Date: Jun 21, 2013 9:43 AM
Author: LudovicoVan
Subject: Re: Matheology § 288

"Sam Sung" <no@mail.invalid> wrote in message 
> Julio Di Egidio write:
>> "Sam Sung" <no@mail.invalid> wrote in message
>> news:kq1ica$juk$

>>> Julio Di Egidio wrote:

>>>> << Edward Nelson criticizes the classical conception of natural numbers
>>>> because of the circularity of its definition. In classical mathematics
>>>> the
>>>> 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'.

>> No,

> 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,
> the
> written history of mathematics was thus classically finitist until Cantor
> invented the hierarchy of transfinite cardinals in the end of the 19th
> century."
> 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
finitist view...