wandering - 20 September 2007 07:54 AM

So, the The Multitude is a thing beyond an atom of itself.

Please define a thing that is beyond an atom of itself, which is not the result of a whole/part relation.

—

I will gladly do it, the moment you give me an explanation of the thing which is constructed and not constructed at the same time from the eternal pink being that is the essence of all essences.

Using your explanation then, I will give you a definition, can’t do it otherwise.

The Traditional Understanding of the Concept of Set (TUCS) is not based on Whole\Part Relations (WPR) for example:

Let *x* be {a,b,c}

By TUCS *x* is a member of {*x*} and it is not a member of {{*x*}}.

TUCS thinking ignores the internal structure of {*x*} in {{*x*}} when it defines the cardinality of {{*x*}} (notated as |{{*x*}}|=1) and as a result, cardinality is not based on Whole\Part Relations (WPR).

I find that TUCS is actually based on Whole\Part Relations (WPR) as its hidden assumption because it uses WPR in order to distinguish between members, for example:

x is distinguished from y only if x and y internal structures are not ignored (WPR is not ignored).

If TUCS ignores WPR it is unable to distinguish more than “a One Thing At a Time” and as a result Cardinality cannot be extended beyond 1.

If Cardinality is extended beyond 1 under TUCS, then WPR is its hidden assumption.

If WPR is TUCS ‘s hidden assumption, then the traditional concept of Set is not based on rigorous foundations, and anything that is based on it has be re-defined in order to avoid WPR as a hidden assumption of the concept of Set.

For more detials, please look at http://www.centerforinquiry.net/forums/viewthread/2924/ .

Thank’s