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Frege begins his argument with the reference that a name has on an object. An identity should refer to one particular object with no other reference to another object. In common practice, we meet words that refer to an object, but it also has a meaning different from the reference that it gives to the identity of an object. If ‘a = b,’ then it should be possible to replace ‘a = b’ with ‘a = a’ without changing the meaning of the expression.
Frege applies the method of replacing the object or reference with another one of the same truth value to solve the puzzle of identity. The development of ideas is similar to abstract nouns that do not have a similar form in any two people. As a result of lacking a common image in different people, Frege suggests that they do not have a reference even though they have a sense.
Frege applies the method of replacement on an adverbial clause, and on an adjectival clause that forms a complex sentence. He also applies the replacement technique on conditional clauses and consequent clauses. In all the cases, he maintains that if the clauses are replaceable without changing the sense of the sentence, then they have a true value. The true value is the reference of a sentence.
Frege begins his argument with the reference that a name has on an object. According to Frege, an identity should refer to one particular object with no other reference to another object. He uses the example of the name ‘moon’ in a sentence. When the moon is used in a sentence, a person may take its reference to be the moon that revolves around the earth. However, the name ‘moon’ could also have its origin that may give someone else another meaning without referring to the moon that revolves around the Earth.
In common practice, we meet words that refer to an object as the name of the object, but it also has a meaning different from the reference that it gives to the identity of an object (Moore 23). Frege labels the identity that the name gives as the reference, and the thought that the word captures as the sense.
Frege also points out that some names have a reference, but do not have a sense. It means that the name does not mean anything apart from identifying the object. In the example of the moon, the word may have another meaning in another language or the same language. When some hear about the moon, the sense and the reference may come to his mind.
Frege captures the issue of identity using two letters, ‘a’ and ‘b.’ The letter ‘a’ can be said to be equal to the letter ‘b,’ which is (a = b). On the other hand, the factual truth is that ‘a = a.’ If ‘a = b,’ then it should be possible to replace ‘a = b’ with ‘a = a’ without changing the meaning of the equation (Moore 24).
However, the two cannot be replaced without changing the meaning. It means that when someone says ‘a = b,’ he refers to only a particular aspect of the letters, such as the quantities that they stand for, but not the shapes. The reason they cannot be replaced is that ‘b’ has a reference it designates that is different from the sense of equality that is portrayed by equating it to ‘a.’
Frege’s thought can be transferred to another example, even though Frege shows that the reference would be different if I do not refer to the same example as his. If I am allowed to give an example similar to ‘a = b’ and ‘a = a,’ consider a man and a woman. Consider a women’s rights activist, who claims that a woman is equal to a man. In that case, ‘woman = man’ is not the same as saying ‘woman = woman.’
The reason is that man has a different ‘sign’ apart from the ‘reference’ of equality given to it against that of the woman. In that case, ‘man = woman’ refers to some particular aspects that the speaker refers to without considering every aspect of man, and woman. It may be that the speaker refers to certain abilities such as their thinking abilities, and the type of jobs that they can do.
However, biologically, man refers to another aspect that portrays some difference from that of a woman. In that case, saying ‘man = woman’ cannot be replaced with ‘woman = woman.’ Another reason is that if a man were equal to a woman in all aspects, the woman would be known as a man without any difference in their sign or reference.
Frege discusses the development of ideas as abstract images that do not have a similar form in any two people. Frege uses the image of Bucephalus, which refers to the horse belonging to Alexander the Great (Moore 26). The reason is that the images are based on imaginations, and descriptions passed by people who had imaginations. According to Frege, different groups of people would have different depictions of the horse’s image.
A simpler example would be that of ghosts. People from different images at the mentioning of the ghost because it has not been seen as a physical object. The image is modified as the ages pass, and the image becomes a collective picture of what people expect about how it looks.
Frege explains that “man has a common store of thoughts, which is transmitted from one generation to another” (Moore 26). Something is only but an idea when it is identified through the passage of imaginations from one group to another. Each person is able to identify ghosts, but no one has ever seen one that is tangible, that is if the statement is true.
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Frege adds that when one refers to ideas, one has to include the time, and to whom it belongs. The reason is that ideas are abstract, subjective, and they change just like the imaginations.
