Deconstructing “On Denoting” Oswaldo Chateaubriand (PUC-Rio, CNPq)

“On Denoting” marks a fundamental turning point in Russell’s philosophical outlook. With the analysis of denoting phrases, the formulation of the distinction of knowledge by acquaintance and knowledge by description, and the implicit use of Ockham’s razor as an eliminative tool, it set the basis for much of Russell’s later philosophical and logical work, including logical atomism, the no-class theory, and the ramified hierarchy of types. Although it has been said that Russell was “a philosopher without a philosophy” (Wood 1959, p. 260), I think that from 1905 on Russell’s philosophy was remarkably faithful to the ideas first presented in “On Denoting”. Not only did these ideas have a lasting effect on Russell’s philosophy, but they also had considerable influence on the development of analytic philosophy as a whole. In this paper I will discuss Russell’s treatment of definite descriptions in “On Denoting”, and will argue that although it is successful in achieving an interesting reduction of contexts involving descriptions to contexts in quantification logic, it contains important ambiguities.1

1. Descriptive terms and descriptive predicates. By a descriptive term I understand a singular term of the form ‘the so-and-so’, such as ‘the present King of France’, ‘the author of Waverley’, and so on. Most descriptive terms are obtained from descriptive functions filling up argument places.2 Thus, the term ‘the author of Waverley’ can be obtained from the descriptive function ‘the author of z’ substituting ‘Waverley’ for ‘z’. As a general notation for descriptive terms and descriptive functions I use ‘ixFx’, ‘ixRxz’, ‘ixRxz1...z n’, and variations on these forms. The basic feature of a descriptive term is (1) "x(ixFx = x « (Fx & "y(Fy ® y = x))).

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I discuss various issues relating to Russell’s theory of descriptions in Chateaubriand 2001 (especially chapters 3 and 11), and summarize some of the points in Chateaubriand 2002. I shall not presuppose these discussions here, but Chateaubriand 2002 would be a helpful complement to my arguments. 2 Descriptive functions are discussed at length in Principia Mathematica *30. Russell also remarks on them in Russell 1919 (pp. 46, 167, 180), and in Russell 1959 (p. 89).

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Similarly, the basic feature of a descriptive function is (2) "x"z1..."zn(ixRxz1...zn = x « (Rxz1...zn & "y(Ryz1...zn ® y = x))). By a descriptive predicate I understand a predicate of the form ‘is the so-and-so’, such as ‘is the present King of France’, ‘is the author of Waverley’, and so on.3 A descriptive predicate of the form ‘x is the F’ is obtained from the predicate ‘x is an F’ by adding a uniqueness clause ‘and only x is an F’—or ‘and nothing other than x is an F’. That is, ‘x is the F’ is the predicate (3) [Fx & "y(Fy ® y = x)](x). More generally, a descriptive predicate of the form ‘x is the R of z1, ..., zn’ is the predicate (4) [Rxz1...zn & "y(Ryz1...zn ® y = x)](x, z1, ..., zn). I use ‘[!xFx](x)’ and ‘[!xRxz1...zn](x, z1, ..., zn)’, and variations on these forms, as a notation for descriptive predicates—and they can be taken as abbreviations for (3) and (4), respectively. It should be noticed that whereas the operator ‘i’ is a variable binding operator that applied to a predicate F gives as a result a singular term ‘ixFx’, the operator ‘!’ applied to a predicate F gives as a result another predicate with the same free variables .4 The basic feature of a descriptive predicate is (5) "x([!xFx](x) « (Fx & "y(Fy ® y = x)). More generally (6) "x"z1..."zn([!xRxz1...zn](x, z1, ..., zn) « (Rxz1...zn & "y(Ryz1...zn ® y = x))). It is important to realize that by (3) and (4) descriptive predicates are part of quantification logic, and do not require additional interpretation. In other words, they are available to users of quantification logic independently of any views about descriptive terms and descriptive functions.

2. Russell’s ambiguous treatment of contexts involving descriptions. 3 4

Not necessarily in the present tense. I.e., ‘[!xFx](x)’ contains ‘x’ free.

