No Doron being mutually exclusive does not require or even infer being “disjoint” (not connected).
Wrong,
Formally, two sets A and B are disjoint if their intersection is the empty set
(
http://en.wikipedia.org/wiki/Disjoint_sets )
(two sets are said to be disjoint if they have no objects in common and therefore they exclude each other by their unique collection of objects).
But this is only one aspect of being mutually exclusive.
The other aspect of being mutually exclusive, is mutuality, which is the ability to observe disjoint collections from a deeper (or higher) level, where at this level there is a common base ground for both collections.
The realm of being mutually exclusive is not totally mutual and not totally exclusive, and its consistency is known only if at least two levels of existence are shared by Whole\Parts Relations, where the Whole is Non-local w.r.t to the parts, and the Parts are Local w.r.t to the Whole.
Your “X” and “beyond X” are both mutually exclusive and mutually dependent. The “contradiction here” is once again just yours in pretending that they are “being disjoint (or exclude each other) at the same level AND being connected (mutual) at a higher level”. Your “X” and “beyond X” are both mutually exclusive and mutually dependent regardless of what “level” you simply want to claim.
Again, the realm of being mutually exclusive is not totally mutual and not totally exclusive, and this is exactly the Organic realm, which is not less than the simultaneous existence of both Mutuality AND Exclusivity.
The Organic realm can't be known if reduced into a one level of existence, and this is exactly what you are doing all along this thread, The Man, and the contradiction, in this case, is a direct result of your own reduction.
Again stop simply trying to posit aspects of your own failed reasoning and your own deliberate “contradiction” on to others.
You do not need me in order to get this contradiction, actually it is the result of your one level self-made reduction.
(mutually exclusive simply means they share that exclusion just as mutually dependent simply means they share that dependence and the only thing “disjoint” or not connected is your understanding)
Again, two sets are said to be disjoint if they have no objects in common, or in other words they are excluded w.r.t each other at their own level of existence. But this is not the end of the story, because (exactly as you wrote) they are shared at a deeper (or higher) level of existence, and those two levels define the Organic realm of Whole\Parts Relations, where the Whole is Non-local w.r.t to the parts, and the Parts are Local w.r.t to the Whole, such that no collection of parts have the Non-local property of the whole.
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Once again:
The permanent existence of distinct object that is not in the range of any given collection (finite or not) that is translatable to <0,1> forms, essentially determines the incompleteness of such collection, or its openness, if you will.
This fact gives us the clue that complete deduction (such that a set of considered collection of axioms really determines a complete framework, within its bounds) is impossible, exactly because any given collection (whether it is a collection of axioms, or not) exists upon a higher level, which is non-local by nature, exactly because it is a form of existence that does not depend for its own existence on any form of existence of many distinct ids.
The abstract and the non-abstract realm are not less than Whole\Parts Relation, where no collection of parts (finite or not) is the Whole.
This is a paradigm-shift of the Mathematical Science for the past 3,500, which is based on the wrong notion that the Whole is the sum of a given collection of distinct ids.
The inverse of the diagonal of any distinct collection of <0,1> forms (finite or not), which is not in the range of the given collection, actually inherently and essentially demonstrates that the Whole is not the sum of parts and also that complete deduction is impossible (there is no such a thing like a complete bounded framework).