Ian Goddard (igoddard@netkonnect.net)
Mon, 22 Jun 1998 15:33:22 -0400

Gerhard Kessell-Haak wrote:

>>IAN: It's an interesting area of inquiry:
>>does the "-" negative notion equate 100%
>>with the "-" logical not notion? What's
>>your case that "negative =/= not"?
>?not? is a universal set theoretic operator, whilst ?-? is an operator
>that is usually associated with Paeno systems/sets.

IAN: That doesn't establish that we
cannot say that the "-" in -A (as in
not-A) and in -4 are compatible with one
another. There are cases for and against
that, but as I see you're not inclined
to make a case to support your claim,
I guess we'll just leave it at that.

>>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
>Wow ?.. there are so many holes in that stream of reasoning that I really
>can?t be bothered pointing them all out (and please, don?t ask me to).

IAN: Taking the time to back up your
assertions is a drag, so I won't ask.
I guess A is A free from not-A and
that is that and no questions.

>I?ve noted that you (and others) repeatedly use terms such as ?degree?,
>and ?measure? - unfortunately these terms are only valid for sets where
>these can have meaning (such as the set of Reals). For example, for the
>set of operators O = {+, -, *}, where O is not a Paeno set, what is the
>difference between {+} and {-} ?

IAN: That's tangential. Glad you
found the time to make a case that
really has nothing to do with the topic.

>>?.. So A = -A and does not = -A at the same time in
>>different contexts. When mystics say A = -A (or
>>something to that effect) they are referring to
>>a primordial context that maps the structure of
>>identity. So what is this "mystical" context?
>To state that ?A = -A?, where the context of the left side is different from
>the context of the right side is logically invalid, and is an abuse of the
>?=? sign.

IAN: That's not what I said.

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