In Our Time - Bertrand Russell

Episode Date: December 6, 2012

Melvyn Bragg and his guests discuss the influential British philosopher Bertrand Russell. Born in 1872 into an aristocratic family, Russell is widely regarded as one of the founders of Analytic philosophy, which is today the dominant philosophical tradition in the English-speaking world. In his important book The Principles of Mathematics, he sought to reduce mathematics to logic. Its revolutionary ideas include Russell's Paradox, a problem which inspired Ludwig Wittgenstein to pursue philosophy. Russell's most significant and famous idea, the theory of descriptions, had profound consequences for the discipline.In addition to his academic work, Russell played an active role in many social and political campaigns. He supported women's suffrage, was imprisoned for his pacifism during World War I and was a founder of the Campaign for Nuclear Disarmament. He wrote a number of books aimed at the general public, including The History of Western Philosophy which became enormously popular, and in 1950 he was awarded the Nobel Prize in Literature. Russell's many appearances on the BBC also helped to promote the public understanding of ideas.With: AC Grayling Master of the New College of the Humanities and a Supernumerary Fellow of St Anne's College, OxfordMike Beaney Professor of Philosophy at the University of York Hilary Greaves Lecturer in Philosophy and Fellow of Somerville College, Oxford Producer: Victoria Brignell.

Thank you for downloading this episode of In Our Time, for more details about In Our Time, and for our terms of use, please go to BBC.co.com.uk slash Radio 4. I hope you enjoy the programme. Hello, on the last day of the year 1900, an ecstatic British academic, wrote to a friend, I invented a new subject, which turned out to be all mathematics for the first time treated in its essence. The academic was Bertrand Russell, and he was referring to the draft of his book, The Principles of Mathematics, which he just completed. it. In this work, Russell sought to reduce mathematics to logic, and later he was to describe

it as the highest point of his life, in his words, an intellectual honeymoon, such as I've never experienced before or since. Bertrand Russell's impact on philosophy was immense and far-reaching. He was a key founder of analytic philosophy, today the dominant philosophical tradition in the English-speaking world. His theory of descriptions is one of the most famous and important ideas in 20th century philosophy, but his influence extended beyond academia. His many of appearances on the BBC made him a well-known figure, and he wrote several books aimed successfully at the general public. With me to discuss the ideas in life, Burton and Russell, a Professor A.C. Grayling, Master of the New College of the Humanities, and a supernumerary fellow of St. Hans

College, Oxford. Mike Beanie, Professor of Philosophy at the University of York, and Hilary Graves, lecturer in philosophy and fellow of Somerville College, Oxford. Anthony Grayling, Virgin Russell was born in 1872 into an aristocratic family. Can you give us something of his background and his childhood. Yes, he was a grandson of Lord John Russell, the man who saw the 1832 reform bill through Parliament, which was the beginning of partial democratisation of our Parliament. And his father and mother died when he was very young,

so he was brought up by his grandparents in Pembroke Lodge in Richmond Park of the Grace and Favour House that Queen Victoria gave to his grandfather. His grandfather died early too, so actually he was brought up by his rather puritanical Scottish grandmother and that had a great influence on him really. It meant that for quite a large part of the early half of his adult life, he was much under the influence of this puritan outlook. He had a brother seven years older than himself, Frank, who became the second Earl Russell, and Frank was an influence too because very importantly he was the first person to introduce

Bertrand Russell himself to mathematics. And was, are we talking about a lone childhood. Basically, are we talking about something in his childhood that impacted on his later work? Oh, yes, very much. It was a very lonely childhood. He wrote in his autobiography that although he loved the, the Park, Richmond Park and the flowers that he saw blooming every spring, nevertheless, he felt acutely this loneliness, living in a household of very, very much older people. His brother had gone away to school, he himself remained at home. And it wasn't until he was in his late teens that he was put in amongst other children, really, when he went off to a crammer. Why didn't they send him to school?

I think he was rather, seemed to them rather sensitive, rather intellectual youth and not a particularly sporty one. His brother was a much more robust character. He described as a significant moment in his life his first encounter with Euclidean geometry. That's right. This happened at the age of 11 and he was introduced to it by his brother Frank. And he was very puzzled by the fact that he was obliged to accept certain axioms without them being proved. And he asked his brother about this. He said, well, why can't we prove the basis of what we're doing here? And his brother said to him, nope, we've just got to accept them, otherwise we can't get on.

