1. Last day, we noted four objections that arise when we consider the workings of proper names. Let us first note that the same problems arise when we look at definite descriptions, phrases of the form ‘the NP’. Our first two puzzles concerned empty names; we have an analogous problem of what a phrase like ‘the present king of France’, either when we say ‘the present king of France is bald’ or when we say ‘the present king of France doesn’t exist’. The third objection concerned nonsynonymous coreferring expressions, i.e., identity statements. The very same problem we expressed in terms of ‘John Paul’ and ‘the pope’ can be expressed using the standard definite descriptions for these things: ‘the evening star’ and ‘the morning star’. Lastly we had objections caused by opaque contexts. Again, if ‘the animal Jones seeks’ is the very same person as ‘the mythical unicorn’ it is difficult to see why we cannot switch such designations salva veritate. So, as far as the objections go, definite descriptions and proper names seem to be in the same boat.
2. To deal with ostensible reference to nonexistents, one might reject K3 but except K1-K2, K4-K6 or one can make Plato’s move and accept K3 but reject K6.
3. Plato’s move in the Euthydemus Paradox provides the basic Platonic insight here.
4. Frege rejects K3.
Frege
There is an online version of Frege’s paper ‘On sense and reference’.
It seems that these kinds of puzzle were first invoked by Frege to confront Mill’s type of theory with what seemed to Frege an unanswerable objection, and to motivate his own approach to these problems.
5. Reference to nonexistents. The behavior of names and definite descriptions in identity statements, now informative, now tautologous, led Frege to say that these expressions have two aspects: Sinn and Bedeutung, a pair of words often, but not universally, translated as ‘sense’ and ‘reference’. The reference is the object in the world, the planet Venus in the case of ‘Hesperus’, ‘the morning star’, etc.; the philosopher Aristotle in the normal case of ‘Aristotle’ or ‘the teacher of Alexander the Great’. Sense determines reference; it is in virtue of its sense that an expression refers to what it refers to. Fregean senses are not meant to be subjective items (like my personal mental image of Socrates deriving from a well-known sculpture allegedly of him), but objective intersubjectively available items. Frege offers the following explanation:
“The reference of a proper name is the object itself which we designate by its means; the idea, which we have in that case, is wholly subjective; in between lies the sense, which is indeed no longer subjective like the idea, but is yet not the object itself. The following analogy will perhaps clarify these relationships. Somebody observes the Moon through a telescope. I compare the Moon itself to the reference; it is the object of the observation, mediated by the real image projected by the object glass in the interior of the telescope, and by the retinal image of the observer. The former I compare to the sense, the latter is like the idea or experience. The optical image in the telescope is indeed one-sided and dependent upon the standpoint of observation; but it is still objective, inasmuch as it can be used by several observers. At any rate it could be arranged for several to use it simultaneously. But each one would have his own retinal image. (On sense and reference)”
The sense is independent of this or that mental representation, it belongs to the domain of “representables.” Why not?
6. Frege lumps together proper names with definite descriptions.
“The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it belongs; but this serves to illuminate only a single aspect of the reference, supposing it to have one. Comprehensive knowledge of the reference would require us to be able to say immediately whether any given sense belongs to it. To such knowledge we never attain.”
Ideally, Frege means ‘Aristotleme is Aristotleyou’ is informative because you and I differ in comprehension. This solves the Puzzle about Identity.
6. Frege goes on to point out that every name has a sense, but not necessarily a reference:
It may perhaps be granted that every grammatically well-formed expression representing a proper name always has a sense. But this is not to say that to the sense there also corresponds a reference. The words ‘the last cardinal before aleph null’ has a sense, but it is very doubtful if they also have a reference. In grasping a sense, one is not certainly assured of a reference.
This permits Frege a solution of the puzzle of negative existentials: empty names have sense, so we can use them to say significant things, but we do not need them to have a reference. Negative existentials are true simply in as much as they state that absence of a reference.
7. Frege next gives his solution to the problem of opaque contexts:
If
words are used in the ordinary way, what one intends to speak of is their
reference. It can also happen, however, that one wishes to talk about the words
themselves or their sense. This happens, for instance, when the words of
another are quoted. One’s own words then first designate words of the other
speaker, and only the latter have their usual reference. We then have signs of
signs. In writing, the words are in this case enclosed in quotation marks.
