Wow! this post really demonstrates your open minded approach and your openness for criticism.
Your only motivation is the survival of your ideas.
You are a cult leader with no cult.
If you have something to say, please demonstrate it in details according to
http://www.internationalskeptics.com/forums/showpost.php?p=4960155&postcount=5567 .
Jsfisher's reply style in
http://www.internationalskeptics.com/forums/showpost.php?p=4960373&postcount=5568 ,
http://www.internationalskeptics.com/forums/showpost.php?p=4960952&postcount=5571 and
http://www.internationalskeptics.com/forums/showpost.php?p=4961199&postcount=5573 IS
an exact example of how to systematically avoid notions and stick to agreed names and notations.
I am doing my best not to be a member of jsfisher's club.
Again, here is a very simple example, which clearly demonstrates my argument about jsfisher's club:
Both jsfisher and me agree that Cardinality is first of all a measurement unit of the existence of things.
Jsfisher's Cardinality is limited to the existence of things in the first level of some collection, for example:
|{{}}|=|{{{}}}|=|{{a,b,c,…}}| = Cardinality 1 , and this is exactly a measurement that is limited only to the first-level of the existing things.
Since Cardinality is first of all a measurement unit of the existence of things, then there is no reason to limit the measurement only to some particular level of existence of the measured thing.
By avoiding this limitation Cardinality is really the measurement unit of the existence of things, which can be demonstrated as follows:
|{}|=0
|{{}}|= 0+1
|{{{}}}| = 0+1+1
...
|{{a,b,c,…}}| = |{a,b,c,…}| + 1
Furthermore, each one of these cases is based on the fact that the outer "{" "}" represents an existence that enables the measurement in the first place, such that:
1) The Cardinality of that existence is exactly
∞ .
2) The Cardinality of no existence is 0.
3) There is no Cardinality that is greater than
∞ and there is no Cardinality that is smaller than 0.
(1),(2),(3) are simple and expose the arbitrary limitations of jsfisher's club about Cardinality, exactly because Cardinality is the measurement unit of the existence of things, and it can't be forced to be limited to any particular existence.
The argument that jsfisher uses in order to support he's forcing on the concept of Cardinality, is this:
"Cardinality is what my club says it is. No generalization of this concept is allowed; therefore any change of that concept is actually a different subject that should be treated independently of the current agreement of my club about this concept (Quote: "I'd suggest you use D for your measurement function.")"
I am doing my best not to be a member of jsfisher's club, which is a club that is based on names\notations and differentiations of names\notations, and it does it exactly in order to avoid notions and their possible generalizations.
The reason for jsfisher's club behavior is very simple:
Their reasoning is based on verbal expressions and they do not bother to research what actually enables verbal expressions, in the first place.
By not avoiding this essential research, I demonstrate exactly how Direct Perception is the exact reasoning for real generalization.
Direct Perception enables real generalization exactly because it is the common base ground of both Intuition and verbal logical reasoning.
It is only a matter of time until Direct Perception will be the real foundation of the mathematical science, and when this happens, Ethics and Logics will be derived from their real source and will be properties of a one (organic) "Tree of Knowledge", exactly as demonstrated in
http://www.scribd.com/doc/17504323/WZATRP8 .
In other words, the verbal-only tongue's waving of jsfisher's club will be transformed to exactly what it really is: some expression of Direct Perception.
you helped me a lot to refine it.