The Sense and Reference According to Gottlob Frege

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Giving the definition of the concepts “sense” and “reference” in relation to the word and speech are among the main tasks of analytic philosophy. Gottlob Frege, a German mathematician and philosopher, decided to clarify the problem of the discussed terms and was a pioneer in this sphere. He proposed a logical basis for distinguishing between these two concepts. In the work “On Sense and Reference,” he formulated the theory of a name. Frege considered the word as a sign referencing a thing. The thing referenced by a word gets the name of the reference of this word which, in fact, is its sense. Frege proposed to name the sense of the word the way of representing the content referenced by the word. Therefore, a word which has one reference can also have different senses, depending on the expression in which it is used.

Frege was a founder of modern logical semantics. He proposed the notion of a semantic triangle. According to it, the name is located on the first top, on the second — the thing referenced by this name, on the third — the sense expressed by this name. Frege proceeded from the fact that two different signs can point to the same object. For example, two expressions such as “the morning sun” and “the evening sun” point to the same object — the star of Sun, but they have different senses. Thus, a sign can be thought in connection with the denotation or reference of a sign with the thing that this sign designates. The sense of the sign is also intended to reflect the way of representation referenced by this sign. That is why “the morning sun” and “the evening sun” are two different ways of explaining the star of Sun. Thus, Frege considered them as the proper names that reference a thing in the broad sense of the word.

Considering the essence of the sense and the reference, Frege introduced the notion of representation as an internal image of a thing arising on the basis of impressions of this thing. The philosopher believed that the idea is always subjective, and it depends on the person. On this basis, he explained the variety of different representations associated with the same sense. Frege pointed to the connection between the sense of the word and the representations. However, he did not identify them. The philosopher determined the sense between the reference and the idea. In essence, it was an attempt to go beyond the purely linguistic analysis of the meanings and senses. Frege took into account the psychological mechanisms of word formation. According to him, the objective world, where a person lives, exists, but it exists only to the extent that it is represented in person’s psyche in the form of subjective representations and corresponding mental images. Therefore, a man can only refer to something that is the content of his/her psyche, and that the person considers as vital or emotionally attractive.

The approach used in determining the sense and the reference of the word is also utilized in determining the essence of the reference of the word of the whole sentence. According to Frege, the sentence, like the word, expresses its sense and determines its denotation. However, in contrast to the word, the sentence always contains some judgment which should be considered as the sense of the sentence. As for the reference to the sentence, Frege defined it as the true sense which means the objective content of the statement. The philosopher used the notion “judgment” to explain the concept of “idea”, defining the reference of the sentence as the objective essence of the statement. He wrote, “a step is already taken from the judgment to the denotatum in the statement is its objective content.” It turns out that judgment is both a thought and a sense of the sentence. However, according to etymology, the sense is something connected with thought but not the thought itself. The words “sense” and “thought” must have different meanings. However, according to Frege, the thought, judgment, and sense of the sentence are synonymous. The reason is the dominant idea about the inseparable connection between thinking and speech, thought and speech, and the impossibility of the existence of wordless thoughts.

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Frege differentiated two aspects, defining the “sense” and the “reference”. The first element is called the reference. It is correlated with the objective content of the proposal and with the features of objective reality. The second aspect is called sense and, as well as the judgment and the thought, is correlated with the subjective content of the sentence where the features of subjective notions of reality are reflected. In this case, the reference claims the special justification. Indeed, in order to understand a sentence, it is sufficient to internalize only the sense of the sentence expressed by its thought. At the same time, there is no need to appeal to the references of names included in this proposal as evidenced by the free operation with proposals containing non-significant terms. However, the need for the reference of names arises when it comes to the sense of the truth of the sentence to determine which knowledge of meaning is not enough. The understanding of sense for this designation is not enough. According to Frege, the predicate is approved or rejected concerning the reference of the name. In this case, the philosopher provided the following analogy, “the sense of the names included in the sentence determines the sense of the whole sentence, and the references of the names determine the reference of the sentence.” However, the need for the reference of names arises once the necessity to determine the truth value of the sentence appears. Hence the reference of the sentence is its genuine sense.

According to Frege’s compositional conception of reference, the reference should be preserved if the incoming sentence is replaced by any other with the same truth value. This condition is violated in the case of sentences containing intentional propositional operators. Frege explained such cases introducing a distinction between the usual and indirect reference of expressions. For example, if “a” sentence contains a question of another sentence “b”, then it means the usual reference of the sentence “b”, but its sense is an indirect reference. Consequently, these sentences are not-referential and do not have to be interchangeable.

Frege assigned the main place to the concept of sense. The philosopher considered it impossible to give the analytical definition of the object, treating this concept as primitive. He introduced the basic categories of “objects” and “functions” in the framework of arguments from language to the world. The object is something that is expressed by a complete symbol, and the function is something that is expressed by an incomplete symbol. Nevertheless, Frege believed that logical objects should be considered as objects in the full sense of the word, since the logical-syntactic characteristics of the complete expressions do not differ depending on whether they are names of logical or material objects. In addition, the exclusion of logical objects prevents the construction of a complete system of laws of logic. Thus, in this case, it is not possible to distinguish the differences between the sense and the reference.

