Bertrand Russell — On Denoting
An overview of Russell’s noteworthy contributions to the philosophy of language through his article On Denoting, including the Theory of Descriptions
Overview of the Text
Through his article ‘On Denoting’ published in 1905, Russell aims to point out how we often mix the often co-existing and overlapping logical and the grammatical forms of sentences with each other. This is a cause of confusion in language.
He clarifies how denoting phrases (he gives the example of ‘the present king of France’) are not merely names or labels, but are complex expressions that need to be analyzed. He believes that such phrases are ‘incomplete symbols’ which do not have a fixed meaning. Rather, their meaning is determined by the context they are being used in. This is where the theory of descriptions comes in. Russell claims that denoting phrases are used not to refer to particular objects or entities, but to a set of properties or characteristics associated with that phrase.
He also elucidates how differing the nature of subject term might be, in logic as well as in epistemology. Subjects can be definite, and they can be indefinite (ambiguous). Those that are definite might be based on either knowledge by description (verbal, non-natural and indirect) and knowledge by acquaintance (non-verbal, natural and direct).
Read Russell on Knowledge by Description and Acquaintance if you’d like to know more about this distinction.
He talks about the problem posed by non-referring terms (like ‘the present king of France’) and how such expressions do not refer to anything and thus, are meaningless.
He also puts forth the paradox of ‘the barber’ to emphasize how treating denoting phrases as if they are names for particular entities can lead to a paradox, and why it is important to think of them as incomplete symbols capable of being understood only in a particular context.
Why is the grammatical and logical distinction important?
The importance of this distinction can be understood with the help of the following example and explanation.
Grammatical form: “The author of Waverley was a novelist.”
Logical form: “There is a unique x who authored Waverley, and x is a novelist.”
The grammatical form of this sentence suggests that there is a specific person who authored Waverley and is also a novelist. However, the logical form reveals that this may not be the case. Instead, the sentence is referring to a unique entity that satisfies certain conditions or properties, such as being the author of Waverley and being a novelist.
In both cases, Russell is highlighting the importance of distinguishing between the grammatical form of a sentence, which can be misleading, and the logical form, which reveals the underlying meaning of the sentence. By carefully analyzing the logical structure of sentences, we can avoid confusion and gain a more precise understanding of how language works.
What is the Theory of Description?
As per the Theory of Descriptions, descriptions do not directly denote or refer to objects, but rather denote descriptions or properties that fit certain object or objects. It explains how we use language to refer to things in the world. This theory applies to both, definite and indefinite descriptions.
Russell’s Theory of Definite Descriptions will be discussed in some detail. This theory is more focused than the general Theory of Descriptions as it applies specifically to definite descriptions that are used to refer to unique entities satisfying certain conditions or possessing certain properties. It can be explained with the help of an example.
“The coffee mug is in the sink.” — In this sentence, “the coffee mug” is a definite description, but it does not refer to a specific coffee mug. Instead, it refers to a unique set of properties that identify the particular coffee mug that is in the sink. The properties include being a coffee mug, and being in a particular sink.
In his article, ‘On Denoting’, Russell is justifying this theory. His justification is twofold: an attack on the theories of meaning given by his contemporaries — Meinong and Frege and a solution to three philosophical puzzles.
A Commentary on Meinong and Frege
Read On Sense and Reference By Gottlob Frege to understand Russell’s arguments better.
Alexius Meinong (1853–1920) and Gottlob Frege (1848–1925 ) believed that definite descriptions denote objects directly.
As per their theories of meaning, in a sentence like “Record Store Day’s first global ambassador has released 10 original studio albums”, the italicized part is a definite description and directly denotes its object — Taylor Swift. So, the words “Record Store Day’s first global ambassador” and “Taylor Swift” are merely different ways of denoting the same human. This understanding seems intuitive. It is a common belief that the subject or the object parts of a sentence are denoted by definite descriptions. This view is attacked by Russell.
Meinong claimed that definite descriptions always denote objects that possess the properties described. Denotation of a description could thus be understood to be synonymous with its meaning. Sentences like “I drew a round square” would still be meaningful, even though the object is a description for a non-existent thing. But for Russell, meaningful statements must have a corresponding object or referent in reality, and Meinongianism allowed for the existence of non-existent objects. Thus, Russell rejected Meinong’s theory as it violated the law of non-contradiction (as per which there exists a non-existent object that could have the contradictory properties of being round and square at the same time).
Frege tried to avoid the aforementioned problem by putting forward a twofold classification of meaning — sense and reference. For a sentence like “Unicorn has magic blood”, there could be a sense without there having to be a reference. But Russell claimed that this twofold division has no value.
Frege’s theory of meaning (the meaning of a sentence is determined by the objects referred to in the sentence) was rejected by Russell because he believed that it lead to a contradiction that he called ‘Russell’s Paradox’. This paradox can be explained with the help of the following example: “The set of all sets that do not contain themselves” — for Frege, would refer to a particular set. But for Russell, the existence of such a set would be contradictory — because if the set contains itself, it does not satisfy the condition of not containing itself; if it doesn’t contain itself, then it does satisfy said condition, and should be a part of the set. This is how Russell discarded Frege’s theory — by highlighting its inadequacy as a good theory of meaning on the account of the contradictions it led to.
