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Primary: Russell (1867) ‘On Denoting’ Strawson ‘On Referring’ Donnellan ‘Reference and Definite Descriptions’
Secondary: Clack, R. J. (1969) Bertrand Russell’s Philosophy of Language, Hague; Nijhoff. Sainsbury, R. M. (1979) Russell, London; Routledge & Kegan Paul. Blackburn, S. and A. Code (1978) ‘The Power of Russell’s Criticism of Frege’ in Irvine and Wedeking, (eds.) (1993) Russell and Analytical Philosophy, Toronto; UTP, pp. 22-36. Noonan, Harold W. (2001) Frege: A Critical Introduction, Cambridge, UK; Polity. Lycan, W. G. (2000) Philosophy of Language, London; Routledge.
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Russell's Theory
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I’ll start by introducing Russell’s theory so that we know where the discussion that follows is going to end up.
Rather than inventing a mysterious ‘sense’ to cover the gaps left by a referential theory of meaning, or accepting that non existent things could be respectable objects of an ontology, Russell thought that the difficulties could be met by supposing that the referential nature of the singular terms of a language was different from how it appeared on the surface. He proposed a logical form for definite descriptions that he claimed could handle the four puzzles for reference.
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Getting to Russell's Theory
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You’ll recall that one of the criticisms of the Millian View (a direct reference theory of meaning) was that statements about things that are known not to exist seem to have no mening on this theory. When somebody tells you that the planet Vulcan exists and has certain characteristics you have no doubt that the statement has meaning. But if Vulcan doesn’t exist then you are simply mistaken about this because there’s no referent to be the meaning as the MV demands. We also found that although Frege’s theory of a related but separable sense and reference for terms in a language was able to make a reasonable attempt at solving some other problems of the MV it was unsatisfactory when applied to the problem of the meaningfulness of sentences about nonexistent objects. Frege thought that this was a real problem with natural language and proposed a replacement.
Russell thought that this was hardly helpful.
a. Statements with non-referring terms
So far as Frege was concerned, then, truth or falsity could not be assigned to a sentence for which some referential term of the sentence failed to have a referent. And it made no difference whether the term failing to refer was a proper name like ‘Pegasus’ or a definite description like ‘the winged horse of Mt Helicon’. Russell begins his attack on the Fregean conclusion – and, indeed on the whole notion of a necessary element of ‘sense’, with a discussion of the referential power of definite descriptions. Let me paraphrase how Russell sets up the problem in ‘On Denoting’:
If we say, ‘the King of England is bald’, that is, it would seem, not a statement about the [sense of] ‘the King of England’, but about the actual [thing] [referred to] [through] [the sense]. But now consider ‘the King of France is bald’, By parity of form, this ought also to be about the [reference] of the phrase ‘the King of France’. But this phrase, though it has a [sense], provided ‘the King of England’ has a [sense], has certainly no [reference], at least in any obvious sense. Hence one would suppose that ‘the King of France is bald’ ought to be [beyond judgment]; but it is not [beyond judgment], since it is plainly false.
Russell’s solution to this was to suppose that the definite descriptions in question should be analysed not on the model of names but, instead, on the model of quantified statements. That is to say, that a sentence like ‘the present King of France is bald’ should be seen as more similar to a sentence like ‘some people are bald’ than to a sentence like ‘Louis XVII is bald’. To be more specific, according to Russell that statement should be analysed as involving the conjunction of three distinct parts, thus:
i. there is a present King of France ii. there is no more than one present King of France iii. anything which is a present King of France is bald.
Each of these is a quantified statement which in our modern notation we would write as
i'. ($x) [Fx] ii'. ("x) [Fx ® ("y) [Fy ® y = x]] iii'. ("x) [Fx ® Bx]
and the conjunction of these parts, i' & ii' & iii', is logically equivalent to:
($x) [Fx & ("y) [Fy ® y = x] & Bx]
which you should read as
There is a thing, x, such that x is a present King of France, and for any thing, y, if y is a present King of France then y is the same thing as x, and x is bald.
Russell saw this as the logical form of all those statements that had the grammatical form ‘the A is B’. The logical form of a statement, which has never been properly defined, you should understand to mean something like the real form of the sentence in a perfectly perspicuous language that makes all its logical relations to other sentences clear. The grammatical form is a mere creature of the contingencies of history and convention and must not be relied upon to perfectly mirror on its surface the real intentions of the speaker.
