Tuesday, April 3, 2007

Analyzing Russell’s ‘On Denoting’

On Russell’s ‘On Denoting’

One of the most fascinating facets of Russell’s philosophy of language is that denoting phrases do not have meaning by themselves. This position departs from the viewpoints of nearly every other philosopher before Russell, even Frege. However, the way that Russell treats language is closer to Frege’s analysis than any other philosopher (excluding philosophy after Russell). Therefore, it makes sense to analyze Russell’s arguments in On Denoting as a contrast to Frege’s theory of sense and reference, in order to identify similarities and spotlight differences. After this process, we will be in a better position to appreciate the uniqueness of Russell’s theory of denoting phrases. In particular, this approach will aid in explaining Russell’s three puzzles and how his theory of denoting phrases solves them.

The beginning of Russell’s article contains two important foundational arguments. One of these arguments splits up a denoting phrase into three types of statements. Although Russell has the impediment of never defining a denoting phrase, he lists plenty of examples:

A man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass in the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. (p. 212)

Through this set of examples, the reader has at least a rough grasp of the idea of a denoting phrase. After Russell introduces these examples to help the reader intuit the idea of a denoting phrase, Russell splits the idea into three categories. A denoting phrase might denote nothing, or it may denote ambiguously, or it may denote one definite object (p. 212).

Denoting phrases are constituents in propositions and sentences, and as such are important to epistemology. Russell argues this, and states that the three categories of denoting phrases are responsible for two different types of knowing. On one hand, we may have knowledge by being directly acquainted with various objects in the world, and Russell calls this knowledge by acquaintance. On the other hand, we may not have direct acquaintance with objects in the world, yet still have knowledge—Russell considers that this is possible simply by being in contact with denoting phrases and statements that refer to objects beyond the scope of our sensory acquaintance. If we have knowledge but fail to be acquainted with the objects of our knowledge, according to Russell, we have knowledge about that something (p. 212).

The above three types of denoting phrases and the two-type theory of knowledge (which strongly resembles Quine’s de re/de dicto distinction), allows Russell to argue in a slightly different direction from Frege. As aforementioned, the most important argument that Russell advances here is that “denoting phrases never have any meaning in themselves, but that every proposition in whose verbal expression they occur has a meaning” (p. 213). This position departs from Frege’s argument that names have a sense and a reference. Russell’s contrasting argument seems to state that names, or rather denoting phrases, do not have a reference, but only have a functional version of a sense/description. This description allows denoting phrases to function so that they do not mean anything by themselves, but display meaning when used to construct propositions.

Russell recognizes Frege’s theory of names. Russell states Frege’s theory as characterizing a denoting phrase as having a meaning and a reference. Russell argues that imbuing denoting phrases with both of these properties is self-contradictory (they produce sentences that are simultaneously false and nonsensical; p. 214). Here Russell utilizes the famous statement: “The King of France is bald.” Russell notices that ‘the King of France’ refers to nothing, yet the whole statement ‘The King of France is bald’ is false. Although it is not clear how Frege suffers from self-contradiction by admitting that a denoting phrase can have a sense and fail to refer to any real object, Russell’s theory clearly has an advantage over Frege’s theory.

By arguing that denoting phrases function in a certain way so that they contribute to the meaning of an entire statement, Russell is able to extract multiple logical statements from a single sentence in English. For example, again consider the sentence, “The King of France is bald.” Russell believes that this sentence entails two logical propositions: (1) X is the King of France, and (2) X is bald. If we simply isolated the denoting phrase, ‘the King of France’, we would be unable to attribute any meaning to that phrase. We could not, according to Russell, declare that X is the King of France, since ‘the King of France’ by itself is not a constituent in a complete sentence. Furthermore, we could not say that X is bald, since we disconnected the existential quantifier ‘baldness’ from the denoting phrase. So, Russell seems be maintaining a fascinating position: denoting phrases have no meaning by themselves, but meaning emerges when denoting phrases interact with other components in a sentence. In Russell’s own words, “A denoting phrase is essentially part of a sentence, and does not, like most single words, have any significance on its own account” (p. 217).

Russell uses three ‘puzzles’ to test a theory of denoting phrases. The first puzzle tests a theory for salva veritate substitutions, the second puzzle tests a theory against the law of excluded middle, and the third puzzle tests a theory against the assumption that using propositional subjects entails existence. I will summarize each of these puzzles and describe how Russell argues how his theory defeats these puzzles.

