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Okay. Let's now move on to Hume's theory of relations.

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Now this is another area where understanding humans potentially quite difficult and complex.

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Right at the beginning of the treatise in book one, Part one, Section five,

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we get a discussion of relations and you might well wonder what on earth is going on there.

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We've seen that. HUME starts off talking about association and how that gives rise to complex ideas.

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And then he sets out to give this taxonomy of the complex ideas.

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And then in the very next section, he says, Well, let's start with relations.

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Here are the different kinds of relations. And you might wonder, is this just boring taxonomy or is there something else going on?

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Well, as I'll explain to you now, there's quite a lot more going on.

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To understand this, let's go back to John Locke. John Locke, as so often is the source of things that feed into humans philosophy.

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So recall that what John Locke was trying to do was explain how all our ideas could be explained as arriving from experience.

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And one of the things he wanted to do, particularly in in book two of his essay concerning human understanding,

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was to go through all the various ideas showing how they could arise from experience.

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So Locke was very much in the business of taxonomy quizzing.

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Listing all the various ideas we have, showing how they can all be explained as arising from experience.

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So if you look through Locke, you'll see that he draws a distinction between different categories of relation.

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What he's trying to do is look at all the various types of relation that there are.

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Well, there's cause and effect relations. Relations of time.

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Relations of place and extension. Identity and diversity.

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What he calls proportional relations.

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Proportional relations, by the way, include both what HUME calls degrees in quality and proportions in quantity or number.

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So it's kind of mathematical relations, broadly speaking.

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He then says that there are lots of other types of relation in the infinite other relations,

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for example, that are natural relations, such as father and son, brothers, countrymen.

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Just noticed, by the way, for future reference, when HUME talks about a natural relation, he doesn't mean what Locke means.

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Okay. When HUME talks about a natural relation, he just means an associative relation that when we think of one thing as related to another,

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it's because the idea of one of them naturally leads our thought to the idea of the other.

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Because they resemble each other, because they're close by, they're contiguous, or because one causes the other, or is the cause of it.

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Okay. That's what he means by natural relation. What Locke means by a natural relation is more or less a blood relation.

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And then the institute, you know, voluntary relations, general citizen, patron and client, constable, dictator.

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These are instituted relations. Relations that come from social relations or politics, etc.

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And there are various moral relations. Okay.

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Now let's think about Hume's taxonomy of relations in relation to locks.

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Well. HUME has a relation called Contra Riot, where Locke has diversity.

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That seems to be something like a way of bringing negation into the whole picture.

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Locke talks about agreement or disagreement of ideas.

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HUME talks about resemblance, and we'll see that he thinks that resemblance enters into every relation.

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He doesn't actually explain why, and it's somewhat mysterious, to be frank.

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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.

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How is that? Well, it's not well explained, and it's not clear what role HUME takes it to play.

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But it is quite intriguing. The lock talks about agreement and disagreement of ideas in very much the same way.

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Locke's agreement seems to be a general sort of logical glue rather than anything more specific.

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So there's quite a similarity between what HUME says about resemblance and what Lock says about agreement.

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Locke doesn't treat resemblance as a single type.

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He recognises all sorts of different kinds of resemblance and talks about them as different relations.

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So countrymen, those who are born in the same country.

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That's a kind of resemblance. And there are myriad resemblances.

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Whereas HUME wants to reduce them all to one general relation of resemblance.

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Now look at these two passages. Now, these are quite well known passages in HUME Scholarship for the following reason.

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Norman Kent Smith, very famous HUME scholar, wrote a major book in 1941, one of the few early 20th century works that still worth reading on HUME.

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Kemp Smith famously made a speculation about Hume's philosophy.

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Kent Smith wanted to say that Hume's philosophy is driven primarily by the moral theory.

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He saw HUME as influenced by Hutcheson. Hutcheson wanted to say that morality is ultimately derived from feeling.

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From sympathy. From our fellow feeling towards other people.

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That's where it comes from. And Kim Smith wanted to say that HUME took over that insight and wanted to apply it to his philosophy generally.

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So when we when we make an inductive inference, for example, HUME says things that imply that that's somewhat different.

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Somewhat similar to feeling we see in a followed by a B again and again and again.

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See, I again, we feel that if he's going to follow.

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So there's actually quite a big structural similarity between what HUME says about induction and what he says about morality.

