The origins of Russell's theory of descriptions according to the unpublished manuscripts INTRODUCTION THE DISCOVERY OF the paradoxes led Russell to reconsider the sort of definition he employed.!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 ofintuitiveness. 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 of the theory of descriptions 101 (Principles, pp. 103-4). This led him to the first theory of types (Appendix B) and the first version of the "no classes theory" (in a letter to Frege),2 which clearly show how Russell accepted great ontological sacrifices. different forms ofterms), and between predicates and relations (as However, there was still a long way to go until the discovery that denotative functions can be derived from propositional functions, which led Russell to the theory of descriptions of 1905. First, the theory of meaning of the Principles contained an en- deavour for distinguishing the logical and psychological involve- ment in meaning, but did not completely clarify the complex distinction between meaning and denotation. Second, a great deal of unpublished work contained: (i) serious attempts of incorporat- ing the objectivity of Frege's semantic notions; (ii) the pre-em- inence of "the" over other denoting functions; (iii) the need for clearly distinguishing knowledge by acquaintance and by descrip- tion in order to state the conditions for understanding proposi- tions. Third was the discovery that the distinction. between meaning and denotation must be discarded, and fourth the theory of descriptions by partially accepting Bradley's claim that certain proper names are only disguised descriptions. to a new complication of this ontology, which consisted in the This allowed Russell systematically to apply an eliminative device, first to definitive descriptions, second to classes (mainly through a substitutional theory), and then to propositions them- selves in favour of propositional functions (through the ramified theory of types). Thus, the main effect of the paradoxes was to make it possible for Russell's definitions not only to construct the defined entities (e.g. numbers, as in the Platonism of the Prin- ciples),butalsotoeliminatethemasmere"incompletesymbols'~ which are not symbols. The second applies only to certain con- cepts and states a logical relation (denotation) between those con- cepts and things, i.e. it consists in the designation or description of a term by a concept (pp. 51, 56). In the following, I shall describe these several stages from 1903 to 1905 (sec. II-IV) and then attempt a methodological interpreta- tion of the resulting theory of descriptions (sec. V), which will lead us to an alternative view of the relationship between Russell's descriptions and ordinary language (sec. VI). 3 These new entities were, however, incompatible with Moore's relational theory of judgment, which could admit only terms, or concepts (I attempt a general study ofMoore's first philosophy in my 1990e, and a description ofRussell's first assimilation of this philosophy in my 1988a). This was a consequence of the formidable problems caused by imaginary proper names (Apollo, etc.), and some difficult denoting concepts not considered by Moore, like the ones involving paradoxical entities (the class of all classes, etc.), or impossible objects (the round square, etc.). It is true that Russell regarded these last entities in full II. ATTEMPTS AT INCORPORATING A FREGEAN SEMANTICS Russell's theory of denotation in the Principles derived from two main ontological distinctions: between things and concepts (as two 2 The letter to Frege is dated 24 May 1903 and may be found in Frege 1976a, pp. 158-60. 4 (see n. 18). A rare exception is the excellent Cassin 1970a. The analysis by Vuillemin (1968a, pp. 73-8) is interesting, but it seems he does not realize the distinction. two different forms of concepts). However, the analysis of plural (or ambiguous) denoting concepts-those expressed by quantifica- tional devices in conjunction with general terms-forced Russell admission of a larger category: objects (p. 58n.), which embraces 3 entities denoted by those concepts. The problem of denoting appeared when Russell realized that in cases where a substantive (a class-concept) is preceded by certain w9rds ("the", "a", "some", "all", "every" or "any"), the result is a denoting concept involving a relation between denoting terms (concepts) and denoted terms (objects) which is very different from the usual, linguistic relation of~eaning:"A concept denotes when, if it occurs in a proposition, the proposition is not about the concept, but about a term con- nected in a certain peculiar way with the concept" (p. 56). A first result was an important distinction which is usually misunderstood.' There are two kinds of meaning. The first applies to words and states a psychological and linguistic relation accord- ing to which words stand for or indicate other things or concepts Thus, both proper names and adjectives (and verbs) indicate terms, but while proper names indicate things, the rest indicate concepts. (Adjectives indicate predicates and verbs relations.) Again, two of these three kinds of terms have a specific relation with other entities (I use this word for lack of another): predicates 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 102 Russell winter 1989-90 The origins of the theory of descriptions 103 denote other terms (as we saw above), but relations have an indefinable connection with truth because they constitute the assertive element of propositions. The third kind of term, things, are only the entities indicated by proper names, but they have no additional relation with other terms. This leads Russell to con- sider the sole denoting concept which presupposes uniqueness- "the': Russell admits the great importance ofthis term, recognizes the merit of Peano's notation,5 and attributes to him the capacity to make possible genuine mathematical definitions defining terms which are not concepts (p. 63). the meaning of a word with its indication-refere.nce (and the meaning of a denoting concept with its denotation). Thus, al- though Russell himself attempted to identify his denoting concept with Frege's Sinn, and therefore he translated "Bedeutung" as "indication" (ibid.), his previous equivalence between Frege's distinction and the pair "denoting concept/entity denoted" implied that Bedeutung cannot be indication, for this is not a denoting-- relation. The consequence was the actual identification between Frege's sense-reference and Russell's indication-denotation. This is incompatible with Frege's intentions because in this way the denoting concept can be the meaning as well as the indication of the denoting expression. Thus Russell was really rejecting Frege's distinction and preserving the identification between meaning and reference.7 This was the basis on which he faced the problem of denoting concepts which do not denote in spite of having a meaning. Rus- sell was not yet prepared completely to accept Bradley's attack against proper names:6 "when meaning is thus understood [in a logical sense], the entity indicated by John does not have mean- ing, as Mr Bradley contends; and even among concepts, it is only those that denote that have meaning' (p. 51). That seems to imply that "the present King of France" (the famous example whose general kind Russell does not yet consider in this work) has neither denotation nor, by the same reason, meaning, although Russell was referring rather to the fact that proper names only denote, but do not have meaning as connotation. Nevertheless, the reinterpretation of Frege in the appendix is not the "missing link" between the Principles and "On Denoting' (as claimed by Cassin 1970a, p. 261). Between these two views there is a collection of unpublished manuscripts which show how the problem of denotation was inseparable from the supposed indefinability of"the" and how, again, the elaboration of a genuine eliminative theory, necessary to dispense with the paradox of 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- ical definitions by eliminating problematic denotations. But when he tried to assimilate Frege's distinction (in the Principles, App. A), he presented it as equivalent to his own distinction between indication and denotation, inside a referentialistic theory of meaning. 7 In this paragraph I follow Cassin 1970a, pp. 259-61. Russell had also many doubts regarding Frege's theory that the reference of a judgment can be the True, and that because ofhis referentialistic theory ofmeaning: "I believe that a judgment, or even 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 1976a, p. 156). Instead of that, for Russell the object ofjudgment is the proposi- tion itself (24 May 1903; ibid., pp. 159-60). Russell starts by equating Frege's distinction with the one between a concept in itself and the entity denoted by it (p. 476). But Frege's referring-relation takes place between a symbol and its object, whereas Russell's denoting-relation is not symbolic: it takes place between two terms. Besides, Frege's distinction makes the coincidence between Sinn (sense-meaning) and Bedeutung (reference) impossible, whereas Russell's semantics can identify 8 Russell himself stated this connection in correspondence with Frege when affirming that, if we admit something as not being an object, at this very point we are falling into a contradiction for we attribute being to this entity (letter of 24 June 1902; Frege 1976a, p. 134). The answer from Frege on 29 June 1902 doubtless contributed to Russell's idea that a function cannot be treated as an object, and therefore to the later need of eliminating "apparent" logical subjects including functions. Frege states clearly that a function (and "the" is a function) cannot be regarded as an entity, for if we do so we attribute to it the status of a proper name, while it is only the sign of a function (the name of a concept). This was a consequence of Frege's ontology of two exclusive classes of entities: objects and functions (including concepts and relations), which are respectively designated by saturate expressions (names) and unsaturated ones (functional expressions). & In my 1990h I try to state that Peano did something more than provide the standard notation. 