Accordingly, a word standing between quotation marks must not be taken as
having its ordinary reference.
In order to speak of the sense of an expression ‘A’ one may simply use the
phrase ‘the sense of the expression “A”’. In reported speech one talks about
the sense, e.g., of another person’s remarks. It is quite clear that in this
way of speaking words do not have their customary reference but designate what
is usually their sense. In order to have a short expression, we will say: In
reported speech, words are used indirectly or have their indirect reference. We distinguish
accordingly the customary from the indirect reference of a word; and its customary sense from its indirect sense. The indirect reference of
a word is accordingly its customary sense. Such exceptions must always be borne
in mind if the mode of connexion between sign, sense, and reference in
particular cases is to be correctly understood.
Extending this to other opaque contexts, Frege is claiming that in ‘Jones believes Orcut is a spy’ ‘Orcut’ refers not to Orcut but to the sense. ‘The man at the door’ may designate the same person, but if I don’t know that, it might not be true that ‘Jones believes the man at the door spies’ and this is possible because the reference of ‘the man at the door’ is not Orcut but the sense of ‘the man at the door’ and that is pretty obviously different from the sense of ‘Orcut’.
Or is it?
There are also criticisms of the proliferation of senses and references entailed by the account of indirect reference. ‘Aristotle’ standardly refers to Aristotle and expresses the sense of ‘Aristotle’. But when used to refer indirectly, ‘Aristotle’ refers to the sense of ‘Aristotle’ and expresses what? Assuming that a sense of a term cannot be identical with the reference of that term, there must be some further sense here that would account for your “Aristotle” and mine. And why should we not go on to refer to it? But then there will be a further sense associated with that reference, and so on ad infinitum.
Before leaving Frege, let us note a characteristic Fregean thought: Words have meaning only in the context of a sentence. The meaning of a sentence is a resultant of the contributions of its component parts.
Russell
For Russell, the paper is available on-line: ‘On Denoting’.
Russell criticizes Frege’s sense/reference contrast and offer his own resolution of the difficulties created by the puzzles in the context of definite descriptions. Since Russell also subscribed to a description theory of ordinary proper names, he agrees with Frege in thinking that whatever is said about the one should be said about the other, though of course, what he did say was significantly different from what Frege said.
Russell’s criticisms of Frege are concerned with Frege’s view of empty names or definite descriptions. It is not enough just to say that such names have a sense but no reference. There does not appear to be any difference between claims about the present queen of England and the present king of France. One is said to be about an existing person, but then what is the other about? It is certainly not nonsense. Part of Russell’s own argument is:
The King in The Tempest might say, ‘If Ferdinand is not drowned, Ferdinand is my only son’.’ Now ‘my only son’ is a denoting phrase, which, on the face of it, has a denotation when, and only when, I have exactly one son. But the above statement would nevertheless have remained true if Ferdinand had been in fact drowned. Thus we must either provide a denotation in cases in which it is at first sight absent, or we must abandon the view that denotation is what is concerned in propositions which contain denoting phrases. The latter is the course that I advocate. The former course may be taken, as Meinong, by admitting objects which do not subsist, and denying that they obey the law of contradiction; this, however, is to be avoided if possible. Another way of taking the same course (so far as our present alternative is concerned) is adopted by Frege, who provides by definition some purely conventional denotation for the cases in which otherwise there would be none. Thus ‘the King of France’, is to denote the null-class; ‘the only son of Mr. So-and-so’ (who has a fine family of ten), is to denote the class of all his sons; and so on. But this procedure, though it may not lead to actual logical error, is plainly artificial, and does not give an exact analysis of the matter. Thus if we allow that denoting phrases, in general, have the two sides of meaning and denotation [sense and reference], the cases where there seems to be no denotation cause difficulties both on the assumption that there really is a denotation and on the assumption that there really is none.
Russell also has a complex argument, using two pairs of sentences (I give only the second pair):
The first line of Gray’s Elegy states a
proposition.
