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Topic: Matheology § 288
Replies: 15   Last Post: Jun 22, 2013 12:23 AM

 Messages: [ Previous | Next ]
 LudovicoVan Posts: 4,165 From: London Registered: 2/8/08
Re: Matheology § 288
Posted: Jun 21, 2013 9:43 AM

"Sam Sung" <no@mail.invalid> wrote in message
news:kq1k8g\$u5d\$1@dont-email.me...
> Julio Di Egidio write:
>> "Sam Sung" <no@mail.invalid> wrote in message
>> news:kq1ica\$juk\$1@dont-email.me...

>>> 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. >>
>>>>
>>>> <http://en.wikipedia.org/wiki/Ultrafinitism#Main_ideas>

>>>
>>> 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...

Julio

Date Subject Author
6/20/13 Alan Smaill
6/20/13 LudovicoVan
6/21/13 LudovicoVan
6/21/13 Tanu R.
6/21/13 LudovicoVan
6/21/13 Tanu R.
6/21/13 LudovicoVan
6/21/13 Tanu R.
6/21/13 fom
6/21/13 LudovicoVan
6/22/13 fom
6/22/13 fom
6/22/13 fom
6/21/13 Tanu R.