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Re: [xmca] Why "Natural" Numbers?

Thanks, Andy and Anna...
I never heard that Cantor's breakdown was caused by a disagreement with Kronecker. Actually, I thought it came when Cantor discovered that every finite length contains an infinite number of infinitely small lengths. He apparently started hearing voices, and never quite lost the conviction that God had put him on earth to help people discover that every moment contains an eternity of instants.
Of course, there is a sense in which Vygotsky's notion of "analysis into units" is also "natural"; it involves discovering the irreducible "basic unit" which "naturally" has all the properties of the phenomenon one wishes to explain. It's interesting that for water that is not simply the molecule but "molecular motion"! One for the counters, and one for the measurers.
David Kellogg
Seoul National University of Education

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