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When Russell starts his analysis of definite descriptions in “On Denoting” (p. 417, 15-36), he considers the example 5

(7) the father of Charles II was executed. “This,” he claims, “asserts that (8) there was an x who was the father of Charles II and was executed.” He then proceeds to analyze (9) x was the father of Charles II as (10) x begot Charles II & "y(y begot Charles II ® y = x), and concludes that (7) becomes (11) $x(x begot Charles II & "y(y begot Charles II ® y = x) & x was executed).6 In this analysis, we see that (7) involves the descriptive term ‘the father of Charles II’, whereas (8) involves the descriptive predicate ‘was the father of Charles II’. The descriptive predicate is correctly analyzed in the natural way in (10), and is then used to analyze (8) in (11). We may say that by means of the use of existential quantification, Russell’s analysis reduces a context involving a descriptive term to a context involving a descriptive predicate. Let me discuss now another example that plays an important role in “On Denoting”, namely (12) Scott was the author of Waverley. In his initial analysis (p. 423, 22-23), Russell interprets (12) as 5

I refer to “On Denoting” and to other works in The Collected Papers of Bertrand Russell by page number and line indications. 6 I use standard quantifications instead of Russell’s formulations with ‘true of’ and ‘false of’, which introduce additional complications.

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(13) Scott was identical to the author of Waverley, which he then analyzes as (14) One and only one entity wrote Waverley, and Scott was identical with that one. Or, in explicit form, (15) $x(x wrote Waverley & "y(y wrote Waverley ® y = x) & Scott = x). However, in (p. 427, 3-5) Russell claims that the proper analysis of (12) is (16) Scott wrote Waverley & "y(y wrote Waverley ® y = Scott). This parallels the analysis of (9) in (10), and is the most natural analysis, interpreting (12) as involving the descriptive predicate ‘was the author of Waverley’. The identity version (13), on the other hand, interprets the copula ‘was’ as ‘was identical to’ in relation to the descriptive term ‘the author of Waverley’, and then reduces the context to a context involving the descriptive predicate ‘was the author of Waverley’ by means of the existential quantification (17) $x(x was the author of Waverley & Scott = x). Which of these two interpretations, (15) or (16), should we attribute to Russell? Although (15) is generally favored in Russell’s works, I think that the distinction between descriptive terms and descriptive predicates was not clear to Russell, and that this led to some confusion about this issue, so that at times he said one thing, and at other times he said the other.7 I hold that the correct analysis of (12) is (16), and I will argue that Russell’s arguments in “On Denoting” involving (15) are questionable. 7

Aside from various contexts in “On Denoting”, the clearest place where Russell takes the predicative interpretation is in Russell 1911 (p. 151, 39-42) where he says: The proposition “a is the so-and-so” means that a has the property so-and-so, and nothing else has. “Sir Joseph Larmor is the Unionist candidate” means “Sir Joseph Larmor is a Unionist candidate, and no one else is”. In the version in Russell 1912 (p. 53) he changes the last sentence to: ‘Mr. A is the Unionist candidate for this constituency’ means ‘Mr. A is a Unionist candidate for this constituency, and no one else is’.

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3. Russell’s first puzzle. Russell’s first puzzle concerns the statement (18) George IV wished to know whether Scott was the author of Waverley. He argues (p. 420, 23-27) that since “in fact Scott was the author of Waverley ... we may substitute Scott for the author of Waverley, and thereby prove” (19) George IV wished to know whether Scott was Scott, which he considers an unlikely result. Russell’s solution (p. 424, 14-17), given after the analysis (15) of (12), is that (18) means (20) George IV wished to know whether one and only one man wrote Waverley and Scott was that man, which, using (15), becomes (21) George IV wished to know whether $x(x wrote Waverley & "y(y wrote Waverley ® y = x) & Scott = x). If we analyze (18) as involving the descriptive predicate ‘was the author of Waverley’, on the other hand, and use (16), the result is (22) George IV wished to know whether Scott wrote Waverley & "y(y wrote Waverley ® y = Scott). Since (22) does not contain a descriptive term, the possibility of using substitutivity of identity does not arise. I will now argue that (22) gives a better solution to Russell’s puzzle than (20)-(21). Did George IV wish to know whether someone wrote Waverley? Presumably not, for he already knew (or assumed) that someone had written Waverley, and what he wished to know is whether Scott was the one who did. Therefore, the addition of ‘one and only one

