On Denoting

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On Denoting is one of the most significant and influential philosophical essays of the 20th century. It was written by Bertrand Russell and published in the philosophy journal Mind in 1905 (reprinted in Logic and Knowledge, 1956). In it, Russell basically revolutionizes the philosophy of language by introducing his famous theory of definite and indefinite descriptions, formulates his thesis of descriptivism with regard to proper names, and characterizes proper names as "disguised" or "abbreviated" definite desciptions.

In the 1930s, F. P. Ramsey referred to the essay as "that paradigm of philosophy" and, more recently, at least one philosopher has even singled it out as "the paradigm of philosophy", calling it a work of "tremendous insight" which had provoked, and continues to provoke, discussion and debate among philosophers of language and linguists for over a century. ^[1]

1 The "denoting phrase"
2 The theory of descriptions
3 Meinong and Frege
4 Resolving the problem of negative existentials
5 References

[edit] The "denoting phrase"

Russell begins by providing several examples of what he means by the expression denoting phrase that he will be discussing throughout the course of the article. It is important to note that denotation, for Russell, is radically different from the Fregean notion of Bedeutung (often interpreted in English as reference, denotation, and so forth) as well as to what more modern philosophers call reference. For Russell, a denoting phrase is a singular noun phrase preceded by a quantifier whose predicate term is satisified by some particular. Such phrases do not contribute objects as the constituents of the singular propositions in which they occur. Denotation, in other words, is a semantically inert property, in this view. Whereas Frege held that there were two distinct parts (or aspects) of the meaning of every term, phrase or sentence (its Sinn and Bedeutung), Russell explicitly rejects the notion of sense (Sinn) and replaces it with the idea of a propositional function (i.e. a function from objects to abstract propositions which are the contents of sentences). This is so because, for Russell, propositions must have concrete, really existing entities as their constituents. Russell provides several clear examples of the sort of thing that he had in mind: "a man, any man, every man, the present King of France... the center of mass of the Solar System, ...." So, for Russell, a denoting phrase can be either a definite description (i.e. a singular noun phrase with the determinative article "the" at the beginning) which "does not denote anything" (meaning designate any specific object) or a definite description which does denote a specific object or, finally, an indefinite description which denotes "ambiguously". Russell, as will be shown later, believes that definite descriptions are not referring expressions but rather, to borrow a term which was later coined by Keith Donnellan, they have "attributive" uses only. They are to be interpreted as strictly logical quantificational formulas which are "general" in nature. At least this has been the general interpreation of Russell among philosphical logicans for nearly a century. However, it is interesting to note that right at the very beginning of the article, Russell distinguishes between cases where "a phrase may be denoting and yet not denote anything (e.g. 'the present King Of France)" and cases where they may denote "one definite object (e.g. "the present King of England)". If this passage is interpreted as saying that descriptions may "refer" to one definite object, then it could be that Russell actually recognized the two distinct uses of definite descriptions (attributive and referential) which Donellan later proposed.

In any case, after clarifying the sense of the term "denoting phrase" and providing several simple examples to illustrate the idea, Russell explains the epistemological motivations for his theory. Russell believes at this point that there are essentially two modes of knowing: knowledge by description and knowledge by (direct) acquaintance. Knowledge by acquaintance is limited to the sense data of the phenomenal world and to one's own private inner experiences, while knowledge of everything else (other minds, physical objects, and so on) can only be known by way of general descriptions.

[edit] The theory of descriptions

Russell starts out by defining the "fundamental" notion of a propositional function. This is basically a modified version of Gottlob Frege's idea of unsaturated concepts. Hence, "'C(x) stands for a proposition in which x is a constituent and where x, the variable, is essentially and wholly undetermined." The notions of everything, nothing and something ("the most primitive of denoting phrases") can then be defined as follows:

$C(E) \leftrightarrow \forall x C(x)$

$C(N) \leftrightarrow \forall x \lnot C(x)$

$C(S) \leftrightarrow \lnot \forall x \lnot C(x)$

where E stands for everything, N stands for nothing and S stands for something. All is taken as primitive and indefinable and the others are defined in terms of it. Russell emphasizes that these notions can have no meaning apart from that which is assigned to them within the propositions in which they occur, all of which are meaningful. This the foundation of Russell's theory of descriptions as he proceeds to illustrate.

