[FOM] The discrete and the continuous

[A. Mani]

On Sunday 04 Nov 2007 5:23:41 pm Thomas Forster wrote:
>  	All of Mathematics can be reduced-to/interpreted-in/etc Set
>  	Theory;

I would like to define Mathematics as the science of exactly representing and 
analysing objects, processes or states of affairs. So this falls out with 
the "reduced-to" possibility. But I do accept that there is a set-theoretical 
interpretation of everything ... however non-classicalist or classicalist it 
may be. I suspect you mean "in a classicalist sense",     
>
>  	Set Theory is Discrete;
There are set theories and interpretations thereof that may be discrete or be 
otherwise.  

>  	The Discrete and the Continuous are two twin pillars of
>  	Mathematics, neither to be explained in terms of the other.

To disclude the possibility of explaining one in terms of the other appears 
too dogmatic. We can see either as a special case of the other and in many 
ways. It is sometimes more difficult to build mathematical models with the 
discrete and then the easier continuous models are approximations.  
>   
 So I accept about some of the first proposition only.

Best

A. Mani

-- 
A. Mani
Member, Cal. Math. Soc