1 Introduction

The basic unit of communication can be said to be the sentence, which can be further divided into detailed elements. Traditionally, philosophers have divided sentences into subjects and predicates, with subjects and predicates containing either proper nouns or common nouns. For example, in “Socrates is a man,” “Socrates” can be considered a proper noun, while “man” in “I am a man” can be considered a common noun. Thus, it can be said that the linguistic expression “Socrates” has meaning because it refers to a specific individual. However, common nouns like “man” pose a challenge: “What does such a common noun refer to?”

In response to this problem, Russell proposed a groundbreaking solution in the early 20th century. His theory of descriptions not only addressed the issues of traditional philosophy but was also hailed as a philosophical paradigm. Stephen Schiffer commented that Russell’s theory not only contributed to defining the new philosophy of language but also remains the dominant theory today.

The purpose of this paper is to review the theory of descriptions from a semantic perspective. Since the theory of descriptions heavily relies on Frege’s semantics, we will first examine Frege’s semantics, then analyze which aspects of Frege’s semantics Russell accepted and which he rejected. Additionally, we will briefly explore how Russell’s semantics functions within his theory of descriptions. At the same time, Strawson’s critique of the theory of descriptions highlights its semantic aspects more clearly. Therefore, in the final section, we will examine Strawson’s critique of the theory of descriptions based on the concept of usage. By analyzing the key points between the two, we can see that Russell and Strawson hold differing views on language. However, it is evident that this difference in linguistic perspectives ultimately stems from their differing philosophical and truth views.

2 Frege’s Semantics

Frege’s fundamental idea in analyzing sentences was to extend the concepts of mathematical functions, variables, and values into the realm of sentences. For Frege, variables correspond to proper nouns in a sentence, and functions correspond to predicate expressions. Frege employed various methods in using proper nouns and predicate expressions. Firstly, proper nouns refer to expressions like “Socrates,” which we typically understand as proper names. Proper nouns also include all descriptions that can refer to a single object, such as “the tallest person in Beijing.” Secondly, predicate expressions include one-place predicate expressions with one variable, such as “x is a philosopher,” two-place predicate expressions, such as “x loves y,” and three-place predicate expressions, such as “y is between x and z.” Generally speaking, there can be n-place predicate expressions.

There are two ways to form a complete sentence. First, a proper noun can be combined with the aforementioned single predicate expression. Second, in general propositions, quantifiers are used to bind variables. For example, the following sentence expresses the same proposition as the general proposition “All men are mortal”:

For every x, if x is a man, then x is mortal.

Frege’s semantics is distinguished by its reference. Thus, it can be said that both proper nouns and sentences have meaning and reference. In the case of proper nouns, in a well-defined scientific language, all proper nouns have a single meaning and a referent. As for sentences, the meaning of a sentence is a proposition, which has truth or falsehood as its reference. However, expressions like “x is a philosopher” are predicate expressions and are considered predicate symbols; they, in themselves, do not have any meaning. Moreover, such expressions cannot refer to any single object.

3 Russell’s Semantics and Theory of Descriptions

Unlike Frege, Russell believed that proper nouns cannot occupy the variable position in predicate expressions. Why did Russell insist that proper nouns cannot be in the variable position of predicate expressions? The reason can be found in Russell’s 1905 paper On Denoting, where he first fully articulated his theory of descriptions. Russell’s primary objective in this paper was to propose a general theory of descriptions. According to Russell, descriptions are divided into indefinite descriptions and definite descriptions. His second objective was to reveal the philosophical implications of this theory.

On the other hand, the first objective also has a negative aspect, which is to refute existing theories. Previous theories held that the referent appearing in the linguistic expression of a proposition was a genuine constituent of the proposition, but this is where the difficulties arise [1].

Frege’s theory can avoid violating Meinong’s law of non-contradiction. According to Frege, referring phrases have both meaning and extension. For example, “the center of the solar system in the first half of the 20th century” has a very complex meaning, but its referent is merely a relatively specific point. Russell argued, “One advantage of this distinction is that it often provides a reason for the expression of identity claims” [1]. However, the situation is different when the referring phrase has no referent. Frege proposed a purely stipulative reference based on definition. For example, “the current King of France” refers to the empty set, “the only son of Mr. So-and-so” refers to the set of all his sons, and so on. Russell rejected this solution on the grounds that, although it is logically sound, it is merely a stopgap measure. We can now see one reason why Russell rejected Frege’s position, namely why he rejected Frege’s stance that descriptions can occupy the variable position in predicate expressions. Assuming Frege’s semantics, in cases like “the current King of France,” where there is no referent, Frege’s reference fails to apply to object distinctions. This is also unreasonable. Therefore, descriptions cannot occupy the variable position in predicate expressions.

