, The truth of mathematics, as Plato says, is unrelated to perception; it is a very peculiar truth, and only involves symbols. Counting propositions, such as "I have ten fingers", are entirely of another category, and apparently (at least in part) to rely on perception. The concept of "finger" is clearly abstracted from consciousness; but what is the concept of "ten"? Here we seem to have reached the real co-phase, or the idea of ​​Plato. We can not say that "ten" is abstracted from the perception, because all can be seen as ten of any kind of thing on any perception, but also

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　　云南省十三五规划摘要:Can be seen as other numbers. If I were to use the word "means" to refer to all the fingers of the whole hand; then I could say "I have two fingers", and this also describes the previous one I used to describe the same number Perceived facts. In this way, in the statement that "I have ten fingers", the perception occupies a lesser position than in a statement of "this is red", and the concept occupies more status. However, this problem is only a matter of degree. On the proposition that the word "ten" appears, our complete answer is that when we analyze these propositions correctly, we

　　They can be found that they do not contain any ingredients that are equivalent to the word "ten". It is more complicated to explain this in the case of such a large number of examples; therefore, let us substitute "I have two hands". This means that "there is a so there is a b, and a and b are not the same. When, and only when, x is a or x is b, 'x is one of my hands' Is true, no matter what x may be. " Here the word "two" did not appear. Indeed, the two words appear, but we do not need to know that they are two, just as we do not need to know whether they are black or white, or may have any other color. Thus, in a strict sense,