?not? is a universal set theoretic operator, whilst ?-? is an operator
that is usually associated with Paeno systems/sets.
Please don?t take the following personally, but if you (Ian) have never met
these terms, I strongly advise that you familiarize yourself with
elementary logic and set theory. The fact that you are attempting to
espouse a philosophy using terms grounded on set theory, logic, and
analysis surely dictates that you should, at least, have a passing
familiarity with these subjects.
>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).
Perhaps somebody on the mailing list who has recently or is currently in
the process of completing an elementary course in logic may wish to.
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 {-} ?
>?.. 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. According to this fashion of reasoning, I could prove that Mary is a
man because all jeans are worn by men (in Italy), Mary is wearing jeans
(in New Zealand), therefore Mary is a man! I'm sorry, but ...... I don't think
so.
However, your ideas have some merit - the set U = { A } is an extremely
boring set, especially if any operators performed on U must result in a
member of U! Things only begin to get interesting once we have U = {A,
B}, from which we could derive boolean algebra and ascribe A the
?meaning? true and B the meaning ?false?.
I could go on (and on), but I think I?ve spent too much time on this already.
Unless you expound your ideas and concepts in a considerably more
rigorous manner, you will find that your ideas will continue to cause
conflict without coming to any conclusion on the validity of your
viewpoint.