The first puzzle deals with substitutions. According to Russell:

If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other in any proposition without altering the truth or falsehood of that proposition. (p. 215)

This analysis matches the idea of salva veritate substitution. When a is identical with b, either denoting phrases may be a constituent of a sentence and will produce identical truth-values (excluding belief contexts). However, Russell recognizes, along with Frege, that replacing b with a may cause a sentence to lose information. For example, if a is identical with b, then ‘a is b’ is true, but the above principle of substitution entails that replacing b with a will produce ‘a is a’. Obviously, ‘a is a’ has lost information from ‘a is b’, so this phenomenon puzzles a theory that allows for salva veritate substitutions.

In order to solve the first puzzle, Russell says that a theory of language must be able to maintain a connection between meaning and denotation. When a theory posits a denotation and a meaning of a denoting phrase in a single statement, this puzzle manifests itself. The solution to this puzzle is to deny that denoting phrases have meaning by themselves. So, a by itself has no meaning, and b by itself has no meaning, but combined, ‘a is a’ and ‘a is b’ posit hypothetical entities, but their meanings are different. Truth-value does not fully capture a statement’s meaning.

The second puzzle involves the rule of logic that defines a sentence’s truth-value as either true or false (and no middle value). This rule creates a puzzle for a theory of language because a statement ‘The King of France is bald’ is either true or false, but an enumeration of (existing) things that are bald and (existing) things that are not bald will never mention the King of France. The puzzle reveals how the sentence ‘The King of France is bald’ can be false, but an enumeration of bald things (or people) fails to account for nonexistent things which a sentence has attributed baldness. The only standing solution to this puzzle prior to Russell is a Hegelian synthesis that puts the King of France into the group of wig wearers. I assume that Russell means this last comment as a joke.

In order to solve this second puzzle, Russell translates the sentence ‘The King of France is bald’ into logical form and identifies a logical ambiguity. One form is affirming the truth of the sentence ‘The King of France is bald’—Russell says that this statement is false. The other form is negating this affirmation: ‘The King of France is not bald’—Russell says that this is ambiguous. It could mean ‘There is an entity which is not the King of France and is not bald’. The sentence is ambiguous because it could alternatively mean ‘It is false that there is an entity which is now King of France and is bald’. The payoff in arguing for this ambiguity is that the first form is a false statement, and the second form is a true statement. Russell distinguishes these two types as primary (the first form) and secondary (the second form) occurrences. A philosopher can challenge this ambiguity when examining a statement in a particular context. When George IV wants to know whether Scott is the author of Waverley, we can inquire with George IV whether he intends his question in terms of a primary or a secondary occurrence.

The third puzzle appears when Russell examines two denoting phrases and measures the difference between them. Either two denoting phrases are identical or they are different. However, when we consider denoting phrases that do not refer to an existing object, Russell argues that we run the risk of introducing contradictions. According to Russell, “it must always be self-contradictory to deny the being of anything; but we have seen, in connection with Meinong, that to admit being also sometimes leads to contradictions” (p. 215).

Russell solves the third puzzle by giving rules for when we analyze the relation between two denoting phrases. When we determine that a and b differ, then this difference is an entity (which exists). On the other hand, when we say that a and b do not differ, then this difference is not an entity (which does not exist). The use of denoting phrases that denote nothing will again produce ambiguous meanings, and this ambiguity follows the same model of primary and secondary occurrences. According to Russell, the way to solve the third puzzle is as follows:

If ‘Apollo’ has a primary occurrence, the proposition containing the occurrence is false; if the occurrence is secondary, the proposition may be true. So again ‘the round square is round’ means ‘there is one and only one entity x which is round and square, and that entity is round’ which is a false proposition, not, as Meinong maintains, a true one. (p. 218)

The sentences that contain denoting phrases that do not exist can be broken down into simpler sentences in logic. Once Russell separates assertions of an object’s existence from descriptions of that object, we can avoid the problem of nonexistent objects suffering from self-contradiction (p. 218).

Like Frege, Russell’s theory rests on an important assumption: denoting phrases describe what they inevitably reference. The difference between Frege and Russell on the issue of reference is in terms of when and how denoting phrases refer. Frege argued that denoting phrases refer.[1] However, Russell thinks that this process only occurs after a denoting phrase is a constituent of a whole sentence. Or, put another way, a denoting phrase can only refer to an object after it combines with an existential quantifier to form a sentence, and never before. The question is still open whether denoting phrases have a sense or affect what they reference. Other theories of language may contest this assumption, stating that endowing proper names with the power over what they reference is erroneous, and that denoting phrases have no important functional attributes whatsoever. I would credit this objection to Mill and Kripke, but I am reticent to do so since I have not yet read Naming and Necessity.

[1] Frege: “The sense of a proper name is grasped by everyone who knows the language or the totality of designations of which the proper name is a part; this, however, illuminates the nominatum, if there is any, in a very one-sided fashion” (p. 200).

Note: The parenthetical page references imply the following publication: Martinich, A. P. (2001). The philosophy of language (Fourth ed.). Oxford: Oxford University Press.

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