Understanding & Evaluating Russell's Theory of Definite Descriptions

Understanding and Evaluating Russell's Theory of Definite Descriptions

- Tom Stringer

Russell's theory attempts, using systematic formal logic, to pin down conditions by which we ascribe significance and meaning to descriptive nouns or Ð''definite description' (DD) phrases in idiomatic natural language (NL). Russell's theory covers the functions of these phrases in NL and outlines his ideas on their nature. From this, he goes on to delineate implications that their transposition into a schema of propositional logic has for NL through examining them within the scope of three "puzzles".

DD's are linguistic devices used in assertions to denote common singular noun's prefaced by a definite article, usually "the." i.e. "the grey monkey" or "the PM of the United Kingdom." Donnellan surmises that DD's have two distinct linguistic functions, attributive and referential . This is to say they can attribute a certain quality to their subject "John's girlfriend is attractive", and secondly to refer or draw attention to a particular subject, "John's girlfriend is Sarah." As shown in this case, DD' s like "John's girlfriend" can be used in both senses in one and the same phrase. Our definition excludes plural descriptions and noun phrases such as "brown monkeys", as well as non compositional noun phrases where the meaning isn't implicit in the words but requires outside reference to make sense; "The average Ghanaian citizen has 3.6 children" is an ambiguous denotative term with no particular object and only has meaning in relation to a mathematically derived average.

Russell's project attempts to ascribe meaning to DD's, at its most simply level his theory runs; a sentence of the form "The X is Y" contains a DD and its truth conditions (when this phrase can be said to be both inductively significant and true) can be cached out;

i) there is at least one X

ii) " " most one X

iii) All X's are Y's

Or putting iii) another way; "there is exactly one X and it is Y." These last two are equivalent and have identical truth conditions. DD's are devices of quantification which don't signify any particular in isolation because they don't introduce objects into the truth conditions of phrases but rather quantify their subject within the context of a proposition. They contain an intrinsic claim of existence and of uniqueness (of its subject); for X to be Y it must first exist, and that it is the only X.

Russell initially considers one way we can cache out DD's so as to give them meaning; the view advocated in different forms by Meinong and Frege that DD's are equivalent to "singular terms" or, "denoting phrases which express meaning and denote a denotation." Singular terms both introduce the status of their object into sentential truth conditions as well as exhaustively stating everything that can be entailed of their object. It isn't the phrase's meaning that is significant, simply the denotation. However, we encounter a problem when considering phrases like "the present King of France is bald" (hereafter PKF) or inversely "PKF is not bald" as, although it has meaning, it denotes no object. So although clearly false, we still understand the assertions, leading to ambiguity about the status of the phrase. Rather than concluding that although meaningful we cannot consider DD' s as having truth conditions, Russell follows this lead and introduces 3 puzzles to test the validity of this theory of denotation.

The first puzzle, Informative Identities, is based on the principle that if A and B are identical then whatever is true of A is true of B. If we take a phrase involving the singular terms "Scott was the author of Waverley," and apply this rule, we conclude that if the two terms are truly identical then "Scott is Scott" is equivalent to "Scott is the author of Waverly." However, this is clearly false as although the second phrase is informative, the first has no content, "one is more relevant than the other" and as the second has more meaning Russell questions how singular terms can exhaustively describe an object if the two phrases are not equivalent.

The second puzzle, Negation Pairs, operates around the law of excluded middle that either "a is b" or "a is not b" must be true. However, a phrase involving singular terms like "PKF is bald" and inversely "PKF is not bald" it seems neither can be true or false but are meaninglessly ambiguous as, to paraphrase Russell, "if we enumerate bald thingsÐ'...and non bald thingsÐ'...PKF is not present in either list." We cannot attribute truth conditions to singular terms with no denotation. This introduces the third puzzle, that of Singular Negative Existential Statements (SNES). Russell considers phrases involving singular terms without objects to suffer "failure of meaning," without significance or a truth value. However, negative statements dealing with a single object i.e. "PKF doesn't exist" are both significant and true but have no meaning as their object doesn't exist. The necessity of including the meaning of a phrase into our considerations of significance regarding DD's is made clear by these puzzles. It seems that to accept this view wouldn't just violate the laws of identity and of excluded middle but would still leave ambiguity around some phrases' meanings. Russell cannot consider singular terms equating to DD's a satisfactory solution and concludes another explanation of DD's is required.

Russell's solution to the first puzzle is that we mustn't consider denotative phrases alone but the entire proposition which gives them meaning. Regarding the problem of non equivalency of identity surrounding "Scott was the author of Waverley" we can solve this by separating the terms into "Scott is Scott," caching out the second as "There is one and only one entity X that wrote Waverley", thus altering the subject predicated by the phrase. The identity of the terms can be seen to be equivalent in the most explicit version of Russell's formula noted earlier:

Phrase 1) Scott is Scott

Phrase 2) i) At least one X wrote Waverley

ii) At most one X wrote Waverley