[FOM] Predicativism and natural numbers
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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