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Bertrand Russell: Names and descriptions

(From my book The Great Philosophers)

Our focus is on Russell’s theory of descriptions, and his view on how ordinary proper names function. Russell considered his theory of descriptions to be one of his most important contributions to philosophy.

A puzzle about existence

Let’s begin by sketching out an ancient and infernal puzzle: how do proper names – such as John, Paris or Jupiter – function? What role do they play in those sentences within which they appear? An obvious suggestion would be that they refer. Take the sentence:

John is tall.

We use ‘John’ to refer to a particular individual. We then assert something about this individual – namely, he is tall. The claim is true if the individual to whom we refer is tall, and false if he isn’t. Another apparent use of a referring expression is:

The tallest building is in Kuala Lumpur.

Here, it’s tempting to suppose we use the description ‘the tallest building’ to refer to a particular building. We then claim that the building in question is in Kuala Lumpur. Our claim is true if, and only if, the building referred to is in Kuala Lumpur.

This is a natural way of understanding how both names and descriptions function, but it famously generates the baffling puzzle of empty reference, with which philosophers continue to grapple: If names and descriptions are referring expressions, how can we succeed in using them to say something true, when they do not in fact succeed in referring to anything?

To illustrate, look at these examples:

        The golden mountain does not exist,


        Pegasus does not exist.

Both sentences are true. However, if the job of a name or description within each sentence is to refer, how can they be true? In each case there is nothing for the name or description to refer to. But then the name or description cannot do its linguistic job. With no reference, surely the sentence might as well contain a gap where the name or description appears, like so:

...does not exist,

which is obviously not a sentence, let alone a true one.

An attractive feature of Russell’s theory of descriptions is its success in explaining how the sentence, ‘The golden mountain does not exist’, can be true (it solves a number of other puzzles too, which we won’t explore here).

Russell’s analysis of descriptions

According to Russell, when we use a description, ‘the F’, in a sentence like so:

The F is G,

we are actually making three distinct claims. We are, in effect,

• At least one thing is F;
• At most one thing is F; and
• Whatever is F is G.

To illustrate, suppose I say, ‘The queen of Denmark is in Brazil.’ According to Russell, I make three distinct claims. First, I claim there is a queen of Denmark. I assert that at least one thing is queen of Denmark. However, I don’t just claim that there exists a queen of Denmark – use of ‘the’ indicates that whoever is queen of Denmark is uniquely queen of Denmark. So, I am also claiming that, at most, one thing is queen of Denmark. Finally, I claim that whoever is queen of Denmark is in Brazil.

Russell here offers us an analysis of a sentence containing a description. The surface appearance of the sentence suggests it is used to make a single claim. According to Russell, appearances are deceptive – the surface appearance disguises the sentence’s true ‘logical form’. We are actually dealing with a conjunction of three distinct claims. A little analysis reveals this hidden logical structure.

An interesting feature of Russell’s analysis of sentences containing descriptions is that it entails descriptions are not referring expressions. To see why, let’s take a brief look at another sort of expression – the quantifier. Consider this expression:

…is happy.

Obviously this is not a sentence. However, we can turn it into a declarative sentence by inserting a referring expression into the gap. So, if I refer to a particular person as John, I can slot ‘John’ into the space, thus:

John is happy.

This sentence will be true if and only if the individual I refer to is happy. Another kind of expression could also be slotted in to produce a declarative sentence. Consider these quantifiers:

No one

Instead of referring to a specific individual, they talk about quantities. The sentence:

Someone is happy,

for example, says that the number of individuals who are happy is at least one.

No one is happy,

on the other hand, says that the number of individuals who are happy is zero.

It’s worth emphasizing that quantifiers are not referring expressions. To say, ‘No one is happy’ is obviously not to refer to anyone at all. Nor do I refer to anyone using, ‘Someone is happy’. For the latter to be true, it doesn’t matter which individual is happy, so long as someone is. There is an obvious contrast here with, ‘John is happy’. If ‘John’ refers to a specific individual, then what I say will be true only if that individual –
the one referred to – is happy. Whether anyone else happens to be happy is irrelevant.

Russell’s solution

You may have noticed that Russell’s analysis of ‘The F is G’ involves quantifiers (‘at least one thing’ and ‘at most one thing’ are obviously quantifiers). For the three claims to be true, all that is required is that something be uniquely F, and that whatever is F also be G. It doesn’t matter what is uniquely F and also G, so long as something is. In other words, no reference is made to any specific individual. So according to Russell, descriptions such as ‘the queen of Denmark’ and ‘the tallest building’ are not, after all, referring expressions. The surface appearance of language deceived us into supposing that they were.

