Russell: descripción y existencia

Abstract

I. In the doctrine of Meinong it is established that phrases like “the round square” and “the mountain of gold”, refer to objects which are not exactly existing objects. Although these objects do not exist, they are “something” and not simply a non-being. Such phrases do not only refer to non-existents but allow the formulation of true propositions about these objects, as, for example, “the mountain of gold is golden and mountainous”. If one cannot say that the objects to which these phrases refer exist, and if one can neither say that they simply reduce themselves to a nonbeing, then, supposing that they are something, the situation posed by Meinong’s doctrine is, apparently, contradictory; as Meinong himself came to express it: “there are objects for which it is valid that there are no such objects”.
The theory of Russell’s descriptions is put forward as a reply to this type of paradoxes. In this principal objection, Russell shows that Meinong’s doctrine goes against the principle of noncontradiction, since it maintains that there are objects which do not exist, which is like maintaining that the round square is round, and also not round. But the reason that Meinong maintains that there are non-existent objects lies in the distinction which he introduces between the subsistence of the object as such and the existence of the object as an actual object. Thus, when we say that there are objects (they subsist) in respect of which it is valid to say that there are no such objects (they do not exist), we perceive clearly that there is no such violation of the principle of non-contradiction.
Consequently, the problem presented to Russell by the doctrine of non-existent objects, within the theory of Meinong, is not so much logical as ontological, because the problem is rather that such objects can subsist and, subsisting, do not exist. Seen in this perspective, Russell would have established the epistemological thesis that phrases such as “the mountain of gold”, considered in isolation, have no meaning, refer to nothing. To believe the contrary, like Meinong, is to confuse phrases which can only have meaning in so far as they form a part of a proposition with symbols which signify per se. Russell would also establish the logical thesis that those same phrases are apparent grammatical subjects, and not logical subjects, correctly speaking. To maintain the opposite, as Meinong did, would be to confuse the logical function of the descriptive phrase with the logical function of the proper name.
II. The epistemological definition of the proper name will be: it is the word that directly denotes an individual in whose denotation lies its meaning; its significance is independent of the word with which it eventually appears bound up. But Russell also gives a syntactic definition of the proper name. In this other definition the proper name is the word which can only figure as subjects in the proposition; that is, the word which may be presented in any proposition that does not contain variables. In fact, while the proper name can only be placed as the subject of the proposition it can only have meaning in so far as it directly denotes an individual, and vice versa.
From this, one makes the first approach toward the meaning of “existence” in Russell, although only by a via negationis; it is not possible to speak of existence at the level of the proper name. As a symbol whose meaning does not extend beyond the immediate denotation of an individual, the proper name is always the symbol of an existent. Therefore, to say “a exists” or “a does not exist”, where “a” is the symbol of a proper name, is equivalent to say nothing, because “a exists” expresses in reality “the existent exists”, which is superfluous, whilst “a does not exist” expresses the same as “The existent does not exist”, which is contradictory.
Thus, “existence” is a concept that cannot be applied to the direct language in which the proper name operates. This, the proper name, denotes an existent regarding which, however, it never indicates “that it exists”.
In sharp contrast with the proper name, defined descriptions, such as “the man who committed the crime”, on the one hand, have no direct reference to an individual, neither do they denote immediate existence in the sense of the proper name, nor, on the other hand, is it possible for them to signify in an independent manner. Firstly because, despite the fact that the described term is one and only one, we can know a variable number of propositions about a described term without knowing effectively who or what in particular that term is; and this is definitely what is expressed by the symbol of the defined description: “(ηx) (Φx)”. Secondly, because a phrase like “the author of Waverley” cannot signify the same as “Scott”, since then “Scott is the author of Waverley”, would be equivalent to the tautology of “Scott is Scott”, which is false, nor can it signify something different from “Scott”, since then “Scott is the author of Waverley” would have to be necessarily false. Therefore “the author of Waverley” does not signify either “Scott” or anything different from “Scott”: that phrase for itself signifies nothing. The descriptive phrase itself is an incomplete symbol, in the sense that, independently, it signifies nothing, and will only come to mean anything if it is used in a propositional context.
If the meaning of the proper name did not extend beyond directly denoting an individual, as Russell maintains, but implicitly or in an un-analyzed form had the same sense which the descriptive phrase has explicitly or in analyzed form and if, moreover, the descriptive phrase denoted in an indirect way (by means of properties) the same individual that the proper name denotes directly, in this case the proper name and description would denote the same, but in a different way. In this case there would be no tautology between “Scott” and “the author of Waverley”, and would leave open the possibility that the proper names could be treated as descriptions, and they as names.
