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CTK Exchange
Steven
Member since Dec-27-09
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Dec-27-09, 11:47 PM (EST) |
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"What is a number?"
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I read Professor Bogomolny's "What's a Number?" but it is not clear to me what a number is. I suppose a number is a relative quantity. I suppose a number also is a relative value, a value being like a quantity but more abstract. Professor Bogomolny suggests at the top of his article that a number is a member of a group of objects with shared characteristics. Quine calls this an element of a class but Professor Bogomolny may be saying the same thing in mathematical terms (sets and categories)which are better. In any case, Professor Bogomolny than describes rational numbers, irrational numbers, and other things. I suppose what Professor Bogomolny is saying is that a number is a member of a group of objects to which one or more of the charactistics described (i.e., the nature of rational numbers, the nature of irrational numbers, and especially theorems of Cantor, apply). Is that what a number is, or is a number simply a relative quantity or value (which also happens to have some of the characteristics described by Professor Bogomolny)? In what sense does a number exist? Numbers appear to exist in nature apart from our consciousness. Thank you for your consideration. |
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alexb
Charter Member
2464 posts |
Dec-28-09, 09:15 AM (EST) |
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1. "RE: What is a number?"
In response to message #0
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>Professor Bogomolny suggests at the top of his article that
>a number is a member of a group of objects with shared
>characteristics. Yes, designating something a number means identifying it as a member of a group of other objects with shared charactersitics, but not only that. It is essential for such groups that their elements are subject to some operations that obey common, say arithmetic, laws. >In what sense does a number exist? Numbers appear to exist
>in nature apart from our consciousness. The sentence "Numbers appear to exist in nature apart from our consciousness" is difficult for me. I have a sense of what is meant but lose it on closer examination. Our consciousness is as natural as our bones. Numbers exist in the same sense as other abstractions. Where do words exist? |
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