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man wrote Waverley’ in (20) is incorrect. If we move that phrase out, we get Russell’s alternative primary interpretation of (18) (23) One and only one man wrote Waverley, and George IV wished to know whether Scott was that man, which he also expresses (p. 424, 17-22) as (24) George IV wished to know, concerning the man who in fact wrote Waverley, whether he was Scott. It is interesting to analyze these a bit. Consider (23). We can read ‘Scott was that man’ as ‘Scott was the man who wrote Waverley’, and interpret this either as a predication, with the descriptive predicate ‘was the man who wrote Waverley’, or as an identity, with the descriptive term ‘the man who wrote Waverley’. Russell’s interpretation is the latter, whereas I think that the most natural interpretation is the former. If we do take the predicative interpretation, then we are essentially stating (18) again, except for the gratuitous addition of the initial claim that one and only one man wrote Waverley. Consider (24) now. Russell suggests (p. 424, 22-23) that (24) “would be true ... if George IV had seen Scott at a distance, and had asked ‘Is that Scott?’”. Russell’s idea is, I suppose, that George IV is asking ‘Is that Scott?’ of the man he saw at a distance. But then it does not matter whether I describe this man as the author of Waverley, or describe him as Scott—as Russell does in the passage I just quoted. Therefore, if (24) is true with this interpretation, so is (25) George IV wished to know, concerning Scott, whether he was Scott. Which means that, with the primary interpretation, George IV did indeed wish to know whether Scott was Scott. My conclusion is that Russell’s first puzzle arises from misinterpreting (18) as involving a descriptive term instead of a descriptive predicate.8 Evidently, however, one may counter that the puzzle could be reformulated using an explicit identity statement, even with the same example. For instance,

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I am not denying, of course, that there is a general problem involving substitutivity of identity in intensional contexts.

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(18¢) George IV wished to know whether Scott was identical to the author of Waverley. I do not find such identity statements at all natural, and I think that Russell gives them their due when he says (pp. 426-427, 34-7): The usefulness of identity is explained by the above theory. No one outside of a logic-book ever wishes to say ‘x is x’, and yet assertions of identity are often made in such forms as ‘Scott was the author of Waverley’ or ‘thou art the man’. The meaning of such propositions cannot be stated without the notion of identity, although they are not simply statements that Scott is identical with another term, the author of Waverley, or that thou art identical with another term, the man. The shortest statement of ‘Scott is the author of Waverley’ seems to be ‘Scott wrote Waverley; and it is always true of y that if y wrote Waverley, y is identical with Scott’. It is in this way that identity enters into ‘Scott is the author of Waverley’; and it is owing to such uses that identity is worth affirming.

That it is completely unnatural to interpret contexts involving a descriptive predicate ‘is the so-and-so’, or ‘was the so-and-so’, as identities can also be seen by considering questions of the form ‘who is the so-and-so?’, or ‘what is the such-and-such?’. For, although anyone can naturally ask ‘Who is the author of “On Denoting”?’, or ‘What is the title of Russell’s first book?’, it seems a bit perverse to ask ‘Who is identical to the author of “On Denoting”?’, or ‘What is identical to the title of Russell’s first book?’.

4. Russell’s second puzzle. Russell’s next puzzle concerns the statement (26) The present King of France is bald, and is the most famous of Russell’s examples. Russell argues (p. 420, 28-32) that by the law of excluded middle, (26) should be either true or false. “Yet,” he says, “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.” Russell’s solution consists in reducing (26) to (27) $x(x is the present King of France & x is bald), with ‘is the present King of France’ as a descriptive predicate which is interpreted in the natural way as

