Three Difficulties in Bertrand Russell's Theory of Descriptions

Abstract

Three difficulties which emerge in Bertrand Russell’s Theory of Descriptions are analysed in this paper. In each case one or several possible solutions of the analysed difficulty are studied together with the consequences which such solutions have with respect to the validity and application of the theory. The problems considered are: first, the one concerning the definition of “definite description”; second, that about the application of the theory to the analysis of proper names which appear in historical discourse and finally the Russell-Strawson controversy with respect to the existential content of sentences whose grammatical subject is a definite description.
In the first part, the question of presenting a general account of definite descriptions is discussed. Three formulations which attempt to define these expressions are examined. The first definition specifies a formal criterion: “a definite description is a phrase of the form ‘the-such-and-such’”. There are two arguments against this formulation, showing that this criterion is neither sufficient nor necessary to explain the semantic features of definite descriptions. After this the following formulation is considered: “A description is a phrase of the form, the term that etc., or more explicitly the term x that satisfies Φ x, where Φ x is some function satisfied by one and only one argument.” Notwithstanding that this characterization includes a semantic notion, it has the disadvantage of excluding empty descriptions, that is to say, those constructed with functions satisfied by more than one individual or by none. Finally, an account of the semantic behaviour of definite descriptions is analysed: “A definite description is a linguistic expression by which it is intended to mention an individual by alluding to a property that only he possesses.” The difficulty of this definition is that it excludes descriptions which a particular speaker believes to be empty.
As a solution to the difficulties which the aforementioned accounts present, a definition is proposed to define the expression “‘α’ is a definite description for a in t” where ‘α’ and ‘β’ are variables of linguistic expressions and ‘a’ and ‘t’ are variables of language users and time instants respectively. The outstanding feature of such a definition is that in its definiendum the concept of “intension” appears, as it is used by Carnap in his article “Meaning and Synonymy in Natural Languages”. Def; α is a definite description for a in t = def. there exists a β such that it fulfills the following conditions:
(a) β is a general term (for a in t)
(b) α contains β (syntactically)
(c) In virtue of the intension of α for a in t (and not merely for empirical questions) the following will hold:
(y) (α denotes y ≡ y is the only individual that has the property associated with β).
The author finishes this section criticising the definition and pointing out some difficulties, namely that it does not apply to some cases of ordinary usage and that it relies on the notion of intension.
In the second part, problems arising from the relation between definite descriptions and proper names in a logical sense is a symbol that represents an object of which one has knowledge by acquaintance and does it without assigning any property to it. However, with the exception of logical proper names, other expressions considered generally to be names are in fact abbreviated definite descriptions. Hence, occurrences of common proper names are replaceable by descriptions and, in accordance with this, it may be said that the meaning of a proper name is formed by the meaning of an associated definite description. Nevertheless, a direct consequence of this interpretation of the relation between proper names and descriptions, is that the latter can vary according to the context in which the names are used, so the meaning of a name might be varied. In this part of the article problems arising from the preceeding considerations are developed. Making use of the formal properties of descriptions, as presented in Principia Mathematica, it is shown that this interpretation does not give coherent results within the context of historical proper names.
The author of the article suggests that in order to consider proper names as abbreviated descriptions, a condition is required: the general terms that the description contains should be specified. It is assumed that the application of this limiting condition would unify the formal and semantic aspects of the theory of descriptions. However, in the article it is shown how in the case of names which appear in historical contexts it is not possible to fulfill this condition. Thus, from this a new difficulty arises in the application of the theory of descriptions; i.e., that it is not possible to extend the results which are specifically obtained for definite descriptions to other singular terms.
In the third and last part of the paper the objections which Strawson raises against Russell’s Theory of Descriptions are analysed. Originally, Strawson thought that Russell was mistaken on the following points: (a) in that whichever person utters a sentence in which the grammatical subject is a definite description he would be formulating a truthful assertion or a false one, and (b) that part of which he would be asserting would be that in reality there exists one and only one object which satisfies the function contained in the description. In the article is stressed that Strawson, in a later paper, withdraws his objection to (a) pointing out that the thesis of truth value gaps and the theory of falsity (the thesis accepted by Russell) present advantages which are not mutually exclusive ((b), however, is not discussed in this paper).
The author then describes two technical meanings for the expressions “false” and “asserts”. Let p and q be any two statements, Def: p is falsetc if it does not fulfill some of its truth conditions.
Taking truth conditions of a statement p, the conditions that ought to be fulfilled in the world for that statement to be true and that appear specified in its meaning, he gives the following definition:
Def: Given two statements p and q, p assertstc q if the truth conditions of q are also truth conditions of p. With these definitions an interpretation of (a) and (b) is given.