[FOM] Re: Explicit construction [etc]

[Franklin Vera Pacheco]

On Sun, 6 Jul 2003 W.Taylor at math.canterbury.ac.nz wrote:

> Harvey Friedman wrote, in passing:
> 
> >>>
> The mainstream of mathematical culture is with the finite and the
> countable. This includes Borel functions between Polish spaces at the
> outer boundary, as it is clearly understood in countable terms.
> <<<
> 
> I didn't cotton on to this comment.
> 
> Could Harvey or elseone please elaborate on it for us?
> 
> Thanks,   Bill Taylor.
> _______________________________________________

   Mr. Taylor

 I don´t understand the part of Polish spaces but it seems to be an 
example of the finite and countable power.
 Clearly all the mathematical work is around the "finite", even the 
countable things. All due to the human incapacity to work with infinite 
objects so far (the non countable, actual, non definable ... ). That is 
why there are no infinite (infinite like above) math theory at all. If I 
where asked to rewrite Friedman´s comment I´ll write it like this:
>>>
 The mainstream of mathematical culture is with the finite. 
This includes Borel functions between Polish spaces at the
outer boundary, as it is clearly understood in countable terms and then in 
finite terms.  
>>>

 I don´t hope this was Friedman idea but this is my reading on his 
comment.

  I would like to use this message to give a question asking for opinions:

 The formal theories of more common use e.g. ZFC do not represent this 
human incapacity (to work with infinite (like above) objects). They  
admit models which are not finite, countable or even definable. 
 So, would it be or not preferable than the every day mathematics work 
and use the language of a formal theory which all models are humanly tractable?
 (By humanly tractable we can understand definable but not   < 
2^2^2^2^2^2.)

best regards.

 
-- 
Name: Franklin Vera Pacheco        /:7)>=[   
Position: undergraduate student                       
Institution: University of Havana                      
Research interest: foundations of mathematics         
                   approximation theory
address: 45 #10029 e/ 100 y 104
        Marianao, Ciudad de la Habana, Cuba.
tel: 260 6043
e-mail: franklin at ghost.matcom.uh.cu