Russell believed that ordinary proper nouns are nothing more than abbreviated descriptions. This argument implies that ordinary proper nouns also cannot occupy the variable position in predicate expressions. However, this claim is difficult to accept because it seems to directly contradict common sense. For example, we can substitute “Socrates” into “x is a man” and use the sentence “Socrates is a man” to communicate. So, why can’t ordinary proper nouns substitute for the variable in predicate expressions?

We have never met Socrates face to face. Therefore, we cannot name him. When we use the word “Socrates,” we are actually employing a kind of device, because we have never met Socrates in person, so we cannot name him. Our thoughts are shaped by phrases like “Plato’s teacher” or “the man who drank poison,” yet these are all within the proper sense of the term name. According to this view, Russell’s claim implies that only expressions that we have personally named are considered proper nouns. [2] But what if we consider words like “this,” “that,” and “I” as proper nouns? However, “this” might be a disguised description because it refers to “the object indicated near the speaker,” “that” refers to “the object indicated from a distance from the speaker,” and “I” refers to “the person who is speaking.” So, it seems that nothing can be called a proper noun because it directly refers to something. The conclusion is that even for ordinary proper nouns, Frege’s distinction of reference does not apply well.

Now we understand why Russell rejected certain aspects of Frege’s semantics. If, as Russell suggests, proper nouns in everyday life cannot occupy the variable position in predicate expressions, then it becomes theoretically impossible to explain how we understand familiar truths like the proposition “The Earth is round” in a strict sense. This is a well-known fact. In other words, this proposition can be expressed in another way, such as, “For every x, if x is the Earth, then x is round.” Although this expression contains neither ordinary proper nouns nor descriptions in the variable position, it still conveys the proposition “The Earth is round.” This formulation addresses the difficulties encountered so far, such as how to analyze referring phrases like “the current King of France” when they appear as the subject of a sentence without reference. It reduces all propositions containing referring phrases to a form that essentially eliminates these phrases. Consequently, since the referring phrase is removed from the linguistic expression of the simplified proposition, no issues arise related to the referring phrase. The theory of descriptions precisely offers such a reduction.

Russell regards the concept of “boundary” as a fundamental concept. Next, “C(x)” denotes a propositional function with x as its component. Now, the concept “C(x) is always true” is no longer analyzed but is considered an indefinable concept. Thus, the most primitive referents—“everything”, “nothing”, and “something”—can be interpreted as follows:

C(everything) means “C(x) is always true.”

C(nothing) means “‘C(x) is false’ is always true.”

C(something) means “‘C(x) is false’ is always true” is false, meaning “‘C(x) is false’ is sometimes true.”

Here, Russell emphasizes that the referring phrase itself has no meaning; the meaning is given by the propositions in which it appears. What Russell attempts to defend are precisely the principles of the new theory of reference, according to which all propositions where they appear as linguistic expressions have meaning. Let’s see how to reduce propositions containing vague referring phrases (indefinite descriptions), such as “I met a man.” According to Russell, this proposition is interpreted as follows:

“‘I met x, and x is a man’ is not always false.”

This can be further reduced as:

“C (a man)” means “‘C(x) and x is a man’ is not always false.”

It is worth noting that through this simplification, the statement entirely lacks the meaning of the phrase “a man” itself. Now, let’s consider how to reduce a proposition with a definite description, such as “The father of Charles II was executed.” This proposition asserts that Charles II’s father, x, existed, and x was executed. “x was the father of Charles II” does not indicate that x and Charles II can be explained as “x begat Charles II.” To reveal the uniqueness of this statement: “If y does not equal x, then y did not beget Charles II.” This gives us the original statement. “x was the father of Charles II” becomes “x begat Charles II, and ‘if y begat Charles II, then y is the same as x’ is always true for y.” Then, the initial proposition “The father of Charles II was executed” is simplified to:

“x begat Charles II, x was executed, and ‘if y begat Charles II, then y is the same as x’ is always true for y and is not always false for x.”

When C represents any statement about the father of Charles II, to explain something like “C(the father of Charles II),” rather than “he was executed,” we only need to substitute C(x). Then:

“C(the father of Charles II)” means “x begat Charles II, C(x), and if y begat Charles II, then y is the same as x, which is always true for y and not always false for x.”

So far, we have seen how Russell’s theory of descriptions simplifies all propositions containing referring phrases to a form where such phrases do not appear at all. Finally, the above statement simplifies to what ordinary language implies as uniqueness: “Charles II had one father, not multiple.” According to Russell, if this condition is not met, then “C(the father of Charles II)”—for example, “C(the present King of France)” or “C(a round square)”—can be said to be false.

