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Posted by Harvey on September 16, 2003 17:15:46 UTC

If a number is a 'unit belonging to X', and 'X' is a human system of procedures obeying certain rules, then an abstract entity is about the world since it is in the context of games played by humans (i.e., math procedures and rules). A 'number' is like the money in Monopoly. It isn't real money in the sense that you can go out and buy something with it, but humans give similar meaning to it just in different contexts. Correspondingly, 'numbers' receive meaning from human experience (e.g., how many apples do you have?), and this is why the concept is meaningful. That meaning comes from human experience and is not completely divorced from it simply because we have entered the domain of a formal system (just as Monopoly money is not completely divorced from real money used to buy things). We can fool ourselves that Monopoly money is not related to real money, but humans already bring those monetary concepts to the game, in fact, this is how the game is originally taught. Mathematicians might think they are completely 'beyond' the tangible concepts, but deep inside their brains are neurons that hold those tangible connections. I can't imagine it is the same for each person. Some might have learned the concept of number from counting apples, and some might have learned the concept of number from counting license plates from Maine, but this learned behavior forms the basis for all that follows and forever, I think, forms our concepts of the abstract things of mathematics.

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