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(28) $x(x is now King of France & "y(y is now King of France ® y = x) & x is bald). Since (27) and (28) are clearly false, the problem with the law of excluded middle is solved. Moreover, Russell argues (p. 425, 1-11) that using the distinction between primary and secondary occurrences we can see that (29) The present King of France is not bald, is true with the secondary interpretation (30) Ø$x(x is now King of France & "y(y is now King of France ® y = x) & x is bald), and false with the primary interpretation (31) $x(x is now King of France & "y(y is now King of France ® y = x) & x is not bald). Hence, Russell’s analyses respect the law of excluded middle and do not go counter the law of non-contradiction. The main objection to Russell’s analysis (28) was given years earlier by Frege, when he argued in “On Sense and Reference” (p. 40) that whereas an assertion involving a descriptive term carries a presupposition that the term uniquely refers, this existence and uniqueness claim is not part of what is asserted. I entirely agree with Frege on this point, and I have argued for it elsewhere, 9 but I will take a somewhat different route here. Before analyzing statements containing ‘the’, Russell analyzes the statement (32) I met a man. “If this is true,” he says (p. 416, 22-25), “I met some definite man; but that is not what I affirm.” He then analyses (32) as (33) $x(I met x & x is human). But why (33) and not 9

Chateaubriand 2001, pp. 102-104.

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(34) $!x(I met x & x is human), where ‘$!x’ means ‘there is a unique x’? For, given that I did meet some definite man, as Russell says, then I can go on to assert something like ‘the man I met wore a yellow hat’, whereas a simple existential statement does not license such use of the definite article. Thus, the assertion (35) $x(x is a philosopher & x is tall), does not license the use of ‘the tall philosopher’. Some uses of the indefinite articles ‘a’ and ‘an’ carry a presupposition of uniqueness, and others don’t; therefore, if we want this to be clear from the logical interpretation, we must find a way to indicate it. Adding the claim of uniqueness to the content of the statement, as in (34), is a way to do it, but it would be better to have an explicit notation to indicate presupposition—because, as Russell says, the assertion of uniqueness is not part of what is asserted in (34). The use of descriptive terms, with the article ‘the’ in the singular, generally carries a presupposition of existence and uniqueness,10 and therefore it is not necessary to indicate it explicitly—but, as Frege claims, it is not part of what is asserted. Descriptive predicates, properly interpreted, function somewhat differently. (12), as interpreted in (16), with ‘was the author of Waverley’ as a descriptive predicate, carries a presupposition of existence through the use of the name ‘Scott’, and explicitly asserts uniqueness with the clause ‘"y(y wrote Waverley ® y = Scott)’. Russell’s move from (26) to (28) can now be analyzed as follows. Consider (26¢) A present King of France is bald, which Russell would correctly analyze as (27¢) $x(x is a present King of France & x is bald). By parity of form, Russell goes from (26) to (27)—as in the move from (7) to (8). But now the descriptive term ‘the present King of France’ gives way to the descriptive predicate ‘is the present King of France’, which does contain an explicit assertion of uniqueness. Hence, Russell takes this as part of the content of (26), and offers (28) as an analysis of (26). 10

A special case is that of negative existentials, discussed in §6 below.

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5. Truth-value gaps. Several of Russell’s arguments concern the (im)possibility of truth-value gaps. According to Russell (p. 419, 16-18), if ‘the present King of France’ were a denoting term that does not denote, then (26) “ought to be nonsense; but it is not nonsense, since it is plainly false.” Again, I side with Frege against Russell on this issue, distinguishing sense and reference. But Russell offers two additional arguments. The first (p. 419, 18-25) involves the following statement: (36) If u is a class which has only one member, then that one member is a member of u, or, in an alternative formulation, (37) If u is a unit class, the u is a u. Let us symbolize this as (38) $x(x Î u & "y(y Î u ® y = x)) ® i x(x Î u) Î u. Russell argues as follows (p. 419, 21-25): This proposition ought to be always true, since the conclusion is true whenever the hypothesis is true. But ‘the u’ is a denoting phrase, and it is the denotation, not the meaning, that is said to be a u. Now if u is not a unit class, ‘the u’ seems to denote nothing; hence our proposition would seem to become nonsense as soon as u is not a unit class.

Russell is assuming that because the consequent of (38) is true whenever its antecedent is true, (38) is always true. But this is incorrect. What actually follows is that (38) cannot be false, because in order to be false it would have to have a true antecedent and a false consequent. If we allow that the consequent is neither true nor false when u is not a singleton, and, with Frege, hold that lack of reference or truth-value of a part of a proposition implies lack of truth-value for the whole, then (38) is neither true nor false when its antecedent is false.11 11

I am treating (36)-(38) as conditional assertions, and the source of Russell’s confusion may be that the antecedents of these conditionals logically imply the consequents. In fact, antecedents and consequents are logically equivalent, in the sense that the truth of each of them guarantees the truth of the other. Take (38), for instance. If the antecedent is true, then the consequent is true, as Russell argues. Conversely, if the consequent

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Russell follows this up with a second argument (p. 419, 26-32) to the effect “that such propositions do not become nonsense merely because their hypotheses are false.” “The King in The Tempest might say,” he says, (39) If Ferdinand is not drowned, Ferdinand is my only son. “Now,” he continues ‘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.

