Analysis Of The Frege's Puzzle
The Frege’s puzzle originates from Frege’s study of identity in his paper On Sense and Reference [Frege, 1892]. So far from the emergence of the Frege’s puzzle, philosophers have given many solutions, but there has not been a perfect one. Among these philosophers, although Frege and Russell did not solve the Frege’s puzzle perfectly, they still provided a good direction for future philosophers. This paper will analyze Frege and Russell's solution to the Frege's puzzle, with a description of the differences between the two and their respective strengths.
The Frege’s puzzle is based on Frege’s understanding of the equality sign in “a=a” and “a=b”, and his point of view about the different cognitive values between these two sentences. Frege first …show more content…
In his paper On denoting, he believes that signs and objects play a role through meaning, and meaning is independent of objects. Besides, meaning is attached to signs, which means objects do not have meaning by themselves. Therefore, according to Russell, the meaning of sign “a” and sign “b” should be analyzed from the perspective of grammatical logic, in order to solve the puzzle. In Russell’s opinion, the meaning of a sentence should not be simply analyzing its predicate term and its subject term through surface grammar, but should be considered within a deeper grammar. For example, when “a” refers to an object, “a” would have the following three extended meanings: 1. There is at least one object. 2. There is at most one object. 3. The object has the property x. Accordingly, when “b” refers to the same object as “a”, “b” would have the following three extended meanings: 1. There is at least one object. 2. There is at most one object. 3. The object has the property y. Thus we can see that sign “a” and sign “b” contain the same extended meanings for the existence of the object, but they also contain different extended meanings for the properties of the same object. Therefore, when “a” and “b” refer to the same object, because of the different meanings they contain, “a=a” and “a=b” have different cognitive
The Frege’s puzzle is based on Frege’s understanding of the equality sign in “a=a” and “a=b”, and his point of view about the different cognitive values between these two sentences. Frege first …show more content…
In his paper On denoting, he believes that signs and objects play a role through meaning, and meaning is independent of objects. Besides, meaning is attached to signs, which means objects do not have meaning by themselves. Therefore, according to Russell, the meaning of sign “a” and sign “b” should be analyzed from the perspective of grammatical logic, in order to solve the puzzle. In Russell’s opinion, the meaning of a sentence should not be simply analyzing its predicate term and its subject term through surface grammar, but should be considered within a deeper grammar. For example, when “a” refers to an object, “a” would have the following three extended meanings: 1. There is at least one object. 2. There is at most one object. 3. The object has the property x. Accordingly, when “b” refers to the same object as “a”, “b” would have the following three extended meanings: 1. There is at least one object. 2. There is at most one object. 3. The object has the property y. Thus we can see that sign “a” and sign “b” contain the same extended meanings for the existence of the object, but they also contain different extended meanings for the properties of the same object. Therefore, when “a” and “b” refer to the same object, because of the different meanings they contain, “a=a” and “a=b” have different cognitive