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Kemp Smith speculated that it was actually the theory of morality that was driving the philosophy

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and that HUME had worked on Book three of the Treatise on Morals before he wrote Book one.

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Now as evidence for that, Kemp Smith gave these examples.

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He said notice when he wants to give examples of causal relations.

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He gives relations that are morally pertinent. There we are.

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That gives evidence that what's really driving Hume's philosophy is the moral theory.

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Well, it's an interesting speculation. It's not particularly popular these days because for all sorts of reasons,

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it just doesn't seem to hold up as a theory of the order in which things were done.

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But what I want to suggest is that there's a more interesting explanation.

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I mean, it is an intriguing fact that when HUME wants to give examples of causal relations, he doesn't give billiard balls.

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He gives moral relations. But suppose you look at these in the light of Locke's taxonomy.

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Remember, Locke had this proliferation of relations,

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including a whole load of what he called natural relations, blood relations, and instituted relations.

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And here is HUME saying all the relations of blood depend upon cause and effect.

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Right. So all blood relations are actually causal relations. The relation of cause and effect.

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We may observe to be the source of all the relations of interest and duty by which men

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influence each other in society and are placed in the ties of government and subordination.

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Okay, so all Locke's instituted relations are causal relations to.

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So what I'm suggesting is this. HUME got hold of Locke's taxonomy of relations.

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Where LOC had a proliferation of relations of similarity.

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HUME puts them all under the heading of resemblance. Well, Locke had blood relations and instituted relations lock.

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HUME 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.

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And they're in Treatise 115. He spells out these categories.

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So he says all the types of relation there are what he calls philosophical relations,

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that is relations as considered by philosophers a resemblance, cause and effect, space and time identity.

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Contrasting proportions in quantity. Degrees in quality.

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Okay.

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So 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.

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Why? What's going on here? Well, his motivation doesn't become clear until book one, part three.

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But one part through right at the beginning, he draws a distinction between two different categories of relation.

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These are commonly called constant relations in constant.

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That's a term he does talk use once apparently referring to this distinction so it's it's worth using that term.

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On the one hand, you've got relations that depend entirely on the ideas which we compare together.

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So resemblance contour 80 degrees in quality proportions in quantity or number.

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So the claim there is that if you take two things and compare them together.

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These relations between them, their resemblance or their contrary royalty or degrees in quality or proportions in quantity or number.

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Those will depend purely on the things you're comparing together.

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On the other hand, there are three inconstant relations. Identity relations of time and place.

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Cause and effect. Now, the last two of those are fairly straightforward, right?

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Time and place. Yes, of course. Take one thing. Take another thing.

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They could remain the same things and yet be in different relations of time and place.

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Causation. Cause and effect. Well, we can think of anything causing anything.

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So whatever. And we might be. Take those ideas. You could have those very same ideas and have one thing causing another.

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Or not causing. It wouldn't change their identity. But what about the notion of identity?

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That's a bit of a strange one to put here, you might think.

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How come how is it suppose that that relation can be changed without any change in the ideas?

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Well, HUME is here talking about identity over time.

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So think of coming across something today.

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And then coming across something next week and wondering whether they're the same thing.

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And the thought would be that you can perceive the thing now and have your idea of that thing next week.

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You can perceive the other thing and have your idea of that.

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And you can speculate whether they are or are not the same thing without actually changing those ideas.

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Okay. So you've got three, four constant relations.

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Three in constant relations. Here is the payoff.

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Who wants to argue later in the treaties that certain things cannot be demonstrated, cannot be demonstratively proved, proved with certainty.

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Going purely from our ideas. One of them is the causal maxim that every beginning of existence must have a cause.

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So that's entreaties. One, three, three. And he argues well since that doesn't include isn't based on in constant on constant relations.

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It cannot be demonstrated. Only things that are based on constant relations can be demonstrated.

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Again in but one of three of the treaties, the first section of that, when he's talking about morality,

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as we've seen, he's going to argue that morality is not founded on reason.

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And as part of that, he wants to say that moral distinctions cannot be demonstrated.

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So again, he says they can't be demonstrated because they involve inconstant relations.

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They're not based purely on constant relations. Now he doesn't actually enunciate this principle as such,

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but his use of it in those two passages seems pretty clearly to indicate that this is the thought that's driving him.

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We've got these seven relations, seven types of relation. We divide them between those that depend only on the ideas.

