In formal semantics and philosophy of language, a definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun.
The definite description is proper if X applies to a unique individual or object.
The definite descriptions "the person in space" and "the Senator from Ohio" are improper because the noun phrase X applies to more than one thing, and the definite descriptions "the first man on Mars" and "the Senator from Washington D.C." are improper because X applies to nothing.
Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content.
Bertrand Russell pointed out that this raises a puzzle about the truth value of the sentence "The present King of France is bald.
But if it is false, then one would expect that the negation of this statement, that is, "It is not the case that the present King of France is bald", or its logical equivalent, "The present King of France is not bald", is true.
A definite description like "the present King of France", he suggested, is not a referring expression, as we might naively suppose, but rather an "incomplete symbol" that introduces quantificational structure into sentences in which it occurs.
Thus, whether "the present King of France is not bald" is true or false depends on how it is interpreted at the level of logical form: if the negation is construed as taking wide scope (as in the first of the above), it is true, whereas if the negation is construed as taking narrow scope (as in the second of the above), it is false.
So we do not have a failure of the Law of Excluded Middle: "the present King of France is bald" (i.e.
On this view, definite descriptions like 'the present King of France' do have a denotation (specifically, definite descriptions denote a function from properties to truth values—they are in that sense not syncategorematic, or "incomplete symbols"); but the view retains the essentials of the Russellian analysis, yielding exactly the truth conditions Russell argued for.
The Fregean analysis of definite descriptions, implicit in the work of Frege and later defended by Strawson[3] among others, represents the primary alternative to the Russellian theory.
The Fregean view is thus committed to the kind of truth value gaps (and failures of the law of excluded middle) that the Russellian analysis is designed to avoid.
The presuppositional character of the existence and uniqueness conditions is here reflected in the fact that the definite article denotes a partial function on the set of properties: it is only defined for those properties f which are true of exactly one object.
It is thus undefined on the denotation of the predicate 'currently King of France', since the property of currently being King of France is true of no object; it is similarly undefined on the denotation of the predicate 'Senator of the US', since the property of being a US Senator is true of more than one object.
Following the example of Principia Mathematica, it is customary to use a definite description operator symbolized using the "turned" (rotated) Greek lower case iota character "℩".