set incompleteness

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.

 

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

 

John M