Types of Denoting Phrases
Russell believes that phrases do not have their own, independent meaning, but are assigned one in context with the proposition they are in. This is called the principle of denoting. He then explains how there are three types of denoting phrases — 1) ones that denote one definite object (example — the present queen of England), 2) ones that denotes an ambiguous, indefinite object (example — a dog), and 3) ones that seem to be denoting but do not denote anything (example — the present king of France).
Definite and Indefinite Terms
As per Russell, the following indefinite terms can be explained as:
- Everything: (x) is always true.
- Nothing: (x) is always false is always true.
- Something: ‘It is false that (x) is always false’ is always true.
More on Definite Descriptions
Russell was especially interested in definite descriptions because of their ontological diligence. These phrases have the form ‘the so-and-so’ and describe a unique entity/object.
For example, in the sentence “The artist who sang my favorite song is British.” — a relationship is asserted between the subject and the predicate, and, at the same time, it is being emphasized that nothing else has this relationship. We can reform this sentence into — “There is one, and only one artist, who sang my favorite song and is British” to better understand its claim at uniqueness.
Primary and Secondary Occurrence
Bertrand Russell introduced the concepts of “primary” and “secondary” occurrences of a term in his theory of descriptions. An understanding of it is essential to understand the puzzles and their solution.
In a primary occurrence, the term can be substituted with its synonym, whereas in a secondary occurrence, the terms occur as a part of the sentence and cannot be substituted. In the above example, ‘poet who wrote ‘Hope is a thing with feathers’’ is a secondary occurrence and hence cannot be substituted.
A term occurs “primarily” when it refers to a particular object or individual, while it occurs “secondarily” when it does not refer directly to an object or individual, but instead describes some attribute or property of the object or individual being referred to.
For example, in the sentence “The king of France is bald,” the term “the king of France” does not refer to any actual king of France (since there is currently no such person), but instead is used to describe the property of being bald. This is a secondary occurrence of the term.
On the other hand, in the sentence “Napoleon was defeated at Waterloo,” the term “Napoleon” occurs primarily, since it refers directly to a specific individual.
This distinction is important in Russell’s theory of descriptions, which seeks to clarify the logical structure of sentences containing definite descriptions such as “the king of France.” Definite descriptions help in understanding the primary occurrences of the subject.
Russell’s Three Puzzles
Russell introduces three puzzles that he think a good theory of denoting phrases should be able to solve. These are based on the three laws of thought — the law of identity, the law of non-contradiction, and the law of excluded middle.
First Puzzle — Identity Puzzle
This puzzle is concerned with the law of identity. As per this law, if A and B are identical, what is true for A is necessarily true for B, and both should be able to be replaced with each other. Consider the following sentence: “Skye wished to know whether Emily Dickinson was the poet who wrote ‘Hope is a thing with feathers’.” If we substitute ‘poet who wrote ‘Hope is a thing with feathers’’ with ‘Emily Dickinson’, it would become absurd to say — “Skye wished to know whether Emily Dickinson was Emily Dickinson.”
Russell proposes a solution to this puzzle by giving the following reasoning — when Skye wished to know something, the ‘something’ must be a proposition with a denoting phrase. Following will be the logical form of the proposition — “One and only one person wrote ‘Hope is a thing with feathers’ and Skye wished to know whether Emily Dickinson was that person.”
Second Puzzle — Negation Puzzle
The second puzzle is concerned with the law of the excluded middle. As per this law, either A is equivalent with B or A is not equivalent with B. If one of two contradictory statements is denied, then the other must be affirmed (either a proposition, or its negation, is true).
Now consider the sentences — “The present king of France is bald” and “The present king of France is not bald”. If one of these is false, it seems as though the other must be true. But France has no ‘present king’, so neither of these sentences can be true.
Through its logical form, Russell points to the emptiness of the subject. He puts forward the following — “Something is a king of France and nothing else is a king of France and it is also bald” and its negation “There is not something that is a king of France and nothing else is a king of France and it is also not bald”. The latter is true and the former is false.
Third Puzzle — Non-Existence Puzzle
This is based on the law of non-contradiction. As per Russell (in opposition to Meinong as discussed earlier in the blog), when we use a definite description to refer to something that does not exist, such as “the round square,” we seem to be saying something that is obviously false. However, we can still use the description in meaningful ways, such as in the sentence “the round square is a self-contradictory concept.”
Russell suggests that we should treat such sentences as asserting the existence of a “concept” or “meaning” associated with the description, rather than the existence of an object that satisfies the description.
Takeaway
Russell’s “On Denoting” is an important philosophical work that teaches us to think critically about the meaning of language.
By carefully analyzing the logical structure of sentences, we can avoid confusion and gain a more precise understanding of language. Russell’s theory of descriptions is a helpful tool for doing this, as it allows us to understand how language is used to describe objects in the world based on certain properties or conditions.
Also read — Russell’s Logical Atomism
Discussion in continuation (after Russell) for the theory of language can be understood through On Referring by P.F. Strawson and Reference and Definite Descriptions by K. Donnellan
