The origins of Russell's theory of descriptions according to the unpublished manuscripts by Francisco A. Rodriguez-Consuegra I. INTRODUCTION THE DISCOVERY OF the paradoxes led Russell to reconsider the sort of definition he employed.! I call such definitions "construc­ tive'~ independently of other stated senses of the expression, because they (i) analyze the concept into "simple" components; (ii) presuppose a reduction-to these components; (iii) try to use ordi­ nary language as a guide; (iv) obtain precise meanings; and (v) imply a certain loss of intuitiveness. Thus, Russell's logicism in The Principles ofMathematics (1903a) appears strange because, whereas it reduces all mathematics to simple logical entities, it gives the same ontological status to reconstructed mathematical objects (i.e. numbers), which are not to he eliminated. The paradox of classes showed that the underlying referential­ ism failed in certain cases, which required therefore a new theory of denotation. In fact, starting from the paradox, the idea of dispensing with certain entities (like the class of all classes) appears for the first time, together with the philosophical import­ ance of the notion of "meaninglessness" of certain ex~ressions 1 As I explain in my 1989a. See my 1987a for an account of "constructive defini­ tions". 99 100 Russell winter 1989-90 The origins ofthe theory ofdescriptions 101 (Principles, pp. 103-4). This led him to the first theory of types differentforms ofterms), and between predicates and relations (as (Appendix B) and the first version of the "no classes theory" (in a two different forms of concepts). However, the analysis of plural letter to Frege),2 which clearly show how Russell accepted great (or ambiguous) denoting concepts-those expressed by quantifica­ ontological sacrifices. tional devices in conjunction with general terms-forced Russell However, there was still a long way to go until the discovery to a new complication of this ontology, which consisted in the that denotative functions can be derived from propositional admission of a larger category: objects (p. 58n.), which embraces functions, which led Russell to the theory of descriptions of 1905. entities denoted by those concepts.3 The problem of denoting First, the theory of meaning of the Principles contained an en­ appeared when Russell realized that in cases where a substantive deavour for distinguishing the logical and psychological involve­ (a class-concept) is preceded by certain w9rds ("the", "a", "some", ment in meaning, but did not completely clarify the complex "all", "every" or "any"), the result is a denoting concept involving distinction between meaning and denotation. Second, a great deal a relation between denoting terms (concepts) and denoted terms of unpublished work contained: (i) serious attempts ofincorporat­ (objects) which is very different from the usual, linguistic relation ing the objectivity of Frege's semantic notions; (ii) the pre-em­ of~eaning: "A concept denotes when, ifit occurs in a proposition, inence of "the" over other denoting functions; (iii) the need for the proposition is not about the concept, but about a term con­ clearly distinguishing knowledge by acquaintance and by descrip­ nected in a certain peculiar way with the concept" (p. 56). tion in order to state the conditions for understanding proposi­ A first result was an important distinction which is usually tions. Third was the discovery that the distinction. between misunderstood.' There are two kinds of meaning. The first applies meaning and denotation must be discarded, and fourth the theory to words and states a psychological and linguistic relation accord­ ofdescriptions by partially accepting Bradley's claim that certain ing to which words stand for or indicate other things or concepts proper names are only disguised descriptions. which are not symbols. The second applies only to certain con­ This allowed Russell systematically to apply an eliminative cepts and states a logical relation (denotation) between those con­ device, first to definitive descriptions, second to classes (mainly cepts and things, i.e. it consists in the designation or description through a substitutional theory), and then to propositions them­ of a term by a concept (pp. 51, 56). selves in favour of propositional functions (through the ramified Thus, both proper names and adjectives (and verbs) indicate theory of types). Thus, the main effect of the paradoxes was to terms, but while proper names indicate things, the rest indicate make it possible for Russell's definitions not only to construct the concepts. (Adjectives indicate predicates and verbs relations.) defined entities (e.g. numbers, as in the Platonism of the Prin­ Again, two of these three kinds of terms have a specific relation ciples), but also to eliminate them as mere "incomplete symbols'~ with other entities (I use this word for lack ofanother): predicates In the following, I shall describe these several stages from 1903 to 1905 (sec. II-IV) and then attempt a