The other important thing about his introduction to geometry was that his brother told him that the fifth proposition of Euclid was one that people found particularly difficult, and Bertrand himself didn't find it difficult. And he said in his autobiography, this was the first indication to me that I might have some intelligence. Mike Beanie, he became a mathematics undergrad in Cambridge in 1890. mathematics, but then he focused on philosophy. Can you take us through the early Cambridge Korea? Yeah, so he studied mathematics for about three years and then he switched to do moral sciences. And at the time, what was dominant in Britain, certainly in the last two decades

of the 19th century, was a movement called British Idealism. And that was the tradition which Russell first worked in philosophy. So idealism is the view that the relevant, the realm of ideas or the mental and physical world is somehow more fundamental than the other realm, so in particular the material or physical world. And so idealism is often opposed to materialism, but actually what Russell gradually moved towards with a more realist view. And the realist is someone who believes that a particular object or realm of objects exists independently of us. If I wanted to draw a contrast between them, one could say that if the idealist in some broad sense thinks that the world is somehow shaped,

or determined by the mind, than the realist of someone who thinks that the world exists independently always. He struck up a friendship with G.E. Moore and then met Italian philosopher, wasn't it? Pina. How did these influence him? He was obviously open to influences, very strongly, wasn't it? Absolutely. So Moore was a year younger than Russell

and had actually started doing philosophy straight away rather than having first studied mathematics. And Russell himself said that, in his rebellion against British idealism, it was more who led the way. And I think what more particularly disliked about British idealism, or idealism in general, was the sceptical implications that it had. So if you think of the world as somehow mediated through our ideas or you think of the world as somehow shaped or formed by our mind,

then you think, well, how do I know what the world's really like? How do I know that you and I actually see the world in the same way? So it looks like lots of sceptical implications follow if you're an idealist. and more in particular didn't like that. In fact, he spent most of his life trying to refute skepticism. And Russell also took that on board. Anthony's mentioned his love of Euclidean geometry.

I mean, if you're wanting to find certainty anywhere, then the obvious place to look is mathematics. But at the same time, according to, at least as Russell read idealism, mathematics is full of contradictions in inconsistencies. And in fact, his first work was, on the foundations of geometry. Hilary Graves, he takes the idea of mathematics on here,

two important mathematical works, the principles of mathematics published in 1903, and Principia Mathematica published about a decade later. What was he aiming to achieve in these books? Is it possible to bring them both together? Sure, I mean, they're definitely both part of the same project. What's bothering Russell here is the issue that Anthony already mentioned in the context of Russell's first encounter with geometry.

So Russell looks at these fundamental, axioms that are taken as the starting points for geometry. And he says, well, that's fine. I can see how if you accept that these things are true, then the rest of geometry follows from them. But how do we know that those axioms are true? Can you give us an example of the basic axioms you're always looking at? Sure.

I mean, they're just things like for any two points of space. There exists a straight line that connects those two points. And Russell's thinking, well, you can wave your hands and say that intuitively, you can see that these things are true. But really, I want to do better than that. This is mathematics. We're looking for certainty. I want proof here.

And that sort of proof is not something that geometry can supply. And Russell then has the same experience when he goes on to look at arithmetic. So the arithmetic of Russell's time starts from the so-called piano axioms. So they are supposed to take as basic things like for any natural number X, X plus one is also a natural number. And again, Russell's thinking, okay, I can see how if you accept those things as basic, we can get the rest of arithmetic therefrom. but how can we prove that those basic things are true? And Russell's response to this is to say,

okay, I'm going to try not taking the fundamental axioms of the various branches of mathematics as basic. I'm going to try giving definitions of them in purely logical terms. So the listeners might be surprised here that he took on 1 plus 1 equals 2 and examined that. Indeed, well, this is to do with the high degree of certainty that Russell wants. He thinks it's not good enough just to say,

intuitively this seems obvious and we'll see that this fear is justified when we get onto the later parts of this story but it's also justified by actual controversies that are going on in real mathematics at Russell's time so he has real cases of 19th century mathematicians you get two mathematicians around a table and they sit there and they look at the same proof

