Date: Jun 21, 2013 9:43 AM
Subject: Re: Matheology § 288
"Sam Sung" <firstname.lastname@example.org> wrote in message
> Julio Di Egidio write:
>> "Sam Sung" <email@example.com> wrote in message
>>> Julio Di Egidio wrote:
>>>> << Edward Nelson criticizes the classical conception of natural numbers
>>>> because of the circularity of its definition. In classical mathematics
>>>> natural numbers are defined as 0 and numbers obtained by the iterative
>>>> applications of the successor function to 0. But the concept of natural
>>>> number is already assumed for the iteration. >>
>>> So what?
>> You have snipped the context.
> You refer to:
>>> What does pi count?
>>> Isn't it a number?
>> pi counts pi, of course...
> ? Sorry then.
The point in fact was "numbers count themselves, how else?"
>>> Take any (uniquely operated) iteration and count the
>>> steps by whichever method you like - the result is isomorphic
>>> to N in whichever 'theory'.
> Why not?
>> confront strict finitism.
> "Classical finitism vs. strict finitism
> In her book Philosophy of Set Theory, Mary Tiles characterized those who
> allow countably infinite objects as classical finitists, and those who do
> not allow countably infinite objects as strict finitists. Historically,
> written history of mathematics was thus classically finitist until Cantor
> invented the hierarchy of transfinite cardinals in the end of the 19th
> They may 'not allow' whatever they want, but cannot 'forbid' appliyng
> endlessly an operation like a successor function to 0.
Indefinitely large yet (ever) finite: there just is no set N in the strict