| 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.
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. 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, 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 (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: x 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 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).
(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). |
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