This argument confuses a descriptive term with a descriptive predicate. The proper interpretation of (39) is: (40) Ferdinand is not drowned ® (Ferdinand is my son & "x (x is my son ® x = Ferdinand), with the descriptive predicate ‘is my only son’, rather than the descriptive term ‘my only son’. And (40) is true either because its antecedent and consequent are true, or because its antecedent is false.

6. Russell’s third puzzle. “Consider the proposition (41) A is different from B,” says Russell, and then argues (420, 34-39): If this is true, there is a difference between A and B, which fact may be expressed in the form ‘the difference between A and B subsists’. But if it is false that A differs from B, then there is no difference between A and B, which fact may be expressed in the form ‘the difference between A and B does not subsist’. But how can a non-entity be the subject of a proposition.

is true, then ‘i x(x Î u)’ denotes the unique element of u, and the antecedent is true. This relation between Frege’s analysis of descriptive terms (in the consequent) and Russell’s analysis of descriptive terms (in the antecedent) is examined in more detail in Chateaubriand 2001 (pp. 106-107) and in Chateaubriand 2002 (p. 220).

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Although nowadays it would be hard to find someone who would express (41) as (42) the difference between A and B subsists, and its negation as (43) the difference between A and B does not subsist, these were reasonable statements at the time, especially considering Russell’s earlier discussion of Meinong’s works.12 However, the important problem that Russell is raising with this example is the problem of true negative existentials. Russell’s analyses are (p. 425, 13-22) (44) There is one and only one entity x such that x is the difference between A and B, and (45) It is not the case that there is one and only one entity x such that x is the difference between A and B. As can easily be seen, these analyses involve descriptive predicates rather than descriptive terms, and are available to any theory that admits quantification logic. In fact, the qualification ‘one and only one’ is superfluous, because the uniqueness claim is already part of the content of the descriptive predicate. Thus, Russell’s analyses come down to (44¢) $x x is the difference between A and B, and (45¢) Ø$x x is the difference between A and B. Although these are still odd, their oddity derives from the nature of the example, not from the analysis. If we take instead (46) The present King of France exists, 12

See Russell 1904 (p. 470) and Russell 1905a (p. 505).

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and (47) The present King of France does not exist, the results are quite natural. For, (46) is (46¢) $x x is the present King of France, which with Russell’s analysis becomes (46¢¢) $x(x is now King of France & "y(y is now King of France ® y = x)), and (47) is (47¢) Ø$x x is the present King of France, which becomes (47¢¢) Ø$x(x is now King of France & "y(y is now King of France ® y = x)). It should be noticed that there are two possible interpretations of (46)-(47), depending on whether one treats ‘exists’ as a predicate or as an existential quantification. With ‘exists’ as a predicate, (46) affirms (and (47) denies) existence of the entity allegedly denoted by the descriptive term ‘the present King of France’. In this case, the analysis of (46)-(47) as (46¢)-(47¢) reduces contexts involving the predicate ‘exists’ and a descriptive term (‘the present King of France’), to contexts involving existential quantification and the corresponding descriptive predicate (‘is the present King of France’). But (46)-(47) can also be interpreted directly in terms of existential quantification and the descriptive predicate ‘is the present King of France’, thus (46$) There is such a thing as the present King of France, or (46$¢) Something is the present King of France, and 13

(47$) There is no such thing as the present King of France, or (47$¢) Nothing is the present King of France. In which case Russell’s analysis is the straightforward reading of these as (46¢)-(47¢).13

