# Re: Atomism = Holism ? - NO!

Ian Goddard (igoddard@netkonnect.net)
Thu, 18 Jun 1998 07:27:23 -0400

At 04:12 PM 6/18/98 +1200, Gerhard Kessell-Haak wrote:

>Since you both seem to have ceased the argument without coming to a
>conclusion, lets see what consequences there are if the assertion that:
>
>XX) A = not(A) (as taken from Ians definition of Holism at
>www.erols.com/igoddard/holistic.htm)
>
>is true.
>
>Define a set universe U = {A, B, C}
>
>This implies that B is an element of not(A).
>
>taking XX, this implies that B is an element of A.
>
>Since A is an atomic entity within U, this actually means that
>
>B = A.
>
>That means that U = {A, C}.
>
>One can continue on in the same fashion, until
>
>U = { A } => U = A.
>
>However, under this definition, not(A) = empty set.
>
>Thus, using assertion XX, one can only come to the conclusion that U is
>an empty set.
>
>As we defined U = {A, B, C}, we can then conclude that {A, B, C} is an
>empty set.
>
>This is blatantly false.
>
>So, assertion XX must be false.

IAN: Your argument is true, but it
does not actually address what I say.

It comes down to the context in which
we use the "=" symbol. Your critique
of my page cited uses the "=" symbol
in a different context than that
which I carefully state there:

Criterion for inclusion in "A"

x is a part of A, IF x is necessary for
the specific existence/identity of A.

If this criterion is valid, it then follows that as:

not-A is necessary for the existence of A,
therefore, not-A is a part of A.
In the same fashion, A is a part of not-A.

IF not-A is a part of A,
IF A is a part of not-A,
THEN A and not-A have the same parts.
ERGO: A = not-A

Assuming you do not see the contexts now
more than you did before (it's not easy),
I'll define them more clearly... asap.
It has to do with equality if relational
dependence vs differentiating features,
the first context returns an = while the
second context returns an =/= and each
context is a feature of the other.

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