially confusing two different notions. And one of them is supervenience and one of them is analyticity. So very roughly supervenience is where the relation between two things depends on their individual properties. If you've given the properties of one thing and another thing, then the relation between them follows as a matter of necessity. Analyticity is different. That is, if you know about A and B, you've given your ideas of A and B, you can deduce the relation, you can see that it follows as a matter of the relations between the ideas. So that's related, if you like, to a prioricity. Follows from the meanings of the terms. So I'm using modern terms here for kind of the closest equivalents to what Hume seems to be talking about. Now I think Bennett is right that there is this confusion in Hume. I have an idea of what's gone wrong here. I think what Hume does is when he's talking about objects or ideas of objects, he gets muddled. Sometimes he's thinking about the properties of objects. Sometimes he's thinking about the properties of our ideas of objects. And since he's talking about issues of knowledge, it's very easy to conflate those two. And I think that's what happens here. He pushes the two together. He's talking at a very abstract level. He's not anchoring it with examples, and so he doesn't see the problem. But I think it's important when reading those early parts of the treatise to know that Hume has this target in mind in order to understand some of what's going on there. Now very briefly, fortunately, Hume doesn't actually rely very much on this dichotomy, only in the two cases that I've mentioned. Most of the time, his criterion for whether something's demonstrable or not is actually based on the conceivability principle of which I've given a couple of quotations there. To form a clear idea of anything is an undeniable argument for its possibility and is alone a refutation of any pretended demonstration against it. Whatever we conceive is possible, at least in a metaphysical sense, but wherever a demonstration takes place, the contrary is impossible and implies a contradiction. So notice, he's not here distinguishing between constant and inconstant relations. He's not relying on that at all. He's simply saying the criterion for something being demonstrable is that the opposite is impossible. And if you can clearly conceive of something, that shows it is possible. So that delimits the possible range of what can be demonstrated. So although I've been rather harsh on Hume's theory of relations, I've suggested that it's motivated by trying to draw a dichotomy for a reason that just doesn't work. Fortunately, it doesn't infect too much of Hume's philosophy. In the inquiry, by the way, the dichotomy makes no appearance at all. He relies on what is commonly known as Hume's fork, which is clearly based on the conceivability principle, the distinction between things that we can conceive and therefore are possible and things that we cannot conceive and tend therefore to be impossible.