‘The first line of Gray’s Elegy’ does not state a proposition.
Russell then says:
Thus
taking any denoting phrase, say C, we wish to consider the relation between C and ‘C’, where the difference of the two
is of the kind exemplified in the above two instances.
We say, to begin with, that when C occurs it is the denotation that we are speaking
about; but when ‘C’
occurs, it is the meaning.... the difficulty which confronts us is that we
cannot succeed in both preserving the connexion of meaning and denotation and
preventing them from being one and the same; also that the meaning cannot be
got at except by means of denoting phrases. This happens as follows.
The one phrase C
was to have both meaning and denotation. But if we speak of ‘the meaning of C’, that gives us the meaning (if
any) of the denotation. ‘The meaning of the first line of Gray’s Elegy’ is the
same as ‘The meaning of “The curfew tolls the knell of parting day”,’ and is
not the same as ‘The meaning of “the first line of Gray’s Elegy”.’ Thus in
order to get the meaning we want [a denoting phrase that denotes the
meaning/sense of “C” when it is used], we must speak not of ‘the meaning of C’, but ‘the meaning of “C”,’ which is the same as ‘C’ by itself. Similarly ‘the
denotation of C’
does not mean the denotation we want, but means something which, if it denotes
at all, denotes what is denoted by the denotation we want. For example, let ‘C’ be ‘the denoting complex
occurring in the second of the above instances’. Then C = ‘the first line of Gray’s
Elegy’, and the denotation of C = The curfew tolls the knell of parting day. But
what we meant to have as the denotation was ‘the first line of Gray’s Elegy’.
Thus we have failed to get what we wanted.
The problem of Substitutivity
Given that STs are meaningful because they denote, why doesn’t substitution hold? It should, given Leibniz’ law. Russell provides an analysis to avoid these objections.
Russell’s theory of descriptions
It remains to interpret phrases containing the. These are by far the most interesting and difficult of denoting phrases. Take as an instance ‘the father of Charles II was executed’. This asserts that there exists an x who was the father of Charles II and was executed. Now the, when it is strictly used, involves uniqueness; we do, it is true, speak of ‘the son of So-and-so’ even when So-and-so has several sons, but it would be more correct to say ‘a son of So-and-so’. Thus for our purposes we take the as involving uniqueness. Thus when we say ‘x was the father of Charles II’ we not only assert that x had a certain relation to Charles II, but also that nothing else had this relation. So, to get a unique equivalent of ‘x was the father of Charles II’, we must add ‘If y is other than x, y did not beget Charles II’, or, what is equivalent, ‘If y begat Charles II, y is identical with x’. Hence ‘x is the father of Charles II’ becomes: ‘x begat Charles II; and “If y begat Charles II, y is identical with x” is always true of y’.
Thus ‘the father of Charles II was executed’ becomes:
(3x)Fx
(x)(Fx à (y)(Fy à y = x ))
(x)( Fx à Bx)
Or,
(3x)(Fx & ((y)(Fy à y = x) & Bx)).
Scope
A further crucial element in Russell’s account are the scope differences that his analysis permits and which he uses to explain some difficulties. Negative claims about non-existent entities can sometimes be construed as true, sometimes as false. Russell suggests that scope differences are the reason:
Thus ‘the present King of France is not bald’ is false if it means
‘There is an entity which is now King of France and is not bald’,
but is true if it means
‘It is false that there is an entity which is now King of France and is bald’.
It all depends on how we reconstruct the scope of the negation (‘not’).
It is fairly easy to see that Russell’s analysis provides a way of tackling Lycan’s four puzzles, and Russell’s fifth, excluded middle, one.
1. Apparent reference to nonexistents
2. Negative Existentials
3. Identity
4. Substitutivity
8. The definite description does not refer, so there is no question about what it refers to when what it appears to mean does not exist. What looks like a subject-predicate sentence turns out to have a quite different logical form.
9. Negative existentials involve a scope error. The present king of France does not exists should be analyzed as, it is false that the present king of France exists which is true and unproblematic.
a. “The werewolf of London does not exist” is not reconstructed as “(x)(Lίx à ~Зx(Lx))” but as “~(Зx)(Lx & ((y)(Lx à y=x) & Зx))”.