6 'lb the point of presenting them as disguised descriptions; see my 1990f. 104 Russell winter 1989-90 The origins of the theory of descriptions 105 come now to this evolution, characterized by the search for an adequate treatment of"descriptive (or denoting) functions'~i.e. for a method to define them constrq,ctively.9 suggested by a note by Russell on the first page that it contains the reason for the new theory of denoting). Finally, I locate the important publication, ''The Existential Import of Propositions" (1905a) between m1904c and m1905a, together with "The Nature ofTruth" (m1905).10 III. THE FIRST TWO MANUSCRIPTS OF 1904 The same approach to Frege led Russell to abandon the semantics of the Principles, as the manuscripts from this period show. The basic traits of this unpublished material are: (i) the application of the distinction between meaning and denotation, including the mutual application to each other, which would finally produce the abandonment of the distinction itself; (ii) the analysis of"denoting (or descriptive) functions" in relation to other kinds of functions (which includes the problem of the indefinability of the definite article); (iii) the several approaches to the notion of "denoting complex" which produced the first substitutional theory and later the theory of descriptions; and (iv) the epistemological implica- tions of all that, which permitted the clear formulation of the distinction (already in the Principles) between intuitive and non- intuitive knowledge, although now with other tenninology. The first relevant manuscript is "On Functions, Classes and Relations" (m1904).1t contains a classification ofthe several kinds of functions according to their complexity and definability, and it introduces for the first time the order (in increasing complexity): descriptions-classes-relations (as three kinds of particular indefinable denoting functions), which remained unchanged till Principia Mathematica. Russell starts from three indefinable kinds offunctions: I accept Richards' 1976a arguments according to which the main manuscripts were written in this order: "On the Meaning and Denotation of Phrases" (m1904a), "Points about Denoting" (m1904b) and "On Meaning and Denotation" (m1904c), but I locate "On Functions, Classes and Relations" (m1904)-which Richards ignores-before all ofthem (it is dated 1904 and is not so complex). Likewise, I locate "On Fundamentals" (m1905a)-which is also ignored by Richards despite its being the most important manuscript of this period-after all of the others, because it is dated June 1905, i.e. immediately before "On Denoting" (as (ii) Propositional functions (<1>',£ as opposed to <I>'x, one of its indetermined values) are those functions whose values are "com- plex meanings containing their respective arguments as constitu- ents, in the way in which a constituent of a propositivn is con- tained in a proposition" (p. 1). That is why their values are ulti- mately always propositions (p. 2). Russell also calls them "mean- ing functions" because they ambiguously denote their values, whereas denoting functions ambiguously denote complex mean- ings, which denote the corresponding values in an unambiguous way. These last functions generate the notion of "denoting com- plex", which takes place if we reach a stage where the variable is not a constituent of the function, in which case we are to consider the meaning of the complex and not its denotation, presumably because the latter is not an entity. Thus, Russell tries to give a (Fregean) objectivity to his semantics without the need of reject- ing the identification of meaning and reference, although he systematically avoids any philosophical discussion of this matter. 9 "Meinong's Theory of Complexes and Assumptions" (1904a) did not presuppose any modification of the theory of denoting from the Principles. Thus, Russell continued translating "Bedeutung" as "indication" when he described Meinong's doctrine according to which language expresses a thought (or mental state) but indicates an object (pp. 43, 63), which seems to show that the former distinc- tions are maintained (see Richards 1976a, p. 31). However, there is also a certain approach to Frege, as illustrated by the fact that the theory finally chosen by Russell (among several examined) was referred to as the one advocated by Frege and Moore (p. 63), and was described as that which asserts the subsistence of false propositions, Le. a theory of truth and falsehood as correspondence between language and facts. (iii) Denoting functions of propositional functions are to be distinguished from propositional functions in that they take propositional functions as arguments (i.e. "the entity for which <I>'x is true"). As denoting functions (f(<I>'2» they have entities as their values, which are neither propositions nor functions (p. 3); and this property is just the one which gives denoting functions their (i) Functions in general (<I>x) are defined as usual, emphasizing the fact that they ambiguously denote a set of entities. 10 All ofthese manuscripts are being edited by A. Urquhart for publication in Vol. 4 of The Collected Papers ofBertrand Russell. 106 Russell winter 1989-90 The origins of the theory of descriptions 107 importance for individuating, describing and defining. However, the property gives rise also to the problem concerning pseudo-enti- ties, which Russell is still not ready to solve. Therefore, after dealing with other definable kinds offunctions, Russell introduces three indefinable denoting functions corresponding to descrip- tions, classes and relations, which seem to suppose a renunciation of the constructive trend from the Principles. phrases ("the table") (m1904a, p. 7). A parallel classification for objects is added: (1) those that can only be denoted ("individuals"); (2) those that can only be meant ("non-functional concepts"), which are declared the more difficult ones, probably because they embrace (at this stage) the problem of subsistence, as opposed to existence; (3) those that can be either meant or denoted ("func- tional concepts"), to which correspond functions. Finally, "term" is proposed to be any object denoted by a constituent word or phrase in a proposition. However, all this is supposed to transform the clear (true or false) Fregean ontology of objects and functions into a chaos, for Russell calls even concepts "objects'~ while concepts The pre-eminence of descriptions over other forms of denotation is definitive. The notation for descriptions is inspired in the Pean- esque symbolism (i.e. "laeb"; see my 1990h), but membership of classes is replaced by propositional functions (i.e. (l£)(<I>X)), which is explained as "a certain denoting function of <l>x, which, if <1>£ is true for one and only one value ofx, denotes that value, but in any other case denotes (P).p" (m1904, p. 5). In this way Russell seems to accept Frege's proposal of a conventional reference to descrip- tions not fulfilling the requirements of uniqueness and existence, i.e. not using the sense/reference distinction because this possibil- ity could lead one to deprive some descriptions of their reference, which, as in Frege, is not acceptable even though we could regard Sinn as something objective. Then classes are introduced, as classes of arguments for which a function is true, through the are functions for Frege.12 The problem of the conditions required for admissible descrip- Fregean symbolism for Wertverlaufen (:t(<I>x)), and finally relations (already in extension, as apparently announced in Appendix A of the Principles), although expressed as denoting functions of the correlation ofx with f<l>(x) for every value ofx: £(f<l>(x)} (p. 6). tions-that they have meaning and denotation-begins in con- sidering the equivalence between expressions. Russell solves it using the Fregean idea: x and yare to be identified when they have the same denotation although different meanings. In apply- ing this theory to imaginary proper names (which have neither meaning nor denotation), problems appear. Thus, "Apollo", as a proper name, must be devoid of meaning, and as it is imaginary it must be also devoid of denotation. This situation forces Russell to accept, at least in these cases, the Bradleian theory that "imagin- ary proper names are really substitutes for descriptions" (p. 4), i.e. they result from a combination of characteristics of which the supposed object named is the only instance. In fact Russell even admits that "genuine proper names, when they belong to interest- Philosophical problems are treated only in "On the Meaning and Denotation ofPhrases" (m1904a). This incomplete manuscript already includes a theory of denotation very different from the Principles as regards the semantics, although still without an admission of Bradley's reduction of proper names to disguised descriptions (except in the case of imaginary proper names). Far from that, Russell seems to have been inspired by John Stuart Mill when he classifies words and phrases into three kinds: (1) those that denote without meaning, i.e. proper names ("Socrates"), which include propositions and some substantives ("death", "blackness"); (2) those that mean without denoting, i.e. verbs ("is'~ "died"), adjectives ("black") and the remaining substantives ("table");l1 (3) those that both mean and denote, i.e. denoting "death" is a proper name (it denotes without meaning), "but it is unlike Socrates in that what it denotes can also be meant" (e.g. in "Socrates died") (m1904a, p. 7), and he also says that "table" is by itself like an adjective (it means without denoting) (p. 1). But both words can at times be used similarly, e.g. as proposi- tional concepts ("the x of S") and as definite descriptions ("the x that arrived on Monday"). 11 Russell is rather obscure when distinguishing between two kinds of substan- tives, respectively belonging to the first and the second groups. He says that 12 See n. 8. It could, however, be said that Russell uses "term" approximately as Frege uses "object~ and that his "objects" approximately include both Frege's objects and concepts. Of course, Russell's objects include his terms (for terms are a kind of objects), but here the parallelism ends, for terms are to be denoted, BO that they can be both individuals and functional concepts; therefore they can by no means be used as Frege's objects, which are the opposite category to that of functions. As for the correspondence between Russell's objects and Frege's objects plus concepts, it is true only when replacing concepts by functions, but then it is trivial. 