Now let’s consider Russell’s second objective, namely, how the theory of descriptions is applied to philosophical problems. Russell presents three problems related to descriptions. Due to the limited scope of this article, we will focus only on the first problem. This problem concerns the issue of how propositions containing definite descriptions seem to violate the law of excluded middle.

According to the law of excluded middle, either “A is B” must be true, or “A is not B” must be true. Therefore, either “The present King of France is bald” must be true, or “The present King of France is not bald” must be true. However, even if we list all things that are bald and all things that are not bald, we would not find the present King of France in either list; a Hegelian inclined toward synthesis might conclude that the present King of France is wearing a wig.

Here, for Frege, a sentence that includes a definite description without a referent is neither true nor false. To avoid the conclusion that “a sentence containing a definite description without a referent lacks a truth value,” Russell treats definite descriptions as quantificational expressions. [3] When we say, “The present King of France is bald,” according to the theory of descriptions, this sentence asserts that there is an x such that x is the present King of France, that no one other than x is the King of France, and that x is bald. But in reality, since no individual has the attribute of being the present King of France, the sentence is shown to be false.

We have already examined the theory of descriptions. It refers to a theory that allows various conclusions to be derived based on the structure of facts. These facts are expressed by the propositions contained within sentences. Some propositions are composed of elements like names or descriptions, which are all ordinary proper names. The theory of descriptions removes referring phrases, such as definite descriptions, from propositions where they appear and reduces propositions where such phrases do not appear. This reduction cannot be achieved through traditional subject-predicate grammatical analysis. Furthermore, the theory can be applied to address certain philosophical problems. For example:

“The most perfect being possesses all perfections. Existence is a perfection; therefore, the most perfect being exists,” is reduced to “There is only one entity x that is the most perfect, and because existence is a perfection, this entity exists.” However, this argument fails as it cannot prove the premise that “there exists a most perfect entity x.”

Russell’s theory of descriptions assumes a semantics where the meaning of a name is its referent, while a definite description in itself has no meaning.

4 Strawson’s Critique

In 1950, Strawson published an essay titled On Referring, which stands in sharp contrast to Russell’s On Denoting. Strawson argued that Russell had a fundamental confusion regarding language.

Strawson referred to the way we use expressions in statements about individuals, single objects, specific events, etc., to refer to each of these as the “uniquely referring use”. [4] He further categorized the expressions used into four types: 1) singular demonstrative pronouns, 2) proper names, 3) singular personal pronouns and singular impersonal pronouns, and 4) phrases beginning with a quantifying or non-quantifying noun modified by a definite article. Strawson focused his attention on expressions used in a singular statement manner that appear as the grammatical subject of a sentence, and stated: “I believe that Russell’s theory of descriptions concerns the last of the four types of expressions I mentioned above and is still regarded by logicians as a norm of ordinary language. I consider it to be widely recognized as an accurate description of the use of such phrases. First, I would like to show that this theory, as it is generally understood, contains several fundamental errors.”

Strawson pointed out that Russell’s perspective is incorrect and used sentences and expressions as steps toward providing a correct solution. The specific reason Strawson made this distinction was that he wanted to demonstrate how each distinction is applied from the perspective of ordinary language. For example, consider the sentence, “The King of France is wise.” 1) This sentence, “The King of France is wise,” can be uttered multiple times. It is reasonable for us to say something about the same sentence in all these instances. This is the sense in which Strawson uses the term “sentence.” 2) However, there are clear distinctions between each usage of this sentence. For instance, if a person uttered this sentence during the reigns of Louis XIV and Louis XV, they would be referring to different individuals, with the first person using the sentence to make a true statement, while the second person would be making a false statement, and so on. This illustrates what Strawson means by “use of the sentence.” 3) Next, if two people simultaneously uttered this sentence during the reign of Louis XIV, it could be said that they used the same sentence, which reflects what Strawson calls “sentence expression.”

Moreover, distinctions can be made regarding the expression “The King of France.” Strawson believed that we cannot say we are using the phrase “The King of France” to express a proposition, whether true or false, because sentences are the only things that can be used correctly or incorrectly. Additionally, we can only use sentences to refer to specific individuals. On the other hand, when using a sentence to refer to a specific person, we use the expression to refer to that person. Therefore, “denoting or referring” is not what the expression itself does, but rather what someone attempts to do by using the expression. In short, referring to something means using an expression. It is a feature of usage, and truth or falsity is a feature of sentence usage. On the other hand, if we refer to a “sentence or expression” as a “type,” can we distinguish between the type, the usage of the type, and discourse about the type? Strawson asserts, “This cannot be done.”

In reality, what we are actually discussing is types. This confusion often arises from not noticing the distinction between talking about things and talking only about the use of types. When we talk about the use of sentences and expressions, we tend to think we are discussing sentences and expressions themselves.