that somebody's offered and mathematician number one says well intuitively this looks to me like a valid proof I accept it. Mathematician number two says well I'm sorry to disagree with you but I have different intuitions I don't think it is valid and Russell's thought is there really should be some rigorous tribunal we could appeal to here if we're just taking what seems intuitively obvious to us as our foundation for mathematics then we have no tribunal to appeal to when different people have different intuitions given that the Russell project was to turn mathematics into logic and given that one plus one equals two

is something that everybody listens to the program we'll intuitively think is right how did you tackle that to turn it into logic right So Russell thinks that if he can give a definition of the number one and a definition of the operation plus one, then he'll be able to prove using the rules of logic alone that one plus one really does equal to. You'll no longer have to accept it as basic. So Russell gives definitions of the numbers using things he calls classes,

and this enables him to complete this project. I want to ask at this stage, something that Mike mentioned, that being influenced by ideas, when he went to Cambridge, which would seem to be the right thing for him to be influenced by when they go to university, especially from such a restricted background.

He turned against it towards an extreme form of realism, influenced by the Austrian philosopher I read here, Alexius Mainong. So why did he believe that? What did he find there? He had an introduction to it from my thought. He did indeed go from one extreme to the other, from idealism to a very, very extreme form of realism premised on the idea

that if things we say seem meaningful to us it must be because the expressions in what we say that refer to things actually have something to refer to if you think that nouns the meaning of a noun is the object that it denotes

then since you can talk about unicorns and fairies there must in some sense be unicorns and fairies in order for that term to denote them so if I say fairies don't exist then in some sense there must be fairies in order for me to be able to say of them that they don't exist. This is a very, very extreme form of realism. This was Meinong's theory. And Meinong said, well, obviously, of course, we don't

really want there to be fairies jumping about at the bottom of the garden. So what we have to think of in their case is that they don't fully exist, but they subsist. There's a kind of second-class existence that they have which enables us to talk about them. And that was the view that Russell adopted. And very amusingly, a much later philosopher, W. V. Quine, described this as Maynong's ontological slum, meaning that the universe was crammed with objects, subsisting objects, just in virtue of the fact that we could talk about them. Mike Beanie, he, Brussels moving through different ideas at this early stage in his life. Another fashionable idea at the time is known as monism, which was associated with F.H. Bradley

at Oxford across the country. What's monism and why did Russell argue against it? So monism is the view that there's only one ultimate reality, and it's particularly characteristic of Bradley's idealism. Bradley thought that everything was interrelated in one whole, and whenever we try to kind of conceptualise something or separate out something in thought, we kind of

distort it. And Russell thought that in the case of asymmetrical relationships, you couldn't actually reduce them away in the way that Bradley thought. So he came to the conclusion, this is another illustration of what Anthony Greding thought, that relations had to be understood as separately existing entities, so that when we talk

about X being larger than Y, There's X, there's Y, they're independent, and then there's a relation that's also independent. So he adopted a kind of form of pluralism, which was in opposition to Bradley's form of monism. Do you, did, as it were, is this some sort of contest going on for the high-ground of philosophy? Did Russell's view prevail at that time?

I think it took a while for it to prevail, but I think the most important thing that happened, you mentioned it earlier, I should say a little bit about that, is Russell's meeting with piano, the Italian mathematician in logic in logician in 1900. So he attended a Congress in Rome. And what piano taught him was the new logic

that he and a German mathematician called Gottlob Frege had started to develop. And you mentioned your introductory remarks that Russell later said this was the high point in his intellectual life. And I think what Russell realized was this new form of logic, which was far more powerful than any logic that had hitherto been available, gave him the resources to solve some of the contradictions problems that he'd seen in idealism. And it's from that point on that he started to use the new logic

to try and solve these problems. Now, Hilary Grosier, we're turning to classes and to Russell paradoxes here, so here we go. Bertrand Russell wanted to reduce mathematics by logic using something he called classes. Can you explain what he meant by classes and why this was important? Sure. So classes are the sort of things

that modern mathematicians use the word set for. So intuitively speaking, the idea is, for any collection of objects that you care to name, there's going to be a set whose members are precisely those objects. Bottles. Yeah, for instance. So your bottle and your cup, there's a set that contains just those two objects and no more.

If people are objects too, then there's a set that contains you, me, Mike and Anthony, and nothing else. In this theory of sets, sets themselves count as objects. So this is important for Russell. So we can now iterate the process. We can consider higher-level sets, which themselves have sets as members.