108 Russell winter 1989-90 The origins ofthe theory ofdescriptions 109 ing people, tend to become names which have meaning" (p. 3). This leads to the general problem of the denotation of definite descriptions: to give an account of these phrases and of the sen- tences where they appear, especially in cases of descriptions which have a meaning but do not denote, i.e. when they cannot really be "logical subjects". Such phrases exist when the definite article precedes a concept-word with no instance.13The solution is different from that of"On Functions, Classes and Relations": now correspondence with facts-such phrases should lack denota- tion-unless "false facts" are admitted. This is perhaps the reason leading Russell to declare the entire question "open" (p. 6). such phrases are declared as lacking denotation but as having meaning. However, Russell immediately must assume the fact that, in any case, they express concepts; that is why it is possible to speak of the "instances" of these concepts although there are not really any instances. And this, again, leads to the problem of subsistence and to the difficult questions concerning the denota- tion of phrases containing such descriptions (e.g. "the present King of France") and of their role as logical subjects (e.g. "the present King of France is bald"). On that basis Russell starts to develop substitutional theory.15 He begins with the following principle: ''When a word or phrase which denotes occurs in a proposition, and is no part of any other word or phrase which denotes (except the whole proposition), then it may be freely varied without our ceasing to have a proposition" (m1904a, p. 8).18 Russell even introduces at this point some sub- stitutional notation, readingXy/x as a "complex meaning" contain- ing a variable term x (which stands for a proper name, contrary to the Principles where it was not so), which is a constituent ofX and can be replaced by y. When Xy/x is part of a proposition, the thing asserted is that denoted by such an expression, which is part of the proposition, in spite of the fact that x is a constituent ofthe meaning ofX. Russell's solution to such problems consists now in denying that "the present King of France is bald" refers to the meaning of the phrase "the present King of France'~ for such a meaning is a "complex concept", so it is not capable of having or losing hair. Therefore: This substitutional theory was doubtless stated in order to obtain a device for constructing entities by avoiding the problems of propositional functions and classes, as asserted by Russell in a 1906 letter;17 but it was finally abandoned (see my 1989a for full details). In that letter Russell gives two reasons for the failure of the theory: the lack of an adequate theory of denotation, and the non-distinction between substitution among constants and deter- mination of a variable as this or that constant. Concerning the problems ofdenotation, the present manuscript was not developed enough to give an account of the cases relevant to the paradox of classes. However, it seems that Russell, as happened in later writings, was somewhat confused when trying to apply. the no- tions of meaning and denotation to each other with the aim of distinguishing between proper names, descriptions and proposi- tional concepts. although the concept is part of the meaning of "the present King of France is bald~ it is not part of the denotation (if any). Thus we shall have to say that "the present King ofFrance is bald" is neither true nor false; for truth and falsehood have to do with what a sentence denotes, not with what it means; and we must take it as axiomatic that the sub- jectofapropositionispartofthedenotationoftheproposition. (P.5) However, Russell does not generalize this result to all false propositions, which would also lack denotation, because this would lead one, contrary to the stated conclusion, to regard truth and falsehood as belonging to the meaning and not to the denota- tion.14 Anyway, this could be dangerous to the theory of truth as Thus, regarding "Caesar died" the verb is unable to denote the constant element ofthe proposition; but, when transformed into a concept, a proper name appears ("death"), which lacks meaning. 13 Russell offers here the famous example of "the present King of France" for the first time; m1904a, p. 4. The same example was used by Husserl in the last decade ofthe last century (personal communication by Ivor Grattan-Guinness). Strawson in his famous criticism (see sec. VI below). 15 Which was the link between descriptions and types; see my 1989a. 16 However, it is admitted that a proper name can be a constituent of a phrase 14 Skosnik suggested correctly in his 1972a that with that view Russell held a position not only opposed to the "On Denoting" one, but parallel to that of we saw above. 17 Letter to Jourdain of 15 March 19,06 (in Grattan-Guinness 1972a, p. 107). which denotes without its bearer being part of the denotation of that phrase, as 110 Russell winter 1989-90 The origins ofthe theory ofdescriptions 111 Russell sees only one solution: to grant to such a proper name the possibility of"denoting a meaning", i.e. to admit that the meaning can be an object: "Death is the name of a function, for it is a proper name denoting an object which can occur as meaning in a complex" (p. 10). With that, Russell was making a great endeav- our to approach the objectivity of Frege's Sinn, thus overcoming his 1903 view (where indication was something psychological). Butin so doinghe made possible a set ofparadoxes ofself-applica- tion in regards to "complexes". The rest of the manuscript is devoted to such problems. The full substitutional theory did not appear until the problem of denotation was solved with the theory of descriptions.18 A phrase such as "the present Prime Minister of England" designates an entity, in this case Mr. Arthur Balfour, while it expresses a mean- ing, which is complex, and does not, as a rule, include the entity designated as a constituent; the relation of the meaning expressed to the entity designated is that ofdenoting. The meaning may be called a description of the entity and the phrase may be called a descriptive phrase. (P. 7) IV. DESIGNATION, EXPRESSION AND DENOTATION Now the problem of pseudo-entities is easily solved: we need only say that there are phrases expressing a meaning and desig- nating no object, as for instance in the case of"the present King of France" (p. 8). We can express the same thing in terms of sense and denotation (or reference), obtaining always the same conse- quence: there is already no need of maintaining the subsistence of such "entities'~19 Likewise, in "On the Meaning and Denotation of Phrases" (mI904a), the names of imaginary people are only apparent names. However, to generalize this conclusion to em- brace false propositions, Russell meets the same challenge against his theory of correspondence as in m1904a: it call be inferred that such propositions lack designation (m1904c, p. 10), a hypothesis that he considers several times but always rejects (e.g. on pp. 28-9). A sign of the difficulties Russell faced in accepting such a hypothesis (which finally led him to the multiple-relation theory of judgment) is that in a manuscript of this same period he maintains that there are entities which do not exist.20 The next relevant manuscript is "On Meaning and Denotation" (mI904c), where such complications are solved by means of a partial return to the theory of the Principles, i.e. by stating a twofold relation clearly parallel to the distinction between indica- tion and denotation, because one ofits terms was psycholinguistic and the other was logical. Russell uses the distinction by Meinong (already in 1904a; see above) between what language expresses and what it indicates, and the Fregean distinction between meaning and reference. As a whole, this has the advantage of returning to denotation as a unique relation, i.e. of avoiding the former complications regarding (i) the denotation of an object by means of a word and also by means of a meaning, and (ii) the treatment of the meaning itself as an object. But this advantage is vitiated by the fact that the new theory forces us to divide the This and other difficulties led .Russell to claim the need for a new theory of the relation between meaning and denotation (p. 13), and for an analysis of the general nature of propositions (p. 14ff.). This includes a consideration of the possibility (which he ultimately rejects) according to which phrases are not to be names ofpropositions, Le. that phrases do not designate them but merely affirm propositions, a view which immediately leads to epistemol- ogical problems concerning the relation between ideas and objects. symbolic relation of the Principles (indication) into two different relations: designation, relating the phrase to what is named (or denoted), and expression, relating the phrase to its meaning, Le. to the object of our thinking (pp. 2-3). In this way denotation remains free of complications and can be a purely logical relation between what is expressed and what is designated (although without forgetting that both are objects). In other words, it can be limited to denoting the meaning. Russell sums up as follows: 19 InalettertoMeinongof15December1904Russellabandonsthebeingofsuch objects in Fregean terms: "I have always believed until now that every object must in some sense have being, and I find it difficult to admit unreal objects. In such a case as that of the golden mountain or the round square one must distinguish between sense and reference (to use Frege's terms): the sense is an object, and has being: the reference, however, is not an object" (Lackey 1973a, p.16). 