10. Informative identities amount to conjunctions: there exists a unique X that is F and G; tautologous identities, on the other hand, says there exists a unique X that is F and F. They stutter. So, “Elizabeth Windsor = the Queen of England” tells us, according to Russell, somebody is queen and there is only one of them and it is Windsor. I.e., (3x)(Qx & ((y)(Qy à y=x) & x = Windsor)).
11. “Co-referring” expressions in opaque contexts contribute different predicates to whatever is being said, so there is no reason to expect to be able to substitute them. In this case, “Jones believes that Smith is at the door” but, unknown to Jones, Smith is a spy. Given the intersubstitutivity of identicals, we would be able to change “Smith” to “a spy” which, given the opaque context, would wrongly attribute the belief that Smith is a spy to Jones. On Russell’s analysis, we simply get rid of the singular terms. And get,
a. Jones believes that at least one person is at the door, and at most one person is there, and whoever it is, spies.
12. Russell’s extra puzzle is worth quoting:
Take the proposition that the present king of France is bald. By the law of the excluded middle, either ‘A is B’ or ‘A is not B’ must be true, i.e, for those who hear things conjunctively, ~(P & ~P) and for those who hear things disjunctively, (~PvP). Hence either ‘the present King of France is bald’ or ‘the present King of France is not bald’ must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of France in either list. We have already seen the scope machinery that allows Russell to dispose of this puzzle. Giving the description narrow scope or Russell’s “secondary” position, the positive is false, the negative true; giving the description wide scope or primary position, both are false, but do not constitute an excluded middle pair (logically, both begin ‘there is an x, such that ...x’).
a. Not: [The present king of France is bald], i.e., it is false
b. Bald: [The not existent king of France], i.e., it is true that a non-existing thing is bald.
c. Applying the analysis inside the scope of the negation in a., we have, ~(3x)(Kx & ((y)(Ky à y =x ) & Bx)).
13. Russell explains away definite descriptions in terms of the application of predicates. But he tells us nothing about how that works. But one might consider it an advance to reduce an apparent variety of ways of using language to two simple categories: Millian names for some demonstratives and the application of predicates.
Objections to Russell’s theory
Strawson against Russell
14. Overall Objection. Strawson represents a very different emphasis, one that stresses the human use of language rather than abstracting away to consider language and the world sub specie aeternitatis. So Strawson reminds us that linguistic expressions do not refer, people refer by using linguistic expressions.
15. Objection one. Strawson rejects one of Russell’s intuitions: that claims like ‘the present king of France is bald’ are false. Rather, Strawson says, we ought to think of them as misfires in an attempt to say something, shooting blanks. They have gone wrong, but in a very different way from that in which we make mistakes about existing objects. The question of truth or falsehood does not arise for them. And so, there is no question about the object referred to by such empty phrases. While Russell says that use of ‘the F’ implies an existential claim ‘there is a unique F’, Strawson’s idea is that this latter claim, or some modification of it, is presupposed, in the mind of the speaker, by using the definite description. Language is a game and playing it involves presuppositions about what’s permitted. Strawson’s belief is that Russell was so crazy about formalization that he cut syntax adrift.
16. Objection three. Another problem arises once we look at definite descriptions that are not so obviously uniquely referring as Russell’s ‘the author of ...’ Lycan offers ‘The table is covered with books.’ There is nothing odd about such a sentence, but it cannot be claimed to be equivalent to the claim that there is one unique table and it is covered with books (Objection Two). Russell focuses on the formal aspects of language so he can get around the problem of speaker assertions. Lycan mentions but rejects the suggestion that such definite descriptions are elliptical for more elaborate and genuinely uniquely referring descriptions because it can’t be formalized. The trouble here is that this extra material becomes part of the logical content of particular propositions with no end in sight. A less extravagant hypothesis is that we are using restricted quantification, just as we are when we say things like ‘everyone likes her’ — we do not mean that every person in the universe likes her, but just everyone within some contextually given social circle. Lycan says the restricted domain interpretation does not require that we restore the unstated restrictions; it is more like the use of a demonstrative pronoun.