So I could form, for example, the set that has precisely one member, and here's the member that it has, the set that contains your bottle and nothing else. So Russell's idea is, okay, let's try identifying numbers, 0-1-2, etc, with particular classes. And maybe this will allow us to execute the logist programme we were talking about earlier. So Russell says in the case of the number three, for instance, I'm going to define the number three to be a particular set. Here's the set we're going to define it as. Ready? So it's going to be a set whose members are themselves sets.

And the sets we're talking about are sets containing precisely three members. So one member of the number three would be the set containing you and Mike and Anthony and nothing else. Another member of the number three would be the set containing, the set that contains your bottle and nothing else, the set that contains your cup and nothing else, and the set that contains your cup and your bottle and nothing else. So the number three on this picture is a set with infinitely many members and every member is a three-membered set.

And the point of all this is, if you've given an explicit definition of the number three in that way, you can then give a corresponding definition of the number two and of the operation plus, and you can use these definitions plus the rules of logic to prove that, for example, 2 plus 3 equals 5,

the kind of thing that our mathematicians normally have to just take for granted. Mike, can you, before you come in, I think that one or two of our listeners might be saying to themselves, so where does this lead to?

I just want to add one thing to tie back to the idea that mathematics is logic. So the key idea is that we actually make use of logical concepts. So if you take the concept of being, identical with itself, which is often taken as a logical concept, and we also think of negation as a logical

concept, so we have the concept not identical with itself. So then we consider, what is it... I'm sorry to be so lumping about all this, but could you give us an example? Well, so we consider the concept not identical with itself, and nothing can be not identical with itself. Everything is at least identical with itself, okay? So we consider

the set of things that are not identical with itself, and that's nothing. We call it the null set. So essentially that null set is being defined in terms of these logical concepts, not identical with itself. Now we've got our first object, the null set, defined purely logically, this is the idea. We have one object, we can then very roughly say that the number one is, as it were, equivalent if you like, to that.

We've got our first object, so we can use that object defined logically to define the number one. We then have two objects, zero and one, which we can use to define number two, and so on. So that's the idea of the logicism. Well, to get back to your question about what's going on here and why you use these logical notions. I suppose one thing one could say is that intuitively the idea of a group, of a set of objects, is much, much clearer and more accessible than the notion of a number. If you ask somebody, what is the number three or what is the word three denote? You have a much more complicated task than using this more intuitive notion. And then you're using that intuitive notion as part

of a definition of number which doesn't involve any reference to numbers. So you're not using any arithmetical concepts at all, but you're using logical concepts and explicating, explaining what the arithmetical concepts are in logical terms. Do you want to add to this? Sure, no. I mean, I just endorse all those comments. I mean, I was telling you the story about which object the number three ends up being on this story so that we can see where we end up at the end of the day.

But Mike and Antony are exactly right. It's a crucial part of the story for the purposes of Russell's project that there is another way of getting there that starts from just logical notions. So we don't have the notion of number sitting there undefined at the very foundations anymore. Anthony Grayling, Russell attempted to reduce mathematical logic. We've been, or you've been talking about that, you three. Then something came up called Russell's paradox, which caused him a lot of problems and lots of other people's problems,

a man to repudiate a lifetime's work, another great philosopher and son. Can you tell us what Russell's paradoxes? was and then the three of you discuss it. Basically, the idea is that Russell, using the notion of a class, which as Hillary pointed out, is now referred

to as a set, but using this notion, he came across the difficulty that some classes are members of themselves. For example, a class is, in being a class, is a member of the class of classes, and there are some classes which are not members of themselves.

So, for example, if you had a class of, let us say, horses. Horses. a horse is not a class. So you get this distinction between kinds of classes or types of classes. And he came across the puzzle that what would you say of a class which was not a member of itself? If it weren't, if you had a class of all those classes that were not members of themselves, would that class be a member of itself or not?

What does a class not being member of itself actually mean? Could you give us an illustration? Well, if we fast forward, let me give you a very clear illustration, which is that you might perhaps arbitrarily define classes as occupying different sort of levels. And you might say that a level two class is only allowed to have level one classes as members. It can't be a member of itself. I mean, a very good example of a class that would be a member of itself is a class, which is a member of the class of classes.

