[FOM] Predicativism and natural numbers

Giovanni Lagnese lagnese at ngi.it
Wed Jan 11 02:27:28 EST 2006

Arnon Avron wrote:

> The basic intuition behind the construction
> of the concept of natural number is "and so on"
> (or the idea of "..."). The natural numbers
> consist of 0, 0', 0'', and so on (or 0, 0', 0'', ... ).

By this definition, how can you infer that omega+omega is not a natural 

> Needless to say, in a language with TC and = the notion of a
> natural number can easily be defined from 0 and successor

Yes, because TC *is* the concept of natural number.
I merely said that it's an impredicative concept. You must take it as 

But one can take as primitive also the concept of powerset. So there must be 
a philosophical reason for taking as primitive the concept of natural 
numbers but not the concept of powerset. And this reason can not be the 


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