The symbol of the defined description is introduced, and it is established how, by being the expression of an incomplete symbol, and by not being a logical constituent of the proposition, it can disappear when defining the proposition that it contains, showing that it is nothing more than a grammatical subject. This introduces the logical analysis of that proposition.
III. An example of a proposition in which a descriptive phrase figures as subject is “the author of Waverley was a poet”.
(a) The first thing that the proposition signifies is that at least one person wrote Waverley, or that “ ‘x wrote Waverley’ is not always false”, in symbols: (Εx), Φx.
(b) In accordance with the unique reference that by definition is ascribed to the definite article “the” with which the proposition opens, it refers at the most to a person. Therefore, what the proposition signifies secondly is that if x and y wrote Waverley, x and y are always identical, or that “ ‘if Φx . Φy, then x=y’ is always true”.
(c) It is from that single term that the proposition which one analyzes affirms that “he was a poet”. Thus, what the proposition thirdly signifies is that if x wrote Waverley, x was a poet. But then the integral meaning of the proposition is a double propositional function —in which we find “x wrote Waverley” and “x was a poet”— duly placed within the existential quantifier, since the first two moments of the analysis reveal that there is at the least and at the most ...
In symbols: (Ε c) : Φx. ≡x. x = c : fc
The important thing is that according to Russell, the proposition affirmed in (a) and that affirmed in (b) are equivalent together to the existential proposition “a term c exists so that ‘x wrote Waverley’ is always equivalent to ‘x is c’ ” —where c is a value which substitutes x and satisfies the function “x wrote Waverley”. But this existential proposition means no more than “the term that satisfies the function ‘x wrote Waverley’ exists”, which Russell expresses by the symbol E! (ηx) (Φx). Thus, the affirmation of existence is now included in the whole proposition in which a descriptive phrase occurs; it is part of what these propositions affirm.
Strawson criticized these results by showing that to say “the present king of France is wise” is not to assert that such a person exists, but that in expressing that sentence one only presupposes that such a person exists. According to Strawson, the above sentence changes to an assertion of existence only if one uses it in clearly defined circumstances to refer directly or actually to that person. But in this case, how can we affirm that an individual exists to whom a sentence refers in the use, when the very use of the sentence already establishes its existence? Actually the concept proposed by Russell is a purely semantic concept, which disregards the circumstantial use of language, constructed from a definition of the definite article “the”. The concept of existence which Strawson advocates is a pragmatic concept of existence from which it would be meaningless to judge the concept of existence proposed by Russell. Strawson’s criticism of Russell’s theory would have been conclusive if it had managed to establish its logical and semantic inconsistency.
Since, according to Russell, a describe term never implies knowledge of who or what in particular is the term which possesses the quality of which the description speaks, but, on the other hand, it is necessary to affirm that the said term exists, since, at the least, and at the most, an individual has that property, one has to conclude that the existent that the propositions mentioned in which a defined description is used, is a single existent which could be designated directly, but which in effect is not designated in this way. Thus, when we say “the term that fulfils the function ‘Φx’ exists” E! (ηx) (Φx) the description or its symbol can only function as an indeterminate formal argument of the function in which it is presented, for which there could or not be a determined value, i.e., an existent. Thus, “existence” is that which, ontologically, could occur as a single value of the said argument. It is of this notion of existence which one treats when one says that, in all propositions where a description occurs, one will find E! (ηx) (Φx) as a part of what is affirmed.
IV. If existence signifies what could occur as a value of the formal argument which constitutes the description, then the description phrase or the proposition that contains it can have meaning even though nothing “real” is referred to by it. But this was not what happened with the proper name. Thus there is a contrast as much by what affects the meaning, which either can or cannot have a proper and description when they refer to existence which one attributes to the symbols, as with what affects the existence itself to which they are bound when they are open to the possibility of speaking either with or without meaning. While it is not possible to speak with sense of whether the named exists or does not exist, one can speak with sense of whether the descriptum exists or does not exist, since in this last case there is the possibility that the value which should satisfy the formal argument of the description exists or does not exist, thus leaving the possibility of affirming or denying it. Therefore, it is only about descriptions, strictly speaking, that we can affirm or deny existence.
From this point of view “the round square does not exist” should not be interpreted as if “the round square” referred to an object about which we can then affirm that it does not exist, or as “there is a certain object (round square) about which we can affirm that there is no such object”, but rather as “there is no single value which fulfills the function ‘Φx’ in the way of a single value”.
Therefore, “existence” is equivalent to say that given a function fx, which becomes a proposition when one assigns a value to the variable x, the expression (∃x) . fx signifies that there is at least a value of x for which fx is true. This definition is valid for defined descriptions, but the value here is single.
What one has attempted to emphasize is that, paradoxical as it may be, the notion of existence applied to defined descriptions does not allude as such toan actual existent, but to an object that could exist.