18 In m1904b the same substitutional notation appears, even closer to that of 1905-06, and a last isolated appearance takes place on p. 49 of ml904c (which is the result of removing to it p. 160fm1904b). 20 "The Nature ofri'ruth" (ml905), p. 7; see my 1987a, pp. 522fT. 112 Russell winter 1989-90 The origins ofthe theory ofdescriptions 113 Then three facts about denoting itself are stated: (i) denotation is indefinable and fundamental; (ii) certain complexes denote some- thing other than themselves; (iii) "propositions are not about the complexes, but are about what the complexes denote" (p. 30). Thus the conclusion of the first part of the manuscript is: arguments appears untenable. We must therefore attempt a different solution" (p. 54). Of course, such a solution could only be arrived at when it was possible to define the more problematic denoting function ("the"), which eliminated the distinction be- tween sense and reference and also the problem of subsistence. The rule must be, that when a denoting complex forms part of a proposition, in the sense of being a constituent of it, and when the complex does not form part of any other denoting complex, then it is what the complex denotes, and not the constituents of the complex, that the proposition is about; further a proposition is about any entity which is designated, not expressed, in the thought of the proposition, and is not part of any denoting complex in the proposition. (P.31) The rest of the manuscript consists of discontinuous "miscel- laneous notes'~ However, in these notes we can find interesting ideas for the future. Perhaps the most interesting for us is the insistence on the indefinability of "the" (Peano's inverted iota is already used), together with the notion of denotation (p. 60). In one of the many logical "experiments" which always characterize his method, he arrives at the possibility of dispensing with "the" through the use of definitions preceded by certain hypotheses. He finally writes: "It is plain that 1 is a fundamental logical notion, and that it would be merely shirking to invent a dodge for getting on without using it" (p. 84). With this approach, Russell achieves a distinction between the constituents of a proposition and the entity that a proposition is about, which he thinks is necessary to overcome the difficulties of his somewhat "mechanical" view of a proposition, according to which the context of the proposition with regard to its constitu- ents is not very important in determining the meaning, which depends mainly on the constituents. Obviously, this view makes it impossible to imagine paraphrastic definitions. The last pages sum up the fundamental traits of Russell's view at this moment: (i) all denoting functions are derived from "the"; however, the corresponding symbol must be put before a proposi- tional function rather than before a variable, which points out the fact that a denoting function of x is derived from a propositional function containing x, If(x,ll) being the symbolic general express- ion of denoting functions (p. 91). This shows the importance of descriptive functions, but (ii) these continue to be linked to the distinction between meaning and denotation, so that the proposi- tions in which these functions appear are about the denotation: "When l(f~) occurs in a proposition, the meaning is a constituent of the proposition, and the proposition is about the denotation" (ibid.). This view continued to make the use of the eliminative device impossible, despite criticisms from Whitehead.21 However, in the second part ofthe present manuscript (devoted to the several forms of variable denotation) Russell gives more and more importance to the idea of context in the analysis of functions, probably through the influence of Frege. So, when he asks for the meaning of f in fx, he arrives at the conclusion according to which f is not a separable entity (p. 45): we must consider the complex (fx) as a whole. In this way he is approach- ing the idea of eliminating certain functions-those leading to the paradox of classes. At this point he even considers that "a function is not an entity in the ordinary sense" (p. 52), and tries, by means of the "substitution-view'~to avoid functions in terms of complexes having only constants as constituents. He argues that these complexes would lack meaning in the dangerous cases like f(f), which leads to a hierarchy of functions and to the denial that every function defines a class (p. 53). Finally, (iii) Russell continually found instances leading him to doubt the distinction between meaning and denoting itself: 'There is something still wrong with my theory of meaning and denota- tion" (p. 94); "the theory of denoting must be reformed" (p. 95). However, he always ended with the impossibility of dispensing with the distinction; Since Russell does not feel sure that functions are nothing, he finishes this part of the manuscript by accepting from Frege the possibility according to which we can assign conventional mean- ings to the cases in which certain functions seem to lack meaning: "Thus the whole theory that functions can be detached from 21 A short list of such criticisms can be found on p. 93. I may mention: (i) White- head's rejection of the view that denoting phrases and proper names are both names; (ii) his thesis that, in propositions, the meaning and the denotation of a denoting phrase are involved in the same way. 114 Russell winter 1989-90 The origins ofthe theory ofdescriptions 115 what we need for denoting phrases is that it should always be possible to substitute for them what they denote without loss oftruth. But this is not true of their meanings. "The father of Socrates" contains Socra~ tes, but his father did not. This is the ultimate ground for distinguish- ing meaning and denotation; and this ground seems irrefutable. (P.96) noted by "Smith" and "marriage'~I can conceive a term denoted by "Smith's marriage" in spite ofmy lack ofacquaintance with the new term; i.e., "to be known by description is not the same thing as to be known by acquaintance" (p. 2). Moreover, since descriptive functions, which denote unambiguous- ly, depend upon propositional functions, and since these denote ambiguously, "the notion of denoting remains fundamental" (ibid.). Itis necessary, for the understanding ofa proposition, to have acquain- tance with the meaning of every constituent of the meaning, and of the whole; it is not necessary to have acquaintance with such constituents of the denotation as are not constituents of the meaning. (P.6) Before explaining the emergence of the key idea (the definabil- ity of "the") and, with it, Russell's coming back to "semantic monism" (Coffa 1980a, p. 56), I need to show that the distinction betweenknowledge by acquaintance and by description was already present at this point. In fact, despite the general belief that this important epistemological distinction appeared as a consequence of the theory of descriptions, the truth is that it can be found in earlier manuscripts (including the terminology). Of course, the distinction was only the adaptation of the former one between intuitive and non-intuitive knowledge, which can be found in the Principles and earlier writings, although in that book we even find the key word "acquaintance'~22 This last remark was intended to give an account ofthose cases in which certain descriptions would lack denotation. For the same reason, once the notion of denotation (as opposed to meaning) disappeared through the theory of descriptions, the distinction was transformed into the supreme principle of the semantic and epistemological monism which characterized logical atomism, in the way that it was stated in "On Denoting": "in every proposition that we can apprehend ..., all the constituents are really entities with which we have immediate acquaintance" (1905b, p. 56). Pages 1-6 of "Points about Denoting" (m1904b) contain the essentials ofthe distinction, which was not modified in "On Mean- ing and Denotation": V. ELIMINATION OF "THE"AS A CONSTRUCTIVE DEFINITION sometimes we know that something is denoted, without knowing what. This occurs in obvious instances, as e.g. if! ask: Is Smith married? and the answer is affirmative, I then know that "Smith's wife" is a denoting phrase, although I don't know who Smith's wife is. (P. 1) The definition offered by Russell in "On Denoting" was the pub- lished result ofhis work in "On Fundamentals'~23Thus, the kernel ofthe famous article was a very concentrated version ofthe puzzle of meaning and denoting from the viewpoint of their mutual application, which is solved in the same way as in the manuscript (i.e. by rejecting the meaning/denotation distinction), including the literal incorporation of some paragraphs and the definition of phrases containing descriptions. The distinction between knowl- This leads to the possibility of distinguishing between the terms with which we are acquainted and those which are merely de- noted. AB I am acquainted (in the example) with the terms de- 22 This shows the continuity ofRussell's epistemology, mainly in the link between acquaintance and indefinability: "The discussion of indefinables-which forms the chief part of philosophical logie-is the endeavour to see clearly, and to make others see clearly, the entities concerned, in order that the mind may have that kind ofacquaintance with them which it has with redness or the taste of a pineapple" <Principles, Preface, p. xv; my emphasis). 