7. Russell’s criticisms of Frege. Russell’s first criticism (p. 419, 6-34) concerns Frege’s informal theory of descriptions, according to which a sentence containing a descriptive term that does not denote is neither true nor false. Russell argues that a sentence such as (26) “ought to be nonsense” on Frege’s view, but that “it is not nonsense, since it is plainly false.” This argument begs the question against Frege, because Frege’s point is precisely that whereas (26) clearly has a sense, it does not have a truth-value. And the reason that it does not have a truth-value, is that there being no such thing as the present king of France, there is nothing for the predicate ‘is bald’ to apply to or not to apply to.14 Russell’s claim that (26) is false presupposes that what is not true is false, which is not at all plain.15 Russell next (p. 420, 3-10) criticizes Frege’s formal account of descriptions that attributes an arbitrary denotation in those cases where a denotation is missing. Here I agree with his claim that “this procedure, though it may not lead to actual logical error, is plainly artificial, and does not give an exact analysis of the matter.” Russell’s main argument, however, is the long argument in pp. 421-423 where he attacks Frege’s distinction of sense and reference directly. This argument is quite clearly fallacious, and it depends on a simple confusion that Russell states at the very beginning. He says (p. 421, 10-15):

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For a more detailed discussion of this issue see Chateaubriand 2001 (pp. 111-115) and Chateaubriand 2002 (pp. 221-223). 14 See “On Sense and Reference”, pp. 32-33. 15 In his reply to Strawson, Russell says (Russell 1957, p. 388) that he “find[s] it ... convenient to define the word “false” so that every significant sentence is either true or false”. He also claims (p. 389) that “[t]his is a purely verbal question”. But this is not so, because there is a very significant difference between predications involving non-denoting singular terms and predications involving denoting singular terms. In the former case, neither the predication nor its (predicate) negation is true, and, hence, both are false in Russell’s sense. In the denoting case either the predication or its (predicate) negation is true, and the other is false. This difference must be explained, and it is not a purely verbal question.

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When we wish to speak about the meaning of a denoting phrase, as opposed to its denotation, the natural mode of doing so is by inverted commas. Thus we say: The centre of mass of the Solar System is a point, not a denoting complex; ‘The centre of mass of the Solar System’ is a denoting complex, not a point.

The problem is that Russell’s term ‘denoting complex’ collapses Frege’s distinction between the phrase and the sense expressed by the phrase. According to Frege, there are three different things involved, not two as Russell claims. First, there is the phrase (48) The centre of mass of the Solar System. By means of this phrase within inverted commas we refer to it, not to its sense (or meaning). Thus (49) ‘The centre of mass of the Solar System’ refers to (or denotes) the phrase (48). The phrase (48) expresses a sense, to which we can refer by (50) The sense expressed by the phrase ‘The centre of mass of the Solar System’, or simply as (51) The sense of ‘The centre of mass of the Solar System’. Hence, it is wrong to say that (p. 421, 23-24) when C occurs it is the denotation that we are speaking about; but when ‘C’ occurs, it is the meaning.

Since when a phrase occurs within inverted commas we are speaking of the phrase, not the meaning, it is easy to detect several fallacious inferences in Russell’s argument. The first comes in the argument (p. 421, 32-38) that concludes as follows: Thus in order to get the meaning we want, we must speak not of “the meaning of C”, but of “the meaning of ‘C’”, which is the same as “C” by itself.

The last statement is incorrect. A second fallacious inference of the same nature comes in the next argument (pp. 421-422, 41-4), which concludes: 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”.

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In fact, even Russell’s use of the variable ‘C’ is problematic in these arguments. Russell’s conflation of the phrase and the meaning is also evident in the following passage (p. 422, 914): This leads us to say that, when we distinguish meaning and denotation, we must be dealing with the meaning: the meaning has denotation and is a complex, and there is not something other than the meaning, which can be called the complex, and be said to have both meaning and denotation.

Part of Russell’s confusion seems to derive from his initial remark (p. 421, 24-31): Now the relation of meaning and denotation is not merely linguistic through the phrase: there must be a logical relation involved, which we express by saying that the meaning denotes the denotation. But 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.