If there is such a thing as logical form, and if the logical form of statements involving definite descriptions is such as Russell described (through the contextual definition of the word ‘the’), then the difficulty of assigning a truth value to a statement involving a definite description that is a singular term that apparently fails to refer disappears, because the singular term that we thought failed to refer “disappears on analysis” (so it doesn’t really exist) and so there just is no failure of reference.
In the present case for example, the statement has been claimed to be logically equivalent to the conjunction i' & ii' & iii'. This means that the statement will be true if all of those conjoined parts are true and false if any of them are false while the others are either true or false. The very first conjunct, i’, turns out to be false, because it is not the case that there is an object, x, such that x is a present King of France, and so the conjunction i' & ii' & iii' cannot be true, and so the whole original statement about the present King of France being bald cannot be true. We can’t yet say that the statement must be false because we have to show that there is a truth value for each part – otherwise we’ll be no better off than Frege. In fact, both the second and the third conjunct turn out to be true because the antecedent of the conditional is false and the conditional that we are using in the logical form paraphrase is defined such that A ® B (read ‘if A then B’) is equivalent to ~A v B (read ‘not A or B’) and this is true in just those cases when the antecedent is false or the consequent is true. Therefore the whole statement is equivalent to F & T & T and is therefore false, just as Russell said it was.
Scope
It might look as if there’s a bit of a difficulty here though. You’ll recall that when I was criticizing Frege’s claim that these problem statements had no truth value at all I said that we’d like to be able to say that such statements would still obey the law of excluded middle. If statement A is ‘the present King of France is bald’, and it has no truth value, and the statement ~A is ‘the present King of France is not bald’ has no truth value for the same reason, then it looks as if the law is broken because ‘A v ~A’ gets no truth value whereas it should be counted as true. Unfortunately , on Russell’s scheme it looks as if A will get the truth value F, and so will ~A. This has the disadvantage of making ‘A v ~A’ come out false, which might even be worse than having no value at all.
Russell is undaunted however. Our problem he says arises from an incorrect understanding of how the negation operates upon a quantified statement. In modern terminology, Russell makes a claim that we must make allowances for differences of scope. To see what is meant by this, let’s consider a slightly simpler quantified statement.
Some present King of France is bald.
Which is just the statement ‘there is a present King of France and he is bald’ (which is our original problematic statement without the uniqueness condition that was imposed for ‘the’.) we write this as
($x) [Fx & Bx]
We can then form both contradictory and contrastive statements thus:
It isn’t the case that some present King of France is bald
which we write as
~ ($x) [Fx & Bx]
and Some present King of France is not bald
which we write as
($x) [Fx & ~Bx]
In these cases the difference in the intention of the contradictory and contrastive statements is flagged unambiguously by the position of the negation operator. In modern terminology we distinguish these situations by saying that the quantifier has narrow scope relative to the negation operator in the first instance, and wide scope relative to the negation operator in the second.
Now, we aren’t likely to confuse the two in such simple cases because the surface form of these statements is sufficiently perspicuous in this respect (a perspicuity which is augmented by the fact that we also have a more idiomatic way of phrasing the contradictory statement as ‘No present King of France is bald’); but when we make statements involving a definite description, the perspicuity of ordinary language is sharply reduced, and there is serious ambiguity as to the proper interpretation. When we make a statement like
The present King of France is not bald
it is not immediately clear whether this is supposed to have the logical form
~ ($x) [Fx & ("y) [Fy ® y = x] & Bx]
which on the basis of the falsity of the original statement we see must be true, or
($x) [Fx & ("y) [Fy ® y = x] & ~Bx]
which on the analogy of the original statement we see must be false. And this ambiguity is not helped by any idiomatic way of phrasing the two statements that distinguishes their logical forms. But the fact that there is this distinction allows us to see how Russell’s formulation can preserve the law of excluded middle, because when the statement A is false then the statement ~A, which is the contradictory and not the contrastive, must be true, and therefore A v ~A comes out true. Thank heavens for that.
I should point out here that Russell’s way of talking about what we’ve been calling scope distinctions is a little different. He talks about occurrences of the phrase ‘the present King of France’ in the normal language as being primary or secondary, whereas our scope distinction is defined in terms of the elements of the logical form. Notice that the phrase ‘the present King of France’ doesn’t occur in the logical form at all. When ‘the present King of France is not bald’ is to be understood as equivalent to ‘it is not the case that the present King of France is bald’ then the denoting phrase is said to have secondary occurrence. When ‘the present King of France is not bald’ is to be understood as equivalent to ‘it is the case that the present King of France is not bald’ then the denoting phrase is said to have primary occurrence.
b. Statements of negative existentials
All that talk about scopes and primary and secondary occurrences seems like a lot of effort to go to to make a simple law of excluded middle come out right, and it might be thought that there’s a lot of epicycles being postulated here that don’t have much use apart from that. But that thought would be wrong. It turns out that the scope distinction allows Russell to offer a solution to other problems that a theory of reference without sense has to face. Take the problem of negative existentials for example.