23 Ihavestudiedthismanuscriptinmy1990g.Thedateofthediscoveryseemsto have been June 1905. In his Autobiography (1: 152) he says only that in the spring he was living in Bagley Wood, and a little after that he discovered the famous device, but in the first page of"On Fundamentals" we can read: "Begun June 7~ and also: "Pp. 18 if, contain the reasons for the new theory of denoting': This coincides with the allusion to the same fact in a letter to Lucy Donnelly of The distinction is somewhat complicated when we need give an account of the difference between meaning and denotation: 13 June where Russell speaks about the solution (Auto., 1: 177). So it seems the discovery took place between 7 and 13 June. 116 Russell winter 1989-90 The origins ofthe theory ofdescriptions 117 edge by acquaintance and by description (here called ''knowledge about" or "definition by denoting phrases") was also incorporated, as well as the elimination of other denoting phrases (those con- taining "a" and "all")114 by similar methods. Likewise, Frege's principle of context is admitted25 when we are told that descrip- tions are unmeaning in themselves, as can be seen when they disappear on analysis.26 Since all of this has been already con- sidered in previous sections, I tum now to the new ideas intro- duced in "On Denoting'. Russell also included the more usual and intuitive version: to say that the author of Waverley had the property cj) is equivalent to: "One and only one entity wrote Waverley, and that one had the property cj)" (p. 51). I think that the published article adds mainly three points: (i) the expression of the main definition in terms of propositional functions together with the previous manuscript definition in Peano's terms of existence and uniqueness (although not in symbolic form); (ii) a better explanation of the puzzle of identity and substitution; (iii) a clarification of the distinction between primary and secondary occurrences of descriptions, and then a solution to the puzzle of the excluded middle. I shall say some- thing brief about each one. (ii) The theory of descriptions in "On Denoting' resolves the problem about identity and substitution caused by the desire of George N to know whether Scott was the author of Waverley. For the mentioned proposition no longer contains "the author of Waverley" as a constituent, and so the paradox does not arise (p. 52). As for the problem of propositions containing descriptions denoting nothing (and the involved ambiguity concerning scopes), it is solved by means of the distinction between primary and secondary occurrences. (1) The admission ofexistence and uniqueness is clear, although not so much as in the symbolic formulation: "when we say 'x was the father of Charles II' we not only assert that x had a certain relation to Charles II [i.e. the existence ofx], but also that nothing else had this relation [i.e. its uniqueness]" (1905b, p. 44).27 Start- ing from this point the formulation in terms of propositional functions is easy; thus, "the father of Charles II was executed" becomes: (iii) Thus "the present King of France is bald" is false and in it the occurrence of the description is primary, whereas "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" (primary occur- rence), and true if it means "it is false that there is an entity which is now King of France and is bald" (secondary occurrence). Therefore, the question whether the present King of France (1) is bald or (2) is not bald ceases to be a puzzle concerning the ex- cluded middle, for (1) is always false, and (2) is ambiguous: if it is the negation of (1) it is true; and if it is false, it is not the negation of (1), so that there is no longer a problem (p. 53). It is not always false of x that x begat Charles II and that x was executed and that "ify begat Charles lI,y is identical with x" is always true ofy. When Russell offered the definitive and published symbolic version in 1910a (and before in 1908a)28 he improved this formula- tion. in particular by dispensing with denoting concepts different from "the" (in *9 "all" and "some" are introduced as primitive ideas by means of the two quantifiers), and allowing the clear distinction between the existence ofa described individual (rather incorrect) and the existential quantification. The two essential definitions are (Principia, * 14.01.02): 24 Thislastelimination,however,ismadebyadmittingthatBradleyclaimedthat categorical universal propositions are really hypothetical (see my 1990f). \jI(IX)(epX) • =.(3b) : epx •=~ .x=b : \jib E ! ( 7 X ) ( e p X ) • = . ( 3 b ) : 4 > x . =• . x = b which express the conditions of existence and uniqueness essen- 25 AlthoughwithnomentionoftheFregeanorthePeanesqueversionsofthesame idea. I have attempted a general comparison of the theories of descriptions by Russell, Peano and Frege in my 1990h. 26 Russell offered a "proof' in My Philosophical Development (1959a), p. 85, claiming that this point was the central issue of the theoJY, but again without mentioning Frege or Peano. 27 For a very complete analysis of the notion of existence, including the involved notions here as well as others, see Grattan·Guinness 1977a, pp. 71ff. 28 The two basic definitions first appeared symbolically in a letter to Jourdain of 13 JanuaJY 1906 (see Grattan-Guinness 1977a, p. 70). 118 Russell winter 1989-90 The origins ofthe theory ofdescriptions 119 tially with Peanesque resources, i.e. in terms of quantification and identity, although adding propositional functions.29 and, therefore, the abandonment of the relational ontology that was implicit in Moore's theory of judgment. Likewise, with the definition of"the" one more thing disappeared: the only possibility of distinguishing between terms which are concepts and terms which are not concepts (see Principles, p. 63). Just at this point the distinction between philosophical and mathematical defini- tions became impossible, at least in theory (see my 1991a, Chap. 5). It is clear that the two expre~sions are definitions, in spite of being definitions in use because of the impossibility of isolating a set ofsymbols lacking meaning. As for the possibility ofdescribing this definition as "constructive" (in my sense ofthe term), it is also clear that the expression defined, where it apparently occurs as a constituent, "is defined in terms of the primitive ideas already on hand" (Principia, I: 30), that is to say, it is reduced to these primitive ideas. In this way the eliminative property of these definitions is somewhat diminished: what they eliminate is an expression which has meaning only when inserted in a proposition to whose general sense it contributes, whereas in the other kind ofconstructive definition (i.e. that ofcardinal number) the entities are directly defined. Thus, although Russell later described both definitions as eliminating "incomplete symbols", in the first case it is the use of an expression that is to be eliminated, whereas in the second it is a certain kind of entity that completely vanishes.3o Such a pre-eminence of concepts also has epistemological conse- quences within Russell's own view. Like every definition, the definition ofdescriptions must reduce what is unknown to what is known, i.e. must present the defined thing in terms with which we are acquainted. Moore saw the problem immediately and wrote to Russell in October 1905: if we are acquainted with all the consti- tuents of the proposition which we apprehend, "Have we, then, immediate acquaintance with the variable?" (They usually used this expression to designate quantification.) In his response Russell admits that the question is puzzling, and he adds:32 The difficulties of interpretation caused by all this are formi- dable. In ontological terms, the theory stated in the Principles suffered a strong attack, especially on the supposed deviation from the rigid Moorean ontology, which admitted only one kind of entity. Thus the division between things and concepts had to be abandoned because with the pre-eminence ofconcepts, which were now able to replace described things, it was no longer possible to regard concepts as terms-and all proper names had now to be disguised descriptions despite the supposed need for logically proper names. at other times I think it is an entity, but an indeterminate one. In the former view, there is still a problem of meaning and denotation as regards the variable itself. I only profess to reduce the problem of denoting to the problem of the variable. This produced the direct opposition between terms and con- cepts, identified respectively with subjects and predicates (ex- plicitly done in 1908a, p. 76). Another cause was the logical needs which forced to some extent the readmission of the subject-predicate pattern (by means of propositional functions31) predicative schemes "cpx" whose values are propositions and where x stands for the subject and $ for the predicate. I included some discussion of this predicat- ive commitment in my 1991a (Chap. 4) and 1989a. It is true that Russell wondered at times whether predication is a relation or not, but at least since the Appendix on Frege in the Principles he always regarded relations in extension, and preserved the old relations in intension only as a handy notation, as in Principia: "I read Schrader on Relations in September 1900, and found his methods hopeless, but Peano gave just what I wanted. Oddly enough, I was largely guided by the belief that relations must be taken in intension, which I have 8Ince abandoned, though I have not abandoned the notations which it led me to adopt" (letter to Jourdain of 15 April 1910; in Grattan-Guinness, 1977a, p. 134). Of course, there are dyadic functions, but also dyadic predicates. Besides, functions can be regarded as relations, relations as classes, and classes as predicates. 29 In my 1990h I have shown that Peano had enough resourses to completely eliminate the definite article (the inverted iota) from any proposition, and that he recommended this line in cases where the required conditions of existence and uniqueness were doubtful, precisely through a sort of definition "in use': Thus the descriptor was by no means "indefinable" in his system. 