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Information about Definite Descriptor

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.

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?

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.

Bertrand 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:
  1. there is an x such that x is the King of France (∃x(Fx))
  2. for every x that is the King of France and every y that is the King of France, x equals y (i.e. there is at most one King of France) (∀x(Fx → ∀y(Fy → y=x)))
  3. x is bald. (∀x(Fx → Bx))


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.

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" (alternatively "it is not the case that there exists an x, therefore x is neither bald nor not 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.

Symbolic form

When using the definite descriptor in a formal logical context, it is common to denote it by the symbol iota:
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.
  • Ostertag, Gary (ed.). (1998) Definite Descriptions: A Reader Bradford, MIT Press. (Includes Donnellan (1966), Chapter 3 of Neale (1990), Russell (1905), and Strawson (1950).)
  • Russell, Bertrand, "On Denoting," in Mind 14 (1905): 479-493. Online text
  • Strawson, P. F., "On Referring," in Mind 59 (1950): 320-344.

See also

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denotation of a word or phrase is a part of its meaning; however, several parts of meaning may take this name, depending on the contrast being drawn:
  • Connotation and denotation are either

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    • law of the excluded middle states that the formula "P ∨ ¬P" ("P or not-P") can be deduced from the calculus under investigation. It is one of the defining properties of classical systems of logic.
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    denotation of a word or phrase is a part of its meaning; however, several parts of meaning may take this name, depending on the contrast being drawn:
  • Connotation and denotation are either

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    • A modal form is a provision of syntax that indicates the predication of an action, attitude, condition, or state other than that of a simple declaration of fact. The modality of a grammatical form is the quality or state in question.
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    The theory of descriptions is one of the philosopher Bertrand Russell's most significant contributions to the philosophy of language. It is also termed Russell's Theory of Descriptions (often abbreviated as RTD).
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    Motto
    Liberté, Égalité, Fraternité
    "Liberty, Equality, Fraternity"
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    republic, for all other uses see: republic (disambiguation)

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    Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, historian, logician, mathematician, advocate for social reform, pacifist, and prominent rationalist.
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    Friedrich Ludwig Gottlob Frege
    Birth: November 8, 1848
    Death: 26 July, 1925
    School/tradition: Analytic philosophy
    Main interests: Philosophy of mathematics, mathematical logic, Philosophy of language
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    law of the excluded middle states that the formula "P ∨ ¬P" ("P or not-P") can be deduced from the calculus under investigation. It is one of the defining properties of classical systems of logic.
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    Sir Peter Frederick Strawson (November 23 1919 – 13 February 2006) was an English philosopher. He was the Waynflete Professor of Metaphysical Philosophy at the University of Oxford (Magdalen College) from 1968 to 1987.
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    Keith Donnellan (born 1931) is a contemporary philosopher and Professor Emeritus at the University of California, Los Angeles. He has made important contributions to the philosophy of language, most notably to the analysis of proper names and definite descriptions.
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    Stephen Roy Albert Neale (born January 9, 1958) is Distinguished Professor of Philosophy and Kornblith Family Chair in Philosophy of Science and Value at the Graduate Center, City University of New York (CUNY).
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    Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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    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.

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    Mind is a well-respected British journal, currently published by Oxford University Press on behalf of the Mind Association, which deals with philosophy in the analytic tradition. It was founded by Alexander Bain in 1876 with George Croom Robertson as editor.
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    The theory of descriptions is one of the philosopher Bertrand Russell's most significant contributions to the philosophy of language. It is also termed Russell's Theory of Descriptions (often abbreviated as RTD).
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    Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for Analytic Philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship
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    Analytic philosophy (sometimes, analytical philosophy) is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century.
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    Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, historian, logician, mathematician, advocate for social reform, pacifist, and prominent rationalist.
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    Sir Peter Frederick Strawson (November 23 1919 – 13 February 2006) was an English philosopher. He was the Waynflete Professor of Metaphysical Philosophy at the University of Oxford (Magdalen College) from 1968 to 1987.
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    Stephen Roy Albert Neale (born January 9, 1958) is Distinguished Professor of Philosophy and Kornblith Family Chair in Philosophy of Science and Value at the Graduate Center, City University of New York (CUNY).
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