[ QUOTE=doronshadmi;4658888]Let us summarize it:
The Ontology of Fusions and Collections
By using an ontological viewpoint of the foundations of the mathematical science we distinguish between fusions and collections. Let us quote from Michael D. Potter's book "Set theory and its philosophy" page 21:
"
But the standard cases have a tendency to obscure the distinction between two quite different ways in which it has been taken that things can be aggregated – collection and fusion. Both are formed by bundling objects together, but a fusion is no more than the sum of its parts, whereas a collection is something more."
This "
something more" is exactly the ability of a collection to be available (to exist) as a measurement tool that is independent of the researched (whether it is a collection –empty or not– or a fusion –empty or not–), which is an ability of existence that a fusion does not have. An empty collection is an available measurement tool that measures nothing, For example |{}|=0. This is not the case with a fusion because an empty fusion is nothing (the measurement tool and the measured are the same, and the measurement is impossible since we have lost our measurement tool). Here is another quote from Michael D. Potter's book "Set theory and its philosophy" page 22:
"
And what if we try to make something out of nothing? A container with nothing in it is still a container, and the empty collection is correspondingly a collection with no members. But a fusion of nothing is an impossibility: if we try to form a fusion when there is nothing to fuse, we obtain not a trivial object but no object at all."
By using a collection as a measurement tool "
a fusion of nothing" is researchable (as shown in the case of the empty set). There are 3 levels of existence that are researchable under the collection's framework, which are: Emptiness, Intermediate, Fullness. Since a collection is a level 2 (Intermediate) thing, then:
1) It is above the level of Emptiness ( for example: {} )
2) It is at the level of collection ( for example: {a,b,c,...} )
3) It is below the level of Fullness ( for example: {_}_ )
Some claims "there is nothing below collection". He is right because "there is nothing" is Emptiness. By following the same ontological notion, we get the opposite of Emptiness, called Fullness. Some claims "there is nothing above collection". This claim is ontologically wrong because "nothing" is below collection. Some claims "there is everything above collection". This is ontologically wrong because "everything" is at the level of collection. Some claims "there is Fullness above collection". In this case he is ontologically right. It must be noticed that the measurement tool is excluded from the measurement's results, for example: |{}|=0 and not 1, |{a,b,c}|=3 and not 4, etc.[/QUOTE]
Doron, you continue to burry yourself with your quote mining, read and understand your own reference
But a fusion of nothing is an impossibility: if we try to form a fusion when there is nothing to fuse, we obtain not a trivial object but no object at all
Now let’s see what you say about an ‘empty fusion’
By using a collection as a measurement tool "a fusion of nothing" is researchable (as shown in the case of the empty set).
So again you are claiming to research what your own reference tells you is impossible (you empty ‘fusion’). You try to scurry around this dilemma by claiming you are using “collection as a measurement tool”, but all you ever measure are those collections. Again it is just your usual malarkey of trying to introduce some independent sub element (particularly into a set that has no elements) that you claim to be non-researchable as being independent and your own reference tells you that it is an impossibility as your ‘empty fusion’. You read too much into and too little of the reference you cite.