You’ll recall that the problem is that for a statement like
The King of France doesn’t exist
the statement if true says that the denoting phrase ‘the King of France’ has no referent and, according to the MV it can’t have a meaning. Or, according to Frege, although it can have a sense, it can’t have a truth value (so it can’t be a true statement). On the other hand
The King of France exists
turns out to be something akin to a tautology.
Let us apply Russell’s analysis of denoting phrases to that statement. Accordingly, we find that it is to be analysed as involving the conjunction of three distinct parts, thus:
i. there is a present King of France ii. there is no more than one present King of France iii. anything which is a present King of France exists.
That seems reasonable – if a bit redundant. Perhaps the reason that we feel the statement is somewhat otiose is that we comprehend this redundancy.
Let us on the other hand consider the analysis of the negative of this statement, ie. that ‘the present King of France does not exist’. The analysis is exactly analogous to the analysis of the statement that ‘the present King of France is not bald’ and shows exactly the same scope ambiguity. If we understand the denoting phrase to have primary occurrence then we say that the statement has the logical form
($x) [Fx & ("y) [Fy ® y = x] & ~Ex]
which you should read as
There is a thing, x, such that x is a present King of France, and for any thing, y, if y is a present King of France then y is the same thing as x, and x does not exist.
This is a pretty odd thing to say, because you start by saying that something does exist ($x) and you finish by saying that it doesn’t exist [~Ex]. The statement seems self contradictory.
Contrariwise, if we understand the denoting phrase to have secondary occurrence then we say that the statement has the logical form
~ ($x) [Fx & ("y) [Fy ® y = x] & Ex]
which you should read as
It is not the case that there is a thing, x, such that x is a present King of France, and for any thing, y, if y is a present King of France then y is the same thing as x, and x does exist.
Which makes much better sense. It just means that there is no one who is the King of France.
In neither case is there a problem of reference, and in the case that the denoting phrase is attributed secondary occurrence it turns out to have a perfectly reasonable interpretation.
c. Opaque Contexts
The same distinction between wide and narrow scopes or primary and secondary occurrences allows Russell to solve the problem of the failure of coreferential terms to be intersubstitutable in opaque contexts salva veritate. The example that Russell gives involves Sir Walter Scott, King George IV, and the novel Waverley. [‘On Denoting’]
If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other in any proposition without altering the truth or falsehood of the proposition. Now George IV wished to know whether Scott was the author of Waverley, and in fact Scott was the author of Waverley. Hence we may substitute Scott for the author of Waverley, and thereby prove that George IV wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman in Europe.
The problem is what we’ve seen before when talking about Hesperus and Phosphorus and Evening Stars and Morning Stars, and so on. We have the sentences
i. George IV wished to know whether Scott was the author of Waverley ii. Scott was the author of Waverley
and we wish to show that it does not follow that
iii. George IV wished to know whether Scott was Scott
Russell says that just as there was an ambiguity in ‘the present King of France is not bald’ due to the possibility of the denoting phrase having primary or secondary occurrence, just so there is an ambiguity in the statement about George IV. If we take it as having primary occurrence then the analysis yields the logical form
($x) [Wx & ("y) [Wy ® y = x] & G(s = x)]
(where Wx is ‘x is an author of Waverley’, s is ‘Scott’, and Gx is ‘George IV wished to know whether x’)
which we should read as
There is a thing, x, such that x is an author of Waverley, and for any thing, y, if y is an author of Waverley then y is the same thing as x, and George IV wished to know whether Scott is x.
And the other premiss in the argument we would naturally give the logical form
($x) [Wx & ("y) [Wy ® y = x] Ù (s = x)]
which we should read as
There is a thing, x, such that x is an author of Waverley, and for any thing, y, if y is an author of Waverley then y is the same thing as x, and Scott is x.
Now, given the assumption of primary occurrence in the first premiss, we can see that this reading tells us that George IV’s curiosity is directed at the thing x, which is the author of Waverley, and he wishes to know of that thing whether it is Scott. It thus seems that, given that the thing in question actually is Scott, that it makes good sense to interpret the statement as claiming that George IV wants to know whether Scott was Scott. As Russell says, it’s rather as if he had seen Scott from afar and asked of the thing, Scott, whether it was Scott. In that case we can accept the logical form of iii as
($x) [Sx & G(s = x)]
and this is a valid conclusion.