30 In fact there are three kinds of incomplete symbols, as I showed in my 1989a. 31 HereIamspeakingoftheusualmonadicpropositionalfunctionsinvolvedinthe theory of descriptions (as well as in the later theory of logical types), i.e. 32 Moore's letter is dated 23 October 1905, and Russell's 25 October. With that Russell probably'was alluding to the power of quantifi- cation in giving an account of descriptions, and therefore to 120 Russell winter 1989-90 The origins ofthe theory ofdescriptions 121 solving the general problem of denotation in the framework of avoiding the difficulties of the paradox of classes (see my 1988f). bers), is psychologically different from a definition of a term that is new to the reader." Hence we acquire new knowledge when we learn a precise definition of a word whose corresponding object we knew by acquaintance, though in a somewhat superficial way. Thus: In the context of the new pre-eminence of the unrestricted variable (Principia, I: 4), which was necessary to avoid definitions depending on hypothesis, it meant, simply, that only concepts could provide the material for definitions, given that the general- ization of the eliminative method could dispense with any kind of the entities admitted until that moment.33 It presupposed the admission of only two kinds of entities: particulars and universals (as happens in his 1912a), and the reduction of the other tradi- tional entities-dasses, relations, mathematical objects, and even propositions-to incomplete symbols. As we know, this trend would finally lead even to the reduction of particulars to univer- sals, as happened in his last works. . the two definitions which embody the theory of descriptions (*14.01.02), though formally they are merely nominal definitions, in fact embody new knowledge; but for this, they would not be worth writing about. The elimination of"the" led to another epistemological problem which is related to the general status of definitions, and it helps to strengthen my arguments for identifying this definition with the constructive ones which characterized Russell's usual method. One ofthe aspects ofthe theory ofdescriptions that was criticized by Moore in his monumental (but somewhat insipid) essay, "Russell's Theory ofDescriptions" (1944a), was this. When Russell said that the several statements which must replace a description are to be interpreted as defining what is meant by the statement which contains that description, an ambiguity arises: we do not know whether definiens and definiendum have the same meaning or whether the first one provides a correct definition of the second (pp. 182-4). It is an essential problem for it concerns the signifi- cance of definitions and their epistemological usefulness. If, as Russell maintained in Principia following Peano, definitions are to be always nominal, then their definienda are only mere ab- breviations. But this view leads always to tautology, with which no definition of Principia could build something really new. This position would be completely unacceptable for Russell and could lead to incoherence between the informative value of definitions and their character of abbreviations. Of course, the new knowledge concerns the structure of certain kind ofphrases (descriptive ones), which, despite their familiarity, had not been adequately analyzed (1944b, pp. 690-1; my empha- sis). In the same line, Russell's response to Moore's objection states that the definition of descriptions is a constructive definition. Russell writes: "the definition of sentences containing descriptive phrases, like various other definitions (e.g. that of cardinal num- 34 AsforinstanceWeitz1944a,Pears1967aandMuguerza1973a.Weitz'sposition has the merit of reducing Russell's method in general to definition, and al- though in practice he distinguished between four kinds of analysis in Russell; these can be easily reduced to the general constructive definitions. Clack 1972a is more acceptable because he makes efforts to admit only one method in Russell, i.e. "reeonstructionism~ but unfortunately he finds neither the keys to assimilate descriptions to the rest of constructive definitions, nor (with the mentioned authors) the link between incomplete symbols and Russell's usual recourses for constructing definitions, which permit us, for instance, to regard physical objects as pseudo-entities (see my 1987a, Chap. 14; 1989a, and 1990c). On the other hand, Black admitted that the reduction implicit in the theory of descriptions can be called definition (1944a, p. 243n.27), but he lacks a general view ofRussell's method, which can be illustrated by his claim that the theory of descriptions was formulated as an analysis of actual meaning in ordinary language. 33 As can be clearly seen with the substitutional theory; see my 1988f. This answer seems definitive against any attempt to hold the thesis, many times maintained even by specialists,3' that Russell applied two different kinds of analysis (and therefore, of defini- tions): the vertical and the contextual or paraphrastic ones. However, we must admit that an important problem arises when the definiendum is eliminated: as an incomplete symbol, it is meaningless but, .at the same time, it can be "analyzed~ It is, of course, the same problem that we have seen concerning the twofold role of definitions. I can offer still another proof that for Russell both types of definition (descriptions and numbers) are to be regarded as 122 Russell winter 1989-90 The origins of the theory of descriptions 123 instances of the same constructive method. Thus in "Logical Atomism" (1924a), when Russell offers a list of such instances, he begins with the principle of abstraction (although already very much weakened; see my 1987b). He includes the definition of cardinal number in terms of a class of classes and the elimination ofclasses themselves, and then adds: "Another important example concerns what I call 'definite descriptions'" (p. 327), which is followed by a brief summary of their elimination method and has tried to solve it by dispensing with these writings. In Russell's case the problem is especially difficult because of the extent ofhis work and the changes and innovations incorpor- other examples. I will add only two comments. The first is that it is not strange that Russell mentioned the elimination of classes before the elimination ofdescriptions; it is true that (as explained in my 1989a) the technique of descriptions was later applied to other "incomplete symbols'~ but Russell had in mind his "no classes theory" from much earlier. ated therein. But just for this reason the historical point of view will be necessary, avoiding the usual trend concerning the belief that the "true" work by Russell begins at this or that precise point. One example among many is the recent article by Cappio (1981a), where it is claimed that there are certain realist traits in Russell's semantics which, belonging to the Principles, survived the theory of descriptions. Cappio adds that such traits are related to the principle of acquaintance, which "appeared" in 1905 mainly with the aim ofpreserving realism (pp. 193ff.), with which theory his whole article is concerned. The truth is that, as I pointed out above, the distinction between the two kinds of knowledge not only is present in manuscripts before the theory of descriptions, but appeared as well in the Principles (including the term "acquaintance") as a result of preserving what was never rejected: the distinction between intuitive and non-intuitive knowledge. The second comment is that both the last quotation and the text mentioned above come from a period much later that the one we are studying now, when Russell had had enough time to realize more clearly the implications of his own method. Particularly, only in 1914 did he admit that the unity ofhis method was based on the "supreme maxim" of substituting logical constructions for inferences, perhaps according to an assimilation of his theory of incomplete symbols in Principia. And he had had time to reflect in It is possible to construct a general framework in which we can insert the present problem and see how important was the conti- nuity in Russell's method.38 Russell started, in his approach to ordinary language, from the Bradleian line: there is a ''logical form" in language which the philosopher must endeavour to extract.37 The climax of such Bradleian efforts was the analysis of categorical judgments into hypothetical ones. With this and other examples (like the identification of proper names and disguised descriptions), Russell's old master attempted to discover the "true meaning" which underlies linguistic expressions. Moore, who was also influenced by Bradley, provided Russell with a model of great care in the analysis of ordinary language, which was always Moore's raw material to work with. But he added another el- detail upon the influence of Wittgenstein and Whitehead, which had led him to a partial abandonment of his linear epistemology (see my 1990c). VI. THE "PROBLEM" OF ORDINARY LANGUAGE The last point leads us to a third problem: whether the theory of descriptions must be regarded as a device for clarifying the ordinary language meaning of descriptions, or for stating a recon- structed language (in the sense of an ideal logical language). It is a problem whose key is completely contained in Russell's previous writings (and not only unpublished ones, but mainly the Prin- ciples and others),35 whereas as far as I know every commentator ement: the use of ordinary language as the best guardian of "intuition'~ or immediate knowledge (of which Bradley also spoke). However, Moore thought that it was necessary to purify it to find the "true meanings" through a sort of analysis avoiding both 35 In our day many authors try to reach the "truth" about certain historical questions by means of personal judgment and starting from very limited relevant material, but as I try to show in this article (and in general in my 1987a) usually it is necessary to handle a greater background, including unpublished material and the study of influences. 38 I have done so in my 1991a, especially Chap. 5. 37 Kaplan (1966a, p. 230) admits, exceptionally, that Russell belonged to this philosophical line, although he seems to ignore the precedent of Bradley. 