Posted by: Alexandre Borovik | May 19, 2011

Be fruitful and multiply

Another brilliant quote from Edward Nelson (Predicative Arithemtic, p. 80):

Of course it is a theorem of axiomatic set theory that formalized Peano Arithmetic is consistent, but this is not what people have in mind who argue that Peano Arithmetic is consistent because its axioms are true statements about \omega. What is at issue here is not the familiar construct of formal mathematics, but a belief in the existence of \omega prior to all mathematical constructions. What is the origin of this belief? The famous saying by Kronecker that God created the numbers, all else is the work of Man, presumably was not meant to be taken seriously. Nowhere in the book of Genesis do we find the passage: And God said, let there be numbers, and there were numbers; odd and even created he them, and he said unto them, be fruitful and multiply; and he commanded them to keep the laws of induction.

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