And in virtue of being a class, it would be a member of the class of classes. The paradox that he came across is very similar to this. It's not exactly the same, so one must be misled by the analogy, but it's a little bit like this because it makes it easier to understand. Supposing you have a barber in a mountain village who shaves just those men, all and only those men who don't shave themselves. So if a man in that village doesn't shave himself, he's shaved by the barber. Now our puzzle is, does the barber shave himself or not?

Because if he doesn't, then he's part of the group who doesn't shave themselves and who's shaved by the barber. So if he doesn't shave himself, then he does. And if he does shave himself, then he doesn't. So this is the paradox. If he shaves all and only the men who shave themselves, then he both does and doesn't shave himself. And this is an analogy of the problem that Russell detected,

which is, what happens if you have a class of classes which are not members of themselves? If it isn't a member of itself, then by definition it is. And if it is, then it isn't. And that's the paradox. Mike Beanie, can you take that into the effect it had on others, particularly on the German philosopher Gottlob Frege? Right, so Gottlob Frege.

So Gottlieg was a logist 20 years or so before Bertrand Russell, so we often think him as the first logist. He was logistic about arithmetic rather than geometry. And he certainly thought before Russell that you could define the numbers in terms of, he called them extensions of concepts, which are essentially sets or classes. and for Bertrand Russell, sorry, for Gottlob Fregear,

Russell Paddock was in fact a serious problem because in his account, just like Russell realised, he did want to talk about classes being members of themselves. This is how he used to generate the natural number sequence to find his classes. So Bertrand Russell wrote to Frege in 1902 just as Frege was publishing the second volume of his great work, The Basic Laws of Arithmetic,

when he was hoping to show that, rhythmity could be reduced to logic. And Frege immediately realized that this was devastating. He wrote back and said, oh, the foundations of my project completely shattered. I don't know what to do. He tried in an appendix to the second volume of his work to respond to it, but in fact we now know that that doesn't work.

And in fact, Fregear ended up having to give up his logic and he concentrated on developing his logical and philosophical ideas instead and left it to Russell to try and resolve the paradox. Russell blew up his own work as well as Frege's work, but was it resolved, Hillary Greaves? Was it resolved? So Russell himself went on. So in 1903 he has principles of mathematics.

This is his first attempt at logicism, but this is the version that falls to the Russell paradox for precisely the same reasons, more or less, that Frege's version of logicism falls to the Russell paradox. Russell's response was somewhat more robust than Frege's. He said, okay, we've obviously got a serious problem here. Our system is infected with paradox at the very foundation

so clearly we can't reduce arithmetic to logic in the particular way we've been trying to so far. But maybe we can start again and do it in a more careful way that we'll avoid this paradox. So this is what Russell spends most of the next 10 years of his life doing, rewriting the Logistic project on more secure foundations. And does he succeed? Yes and no.

Silly me not to realise that. What were the secure foundations that he thought he'd found? So Russell developed something that he calls type theory. And here the idea is he takes a step back and looks at the Russell paradox and tries to arrive at a diagnosis of how we managed to end up with a paradox here. And Russell's thought is, okay, the reason we've got this paradox is that in the, let's call it, naive set theory that we've been using so far, we have permitted a certain kind of self-reference.

So we started talking about the class of all classes that aren't members of themselves. And Russell thinks, okay, the reason we've incurred a problem is that when we do that, in some sense, by saying the class of all classes that aren't members of themselves, we're presupposing that all the classes are already there laid out. But then we're using that notion to define another class, the class of all classes that aren't members of themselves,

and we want it to be the case that that new class we've just defined, itself ends up being a member of the collection that was supposed to be there in the first place. So Russell thinks this is where we've gone wrong. What we need to do is write down a foundational theory that forbids that kind of self-reference. And if we can do that, we'll rebuild arithmetic based on these new foundations.

And that's what he proceeds to do with his theory of types. So I'll add one thing just very quickly. So Frege thought that one could, talk very naively, if you like, about all objects where this includes classes as well as everyday objects. And one thing that the theory of types suggest is that actually we need to sort of have a hierarchy of objects. So there's ground level objects, there's classes of those objects, there's classes of those objects, and you can't treat classes higher up as somehow members of classes low down. So that makes us think that actually the world of objects

is actually more structured and complicated than we originally thought. And I think this has been quite influential in Flossi since, that we can't just think there's a simple domain of all objects, but we have to actually try and sort out what kinds of objects they are and what their relationships are. Let's turn to the theory of descriptions, which is arguably Russell's most famous idea, Anthony Grayling. Can you explain what that is? It's a theory that comes out of the early commitment Russell made to the idea that the meaning of a word is the object it denotes. This was what he acquired from Meinong's view about the nature of meaning. It's not a very good theory of meaning by the way, but it prompted this rather interesting attempt to solve a difficulty.

