Frege's The Foundations Of Arithmetity Analysis

In Frege’s book The Foundations of Arithmetic, Frege states three fundamental principles in order to inquiry the logic in language, and the concept of Number in a logical way. This paper will elaborate the second principle to oppose empiricists’ perspective on concept of Number, in order to support Frege’s definition of number. The second principle, namely the context principle, states that, “never to ask for the meaning of a word in isolation, but only in the context of a proposition” [Frege, 2]. Frege argues that a word does not have a meaning unless it is considered with the context of a proposition it is in.
The majority of philosophers at that time, when Frege publishes theses principles, are empiricists, who believes “all knowledge
However, physical objects exist in space and time, and numbers are obviously not objects in space and time. We can say where a physical object appears and disappears, but there is no way for a number to appear or disappear. Numbers do not come from experience, but exist objectively. Just as in Frege’s example, "the North Sea is 10,000 square miles in extent"[Frege, 7], that it is an objective fact that the area of the North Sea does not depend on the subjective impression of people, which means the area of North Sea would not be disappear when people does not think of it. Same as another example Frege provides, “when we speak of the equator as an imaginary line, … it is not a creature of thought, the product of a psychological process, but is only recognized or apprehended by thought” [Frege, 8], which Frege makes a point here is that to recognize something does not mean to create something. More specifically, number is not a product of creation, but it is something exists
However, numbers should not be limited to intuitive, because different people will have different intuitive. If numbers come from intuition, then different people should have different interpretations of different numbers in different places or at different times. For example, person A might have an intuition that the object P weighs 5 kg, while person B might have an intuition that the object P weighs 10 kg. In addition, the assertion that ideas are obtained through intuition ultimately leads to psychology, which is to interpret numbers as ideas in the mind. However, the numbers do not have the idea of mind. For the two numbers "1" and "2", we do not have a bigger “1” or a smaller “2”, that we cannot explore the concept of number without considering the context of proposition it is in. For example, for “a person” and “a group of people”, the quantity of the “a” of “a group of people” is larger than the “a” in “a person”. Moreover, Frege indicates that when seeing numbers as the context of “countable”, they do not only involve intuitable, but also involve everything thinkable [Frege, 4], that what can be intuitive can also be think of, but what can be think of is not necessary