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Russell's Theory of Descriptions
Thomas C Ryckman
 
Bertrand Russell's Theory of Descriptions (RTD) can be appreciated against the background of Russell's view about the connections between language and the world, although this view is not itself a part of the theory. Russell held that one can infer things about the nature of the world by examining the language that truthfully describes the world. In his Principles of Mathematics (1903), he held that every well-formed denoting phrase denotes, and that definite descriptions, phrases of the form of "the-so-and-so," denote the right things-things satisfying the descriptions. This view suggests that such definite descriptions as "the golden mountain,"  "the round square," "the winged horse of Greek mythology," and "the greatest conceivable being," do, in fact, denote things that fit or satisfy them. RTD, originally set forth in Russell's, "On Denoting," (1905)represents his attempt to account for the meaningfulness of sentences in which such expressions occur in a way that does not commit him to the existence of such entities.


RTD is used to analyze sentences in which definite descriptions occur in places in which proper names may occur. It is an early work in analytic philosophy, and represents one form of philosophical analysis.


Such a sentence as,
(1) John is bald.
is a subject-predicate sentence containing an occurrence of the proper name "John." The sentence,
(2) The tallest spy is bald,
appears to be a subject-predicate sentence in which the definite description, "the tallest spy," occurs the place in which the proper name, "John," occurs in (1). The theory entails that these two sentences should not be treated in the same way; definite descriptions should not be treated as if they were proper names. Russell maintained that although sentences like (2) have the grammatical form of subject predicate sentences, they do not have the logical form of subject-predicate sentences, and that the correct analysis of such a sentence as the (2), will not treat it as a subject-predicate sentence. He was led to this position by three motivating puzzles.

A. Scott and the author of Waverley.
B. The King of France.
C. The Difference between A and B.

A. Scott and the author of Waverley.

Russell observed that a sentence like,
 

(3) George IV wished to know if Scott is the author of Waverley,
 

might well be true, even though
 

(4) George IV wished to know if Scott is Scott,
 

was false and
 

(5) Scott is the author of Waverley,
 

was true. If (3) is true, then it would appear that George IV was uncertain about the truth of (5) and if (4) were true, it would appear that George IV was uncertain about the truth of
 

(6) Scott is Scott.
 

Furthermore, if (5) is true, and the expression "the author of Waverley," functioned as a proper name in (5), then (5) would appear to say the same thing as (6). Yet, if (5) and (6) said the same thing, it is hard to see how (3) could be true while (4) is false.

B. The present king of France.
 

Russell observed that sentence,
 

(7) The present King of France is bald,
 

is not true. France is not a monarchy. He also maintained that
 

(8) The present king of France is not bald,
 

is not true. For the set of non-bald things does not contain a present king of France. The law of excluded middle,

LEM For any proposition p, either p is true or not-p, the negation or denial of p, is true,

seems to imply that there is no middle ground-for any given sentence, either that sentence or its denial is true. Since (7) is not true and (8) is the apparent denial of (7), it would seem to follow that (8) is true. We have seen, however, that there are reasons for thinking that (8) is not true.

C. The difference between A and B.
 

Two quantities, A and B, are of the same magnitude: A-B=0. Hence, there is no numerical difference between A and B. We might then think that
 

(9) There is no difference between A and B,
 

is true; this, in turn, suggests that
 

(10) The difference between A and B does not exist,
 

is true. (10), if true, would appear to attribute non-existence to the difference between A and B; that would seem to entail that the difference between A and B is such that it does not exist. However, how can the difference between A and B be such that it does not exist, if, in fact, there is no such thing as the difference between A and B? Hence, it seems that there is no was to deny truthfully that a given thing exists.
 

Russell's Theory in Application to these puzzles.

Russell's solution to these puzzles is to stop treating sentences containing definite descriptions as if the descriptions functioned as proper names. Russell had treated such expressions as, "the current king of France," "the round square," and "the difference between A and B," as he treated proper names, and would treat sentences in which such expressions occur as grammatical subjects as if they were genuine subject-predicate sentences. Under RTD, such sentences would be regarded as existentially quantified general sentences.