And the difficulty is the over-rich universe of things that you get if every meaningful expression must have something out there that it denotes. So what Russell did was to say, actually, most of the words that we think of as denoting or naming objects in the world are not really denoting expressions. they're really disguised descriptions of those things. And there are only two, or perhaps if you take the plurals of them, four words that directly denote. And these two words are the demonstrative pronouns, this and that. And the reason why they are guaranteed to refer to something is that whenever you use a demonstrative pronoun,

as you get from the actual label of it, you're demonstrating, you're pointing at the thing that you're talking about. This is a glass of water or that is a microphone. all the other expressions, all the other nouns and names, disappear when you look at the underlying logical structure of the sentence in question. The example that he used was, The present King of France is bald. Now, supposing there not to be a King of France at present, if you said the present King of France is bored,

you feel that because there isn't a King of France, that sentence must be false. But in what way is it false? Well, first one has to remind oneself of the fact that what Russell wants, was that our language like our logic should be, in the technical term, bivalent. That is, have only two truth values, true and false. And if it isn't true, then it's false. If it isn't false, then it's true. And in the case of a sentence like the present king of France is bald, it seems a bit difficult to know how to explain its falsity, given that it looks a bit like, you know,

a complex question. You can't say either yes or no. You've got to unravel some implications or presuppositions anyway of that question. What he did, therefore, was to say, A sentence like the present King of France is bored is actually three sentences when you dig down into its underlying form. And the three sentences are, there is a King of France. Anything whatever which has the property of being King of France is identical to that thing. And that rather complicated little utterance takes care of the definite article, the which seems to imply uniqueness.

And the third one is, whatever that thing is, it is bored. So you have, there is a King of France, anything else that King of France is identical with that thing, and that thing is bald. And that is the theory of descriptions. It shows that the apparent subject expression in a sentence is, in fact, a description. Now, the example I've given you, the present King of France, that is a description. If I were to say Louis, meaning the person who's King of France, is bald, then it would turn out that Louis, an apparent name, can be analyzed into the is something X such that X has the property of being Louie, anything whatever that has that property is identical with that thing, and that thing is bald.

Mike Beeney, how important was this in philosophy in general? Okay, so just taking out of them. What was really crucial in the theory of descriptions was the contrast that then opens out between grammatical form and logical form. So it looks like the present king of France is bored as a simple subject-predicate proposition, saying of something that it has a property, but Russell's suggesting that actually it a far more complex logical form. It's actually made up, as Anthony says, of three sentences.

Now, this was immensely important. In a sense, this idea can be generalized. So we can take a lot of sentences that look as if they're about one thing and say, well, actually, they're not. So here's another example to illustrate the idea. So I might say, my wife has three children. We understand what that means.

You know who my wife is, perhaps. And you know what it is to have three children. Now you compare that sentence, which is straightforward, I think, to understand, with the average woman in York, let's say, has 2.2 children. Now, there is no such person as the average woman in York.

Maybe a BBC documentary might try and find some such person, but even if you were, there's no way that such a person would have 2.2 children. So when we say something like the average woman has 2.2 children, what we're actually saying is something much more complicated, namely, if you count up

the number of women in York, and you count up the number of all their children, and you divide the latter by the former, you get the answer 2.2. So, We can analyse a sentence, in other words, in such a way that we reveal, as a world, what we're really committed to. There are people living in York, and we can talk about the average woman as a kind of, and this is the term that Russell started to use, a kind of logical fiction or logical construction out of those individual people. Another example might be we talk about committees.

The committee made a certain decision. But of course, a committee as such isn't an entity that makes decisions. It's the individual members of a committee. So the full analysis of, say, a statement such as a committee made a certain decision, is this is what happened at the individual level. And that, I think, opens up a tremendous project of trying to understand what the various sentences that we use mean. Hilary Graves, Russell also wrote about knowledge. Would you tell us about the distinction he made between different types of knowledge? Sure.