Now let’s return to the puzzle of explaining how ‘The golden mountain does not exist’ can be true. How do we apply Russell’s theory here?

Well, that sentence is just the negation of:

The golden mountain exists,

which, according to Russell, says:

1. At least one thing is a golden mountain; and
2. At most one thing is a golden mountain.

(Note that we do not add, ‘Whatever is a golden mountain exists’, as (1) and (2) together already assert that there exists exactly one such mountain.)

Russell’s analysis of ‘The golden mountain does not exist’, therefore, is:

It is not the case that:
1. At least one thing is a golden mountain; and
2. At most one thing is a golden mountain.

Because (1) is false (there are no golden mountains), so the original sentence comes out as true. Our puzzle was to explain how, ‘The golden mountain does not exist’ could be true. Russell’s theory allows us to solve that puzzle.

Russell on meaning

Russell’s theory of descriptions allows him to solve a second puzzle generated by a further assumption concerning sentences such as, ‘The golden mountain does not exist’.

The meaning of a referring expression is just the thing to which it refers.

For example, if ‘John’ refers to a person, then that person is the meaning of ‘John’. Russell accepts this, supposing that, for referring expressions, meaning equals reference.

Of course, if this simple theory of meaning is correct, and if the description ‘the golden mountain’ is indeed a referring expression, then not only is it puzzling how the sentence,

The golden mountain does not exist,

can be true, it is equally puzzling how it can succeed in saying something meaningful – for it contains a meaningless expression.

By applying his theory of descriptions, Russell shows how the sentence could still be meaningful even if there are no golden mountains. Russell retains the theory that meaning equals reference, but abandons the theory that descriptions are referring expressions.

However, the theory that meaning is reference is dubious. Many contemporary philosophers of language reject it. One of the most important critics of the theory is Ludwig Wittgenstein (see page 156), who suggests that, rather than thinking of meaning as reference, it is usually more helpful to think of meaning as use . Clearly, a name or description might still have a use even if it lacks any reference (‘Santa Claus’, for example, has a clear use, despite the fact that we don’t use it to refer to anyone). Notice that, if meaning equals use, then we don’t need Russell’s theory of descriptions to explain how, ‘The golden mountain does not exist’ can be meaningful (though perhaps we still need it to explain how the sentence can be true).

Ordinary proper names

A puzzle remains. We have explained how, ‘The golden mountain
does not exist’ can be true, but we have not yet explained how, ‘Pegasus does not exist’ can be true. ‘Pegasus’ is not a definite description, but a proper name. So Russell’s theory cannot directly be applied. How does Russell solve the puzzle here?

As commonly interpreted (not every philosopher interprets Russell in this way), Russell solves this puzzle by suggesting that ordinary proper names are, in effect, definite descriptions in disguise.

Suppose that ‘Pegasus’ is synonymous with the description, ‘the winged horse’. Then the sentence, ‘Pegasus does not exist’, has the same meaning as, ‘The winged horse does not exist.’ So we can now apply Russell’s theory of descriptions.

Of course, the suggestion that ordinary proper names are not referring expressions is counter-intuitive. In fact, while Russell’s theory of descriptions is still widely accepted, many contemporary philosophers of language believe Russell was wrong to claim that proper names are synonymous with definite descriptions. The chapter on Saul Kripke (see page 199) says more on this.

If proper names are not synonymous with definite descriptions, then we cannot apply Russell’s theory of descriptions to explain how, ‘Pegasus does not exist’ can be true. That puzzle remains.


Kevin said…
To determine whether the tallest building is in Kuala Lumpur, I would search all of the objects that are of class building, run a method that chooses the object with the largest height field, then evaluate whether the country field is equivalent to Kuala Lumpur. If the set of objects in class building is empty, then it will return false. A similar process occurs when evaluating the other claims so I fail to see where the problem is. It would the same as if there were no buildings at all. I don't see where the problem is.

Why do we need a physical thing to point at when we evaluate such claims using such a simple method that doesn't rely on the existence of said things? Is the problem that people are mistaking the output of the method to be a concrete reference point? As in, when evaluating the claim of the tallest building, people skip the step of actually finding the tallest building and simply check to see if X building is in Kuala Lumpur?
Richard Wein said…
I'm with Wittgenstein.

Some of the things Russell says here are reasonable. For example, there's nothing wrong per se with saying that words can refer to things. We meaningfully use such talk in ordinary language:
"Who are you referring to when you say 'John'?"
"I'm referring to that man over there."

