A definite description is an expression beginning with the word 'the' and intended to refer to a single entity. Examples are 'the book on that table', 'the Dalai Lama', 'the positive square root of two', and 'the Man in the Moon'. In Gottlob Frege's system of logic these were regarded as singular referring expressions, akin to proper names like 'Venus', 'Mount Everest', or 'Madame de Pompadour'. Bertrand Russell showed in his 1905 paper 'On Denoting' that this analysis was untenable: they need to be regarded as complex components of the proposition they're part of. They are quantified expressions, with 'the table' acting like 'all tables' or 'some tables'.

Russell's analysis is still regarded as correct for at least some definite descriptions, and modern debate has been about whether there are any that actually do behave as referential devices.

Problems with a referential analysis

Problems with treating them as references include what happens with nonexistence and substitution. There is no present King of France, so how do we assess 'The present King of France is bald'? True, false, or indeterminate? It clearly means something: the meaning is quite straightforward; so the denotation, or what it refers to out there in the world, is not in this case determined by the meaning. Many people feel this is neither true nor false; but you can make a clearly true statement about a non-existent referent: 'The Tooth Fairy does not exist'. Meinong got around nonexistence by saying that they subsist, i.e. sort of exist for talking about but sort of don't exist, thus giving rise to Meinong's jungle.

One problem of substitution is that 'The Morning Star is the Evening Star' is informative in a way that 'The Morning Star is the Morning Star' is not. Another is that intensional contexts (after verbs of saying or thinking) are opaque to substitution: 'Arnold believes the Morning Star is visible only in the morning' does not have the same truth value as the sentence formed by substituting another name, 'the Evening Star', for the same referent. (Although in a de re sense he does believe this too, but this is not what we would normally say.)

Russell's analysis

In 'On Denoting', and later formalized in Principia Mathematica, Russell said that definite descriptions contain both an existential and an implicational claim. In saying 'the X has property P' we are saying that there is one and only one thing that satisfies description X, and if anything satisfies description X then it has property P. So there is one present King of France, and there is no more than one present King of France, and whoever is present King of France is bald. This is a conjunction: it is false if any of its parts is false, and since there is no present King of France, it follows that 'The present King of France is bald' is false in Russellian terms (rather than indeterminate).

Under this analysis there is nothing in the logical structure that corresponds to 'the X': the grammar has been distributed across several logical components.

There are at least three things Russell avoided talking about: plurals, anaphors, and incompletely specified or abbreviated descriptions. With plurals, surely a description that picks out exactly two or five individuals is amenable to the same treatment as for one; while those like 'the citizens of Mongolia' that pick out some unspecified number might need to be treated as universal quantifications. Anaphora is when a word doesn't have a reference of its own but picks it up from a previous mention: typically pronouns like 'she' or 'herself', but it is possible to use definite nouns anaphorically: 'I told John I was an astronaut and the fool believed me.' And there is a uniqueness problem in in

Criticisms and refinements

P.F. Strawson picked up on the incomplete descriptions: we routinely say 'the book' and 'the table', and on a literal reading of Russell's theory these should imply there is only one book and one table in the world. In fact of course the context of the utterance makes clear that the uniqueness claimed is within a delimited domain. Strawson also thought Russell had the wrong intuition about non-existents: 'The present King of France is bald' is not false, but fails to work because the presupposition it contains is not met.

Strawson distinguished between the sentence and its use, the utterance of it being a speaker's act of using the sentence to make a claim. Throughout the history of France people have been able to speak about 'the present King of France', sometimes making true statements about Louis XIV, or false statements about Louis XV; it is not the sentence itself that contains the reference or the truth conditions, but the occasion of a particular utterance of it. Uttered at a certain time, it may successfully refer to Louis XV, but at other times the presupposition that there is such a king will fail.

Keith Donnellan drew a distinction between referential and attributive uses of definite descriptions. He said that sometimes a description was just used as a way of picking out a particular individual, and its precise content was not essential to the truth or reference of the utterance. He contrasted this referential use with an attributive one, where we are using the contents of the description as essential, and saying that whatever satisfies that attribute is the thing we mean.

One of his examples was 'the man drinking a martini'. You can point someone out at a party, making clear who you mean by indicating the one with a drink in a martini glass. You mean him, a certain man with a certain name: and if it turns out he's only got mineral water in his martini glass, you still meant him, not someone else. If unbeknownst to you another man is actually drinking a martini, you certainly didn't mean that other man. So in this case 'the man drinking a martini' refers to an individual. But if at a temperance society meeting it is rumoured that someone was seen drinking a martini, the chairperson might ask for the man drinking a martini to stand up and confess: they don't know in this case who the person was, or even if there is one, but they mean anyone who fits that attribute.

Saul Kripke criticizes this distinction, saying that it belongs to pragmatics, the way we understand what speakers mean in particular circumstances. At the party, 'the man drinking a martini' does not mean the teetotaller Smith, even though the speaker intended to refer to Smith, and is probably understood as referring to Smith. He points out that you need a pragmatic explanation of misdescription for proper names anyway. Suppose you see Smith raking up the leaves, but you mistake him for Jones, and say 'Jones is raking up the leaves'. You have referred to Smith by calling him 'Jones', and a hearer would probably understand you as doing so, depending on the context. So there is a semantic reference to one individual, and a speaker's reference to another. It is then unnecessary to posit a systematic ambiguity in the word 'the'.

See my essay 'Logic and Pragmatics of Attributive and Referential' for a lot more detailed discussion of this.

Russell, B. 1905. 'On Denoting', in Mind 14.
Strawson, P.F. 1950. 'On Referring', in Mind 59.
Donnellan, K. 1966. 'Reference and Definite Descriptions', in Philosophical Review 75.
Kripke, S. 1979. 'Speaker's Reference and Semantic Reference', in French et al. (eds), Contemporary Perspectives in the Philosophy of Language.

All the above and many other important readings are collected in:
Ostertag, G. (ed.) 1998. Definite Descriptions: A Reader, MIT.

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