Strawson believed this was the source of Russell’s confusion. Meaning pertains to the function of sentences or expressions, while referring and truth value relate to the functions of expression use and sentence use, respectively. Providing the meaning of an expression means offering general guidelines on how to use that expression to refer to specific objects, whereas providing the meaning of a sentence means indicating how to use that sentence to make correct or incorrect claims. Russell’s error arose from the assumption that a sentence must have a meaning. However, referring and meaning are entirely different. Russell also failed to distinguish between the use of expressions and expressions themselves. He conflated referring and meaning because he confused expressions with the expressions used in specific contexts. If I talk about my phone, I can take out the object I am referring to from my pocket, but I cannot extract the meaning of the expression “my phone.”

Returning to “The King of France is wise,” Strawson indicated that Russell’s two views on this sentence are mistaken:

(1) The person currently uttering the sentence is either making a true claim or a false claim.

(2) The speaker is asserting that there is indeed a current King of France.

(In fact, Russell never claimed this.) Strawson believed that the question of whether “The King of France is wise” is true or false does not fundamentally exist. This is because there is no such person as the King of France. Regarding (2), the statement “The King of France is wise” does not logically imply the existence of a King of France. When facing question (1), we say “France has no king” because we are not asserting that “The King of France is wise” is false. Instead, by making this statement, we are providing a reason why question (1) does not arise [4].

According to Strawson, the statement “The King of France is wise” is certainly meaningful. Even if we utter the sentence “The King of France is wise” but actually refer to no one, this does not mean the sentence loses its meaning. We just cannot refer to anyone with the fully meaningful phrase “The King of France.”

So far, we have seen how Strawson criticizes Russell’s semantics. Strawson first categorizes singular referring expressions into four types. In this context, Russell’s descriptive or referring phrases are expressed as “phrases beginning with a singular quantifying or non-quantifying noun modified by a definite article,” which Strawson classifies as the fourth type. Strawson provides an example of a sentence containing such a phrase: “The King of France is wise.” According to Strawson, we must distinguish between sentences, the use of sentences, and the expression of sentences. Thus, a sentence (strictly speaking, a proposition) itself is neither true nor false. Instead, it is the speaker using the sentence who makes a true or false claim with that sentence. Moreover, we need to differentiate between expressions, the use of expressions, and discourse about expressions. We can only talk about specific people or specific objects by using sentences. However, according to Strawson, we tend to confuse the use of sentences and the use of expressions with the sentences and expressions themselves. Discussing the meaning of an expression or sentence involves providing guidance on correctly using that expression or sentence to make statements or claims in all cases. In summary, Strawson completely rejects Russell’s semantics.

5 Conclusion

Strawson argues that Russell’s focus on mathematics and logic led him to overlook everyday language. Strawson has been criticized for confusing the problem of description with the problem of egocentricity. [5] Russell believed that mathematical propositions are fundamentally not centered on the speaker. Judgments on the differences between these two positions will later be reflected in the views of H. Putnam, S. Kripke, and K. Donnellan, as their perspectives stem from criticisms of Russell’s views.

Let us once again summarize the positions of Russell and Strawson on this issue. Russell and Strawson have fundamentally different views on language. For Russell, words and sentences are the source of meaning. However, for Strawson, it is people who are the source of meaning. In other words, for Russell, the primary focus of linguistic study is semantics. For Strawson, the focus is pragmatics [6]. The two schools have different perspectives on philosophy and language. For example, Russell’s philosophical viewpoint is to use carefully designed artificial languages as tools to explore the structure of reality. Here, exploring the structure of reality means seeking truth, which in turn means treating philosophy as a discipline. Just as physics, chemistry, or medicine are not studied using everyday language, everyday language also requires precision and accuracy. On the other hand, philosophers of everyday language believe that philosophical problems do not arise from everyday language itself but from the distortion and misunderstanding of everyday language by philosophical theories.

We can now speculate on how Russell’s and Strawson’s philosophical viewpoints influence their views on language and how they lead to different semantics. According to Russell, a precise language, such as the language of science, is needed to explore reality. The truth of reality is independent of the perceiver of truth. Therefore, the language expressing truth can be studied independently of the speaker. In contrast, for Strawson, philosophical problems arise from the misuse of everyday language. Therefore, we must explore the correct use of everyday language. Thus, language cannot be studied independently of the speaker’s use of language.

Thus, there remain at least two issues. One is that the semantic differences between Strawson and Russell seem to stem from their differing philosophical viewpoints, which are in conflict with each other. The other concerns the aforementioned issues of description theory and the distinction of speaker-centeredness. The distinction issue will again depend on differing views of truth. All these issues cannot be resolved here. Once these issues are addressed, we will be able to evaluate Russell’s theory of descriptions and Strawson’s critique of it, and further assess the related theories that followed.