Denoting Phrases

Frege's Theory of Descriptions

Russell’s Theory of Descriptions


(A) Russell’s Theory

On Frege’s view, if a name lacks a Bedeutung, then any sentence in which the name occurs also lacks a Bedeutung. To make use of such names in ‘scientific’ discourse, Frege therefore suggested that they be assigned the null set as their referent (for details, see FR, pp. 384-5). Russell regarded such a stipulation as ‘plainly artificial’, and he also objected to Frege’s theory of sense on the ground that it offered no way of saying what the sense of a name was (see FMS, pp. 181-2). Instead, Russell developed his famous ‘theory of descriptions’. Consider Russell’s example:

(K)   The present King of France is bald.

On Russell’s analysis, this is equivalent to the conjunction of the following three propositions, with their formalizations in square brackets:

(K1)   There is at least one King of France.   [(x) Kx]

(K2)   There is at most one King of France.   [(x) (y) ( (Kx & Ky) x = y)]

(K3)   Whatever is King of France is bald.    [(x) (Kx Bx)]

Put together, we have:

(K')   There is one and only one King of France, who is bald.

(K*)   (x) (Kx & (y) (Ky y = x) & Bx).

The two important features of this analysis, as far as Russell was concerned, were firstly, that it allowed propositions containing denoting phrases to possess a truth-value even if there was nothing denoted (in fact, to be false in this case, since (K1) would be false), and secondly, that it showed how such propositions could be understood (i.e. their meaning grasped) independently of any acquaintance with the denotation (if any) of the denoting phrases. All that is required is knowledge of the properties represented by ‘K’ and ‘B’ and the logical constants (including the quantifiers). In (K'), the phrase ‘The present King of France’ (‘The K’) no longer appears – it has been ‘analysed away’; and it is this that underpins Russell’s claim that definite descriptions (of the form ‘The K’) have no ‘independent meaning’ of their own.


(B) Strawson’s Response


(i) Sentences and Statements

Strawson’s essential strategy (in ‘On Referring’) is to distinguish between sentences, which can be characterized as meaningful (significant) or not, and statements (‘assertions’, or ‘uses of sentences’, as Strawson himself calls them), which are the appropriate candidates for the assignment of a truth-value; and he argues that Russell has confused the two. Whilst ‘meaning’ is a function of the sentence or expression, Strawson writes, ‘mentioning and referring and truth or falsity, are functions of the use of the sentence or expression’ (p. 9).

According to Strawson, whilst the sentence displayed by (K) is meaningful, it fails to make, if used today, a true or false statement, just because, in this case, there is a failure of reference. In his Introduction to Logical Theory, Strawson distinguishes between entailment and presupposition, his point then being that in stating that the present King of France is bald, one is presupposing that there is a King of France.


(ii) Clarification of the Dispute

(a)  As Strawson initially presented his argument, it was unclear whether he thought that reference-failure resulted in a statement that was neither true nor false or in no statement at all. In ‘Identifying Reference and Truth-Values’, he suggests that it was the former that he had in mind.

(b)  In his reply to Strawson (‘Mr Strawson on Referring’), Russell suggests that the issue as to whether a proposition with a denotationless expression is false or neither-true-nor-false is ‘a mere question of verbal convenience’ (p. 179); and in Strawson’s own later reflections on the dispute, he writes: ‘What we have here is the familiar philosophical situation of one party being attracted by one simplified, theoretical – or ‘straightened out’ – concept of truth and falsity, and the other by another . . . ordinary usage does not deliver a clear verdict for one party or the other’ (p. 82), a remark which Russell would no doubt endorse. However, Russell makes clear that his intention was to provide expressions with a more precise sense than their ordinary, vague sense; whilst Strawson, though agreeing that ‘ordinary language has no exact logic’ (‘On Referring’, p. 27), thinks that this can distort our understanding of cases where the ‘straightening out’ is less applicable – cases where there is a different ‘topic or centre of interest’ (p. 92).

(c) In ‘Reference and Definite Descriptions’, Donnellan suggests that both Russell and Strawson have failed to appreciate the distinction between two different uses of definite descriptions – the attributive use and the referential use: ‘A speaker who uses a definite description attributively in an assertion states something about whoever or whatever is the so-and-so. A speaker who uses a definite description referentially in an assertion, on the other hand, uses the description to enable his audience to pick out whom or what he is talking about and states something about that person or thing’ (§3). This characterization of the attributive use still leaves open whether there is any reference to an object, but Donnellan’s understanding of the referential use is clear. Here the basic point is that a statement such as ‘The man in the corner drinking martini is a professor’ can be true even if the identifying description is false, as long as it picks out the intended object and says something true of that object. However, Donnellan’s discussion of this latter possibility seems in turn to ignore the distinction between what is strictly said on a particular occasion, and what has been conveyed. Being more precise in what is said, there would have to be a rephrased statement (in what sense would this still be the same statement?), so that the charge of ignoring the ‘referential’ use hardly seems a serious objection to either Russell or Strawson. Any ‘misdescription’ in identifying an object is parasitic upon correct descriptions, and these would seem neither ‘referential’ nor ‘attributive’ as Donnellan uses these terms.