Such a sentence as
 

(11) Some person is wise,
 

Is an existentially quantified sentence. Russell would analyze, or interpret, (11) as
 

(12) There is an x such that x is a person and x is wise.
 

Russell maintained that despite their apparent grammatical form-that of subject-predicate sentences-the sentences that give rise to the puzzles are in fact existentially quantified sentences. They have the grammatical form of subject predicate sentences but the logical form of existentially quantified sentences, and it is the logical form of sentences that should serve as our guide for drawing inferences from sentences
On the analysis afforded by RTD,
 

(5) Scott is the author of Waverley
 

is analyzed as
 

(5') There is an x such that x authored Waverley, x alone authored Waverley, and x is Scott.
 

Therefore, on this analysis,
 

3) George IV wished to know if Scott is the author of Waverley,
 

Which contains (5) as an embedded clause, is analyzed as
 

(3') George IV wished to know if there is an x such that x authored Waverly, x alone authored Waverley, and x is Scott.
 

It is generally recognized that (3') could be true even if (4) is false, and, hence that, as analyzed by the theory, that (3) can be true even if (4) is false.

Sentence
 

(7) The present King of France is bald
 

is analyzed as
 

(7') There is a x such that x is a present King of France, nothing else is a present king of France, and x is bald.
 

This sentence is false; France is not a monarchy. The theory yields two analyses of the sentence
 

(8) The present king of France is not bald.
 

One of the two analyses is,
 

(8w) There is an x such that: is a present King of France, nothing else is a present king of France, and x is not bald.
 

The other of the two analyses is,
 

(8n) It is not the case that there is an x such that: x is a present King of France, nothing else is a present king of France, and x is not bald.
 

(8w), the interpretation of (8) on which the definite description gets "wide scope," is false; it falsely asserts that there is a present King of France, and then goes on to assert that there is just one such king, and that he is bald. But since France is not a monarchy, there is no present king of France. (8n), the interpretation of (8) on which the definite description gets "narrow scope," is true; for it asserts the denial of (7'), and (7') is false. In this way, Russell satisfied the requirement that either (7) or its denial is true; for, strictly speaking, (8n), and not (8w) is the denial of (7')--and (7') is the theory's analysis of (7).


Finally,
 

(13) The difference between A and B exists.
 

Is analyzed as
 

(13') There is an x such that x is a difference between A and B and x alone is a difference between A and B,
 

and (13') can be false in the case where there is no such thing as the difference between A and B. Hence, in this way, on can truthfully assert the non existence of something. That is,

(14) The difference between A and B does not exist,

would be analyzed as

(14') It is not the case that there is an x such that x is a difference between A and B and x alone is a difference between A and B.
 

RTD also analyzes sentences that contain indefinite descriptions. Such a sentence as
 

(15) A man is running,
 

contains the indefinite description, "a man," in a place that could be occupied by a proper name. Russell maintained that such expressions should not, however, be treated as proper names, and would have offered something like,
 

(15') There is an x such that x is a man and x is running,
 

as an analysis of (15).

List of Selected Works
Russell, Bertrand, The Principles of Mathematics, Cambridge University Press. (1903)
Russell, Bertrand, "On Denoting", Mind, 14, 479-493. (1905) Reprinted in Russell, Bertrand, Essays in Analysis, London: Allen & Unwin, 103-119. (1973)

Internet Resources:

On Denoting: http://www.santafe.edu/~shalizi/Russell/denoting/. One of many links the Russell's original article.

Bertrand Russell: http://cd1.fisher.su.oz.au/stanford/entries/russell/ Entry by A. D. Irvine in Stanford Encyclopedia of Philosophy.

 

(Comments welcomed: email.)

© 2000 Thomas C. Ryckman