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According to Frege, the objectivity of reference follows from the idea of the objectivity of logic. The philosopher considered the revelation of truths as the aim of science. The goal of logic as an objective science is to discover the laws of truth. The laws of logic indicate not the psychological laws of why something is considered as true but the laws of truth itself. The objectification of the truth value of sentences is closely connected with the objectification of the sense of sentences and thoughts. According to Frege, such premise cannot lie at the basis of logic as an objective science, because it necessarily leads “to epistemological idealism, since such sides as the subject and the predicate that is distinguished in thought should belong to the sphere of the psychic.” However, in this case, due to the fact that every act of understanding is realized through judgment, the bridge to the reality of the objective world is collapsing. For example, there is a judgment of the identity a = b, then it can be assumed that its sense consists of linking the senses of the terms “a” and “b”. Consequently, this judgment is true, because the objective senses of these terms are objectively related.

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Introducing the distinction between the reference and the sense, Frege identified the first concept more clearly than the second. Therefore, the concept of a reference is introduced without definition. In turn, the concept of sense is defined through the concept of reference as a way of indicating. Frege also justified the necessity of referencing by human intentions. When people pronounce the word “moon”, they do not mean the idea of the moon, but they intend to talk about the object. However, if the objectivity of the intentions is not recognized then Frege’s whole objectivity is collapsing. The philosopher believed that senses have nothing in common with the truth. The direct consequence of this approach is the inference about the inadmissibility of unrepresentative names in logic. Since logic is the science of truth, an ideal logical language cannot contain empty terms, because sentences that include such terms cannot be true. However, the thesis of the independence of truth from sense encounters a serious obstacle in Frege’s theory. This is an indirect reference when a leap from object to sense occurs, and sense becomes the reference. In this case, the truth certainly becomes dependent on the sense.

Additionally, Frege treated the truth and the falsity, in the context of “reference” and “sense”, as abstract objects. If the sentence has a truth value, then it, in turn, is determined by the thought expressed in the given sentence. Frege wrote, “The true value is the meaning of a sentence, the sense of which is thought.” Accordingly, only the senses of sentences that may be true or false are thoughts. The sentences that express orders, questions, or exclamations that express someone’s feelings have sense, but they are not thoughts. Frege considered the natural language as the instrument of accumulating objective knowledge. The philosopher insisted that the sense and the reference of a sign should be distinguished from the representation associated with it. If the sense of the sign is a sensible object, then the human representation of this object is an internal image that arose from the memories of sensory impressions and the acts of human internal or external activity. It is often permeated with emotions. An idea of a person is not always connected with the same sense. The submission is subjective and means that the representation of one individual is not the same as the representation of others. Thus, the representation differs significantly from the sense of the sign. It is also necessary to indicate the reference to whom it belongs and what time it relates for. Sometimes, it is possible to indicate the difference between the references of different people, but an accurate comparison is not possible, since diverse references cannot exist in one sense at the same time. Therefore, the sense of one’s own name is the object itself that is denoted by that name. The idea is completely subjective. The sense lies between them, although not as subjective as the idea.

Bertrand Russell also developed Frege’s semantic ideas. In the article “On Denoting”, he studied the denoting expressions that address statements to objects. They guarantee the connection between language and reality, and the objective, informative nature of communication. However, the use of propositions is due to the fact that they do not always correspond to objects. Russell distinguished three main difficulties in using them, since the external linguistic form of denoting expressions may be inadequate to their actual status in the language. The improper analysis of the sentence that involves denoting phrases is possible. The analysis alleviates the difficulties when the propositional function plays a decisive role. Since the indicated expression has sense only in the composition of a certain utterance, it is also analysed. The theory of description, used instead of a name, develops these ideas. Russell, relying on the sense and the reference of Frege, distinguished the semantic properties of proper names and descriptions. He also differentiated between the definite and the vague descriptions, separate descriptions, and proper names. They have different logical-semantic nature and differently designate the object. The original name indicates the specific name carrier. The descriptions are not indicative expressions and may not correspond to any medium. That is why, according to Russell, the linguistic difficulties arise from the interchangeability of names and denoting as well as the shifting of their logical and semantic functions.

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Despite the obvious harmony of Frege’s idea about the essence of sense and reference, it contains a number of controversial points concerning the foundations of his ideas. As previously noted, the notion that words denote objects and phenomena that constitute the content of objective reality is controversial. The examination of words from the point of view of their genesis shows that the appearance of words is preceded by the processes of subjective reflection of objects and phenomena of reality and the formation in the psyche of their subjective images or ideas about them. These ideas about objects and phenomena of reality are the basis for the formation of words and various word combinations. Relaying on Frege’s terminology, the sense of the word is not a thing, but an idea of a thing, and the reference to a statement is not an objective reality, but an idea of this reality. “On Sense and Reference” is characterized by the incompleteness and not always valid conclusions as well as, sometimes, the complexity of the presentation. Nevertheless, it is a significant contribution to the development of philosophy and logic.

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