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. For example: "the first person in space" and "the 42nd President of the United States of America", are proper. 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 largest prime number" are improper because X applies to nothing. Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content. To meet Wikipedias quality standards, this article or section may require cleanup. ... This word has distinct meanings in other fields: see denotation (semiotics) and connotation and denotation. ... In music, modality is the subject concerning certain diatonic scales known as modes (e. ...

Russell's analysis

Main article: Theory of descriptions

France is a republic, and has no king. Consider the statement "The present King of France is bald." Is this statement true? Is it false? Is it meaningless? The theory of descriptions is one of the philosopher Bertrand Russells most significant contributions to the philosophy of language. ... Forms of government Part of the Politics series Politics Portal This box:      For other uses, see Republic (disambiguation). ...

It does not seem to be true, for there is no present King of France. But if it is false, then one would suppose that the negation of the statement is true, that is, "The present King of France has hair (is not bald)." But that seems no more true than the original statement.

Is it meaningless, then? One might suppose so (and some philosophers have; see below), because it certainly does fail to denote in a sense, but on the other hand it seems to mean something that we can quite clearly understand.

Russell, extending the work of Gottlob Frege, who had similar thoughts, proposed according to his 'theory of descriptions' that when we say "the present King of France is bald", we are making three separate assertions: Bertrand Arthur William Russell, 3rd Earl Russell OM FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician and advocate for social reform. ... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, IPA: ) was a German mathematician who became a logician and philosopher. ...

1. there is an x such that x is the King of France
2. there is no y, y not equal x, such that y is the King of France (i.e., x is the only King of France)
3. x is bald.

Since assertion 1 is plainly false, and our statement is the conjunction of all three assertions, our statement is false.

Similarly, for "the present King of France is not bald", we have the identical assertions 1 and 2 plus

4. x is not bald

so "the present King of France is not bald", because it consists of a conjunction, one of whose terms is assertion 1 is also false.

The law of the excluded middle is not violated because by denying both "the King of France is bald" and "the King of France is not bald," we are not asserting the existence of some x which is neither bald nor not bald, but denying the existence of some x which is the King of France. The law of excluded middle (tertium non datur in Latin) states that for any proposition P, it is true that (P or ~P). ...

There is a second way of stating "the present King of France is not bald". Instead of substituting x in the sentence "x is not bald" as we have done above, we may negate (1) yielding "it is not the case that there exists an x and x is bald". This sentence is true as opposed to the statement obtained by the previous method. Second, it is easier to see that it does not violate the law of excluded middle. Russell's analysis has been attacked by P.F. Strawson, Keith Donnellan and others, and it has been defended and refined by Stephen Neale. Peter Frederick Strawson (born November 23, 1919 in London) is a philosopher associated with the ordinary language philosophy movement within analytical philosophy. ... Stephen Neale is Professor of Philosophy at Rutgers University. ...

Symbolic form

When using the definite descriptor in a formal logical context, it is common to denote it by the symbol iota: Logic, from Classical Greek λόγος logos (the word), is the study of the principles and criteria of valid inference and demonstration. ... For programming language, see Iota and Jot. ...

ψ(ιx(φx)) ≔ ∃x(∀y(φy ↔ y = x) ∧ ψx).

References

• Donnellan, Keith, "Reference and Definite Descriptions," in Philosophical Review 75 (1966): 281-304.
• Neale, Stephen, Descriptions, MIT Press, 1990.
• Russell, Bertrand, "On Denoting," in Mind 14 (1905): 479-493. Online text
• Strawson, P. F., "On Referring," in Mind 59 (1950): 320-344.

The Philosophical Review is a quarterly journal edited by the faculty of the Sage School of Philosophy at Cornell University and published by Duke University Press. ... MIT Press Books The MIT Press is a university publisher affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts. ...

See also

The theory of descriptions is one of the philosopher Bertrand Russells most significant contributions to the philosophy of language. ... Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. ... Analytic philosophy is a generic term for a style of philosophy that came to prominence during the 20th Century. ... Bertrand Arthur William Russell, 3rd Earl Russell OM FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician and advocate for social reform. ... Professor Sir Peter Frederick Strawson (November 23, 1919 – 13 February 2006) was an English philosopher. ... Stephen Neale is Professor of Philosophy at Rutgers University. ...

External links

• Stanford Encyclopedia of Philosophy