Of course, Torgny stops, in the UD Argument, at step 0. He disbelieves  
"classical computationalism".

The "yes doctor" is made senseless; because "he is a zombie", and  
Church thesis becomes senseless, because he is ultrafinitist, and  
Church thesis concerns functions from N to N, or from N to 2, and NXN  
to N, ... It concerns those computable and non computable objects. N=   
{0, 1, 2, 3, ...}.

But yes, we need N, and its structure (N,+,x). We cannot prove that N  
exists. But we can postulate its existence, give it a recursive name,  
and generate and develop more and more simple and powerful theories  
about it and its structure. Usual math use N, and its images all the  
times. Only a philosopher can be paid to doubt N. A good thing!

Without N, no universal machine, no universal person.

And no Mandelbrot Set M is available for an ultrafinitist, given the  
bijection between N and the little Mandelbrots (those the M set is  
made of!).

A beautiful illustration that the M set summarizes its "histories", 2  
times, 4 times, 8 times 16 times, 32 times ... around its little  
Mandelbrot sets, (or around its histories ...).  In the zoom here, a  
feature of the history is "going near the tail of a little Mandelbrot  
set", and both the music and image coloring (different in the zoom in  
and the zoom out) illustrates that "Hopf bifurcation" where the  
neighborhoods are multiplied by two, iteratively, and with an  
accelerating frequence, so that the limit (of 2^n) gives a little  
mandelbrot set (or ...).


On 10 Jun 2009, at 18:24, Bruno Marchal wrote:

> On 10 Jun 2009, at 02:20, Brent Meeker wrote:
>> So we believe in the consistency of Peano's arithmetic because we
>> have a
>> physical model.
> Why physical? And do we have a physical model? I would say we belive
> in the consistency (and soundness) of PA because we have a model of
> PA, the well known structure (N, 0, +, *).
> If comp is true, there is no physical model at all. (But this is not
> something on which I want to insist for now).
> Bruno
> http://iridia.ulb.ac.be/~marchal/
> >


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