Frege examines the different meanings that can be derived from the sentence. Frege explains that the signs used in a sentence should correspond to a certain sense, but languages fail to give a single meaning derived from a group of words. A sentence should have a reference (Moore, 28). The reference can also be the proper name of an object. Reference stands for the truth value of a sentence. The truth value of a sentence is its ability to stand alone and make sense.
A proper name should designate a single identity in a sentence. Its reference should be a single object. Frege uses the example of the sentence, “Odysseus was set ashore at Ithaca while sound asleep” (Moore 28). Frege expresses that ‘Odysseus’ does not have a single reference. The reader is not certain which Odysseus is being referred to unless additional descriptions are provided.
He describes that people want a proper name to have both a sense and a reference. When Odysseus is considered as a work of art, then a reference and a sense are obtained. In that case, the reader would be able to connect Odysseus with the ancient Greek hero in an epic poem.
In the middle part, Frege reinforces the method of replacing the object or reference with another one of the same truth value to solve the puzzle of identity. If the sentence does not change its sense, the reference has no identity. When the sentence changes its sense, the reference has an identity. Frege explains that “all true sentences have the same reference, so do all false sentences” (Moore 30). One should be able to replace a clause in a sentence without making a false statement true.
Quoting someone’s words may refer to a group of signs that have a different reference to the original sentence, especially when the reference is an indirect quote. The indirect quote transfers a thought. According to Frege, a thought does not have a reference. Frege compares an indirect quotation with an abstract noun introduced with ‘that.’
In using replacement to elaborate the reference of a sentence, Frege applies it to the example of Venus and morning star. When you refer to the morning star, you might be referring to a bright star on the eastern side of the sky, and to a planet when referring to Venus. It follows that Venus and morning star cannot be used all the time interchangeably, even though they refer to the same object. They do not have the same sense, even though they have the same reference.
Frege explains that commands and requests do not have a reference. They are not thoughts but can be compared with the thoughts. They do not have a truth value to stand alone and make sense. The sense of the sentence may be lost when quoting a sentence that does not have a reference. Quoting a command is similar to the situation of using no reference as a reference in another sentence. Only direct speech may keep the same sense. A command and a request bear an abstract noun in the form of emotions.
Frege applies the method of replacement on an adverbial clause, and on an adjectival clause (Moore 37 & 38). The adverbial clause he uses is attached to the tense when something occurred. The adjective clause gives an additional description of the object. He shows that in the adjective clause, it is possible to replace one part of the complex sentence without losing its sense. In the adverbial clause, replacing it with a clause with a similar truth value may change the sense of the sentence. It shows that the clauses are not similar.
Frege uses the concept of identity to explain that it is not possible to replace part of a whole sentence and maintain its sense, unless the sentence has an object, more than a single thought, and is attached using conjunction. When a sentence has two thoughts and does not have conjunction, it is not possible to replace a part and maintain the sense. He explains that the subordinate clause is used in the same way a noun (Moore 34).
Frege’s argument can be applied in the case of using references in sentences. It is either the quotes accompany other clauses in a sentence, or they only transfer a thought. They may transfer the reference or truth value of the quote into another complex sentence.
Frege develops his argument from the simple example of a letter, which makes it easier to see the difference. It is true that saying ‘a = b’ cannot be replaced by ‘a = a’ because ‘b’ depicts an additional concept that has not been considered in the equation. Frege’s discussion may be important in the use of references in sentences.
Quoting does not necessarily mean that we have transferred the same reference (truth value) of the sentence into a new one. It may be true if it is a direct quote that transfers the entire sentence. Indirect quotations, only the thought may be transferred, and sometimes it inaccurately retains the sense that it had in the original sentence.
A name may provide a reference to an object as well as a sense, which is a meaning different from the object. Frege implies that if two objects cannot be used interchangeably, then they cannot be completely identical. He uses the case of replacing ‘a = b’ with ‘a = a’ to form his replacement approach in solving the puzzle of identity.
His argument in this simple example is easily verifiable. It is true that they cannot be replaced because ‘b’ has another sense that differentiates it from ‘a.’ However, they share a reference. He extends his argument in the replacement of clauses in sentences to show that most quotes only transfer thoughts and not references. References are the true value of sentences. The reference can only be transferred when a direct quotation transfers the whole sentence.
Moore, Adrian (ed.), Meaning and Reference, Oxford: Oxford University Press, 1993. Print.