On the other hand, we are much more naturally inclined to treat the denoting phrase of i as having secondary occurrence, with the logical form
G( ($x) [Wx & ("y) [Wy ® y = x] & (s = x)] )
which we should read as
George IV wished to know whether there is a thing, x, such that x is an author of Waverley, and for any thing, y, if y is an author of Waverley then y is the same thing as x, and Scott is x.
and in this case the logical form of iii would be
G( s = s )
which certainly doesn’t seem to be a valid conclusion.
d. Frege’s puzzle
Now that we’ve seen how Russell’s theory of definite descriptions can handle three of the puzzles of reference that Frege’s theory of sense was supposed to handle it only remains to be sure that it can also handle the puzzle of identity. Recall that this was a puzzle that if two terms were coreferential and if meaning was reference then making an equation between them told us nothing new. We’ve seen plenty of such identity statements in this lecture. For example
The author of Waverley is Scott
And we know that according to Russell this has the logical form
($x) [Wx & ("y) [Wy ® y = x] & (s = x)]
Just looking at this logical form tells us all we know about why the statement is meaningful: it isn’t really an identity statement but is rather a complex predication, and a predication is exactly telling us something about the thing being predicated of.
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| Strawson’s Objections to Russell’s Theory
of Descriptions
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Of course there are those who find fault with Russell’s solution to the problem of reference. A particularly good source of arguments against Russell is the (recently deceased) Strawson ((1950) ‘On Referring’, Mind, 59: 320-44) The general complaint that Strawson has about Russell’s theory is that Russell seems to imagine that reference is something that is properly attributed to abstract objects like, perhaps, propositions, or more concretely, sentences types, or, even more concretely, actually tokened sentences. Strawson thinks this is just nonsensical: that referring is not something done by sentences but by people who use sentences. People, people who use sentences, are the referringest things in the world.
1. Failure to refer.
Recall that Russell says that when someone says that ‘the present King of France is bald’ the Fregean and the Millian are wrong to say that there is just no truth value to that statement. Russell says that, of course, if someone made that claim we’d tell them that they were wrong; that it was a false claim: and because of the way that Russell interprets definite descriptions, the logical form of the statement does indeed come out to be a false statement. But Strawson says that this is just wrong and Russell’s predecessors were right. If someone made such a statement we would not claim that it was false; we would say instead that the person making the statement had used an inappropriate sentence for their purposes. Actually, we’d probably say something like ‘What are you talking about? There is no present King of France.’ There is no referring going on, and the sentence, which appears to refer, therefore fails to make a statement.
2. Failure to assert.
According to Russell’s theory, when someone makes a claim about the author of Waverly, as when they say that the author of Waverly is a fine stylist, statement makes several assertions; one of which is the assertion that there is one and only one thing that is an author of Waverley. Just think back to the paraphrases that we made of such statements with their declarations that ‘there is an object such that … and if any other object is like that then it is the same object and …’ and so on. But Strawson thinks that this too is a misreading. The statement makes no such assertion about the existence of such an object – it is no part of its role to make such a claim. Instead, we should think of the statement as presupposing that there is such an object.
Unfortunately, this is really a bit of a misreading of Russell’s position, because he’s not actually making a claim that the intention of the statement in question can be considered to be the same as the intention that one would have if one made a statement that was an acceptable English-language paraphrase of the logical form of that statement. The logical form is just that. It shows what the logical relations of the statement are to other statements. An assertion is an act – and it is quite a different thing from a logical consequence. We’ll look at assertions and other sorts of linguistic act in the section on pragmatics later in the course.
3. Contexts of use
‘The table is here’ refers to which table? It seems to refer to a particular table which – but which particular table is something that has to be determined by the context in which the sentence is uttered. In Strawson’s view this indicates that the meaning of a statement or of a definite description that occurs in a statement cannot be determined by the sentence in which that definite description occurs.
