On 04 Jul 2009, at 18:24, John Mikes wrote:

> Dear Bruno, I mentioned that I have something more on the 'set' as  
> you (and all since G. Cantor) included it in the formulations. I had  
> a similar notion about my "aris-total", the definition of Aristotle  
> that the 'total' is always more than the 'sum' of its components. Of  
> course, at the time when A. thought about it, 'components' were only  
> 'physical objects' included in an ensemble as individual and  
> unrelated noumena.

We will see how we can do something similar with set. few  
mathematicians are really interested in sets, but in sets together  
with a structure (usually determined by operations and relations on  
the set.

> If you advance in our epistemic cognitive inventory to a bit better  
> level (say: to where we are now?) you will add (consider) relations  
> (unlimited) to the names of 'things' and the increased notion will  
> exactly match the 'total' (what A was missing from the 'sum'). It  
> will also introduce some uncertainty into the concept (values?) of a  
> set.

I am not sure that I understand.

> I see a similar situation with your ways writing of  
> 'sets' (1,2,3...) - or: ( 1, 2, 3... )

I guess you mean {1, 2, 3 ... }. "{" and "}" are standard, and "(" and  
")" will be reserved for other things, like delimiter of expression,  
like in (3+4), or the notion of couples (soon to be introduced).

> neglecting the additional relations maybe expressed in the  
> (neglected) commas, spaces, even the parentheses. All may mean  
> something and that meaning gives completeness to the entire set  
> beyond the 'factual' elements 1 2 3 . I don't know 'what', but for  
> sure something well pertinent. In infinite sets such uncertainty may  
> amount to infinite uncertainty.

I don't see anything uncertain in most infinite sets. But this will be  
scrutinized soon, or a bit later ... Some sets will appear more  
complex than other, and *some* set will have "uncertainties" attached  
to them, but to understand this we have to progress a bit more.


You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to
To unsubscribe from this group, send email to
For more options, visit this group at

Reply via email to