[FOM] Existence of natural numbers.

Daniel Mehkeri dmehkeri at gmail.com
Sat Jul 16 13:46:40 EDT 2011

 > May I throw your question back to you and ask what you think it means 
 > for a mathematical abstraction such as the number 7 exists?

Mathematical abstractions in general open up a whole range of issues. 
The natural numbers are special, so let's consider just them.

 From P(0) and (forall x)(P(x) implies P(x+1)), I conclude P(7). So does 
everyone. But I also conclude P(2^(2^10)) and P(Graham's number). A few 
won't. In this sense, everyone knows that 7 exists, but some people deny 
that Graham's number exists.

It seems to me that this captures everything about whether a natural 
number exists or not. Is that naïve of me? Can there be another sense to 
this question?


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