Theory of Descriptions

by Dennis Bradford

in intellectual well-being

Russell’s Theory of Descriptions is a paradigm of analytic philosophy, which has dominated philosophy in the English-speaking world for over a century. It is the single most famous argument ever proposed by an analytic philosopher.

Russell presented it in a paper called “On Denoting” in the journal Mind in 1905, pp. 479-493. Quotations in this post are from that article.

Permit me to present the Theory of Descriptions in a clarified, simplified form and briefly evaluate it. [For more details, see my doctoral dissertation.]

How is it possible to think about what does not exist?

That’s the problem that prompted Russell to develop the Theory of Descriptions. It is a puzzle!

Consider any judgment of the form “x does not exist.” If that judgment is false, presumably it is about x. So it would seem that, if it were true, it ought also to be about x. However, in this case, since if it were true x would not exist, there exists no x for the judgment to be about!

How could the truth value of a judgment affect what it is about? Isn’t that backwards? Don’t we first understand what a judgment is about and then determine its truth value?

Russell developed the Theory of Descriptions because he did not want such judgments to be about nonexistent objects. He asks, rhetorically, “[H]ow can a nonentity be the subject of a proposition?”

Since he thinks it cannot, Russell developed the Theory of Descriptions in order to eliminate the appearance of reference to nonexistent objects.

He’s explicit about that. He wants to deal satisfactorily with (i.e., eliminate) the “whole realm of non-entities, such as ‘the round square,’ ‘the even prime other than 2,’ ‘Apollo,’ ‘Hamlet,’ etc. . . . All these are denoting phrases which do not denote anything.” With the Theory of Descriptions, “there are no unreal individuals.”

The argument in favor of the Theory of Descriptions is valid: A or B, not A. hence, B. “The evidence for the above theory is derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur.”

Since the quality of his reasoning is impeccable, all that remains is to determine whether or not the argument is sound (in other words, whether it has all true premises in addition to logical validity).

Let’s get clear on the first premise. What are the two underlying alternatives?

“[W]e must either provide a denotation in cases in which it is at first sight absent, or we must abandon the view that the denotation is what is concerned in propositions which contain denoting phrases. The latter is the course that I advocate.”

Russell designed the Theory of Descriptions as an alternative to the two ways available to take the former course, namely, Meinong’s and Frege’s.

Russell argues that the problem with Meinong’s “solution,” which admits that all denoting phrases signify objects (whether they exist or not), is that it admits objects that fail to obey the law of contradiction, which is absurd.

Russell argues that the problem with Frege’s “solution,” which makes troublesome denoting phrases signify the null class, is that it is “plainly artificial, and does not give an exact analysis of the matter.”

The chief idea behind Russell’s “solution,” the Theory of Descriptions, is that: “a denoting phrase is essentially part of a sentence, and does not, like most single words, have any significance on its own account.”

For example, consider the denoting phrase “the author of Waverley,” which is just the kind of phrase likely to cause a problem. A sentence that contains it should be rewritten so that the offending phrase disappears.

According to the Theory of Descriptions, the sentence ‘The author of Waverley was a man’ should be rewritten as: ‘At least one entity is author of Waveerley, at most one entity is author of Waverley, and that one, whichever one it is, was a man’ or, more simply, “One and only one entity wrote Waverley, and that one was a man.”

Notice that there are no phrases that remain in the rewritten sentence that could normally be used to refer to an individual. If one were to apply Russell’s procedure to all occurrences of possibly offending phrases, one would successfully eliminate all potentially offending phrases.

Russell provides further support for the Theory of Descriptions by arguing that it can be used to solve three puzzles. (If you are interested, I review this part of his argument in my The Concept of Existence, pp. 98-101, or, of course, you can read his original article.)

What, if anything, is wrong with Russell’s procedure?

Consider what Russell considers to be its value: it “gives a reduction of all propositions in which denoting phrases occur to forms in which no such phrases occur.” In other words, it eliminates denoting phrases like definite descriptions from the sentences in which they occur.


Does that solve the problem about how it is possible to think about what does not exist?

How could it? It takes the problem to be a problem about language, about how language supposedly misleads us into thinking that there are nonexistent objects.

As Strawson argued nearly half a century later, the Theory of Descriptions fails to do justice to denoting phrases used referringly. At best it provides a way to rewrite such phrases correctly to capture their meaning when denoting phrases are used nonreferringly.

(Russell himself never attempted to eliminate all denoting phrases used referringly [because he retained logically proper names that label individuals]. Quine took that step.)

In other words, the puzzling fact that the Theory of Descriptions does not even appear to solve is this: It is possible to think about what does not exist. Therefore, this is not merely a puzzle in the philosophy of language.

Since this undermines the reason to accept Russell’s first premise, his argument is unsound.

Furthermore, even if one were to execute the Theory of Descriptions in ordinary language and create a more ideal language in which all denoting phrases were eliminated (thus eliminating all denoting phrases that are used to refer to nonexistent objects), it would be impossible to execute that plan without using the concept of existence.

This is critical because, if existence is a concept (principle of classification), then there are entities to which it is applicable and nonentities to which it is inapplicable. However, the puzzle is how can there be nonentities to which it is inapplicable!

It is my view that Meinong’s alternative, properly emended, is able to solve the three puzzles mentioned by Russell (see my The Concept of Existence, pp. 101-102.). That, though, is a topic for another occasion.

Russell’s Theory of Descriptions is an interesting but misguided attempt to solve an important problem.

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