Russell, of course, has some options here. Rather than discounting the whole business as being hopelessly bound by context he can attempt to expand the description of the table so that it is actually a uniquely satisfied description. He would then have to claim that the statement contains – in some real sense – this expanded description; that it abbreiates it in some way. You will appreciate that this response would require that the description, any description really, must refer to a great deal more of the world than is usually supposed. If I’m referring to this table here then I have to describe it in terms of its position in this classroom, in this university, perhaps at this time of day, and so on. We would probably think that none of those necessary coordinative objects should have any role in the determination of the meaning of ‘the table’. We feel that they should be quite irrelevant. The story become even more unlikely when we realise that there are any number of ways that the table could be distinguished from all other tables. Perhaps I can refer to the table immediately before Jamie, or to the one just left of Tanya, or 5.2763 km from Toowong PO on a line from that point through the letterbox of 27 Macquarie St. In that case, if there is a real meaning to these definiet descriptions, then one of those complete descritions must be the correct complete description. But which one? We have absolutely no preexisting intuitions relevant to making this distinction. Some people have assumed that Russell could appeal to restrictions on the domain of quantification, where the restriction is something that is presuposed somehow by the conversation. It’s claimed that if the restrictin is in the quantification rather than in the material in the scope of that quantifier that somehow this is less objectionable than otherwise. I don’t see it myself. How do quantifiers actually become restricted?
4. Non-referring definite descriptions
It is not always the case that definite descriptions have a referring function. In sentences such as
Who is the present King of France?
or
Let me be the King of France.
the definite descriptions obviously don’t have referential roles and so they can’t be analyzed out in the way that Russell supposed that they could.
I’m not so sure that this is a very strong argument against Russell’s position. He may be able to retort that his was a theory defined in terms of denoting phrases, and if some language elements had additional uses other than as denoting phrases that would be nothing unusual. Languages generally are massively redundant.
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Donnellan’s Contribution to the Theory of Descriptions
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Russell takes descriptions to be making an association between a thing and some properties of that thing (roughly speaking) and their referential function is a consequence of their ability to match an object with the attributed attributes. Donnellan describes this as the attributive function of descriptions, but it is not, he thinks, their only use. They are also used in a sense that he calls referential, where the possession or otherwise of the attributes on thte part of the intended referent is not essential to the success or failure of the reference.
We are aware, of course, that some names look like definite descriptions, The Roma Street Station is such a one. We are not surprised that a ‘description’ of this sort should have a principally referential function; and, in fact, we very rarely use it in any other way. But descriptions which are not obviously really names are also frequently used in a referential fashion. The standard example is
Smith’s murderer is insane.
If this is used by a policeman or a friend of Smith who does not yet know who murdered Smith, then we interpret it as meaning that there are circumstances that lead one to believe that whoever it was that murdered Smith, that person is insane. This is an attributive use of the definite description ‘the murderer of Smith’. On the other hand, the phrase may be used by some random bystander at the time that the police made an arrest. We interpret the phrase as meaning that the person whom the police have arrested for Smith’s murder, who is gibbering and drooling and wearing no more than an inflatable duck, is insane. This is a referential use of the description ‘the murderer of Smith’ because its intention is to point to a particular person.
Note that it does not matter whether the person being arrested in that scenario is really the murderer of Smith. If they were entirely innocent (those still presumably quite mad) the reference would be quite successful, and we would count the statement as a true statement. It gets more strange too, because if I already knew for a fact that the person being arrested was innocent, I could not successfully refer to the real murderer by using the description ‘the murderer of Smith’ while the rest of the world – or the person I was talking to – believed the contrary. We can imagine cases, too in which we have to deliberately misattribute properties to someone to whom we wish to refer, in order that the person who we think believes that we believe something incorrect will understand our reference. If I believe that you believe that I believe that Smith was killed by person X, even if we both know that he was killed by person Y, then my statement to you about the murderer of Smith is a statement about X, and not about Y. Doubtless we could go in this this manner forever, but I think you should get the point.
Donellan is basically saying that there’s an ambiguity in the use of definite descriptions which means that they are sometimes best understood in the Russellian way, and sometimes best understood in the Strawsonian way – and it’s a mistake to insist that one or the other is the unique correct understanding.
Problems for Donnellan
1. Analogues
The fact that we can sometimes use definite descriptions referentially is taken to point up a specific function belonging to those terms that comes into play in certain situations. But we can do the same sort of thing even with straightforward names. If I’ve mistaken the name of one of my students and say in a class
Caroline is wearing a red blouse
Whereas in fact it is Kate who is wearing that colour, I may still succeed in saying a true thing to the other people in the class. Does this mean that the name Caroline has both referential and attributive uses?
2. Pragmatism
Kripke’s response to this sort of thing is to discount it entirely. This ambiguity that Donnellan proposes has something to do, he says, with a distinction between speaker’s meaning and the implicit meaning of the linguistic item used to convey that meaning. We may ask however, whether it is possible to draw such a clear distinction between those two type of meaning.
We’ll come back to this sort of thing later on, for the present it might be worth your while wondering whether Donnellan’s distinction – supposing it can be made principled – can assist with the problems that the description theory faces.
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