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

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> 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. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---