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Call those constant relations and those which depend on something else, you know, situation in time and place or whatever it might be.

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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.

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Right. Seems plausible. And he uses it, as I say, to to argue that the causal maxim can't be shown to be intuitively true.

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Therefore, incidentally, it can't be demonstrated. And that moral relations cannot be demonstrated.

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Now. Sadly, that's complete nonsense. It's a great shame, but it just doesn't work.

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So let's look at some examples. Every mother is a parent.

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That's intuitively true, isn't it? Every mother is a parent.

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And yet on Hume's conception, mother is a causal relation.

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Indeed, that seems plausible. It's the causal relation. Parent is a causal relation.

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So here we have a proposition that involves two causal relations.

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It doesn't mean it can't be demonstrated. Or anyone whose paternal grandparents have two sons has an uncle.

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Great. If your paternal grandparents have two sons, well, one of them must be your father.

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The other one's an uncle. So again, we've got a relation.

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We've got a proposition that can be demonstrated, even though it involves causal relations.

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And then we've got one I've put one at the top involving identity.

140
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If A equals B and B equal C, then I equals C and transitivity of identity.

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Intuitively true. Anything that lies inside a small building lies inside a building.

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It involves the relation of contiguity. But nevertheless, it can be demonstrated.

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So huge principal in the abstract.

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Sounds quite plausible, right? You think? Well, the only way you can demonstrate something a priori is if it involves relations that are constant.

145
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Hmm. That seems about right. But then when you start looking at examples, it falls apart.

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What's gone wrong?

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Well, I only know of one person in the literature who's actually discussed this, you know, in ways that I think are really illuminating.

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And that's Jonathan Bennett. Two works there.

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Incidentally, the website will contain links to all these various things.

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So if you want to chase them up, you're very welcome to do so.

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What Bennett suggests is, is that HUME is essentially confusing two different notions.

152
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And one of them is super vengeance and one of them is Analytic City.

153
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So very roughly, super vengeance is where the relation between two things depends on their individual properties.

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If you're given the properties of one thing and another thing, then the relation between them follows as a matter of necessity.

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Analysis city is different. That is, if you know about A and B, you're given your ideas of A and B, you can deduce the relation.

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You can see that it follows as a matter of the relations between the ideas.

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So that's related, if you like, to a prior essity follows from the meanings of the terms.

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So I'm using modern terms here for kind of the closest equivalent to what HUME seems to be talking about.

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Now, I think Bennett is right that there is this confusion in whom I have an idea of what's gone wrong here.

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I think what HUME does is when he's talking about objects or ideas of objects, he gets muddled.

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Sometimes he's thinking about the properties of objects. Sometimes he's thinking about the properties of our ideas of objects.

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And since he's talking about issues of knowledge, it's very easy to conflate those two.

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And I think that's what happens here. He pushes the two together.

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He's talking at a very abstract level. He's not anchoring it with examples.

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And so he doesn't see the problem. But I think it's important when reading those early parts of the treaties to know that

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HUME has this target in mind in order to understand some of what's going on there.

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Now very briefly, fortunately, HUME doesn't actually rely very much on this dichotomy only in the two cases that I've mentioned.

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Most of the time, his criterion for whether something is demonstrable or not is actually based

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on the conceive ability principle of which I've given a couple of quotations

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there to form a clear idea of anything is an undeniable argument for its

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possibility and is alone a refutation of any pretended demonstration against it.

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Whatever we conceive is possible, at least in the metaphysical sense.

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But wherever a demonstration takes place, the contrary is impossible and implies a contradiction.

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So notice he's not here distinguishing between constant and inconstant relations.

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He's not relying on that at all. He's simply saying the criterion for something being demonstrable is that the opposite is impossible.

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And if you can clearly conceive of something that shows it is possible so that the limits, the possible range of what can be demonstrated.

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So although I've been rather harsh on Hume's theory of relations,

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I've suggested that it's motivated by trying to draw a dichotomy for a reason that just doesn't work.

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Fortunately, it doesn't infect too much of Hume's philosophy in the inquiry.

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By the way, the dichotomy makes no appearance at all.

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He relies on what he's commonly known as Hume's fork, which is clearly based on the conceive ability principle,

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the distinction between things that we can conceive and therefore are possible,

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and things that we cannot conceive and tend therefore to be impossible.