methodological interpreta­ tion ofthe resulting theory ofdescriptions (sec. V), which will lead 3 These new entities were, however, incompatible with Moore's relational theory us to an alternative view of the relationship between Russell's ofjudgment, which could admit only terms, or concepts (I attempt a general descriptions and ordinary language (sec. VI). studyofMoore's first philosophy inmy 1990e, and a description ofRussell's first assimilation of this philosophy in my 1988a). This was a consequence of the II. ATTEMPTS AT INCORPORATING A FREGEAN SEMANTICS formidable problems caused by imaginary proper names (Apollo, etc.), and some difficult denoting concepts not considered by Moore, like the ones involving Russell's theory of denotation in the Principles derived from two paradoxical entities (the class of all classes, etc.), or impossible objects (the main ontological distinctions: between things and concepts (as two round square, etc.). It is true that Russell regarded these last entities in full only after the theory of descriptions, but there are some places where we can see that he realized their great importance for a correct theory of denotation (see n. 18). 2 The letter to Frege is dated 24 May 1903 and may be found in Frege 1976a, pp. 4 A rare exception is the excellent Cassin 1970a. The analysis by Vuillemin 158-60. (1968a, pp. 73-8) is interesting, but it seems he does not realize the distinction. 102 Russell winter 1989-90 The origins ofthe theory ofdescriptions 103 denote other terms (as we saw above), but relations have an the meaning of a word with its indication-refere.nce (and the indefinable connection with truth because they constitute the meaning of a denoting concept with its denotation). Thus, al­ assertive element of propositions. The third kind of term, things, though Russell himselfattempted to identify his denoting concept are only the entities indicated by proper names, but they have no with Frege's Sinn, and therefore he translated "Bedeutung" as additional relation with other terms. This leads Russell to con­ "indication" (ibid.), his previous equivalence between Frege's sider the sole denoting concept which presupposes uniqueness­ distinction and the pair "denoting concept/entity denoted" implied "the': Russell admits the greatimportance ofthis term, recognizes that Bedeutung cannot be indication, for this is not a denoting-­ the merit of Peano's notation,5 and attributes to him the capacity relation. The consequence was the actual identification between to make possible genuine mathematical definitions defining terms Frege's sense-reference and Russell's indication-denotation. This which are not concepts (p. 63). is incompatible with Frege's intentions because in this way the This was the basis on which he faced the problem of denoting denoting concept can be the meaning as well as the indication of concepts which do not denote in spite of having a meaning. Rus­ the denoting expression. Thus Russell was really rejecting Frege's sell was not yet prepared completely to accept Bradley's attack distinction andpreserving the identification between meaning and against proper names:6 "when meaning is thus understood [in a reference.7 logical sense], the entity indicated by John does not have mean­ Nevertheless, the reinterpretation of Frege in the appendix is ing, as Mr Bradley contends; and even among concepts, it is only not the "missing link" between the Principles and "On Denoting' those that denote thathave meaning' (p. 51). That seems to imply (as claimed by Cassin 1970a, p. 261). Between these two views that "the present King of France" (the famous example whose there is a collection of unpublished manuscripts which show how general kind Russell does not yet consider in this work) has the problem of denotation was inseparable from the supposed neither denotation nor, by the same reason, meaning, although indefinability of"the" and how, again, the elaboration of a genuine Russell was referring rather to the fact that proper names only eliminative theory, necessary to dispense with the paradox of denote, but do not have meaning as connotation. classes, depended on the role of functions as logical subjects.8 I However, before accepting Bradley's view Russell sincerely attempted to work with Frege's distinction between Sinn and Bedeutung, in order to strengthen the foundations of mathemat­ 7 In this paragraph I follow Cassin 1970a, pp. 259-61. Russell had also many ical definitions by eliminatingproblematic denotations. But when doubts regarding Frege's theory that the reference of a judgment can be the he tried to assimilate Frege's distinction (in the Principles, App. True, and that because ofhis referentialistic theory ofmeaning: "I believe that A), he presented it as equivalent to his own distinction between a judgment, oreven a thought, is something so entirely peculiar that the theory of proper names has no application to it" (letter to Frege, 20 Feb. 1902; Frege indication and denotation, inside a referentialistic theory of 1976a, p.