It is quite true that the relation of meaning and denotation is not through the phrase. Indeed, according to Frege, it is the relation of the phrase to the denotation that goes through the meaning. The meaning, or sense, which is a manner of presentation, may or may not determine an object (say), and if it does, then this object is the denotation of the phrase. But saying that “the meaning denotes the denotation” leads Russell to disregard the phrase entirely, and to conflate phrase and meaning as “the denoting complex”. Russell’s final claim is also quite curious, for as I mentioned at the beginning “On Denoting” already contains the doctrine of knowledge by acquaintance and knowledge by description, according to which most “things” can only be got at by means of denoting phrases.16 And even aside from that, it is not at all surprising that abstract entities—as Frege held senses to be—can only be got at by means of denoting phrases. In fact, this will hold for any entity to which one cannot point.

8. Conclusion. Although my examination of Russell’s paper has been largely critical, my conclusion is not negative. On the contrary, I think that Russell had good insights about descriptive predicates, which suggested to him the possibility of a reduction of contexts involving descriptive terms to contexts involving descriptive predicates. The reduction consists in taking any sentential context

16

This is made quite clear at the beginning (p. 415, 16-35) and at the end (p. 427, 8-29) of “On Denoting”.

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(49) ... ixFx ... involving a descriptive term ‘ixFx’, and analyzing it as a sentential context (50) $x([!xFx](x) & ... x ...) involving the descriptive predicate ‘[!xFx](x)’. This reduction has several interesting features, some of which I list below. I. Whereas (49) may lack a truth-value, (50) is always either true or false. II. Although (49) and (50) need not be materially equivalent, for (49) may be truth valueless and (50) false, they are logically equivalent, in the sense that each is a logical consequence of the other, as can be seen from (1) and (5). In other words, if (49) is true, then (50) is true; and vice versa. III. Although there may not be a difference in truth-value in the reductions of a context (49) and of the corresponding negative context with the primary interpretation (50), the difference can be recovered by distinguishing secondary interpretations. Therefore, both the principle of excluded middle and the principle of contradiction are preserved. IV. The reduction gives a natural and adequate interpretation of negative existentials. However, whereas I do agree that the analysis of descriptive predicates, as in (10) and (16), is correct both as an analysis of their use in English, and as an analysis of their logical form, I disagree with claims that Russell’s reduction gives a correct analysis of the use of descriptive terms in English, and that it reveals the “real” logical form of statements involving descriptive terms. The position that I defend (Chateaubriand 2001, 2002) is that the proper analysis of descriptions involves a combination of Russell’s insights about descriptive predicates with Frege’s insights about descriptive terms.17

References

17

I am grateful to Abel Lasalle Casanave and to John Corcoran for helpful remarks on an earlier version.

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Chateaubriand, O., 2001, Logical Forms: Part I - Truth and Description, Campinas: Unicamp (Coleção CLE). Chateaubriand, O., 2002, “Descriptions: Frege and Russell Combined,” Synthese 130, 213226. Frege, G., 1892, “On Sense and Reference,” in M. Black and P. Geach (eds.) Translations from the Philosophical Writings of Gottlob Frege, Oxford: Blackwell, 1960. Russell, B., 1904, “Meinong’s Theory of Complexes and Assumptions,” Mind 13, 204-219, 336-354, 509-524. Reprinted in Russell 1994, 432-474. Russell, B., 1905a, “The Nature of Truth”. In Russell 1994, 492-506. Russell, B., 1905b, “On Denoting,” Mind 14, 479-493. Reprinted in Russell 1994, 415-427. Russell, B., 1911, “Knowledge by Acquaintance and Knowledge by Description,” Proceedings of the Aristotelian Society 11, 108-128. Reprinted in Russell 1992, 148-161. Russell, B., 1912, The Problems of Philosophy, London: Williams and Norgate. Russell, B., 1919, Introduction to Mathematical Philosophy, London: George Allen & Unwin. Russell, B., 1957, “Mr. Strawson on Referring,” Mind 66, 385-389. Russell, B., 1959, My Philosophical Development, London: George Allen & Unwin. Russell, B., 1992, The Collected Papers of Bertrand Russell, vol. 6, edited by J. G. Slater, London: Routledge. Russell, B., 1994, The Collected Papers of Bertrand Russell, vol. 4, edited by A. Urquhart, London: Routledge. Whitehead, A. N. and Russell, B., 1910, Principia Mathematica, vol. 1, Cambridge: Cambridge University Press. Wood, A., 1959, “Russell’s Philosophy: A Study of its Development”. Unfinished manuscript printed in Russell 1959, 255-277.

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