The fundamental problem lies in Russell's view that sentences have a true logical form. I think this leads him into over-rigid (and consequently sometimes misguided) analyses of what sentences must be doing.
Joel Lim said…
I think there is indeed a fallacy when we say that something does not exist. I don't think it can be possible to proof that logically coherent possibilities don't exist. When we say "a pink elephant does not exist" it's actual meaning is "to my knowledge there are no pink elephants", as in the case of Hume's black swans. We only prove positive statements. For when I say all that is in the room is air, it follows that no other thing exists in the room. I'm currently alone. To prove that there is nobody with me, it must be shown that all the other objects in the room is something else. 'Pegasus does not exist' is not true. It is an implicit statement of our ignorance.
My definition proposal for "atheist", in Wiki Portal:
One of my favorite philosophical papers is Russell's 1905 paper, "On Denoting", which is where the gist of this discussion originates.

Russell so clearly dispenses with any metaphysical problems alleged to result from assertions that "such and such does not exist".

Whether seemingly referring terms mean what he says they mean or not, it seems reasonable that in demonstrating that "The present King of France is bald" is false (or not true), one need say no more than his analysis requires.

Such a denial does not commit one to some realm of non-existent entities. That much seems obvious to me. Apparently, it was not obvious to those whom his paper was directed.

What perplexed me when I read this paper, and perplexes me to this day, is that there was any metaphysical problem needing addressing in the first place.

The semantics of these expressions is another matter. However, it never dawned on me that in saying that something did not exist, I was committed to such dubious entities.
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Richard Wein said…

Thanks for mentioning "On Denoting", as that prompted me to find the paper (online) and read it.

You wrote: "What perplexed me when I read this paper, and perplexes me to this day, is that there was any metaphysical problem needing addressing in the first place."

Me too. But, as you seem to be defending Russell, I would suggest that Russell too sees the "problem of empty reference" as needing to be addressed. His purpose in that paper is not just to refute the solutions of others, but also to give a solution of his own. My view is that all the disputants (including Russell) are addressing a non-existent problem. My own goal is not to give a better solution, but to point out the misguided nature of the question. Alternatively, we might call it "deflating" the problem. At any rate, it's a very different sort of "solution".

We usually talk about reference in the context of clarifying meanings. "Who are you referring to?" "I'm referring to him." Or, "What does 'Pegasus' refer to?". "It refers to a mythical flying horse." This sort of language is useful and reasonable. As I think you appreciate, given your comment, it makes no sense to say to the latter person, "Oh no it doesn't. It can't do, because no such horse exists." But similarly, if I was talking about a fictional present king of France, or mistakenly believed France had a king, I could reasonably explain what I was referring to. So it makes little sense in those cases to say that I'm not referring to anything. But nor is there any point in saying that I am referring to something, outside of a context like this one (a context of explaining meaning). The philosopher typically extracts the question from any context, asking the bare question, "Does this expression refer to anything?" Deprived of context, the question is meaningless, and that's why philosophers can't agree on an answer. There isn't a right answer. (And that includes Russell's answer that it doesn't denote anything.)

These problems arise because our natural instinct is to treat language as something ideal, which can be interpreted free of any context. I think Russell largely retains such an idealised view of language. He does occasionally refer to a specific context, such as when he talks about what George IV meant by a certain sentence. But generally he ignores context. Looking at this another way, it's not abstract expressions that refer to things. It's people who refer to things when they use expressions. It's often convenient to talk about language in the abstract. But we will be misled if we don't keep thinking back to real contexts.

Taking language so far outside its normal context of use that it loses any meaning is what Wittgenstein called "language going on holiday".

By the way, I'm not saying that Russell's analytic reductions are wrong. They may be reasonable approximations for typical contexts, just as "unmarried man" is a reasonable approximation to "bachelor", and (in my opinion) "justified true belief" is a reasonable approximation to "knowledge". But I don't think they solve any significant problems.
Richard Wein:

Thank you for your comment!

It is not that I am defending any semantic theory of Russell's so much as endorsing what seems to me to be his metaphysical position regarding assertions of non-existence.

I do not have a strong opinion on the issue of whether terms refer/denote/mean/rigidly designate,etc....

My view is simply, consistent with Russell, that if one counted the objects in the world and determined that there was no object such that it was uniquely King of France and bald, that one would have to count another "object", i.e. the non-existent bald King of France.

Whether "the present King of France" does not "refer" to anything, in ordinary language, is another matter.

If someone were casually speaking of the King of France, I would correct them by simply saying that France does not have a King. The speaker would understand me clearly without adding that his error was in using a non-referring expression, "the King of France". Agreed.

However, I do think that if one were to translate the speaker's statement into Russell's notation, demonstrate that nothing satisfies the schema, (x)...., that the speaker would agree that nothing much more was intended by his statement.
Correction: would not have to count...
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