The phrase "the father of Charles II was executed" is interpreted as the following quantificational assertion:

$\exists x (F(x) \land \forall y (F(y) \rightarrow x=y) \land E(x)))$

In other words, there is one and only one thing x such that x is the father of Charles II and x was executed.

So, if C represents any statement at all about the father of Charles II, the statement 'C (the father of Charles II)' always implies:

$\exists x (F(x) \land \forall y (F(y) \rightarrow x=y)$

It follows that if there is not one and only one entity that satisfies the above, then every proposition that contains the descriptions is false. In this way, Russell points out, it will turn out that all statements containing non-referring descriptions (e.g. "The present king of Samothrace is a great writer") are false. Russell's theory reduces all propositions which contain definite descriptions into forms in which they do not.

[edit] Meinong and Frege

He then criticizes Meinong's theory of objectives which, according to Russell, is ontologically promiscuous and self-contradictory. Both of these accusations, however, seem to be the fruit of a misunderstanding of Meinong's views. Russell accuses Meinong, for example, of believing that "the present King of France" both exists and does not exist. However, Meinong does not attribute existence (or any other sort of being) to non-existent objects. Russell also accuses Meinong of violating the law of non-contradiction by asserting that the "round square" is both round and not round. Meinong, on the other hand, maintains that the laws of logic do not apply to such phenomena as "impossible" objects which have no being.^[2]

Russell also goes on to critique Frege's distinction between sense and reference. According to Russell, his theory is to be preferred to Frege's on at least two counts: in the Fregean view, although descriptions (or names) without referents have meanings, their truth value is indeterminate and hence they are nonsense, while, according to Russell's theory of descriptions, these statements are quite meaningful but they are simply false. Also, the theory of descriptions resolves the same sorts of semantic puzzles that the sense-reference distinction was intended to resolve, but without the unnecessary ontological baggage of a third realm of abstract entities (meanings and propositions).

[edit] Resolving the problem of negative existentials

One of the fundamental puzzles that Russell hopes to resolve with the theory of descriptions is the problem of non-referring expressions or, as they are now called, negative existentials. He finally explains how his theory resolves this problem after invoking a distinction between what he calls primary and secondary occurrences of denoting phrases.

Since definite descriptions are just quantificational devices on Russell's view they can enter into scope relations with other logical operators. In the case of negative existentials, there is an ambiguity between two different (primary and secondary) readings of the quantificational assertion. For example, Russell uses the case of "the present King of France is not bald." Here the two possible readings are:

$\exists x (K(x) \land \forall y (K(y) \rightarrow y=x)) \land \lnot B(x))$

$\lnot \exists x (K(x) \land \forall y (K(y) \rightarrow y=x)) \land B(x)$

In the first case, the statement is false because it quantifies over non-existent entities. In the second case, the statement is true because it is not the case that there is a present King of France. "Thus all propositions in which 'the King of France has a primary occurrence are false: the denials of such propositions are true, but in them 'the King of France has a secondary occurrence."

Russell resolves the problem of ambiguity in propositional attitude reports in a similar manner. He refers to an example similar to Frege's puzzle about identity: "George IV wondered whether Scott is the author of Waverly." In this case, it is obvious that King George is not wondering whether Scott is identical to Scott. Russell rejects Frege's solution of distinguishing between sense and reference. Quantificational descriptions are sufficient to of him'handle the de dicto / de re ambiguities. So, for example, in the general case, the sentence "George IV wondered whether Scott is Sir Walter" can be interpreted as:

George IV wondered whether the x that... is identical to the y that....

where ... stands for some definite description such as "the clever fellow who wrote Ivanhoe" and ....stands for something like "the elegant gentleman seated next to the Princess". In the de re case, the above sentence can be interpreted as follows instead:

the x that... is such that King George wondered whether x is identical to the y that....

Finally, Russell suggests that fictional names such as "Apollo" can be treated as abbreviated definite descriptions which refer to nothing. All propositions which contain names of such fictional entities are to be treated in the same manner as the negative existentials described above.

[edit] References

^ Ludlow, Peter, "Descriptions", The Stanford Encyclopedia of Philosophy (Summer 2005 Edition), Edward N. Zalta (ed.), URL=http://plato.stanford.edu/archives/sum2005/entries/descriptions/
^ Grossman, Reinhardt. "Alexius Meinong". The Oxford Companion to Philosophy (ed.) Ted Honderich. 1995