So in the first instance, we have a distinction in the background between two ways in which we use the word knowledge in English. So on the one hand, I can know an object, I can know my brother or your cup of water. On the other hand, I can know truths, I can know that this table has a great op and so on. So Russell is talking specifically about the first category, knowledge of objects. And he wants to probe further the various ways in which we can have knowledge of objects. One of the things he's reacting against is an idea that he takes the idealist to hold to, which is the idea that really, in order to know anyone objects, you would have to know literally all the truth there are about that object.

So on this account, as Russell understands it, I can't really say that I know you, unless I know not only what you look like, but also what your bank account number is and who your paternal grandfather was and so on. So clearly Russell's thinking, well, this is going to lead to the consequence that we don't actually know any object at all.

That can't be the full story. What can we say instead? So his idea is, okay, there are two ways that we can know an object that are less demanding than that. the first way applies to objects that we've come into more or less direct contact with. So at a first pass, he would say that I know you by acquaintance because I've met you. But then he thinks, well, there also seems to be a sense in which we know other objects that are more remote from us in the universe and maybe ones that we haven't come into any direct contact with.

So for Russell, an example of this might be, I know David Cameron. But then he thinks, well, hang on, I haven't met David Cameron. so how does this work? And his account of how this works draws on his theory of description. So his idea is, well, sometimes I'm in the position of knowing a certain truth. And the relevant truth here is going to be the truth that one and only one object is the present Prime Minister of Great Britain. So Russell's thought is, okay, if I know that truth and if in fact, whether I know it or not, David Cameron happens to be the object that satisfies that description,

then we'll say that I know David Cameron by description, even though I don't know him by acquaintance. And acquaintance is the direct contact way of knowing objects. So Russell thinks that this distinction has wide-ranging implications, both for the theory of knowledge, the theory of how we know truths, and for the theory of how our words get to refer to items out there in the world. And Anthony Grohling. And because he was an empiricist, he wanted to establish that all the things that we know by description

can ultimately be traced back to some things that we know by acquaintance. And this is a very, very important point for him, because despite the fact that he changed his mind and changed his views about how you work out a theory to this effect, right the way through his philosophical career, he was very anxious to show how science, natural science, can ultimately be based on empirical foundations, how you could trace back all the things that we know by description

to things that we know by acquaintance. Can we talk about Russell and language and the influence he had on language, more specifically than we have. Do you want to start with that, Mike? Mike Beeney. Yes, so the theory of descriptions, I think, is pretty much a basic topic in the philosophy of language. So if someone's studying the philosophy of language, they perhaps start with Frege's famous distinction between sense and reference, but then the theory of descriptions is often seen as one of the most important works in philosophy of language. And I think subsequent to Russell, people start to question whether Russell offers an adequate account of that.

So as Anthony said, what's sort of important in the theory of descriptions is that you're saying that there's an important difference between names that stand for objects, the meaning of a name is the object that stands for, and definite descriptions which are sort of analyzed away into more complicated form. And so there's this fundamental distinction between names and definite descriptions, but along comes other philosophers, and most notably Peter Strawson, writing in 1950, and says, well, hold on a minute, we have to recognize that actually, names and definite descriptions in many ways function the same way. They both seek to refer to something. So what Anthony is identified as the first two sentences in a proper analysis of the present King of Francis Board is actually sort of take for granted. It's presupposed rather than something

that we're actually asserting when we say that the President King of Francis Ball. And the most important thing is that we're identifying, we're using the definite description to pick out an object and then saying something about it. So Stawson comes along later and says, well, I don't buy this distinction that you're making out between names and definite descriptions.

So it starts up a whole discussion about the relationship between those two kinds of expressions. Hilary Grimes. Well, I think we can usefully identify three rather distinct ways in which Russell's theory of descriptions was influential. So, I mean, the first one is, as we've said, it's still accepted today. We now teach it to our first-year students

as basically the right way to understand sentences that start with the word the. The second point also we've already seen, Mike mentioned that Russell's, approach to the theory of descriptions introduced some new tools which then had applications very much more widely within philosophy

of language. So we saw the distinction between grammatical form and logical form and Russell pointing out the way in which if you don't pay attention to this, you will be led astray. But then the more broad methodological point is Russell's approach to the theory of descriptions is widely

regarded as an absolute paradigm of what we now call analytic philosophy which Russell more or less invented. So the idea here is we are definitely still interested in the big questions. So as with Russell's theory of descriptions, there one of the main motivations was, let's try and get clear on whether there's any sense in which fairies exist or whether, on the other hand, we can get away without saying they exist at all. We're still interested in those matters that are themselves beyond the domain of language.