124 Russell winter 1989-90 The origins ofthe theory ofdescriptions 125 lexicography and mere stipulation.3s With this background Russell began his Principles, in order to The history of the interpretors of the theory can be divided into two groups: those having a tendency to regard it as a resource to describe (or at least to give an account of> ordinary language, who usually end by judging it to be erroneous, and those who regard it rather as one logical and conventional artifice among others to improve formal systems. So expressed, it is easily understood that most commentators belong to the first group, perhaps because Russell often speaks in a somewhat careless way about this topic. But the truth is that neither ofthe two views is admissible, partly for the reasons alluded to above and partly because of the simple fact that, for Russell, it was a question ofcorrection rather than of linguistic conventionality (Gadel 1944a, p. 130). preserve the admissible part of Bradley (his methodological and analytical resourses) and almost the entire Moore, in so far as they were compatible with the requirements of Peano's logic and Cantor's transfinites. That is why in his valuation of the Cantor- ian analysis (continuity, for instance) Russell remains always between the Scylla of precision, which starts from ordinary language and purifies it, and the Charybdis of stipulation, which is very much closer to mere formalism. Russell could not choose the first one because that would suppose a withdrawal from the guide of ordinary language,a9 but he could not choose the second one, which could hardly be regarded as true philosophy or one based on an intuitive analysis in search of the true indefinables. This strange compromise, which appears especially in the tension between philosophical and mathematical definitions, allowed Russell to finish the Principles within Moore's general framework of the identity between logical, ontological and epistemological terms, while always trying to preserve the "whole and part" pattern, i.e. the belief that the meaning of complexes must be found in their constituents. Those in the first group have two essential recourses: (i) the search for counterexamples, i.e. of valid grammatical expressions unable to be explained through the theory, and (ii) the rejection of the relationthat, according to Russell, there is between descrip- tions and the phrases destined to replace them, including the unavoidable link with the problem of truth. Both recourses were first introduced by Moore in his 1944a: the first one through his example of "the whale is a mammal" and similar sentences; the second by doubting that the mentioned relation was implication, or that it can be said that the original description can be "defined" in terms ofthe phrases replacingit. Startingfrom here, an almost infinite literature (very well classified and evaluated by Sainsbury 1979a, pp. 133ft'.) has developed, from which I shall choose only the famous example of Strawson's "On Referring" (1950a) because he opened an epoch and because we have a response by Russell. Only at this point can we ask: in which way, if any, did the theory of descriptions change all that? The answer, of course, is also historical: the eliminative construction of the definite article showed immediately that there are apparent and real constitu- ents. But only when the new technique was generalized, and Russell had transformed a whole series ofentities before regarded as real ones into incomplete symbols, did he realize that we can admit only a few real constituents-in fact, only the bearers of proper names, i.e. those with which we can have acquaintance. Therefore only a study of that generalization (such as the one I attempt in my 1989a) can provide the semantic and ontological implications of incomplete symbols. The essentials of Strawson's criticism, apart from his well- known examples, are: (i) the distinction between a statement and its particular usage; (ii) the assertion that, in whatever applica- tion of the theory, the relation between definiendum (D) and definiens (D') is not implication (and therefore is not mutual implication or logical equivalence), but presupposition. But as Russell, supposedly, did not realize this point, (iii) he maintained that part of what we affirm with D is D', which does not happen with presupposition. By the same reason, in the cases of non- existent objects Strawson40 maintains a position similar to that of 38 I have attempted a general study of the Bradleian heritage in the early Moore and Russell in my 1990f and 1990e. 39 It is true that Russell often spoke as ifordinary language was completely to be rejected because of its implicit bad metaphysics, but after the assimilation of techniques from Bradley and Moore he was convinced that only through it can true logical form be extracted. Thus, it was always his best guide against mere formalism and conventionalism in the construction of definitions (see sec. I above). 40 And also to that by Russell in the manuscripts, as I pointed out above. Thus, when Watling (1970a, pp. 67-9) made efforts to hold this position (with other arguments), he did not know how close he was to the historical truth. 126 Russell winter 1989-90 Frege, holding that (iv) if D' is false, then D is neither true nor The origins ofthe theory ofdescriptions 127 false, whereas for Russell, in this case, D would be false.41 Russell's reply, "Mr. Strawson on Referring" (1957a), concen- trated on (i) and (iv), which are the result of(ii) and (iii). On (i) he answers alluding, somewhat cryptically, to his theory ofegocentric particularsandmaintainingthatifin"thepresentKingofFrance is bald" we replace "present" by "in 1905", then Strawson's objec- tion falls (1957a, p. 239). As has been shown by Austin (1978a), Russell was alluding to egocentric words (later also called "indexi- I find it more convenient to define the word "false" so that every signifi- cant sentence is either true or false. This is a purely verbal question; and although I have no wish to claim the support of common usage, I do not think that he [Strawson] can claim it either. (lbid.)43 cal terms"), which allow the same sentence to be used to say different things in different situations. In this way it demon- strates how Russell had in mind the complete distinction between a statement and its particular uses, and therefore it suffices to eliminate these words to solve the problem. With regard to these arguments, we must declare that the tradition according to which the theory of descriptions was an attempt to give an account of the common usage of descriptions (in a line stated by Black 1944a), is a dead tradition (see Carnap 1947a, p. 33), despite the fact that we can still find seekers of counterexamples. Dummett (1981a, p. 133) has admitted this in the context of Russell's answer to Strawson. In that context, which certainly supposes an approximation of Russell to Frege, Dummett situates what he calls the most important difference between them: Russell's rejection of the sense/reference distinc- tion (p. 134). And he does so by emphasizing Russell's need to maintain a realist theory of proper names; that is why he tried to present descriptions as something different from singular terms, whereas Frege attempted to minimize this difference. But this had a great disadvantage, also pointed out by Dummett (p. 163): it forced Russell to begin the search for true "logically proper names~ As for (iii), Russell never held it (see Linsky 1967a, p. 97). He spoke only of "correct analysis" with no allusion to what persons could mean when uttering D: "My theory of descriptions was never intended as an analysis of the state of mind of those who utter sentences containing descriptions", but rather "to find a more accurate and analyzed thought to replace the somewhat confused thoughts which most people at most times have in their heads" (1957a, p. 243). Hence Russell's position must be clearly located in the ambiguity referred to above (about the tradition of the true "logical form"),Le. between the view of definitions as useful but conventional resources, and the alternative view of them as technical improvements which have to be true. That is why he alludes both to the improvement of ordinary language in terms of mere "precision", which could be made by cultivated It is well known that such a search, together with his principle of acquaintance, led Russell to admit only egocentric particulars as genuine proper names, and finally even to eliminate them, in An Inquiry into Meaning and Truth (1940a) in terms of univer- sals." Thus the realist ontology which Russell still held in 1905 made it impossible to generalize the eliminative recourse to all proper names (genuine or not), which was put in practice by Quine in absence of that or any ontology.45 persons, and to the right of philosophy to build up a language differing from that of daily life, Le. a technical language (p. 242). Finally, Russell replies to (ii) and (iv) with the single device of admitting that to say that D is false, when D' is false, or to say that it is not true (although significant), is "a mere question of verbal convenience" (p. 243).42 In the same vein of hesitation in respect to ordinary language, Russell adds: I conclude by insisting that for Russell the definition of the 41 Accordingtotherelationofpresupposition.DpresupposesD'iffthenecessary condition for D to have some troth value is that D' is troe; see Linsky 196780 pp.98-9. Russell, mainly with the argument that we cannot maintain that proper names are to be descriptions because we can speak only about descriptions as opposed to proper names. However, Frege, who wanted to avoid the search for genuine proper names, preserved all descriptions with only the device of a conventional reference (see Dummett 197380 pp. 160ff.). 42 Curiously, Russell himself maintained in m1904a that in such a case D must be neither troe nor false. 43 Orayen (1975a, pp. 95ff.) has developed the suggestion by Russell about the possibility of defining "false" in such a way that his theory can be maintained against Strawson's arguments. 44 See my 1990h. ~ Welding 1972a has shown that Quine's view is hardly consistent with that of 128 Russell winter 1989-90 The origins ofthe theory ofdescriptions 129 BIBLIOGRAPHY definite article was a new application of his method of construc- tive definitions (in my sense of this term), with all the usual disadvantages and ambiguities, but with the great advantage of allowing him to deal with the elimination of classes and other incomplete symbols in a definitive way. Hence a satisfactory interpretation of the theory must be mainly ontological. As Clack wrote (1972a, pp. 60-1), although such a theory was formulated to clarify the logical structure of certain propositions (descriptive ones), it is also a technique to clarify the ontological presupposi- tions ofthese propositions. So, although we can interpret it as the mere rejection of Frege's celebrated distinction, we must not forget that the main purpose of the new semantic monism was to insert the new problems into the framework of the simple ontol- ogy of the Principles, returning to the distinction between intu- itive and non-intuitive knowledge with a new terminology. The page numbers in the above references are always those of the last edition listed here. Thus there is no more reason to deal with the "problem" of common usage than with the rest ofthe definitions constructed by Russell, as for instance those of cardinal number,46 continuity, geometrical spaces, etc. However, the technical use ofthe key idea ofthe theory ofdescriptions could not have been more fruitful; not only in later uses by Russell himself, but also in its application, in combination with similar ideas from Whitehead, to ambitious constructions like that of the Aufbau by Carnap.47 Published Writings by Russell Department ofPhilosophy Institute S. Vilaseca 43205 Reus, Spain, and McMaster University Hamilton, Ont., Canada48 published in 1973a, pp. 165-89. (1908a) "Mathematical Logic as Based on the Theory of Types~American 46 The attempt of Benacerraf 1965a is interesting because he applies the same idea to the definition of cardinal numbers. This has the advantage (indepen- dently ofhis doubtful success) of pointing out the absurd situations produced by the use, as ordinary language, of a reconstructed language. Unwin. (1924a) "Logical Atomism~ In Contemporary British Philosophy. Ed. J.H. 47 See my 1990d. 48 I am especially grateful to Nicholas Griffin for his comments on a draft of this 1956a, pp. 323-43. (1940a) An Inquiry into Meaning and Truth. London: Allen & Unwin. (1944a)"MyMentalDevelopment~InSchilpp1944a,pp.3-20. (1944b) "Reply to Criticisms~ In Schilpp 1944a, pp. 681-741. (1956a) Logic and Knowledge. Ed. R.C. Marsh. London: Allen & Unwin. (1957a) "Mr. Strawson on Referring~ Mind, 66: 385-9. Reprinted in article, which clarified many paragraphs and arguments, as well as for his detailed and patient work to improve my English. I would like to express my thanks also to I. Grattan-Guinness, who read an early Spanish version and sent me many useful comments. My thanks are also due to Kenneth Blackwell for all the help and information provided. All unpublished material is contained in the Bertrand Russell Archives, McMaster University, where the copyright is held. 1959a, pp. 238-45. (1959a) My Philosophical Development. London: Allen & Unwin. (1967a) The Autobiography of Bertrand Russell. Vol. 1: 1872-1914 Unpublished writings by Russell Correspondence with a.E. Moore, 1896-1905. (m1904) "On Functions, Classes and Relations~16 fos. (m1904a) "On the Meaning and Denotation of Phrases~ 25 fos. (m.1904b) "Points about Denotin~ 18 fos. (mI904c) "On Meaning and Denotation~73 fos. (mI905) "The Nature ofTruth~24 fos. (mI905a) "On Fundamentals~ 81 fos. (1903a) The Principles ofMathematics. Cambridge: University Press. (1904a) "Meinong's Theory of Complexes and Assumptions~Mind, 18: 204-19; 336-54; 509-24. Reprinted in 1973a, pp. 21-76. (1905a) "The Existential Import ofPropositions~Mind 14: 398-401. Re- printed in 1973a, pp. 98-103. (1905b) "On Denotin~ Mind, 14: 479-93. Reprinted in 1956a, pp. 41-56. (1906a) "On the Substitutional Theory of Classes and Relations~First Journal ofMathematics, 30: 222-62. Reprinted in 1956a, pp. 59-102. (1910a) Principia Mathematica. With A.N. Whitehead. 3 vols. Cambridge: University Press, 1910-13. (1912a) "On the Relation of Universals and Particulars~Proceedings of the Aristotelian Society, 12: 1-24. Reprinted in 1956a, pp. 105-24. (1919a) Introduction to Mathematical Philosophy. London: Allen & Muirhead. 1st. ser. London: Allen & Unwin Pp. 356-83. Reprinted in London: Allen & Unwin. 130 Russell winter 1989-90 (1973a) Essays in Analysis. Ed. D. Lackey. London: Allen & Unwin. The origins of the theory of descriptions 131 Writings by Other Authors McColl, H. (1905a) "Symbolic Reasonin~ Reprinted in Russell 1973a, pp. 308-16. Austin, J.w. (1978a) "Russell's Cryptic Response to Strawson~ Philosophy and Phenomenological Research, 38: 531-7. Moore, G.E. (1944a) "Russell's Theory ofDescriptions~In Schilpp 1944a, pp. 177-225. Ayer, A.J. (1971a) Russell and Moore: the Analytical Heritage. London: Macmillan. Mosterfn, J. (1968a) "'!'eorfa de las descripciones~Unpublished Ph.D. thesis, Barcelona Univ!ilrsity. Benacerraf, P. (1965a) "What Numbers Could Not Be~ In Benacer- raf/Putnam 1983a, pp. 272-94. Muguerza, J. (1973a) "Sobre la ontologia del atomismo 16gico de Russell~ Pensamiento, 29: 287-12. Benacerraf, P. and Putnam. H., eds. (1983a) Philosophy ofMathematics. 2nd ed. Cambridge: University Press. Orayen, R. (1975a) "Tres dificultades en la teorfa de las descripciones de Bertrand Russell~Cr£tica, 7: 69-104. Black, M. (1944a) "Russell's Philosophy of Language~ In Schilpp 1944a, pp.229-55. Pears, D. (1967a) Bertrand Russell and the British Tradition in, Philos- ophy. London: Collins. , Bacher, .M. (1904a) "The Fundamental Conceptions and Methods of Mathematics", Bulletin of the American Mathematical Society, 11: 115-35. - - , ed. (1972a) Bertrand Russell: a Collection ofCritical Essays. New York: Doubleday. Cappio, J. (1981a) "Russell's Philosophical Development~ Synthese, 46: 186-205. Quine, W.V. (1966a) "Russell's Ontological Development~ Journal of Philosophy, 63: 657-67. Carnap, R. (1947a) Meaning and Necessity. Chicago: Univ. Press. 2nd ed., 1956. Richards, J. (1976a) "Pre-'On Denoting' Manuscripts in the Russell Ar- chives~ Russell, no. 21-2: 28-34. Cassin, C.E. (1970a) "Russell's Discussion of Meaning and Denotation: a Re-examination". In Klemke 1970a, pp. 256-72. Rodrfguez-Consuegra, F.A. (1987a) "El metodo en la filosoffa de Bertrand Russell. Un estudio sobre los orfgenes de la filosofia analitica a traves de la obra de Russell, sus manuscritos ineditos y los autores que mas Ie influenciaron". Unpublished Ph.D. thesis, University of Barcelona. (Microfiche copies available on request.) Clack, R.J. (1972a) Bertrand Russell's Philosophy of Language. The Hague: M. Nijhoff. Coffa, J.A. (1980a) "Russell as a Platonic Dialogue: the Matter of Denot- ing", Synth,ese, 45: 43-70. - - (1987b) "Russell's Logicist Definitions of Numbers 1899-1913: Chronology and Significance", History and Philosophy of Logic, 8: 141-69. Dummett, M. (1973a) Frege's Philosophy of Language. London: Duck- worth. - - - - - (1988a) "Bertrand Russell 1898-1900: una filosoffa de la matema- tics inedita~Mathesis, 4: 3-76. - - (1981a) The Interpretation of Frege's Philosophy. London: Duck- worth. - (1988b) "Elementos logicistas en la obra de Peano y su escuela~ Mathesis, 4: 221-99. Q)del, K. (1944a) "Russell's Mathematical Logic~ In Schilpp 1944a, pp. 125-53. - (l988c) "Bertrand Russell 1900-13: los principios de la matematica, parte 111~ Mathesis, 4: 355-92. Grattan-Guinness, I. (1972a) "Bertrand Russell on His Paradox and the M u l t i p l i c a t i v e Axiom~ J o u r n a l o f P h i l o s o p h i c a l L o g i c , 1 : 1 0 3 - 1 0 . - - ( 1 9 8 8 d ) " B e r t r a n d R u s s e l l 1 9 0 0 - 1 3 : l o s p r i n c i p i o s d e l a r r i a t e m a t i c a , parte ~~ Mathesis, 4: 489-521. - - .- (1977a) Dear Russell-Dear Jourdain. London: Duckworth. Griffin, N. (1977a) "Russell's 'Horrible Travesty' ofMeinon~Russell, no. - - (1989a) "Russell's Theory of Types, 1901-10: Its Complex Origins in the Unpublished Manuscripts". History and Philosophy ofLogic, 10: 131-64. 25-8: 39-51. Jager, R. (1972a) The Development of Bertrand Russell's Philosophy. London: Allen & Unwin. Kaplan, D. (1966a) "What Is Russell's Theory of Descriptions?~ In Pears - - - - (1989b) "La 'perdida de certidumbre' en la matematica y la ciencia contemporaneas~ Forthcoming in Mathesis. 1972a, pp. 227-44. Klemke, E.D., ed. (1970a) Essays on B. Russell, Urbana, TIL: U. of m. P. Lackey, D.P. (1973a) "Three Letters to Meinon~ Russell, no. 9: 15-18. Largeault, J. 1970a Logique et philosophie chez Frege. Paris: Nauwe- - (1990a) "Bertrand Russell 1895-98: una filosoffa prelogicista de la geometrfa~Di6.logos, 55: 71-123. laerts. - (1990b) "Russell's First Technical Philosoph~ Essay-review of I. Winchester and K. Blackwell, eds., Antinomies and Paradoxes: Studies in Russell's Early Philosophy (Hamilton: McMaster U. Library P., Linsky, L. (1967a) Referring. Atlantic Highlands, N.J.: Humanities P., 1980. 132 Russell winter 1989-90 1989); also published as Russell, n.s. 8, nos. 1-2 [1988]). Forthcoming in History and Philosophy ofLogic, 11, no. 1. - - (1990c) "El impacto de Wittgenstein sobre Russell: 11ltimos datos y vision global". Forthcoming in Theoria. - - (1990d) "El logicismo russelliano: origen, evoluci6n y significado filos6fico". Forthcoming in Cr£tica. - - (1990e) "La primera filosoffa de Moore~ Forthcoming in Agora. - - (1990f) "La influencia de Bradley en los orfgenes de la filosofia analftica". Forthcoming in ER, Revista de filosofta. - - (1990g) "Some New Light on Russell's 'Inextricable Tangle' about - - - - Meaning and Denotation". In preparation. - (1990h) "A Comparison among the Theories of Descriptions by Frege, Peano and Russell". In preparation. - (1990i) "Bertrand Russell 1920~8: una filosofia de la ciertcia entre elholismoyelatomismo~ ForthcominginDidlogos. - (1991a) The Mathematical Philosophy ofBertrand Russell: Origins and Development. Naples: Bibliopolis, forthcoming. - (1992a) "Mathematical Logic and Logicism from Peano to Quine~ In I. Grattan-Guinness, ed., Encyclopaedia ofthe History and Philosophy ofthe Mathematical Sciences. London: Routledge, forthcorirlng. Sainsbury, R.M. (1979a) Russell. London: Routledge. Schilpp, P.A., ed. (1944a) The Philosophy ofBertrand Russell. 4th ed. La Salle: Open Court, 1971. Skosnik, J. (1972a) "Russell's Unpublished Writings on Truth and Denoting", Russell, no. 7: 12-13. Strawson, P.F. (1950a) "On Referring~ In Klemke 1970a, pp. 147-72. Vuillemin, J. (1968a) Ler;ons sur la premiere philosophie de Russell. Paris: Colin. Watling, J. (1970a) Bertrand Russell. Edinburgh: Oliver. Weitz, M. (1944a) "Analysis and the Unity of Russell's Philosoph~ In Schilpp 1944a, pp. 57-21. Welding, S.O. (1972a) "Russell's Theory of Definite Descriptions as Opposed to Quine's Singular Terms~ Revue internationale de philoBo- phie, 26: 513-33.
Subscribe to:
Post Comments (Atom)
Posts
No comments:
Post a Comment