So it's certainly not the case that we're just talking about words. On the other hand, Russell's approach to descriptions illustrates the fact that if we don't pay very careful attention to how language works, we will be led astray in our thinking about those non-linguistic questions. So that combination of a focus on the big questions with approaching them via careful attention to language very much characterises the creed of 20th and indeed 21st century analytic philosophy. But lots of people look to Russell as the originator and the model for this new method.

That's right. And very important philosophical ideas have been, part of their importance in the reactions that they provoke, the disagreements they provoke. For example, Ludwig Wittgenstein, who had been a pupil of Russell's before the First World War in Cambridge, in his later philosophy, Vickenstein's later philosophy, reacted very sharply to the idea that language has underlying logical structure, which requires analysis. Instead, he thought that meanings lie in the surface of language and in the uses in particular that we make of them, and that we mislead ourselves. In fact, if we think that there is something, that we have to unearth.

And interestingly, in Wittgenstein's earlier philosophy, expressed in the tractatus, logico-philosophagus, which was written pretty well out of the encounter that he had with Russell, he has an even more radical view of a denotive theory of meaning where names denote objects, more radical and more systematic

than Russell's own early view on this. But then there was a kind of complete reversal of view in Wittgenstein's later work. And you can see Wittgenstein's, data work as being a major reaction to this idea that underlies the whole approach in analytic philosophy. We haven't talked about a great deal that he did in the political sphere and in the popularising sphere and in the broadcasting affair. What would you think his legacy was than Hillary, Hillary Graves? Well, I think the reason Russell is still an inspiration to so many of us today is that he combines

absolute rigor and clarity with taking on just about every topic that there are. is. So you've mentioned he was widely involved in social and political affairs throughout his life. He also wrote several books on ethics. Russell himself thought of ethics as not really part of philosophy and sharply separated it from his philosophical work. But I think lots of us would say we don't have to take that part of Russell on board. We will take him as a model of somebody who applies clarity, rigor, logical reasoning to every topic you care to name. So in other words, we don't have to go down the route that some people criticize some parts of academia for day of sacrificing the wider view in the interests of narrow specialism and being able to do

one thing very well. Russell did everything, but did all of it very well. Mike Gini. So I think in terms within philosophy, then, the theory of descriptions in particular was enormously influential. I think without Russell, we simply wouldn't have analytic philosophy in the way that we recognise it. But also, he did write a number of popular books. I suppose the most important, I think it was the best-selling book was his history of Western philosophy, which must have introduced tens of thousands of people to philosophy. It introduced me, for example. It's a book that I read as a student, read as a school child and decided

that I needed to do philosophy because of it. But I think looking back on that now, I think that Russell rather caricatures the views that he talks about, but there's no doubt that he had this ability to give nice accounts, often witty and

sometimes sarcastic, sometimes caricatures of the philosophers that he tackled. And I think that's been quite influential and people have enjoyed reading Russell. I think he makes philosophy exciting and something that they want to think about and work on. Finally, Anthony Grayland. Well, Russell writes wonderfully well, and he is very witty, as Mike says,

and that's a great help. But I think he actually had a massive impact in a way on social thinking. He was politically engaged all his life. Before the First World War, he stood for Parliament and on behalf of women's suffrage that were provoked for women. In the 20s, he stood as a Labour candidate in elections. He was very committed in the First World War to pacifism. he in the 50s and 60s, of course, was energetically opposed to the proliferation of nuclear weapons.

So he was a very engaged intellectual. And his writings on popular subjects, especially on things like marriage, divorce, sexual morality, they were, I think, part of the story that needs to be told about how, after the Second World War, and especially in the 1960s, there was a great liberalization of outlook. and he is one of the presences, really, in that story. Without it, without his book, especially Marriage and Morals, which was cited in his Nobel Prize award, we might not have moved with quite the similarity that we did

to our more tolerant age. Well, thank you very much. Thank you, Hilary Graves, A.C. Grayling, Mike Epini. Next week, we'll be talking about the thousand-year-old Persian epic poem, Shana Mae of Fedosi. Thank you very much. There are many more Radio 4 arts and discussion programmes to download for free. Find these on the website at BBC.co.com.uk slash Radio 4.