Here's an obvious example where A = -A:
If A = 30% of U and -A = 70% of U, in the context
of volume we say that A =/= -A, or the volumes of
A and -A are different. If A = 50% and -A = 50%,
then A = -A with respect to volume. With respect
to location, color, etc, it may be that A =/= -A.
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?
If we should ask, what is the degree to which a thing,
A, is a required feature of the identity of A, and what
is the degree to which another thing, -A, is a required
feature of A, we find that the answer is that the degree
to which A requires A is EQUAL to the degree that A re-
quires -A for A to exist. So "the degree of A" = "the
degree of -A" with respect to the degree to which
either is necessary for the existence of A, and
in this fundemental context, indeed A = -A.
That's the true meaning of the mystical axiom: A = -A.
Even if A = 90% of the spacetime volume of U, while -A
only = 10%, the identity of A requires that 10% to a
degree that is equal to its requirement for the 90%.
A = -A expresses the equality of identity dependence.
Saying "A =/= -A" says, "A is different than -A,"
and it's precisely the difference between A and -A
(with respect to features of identity such as color,
size, speed, etc.) that is the basis of the relational,
or differential, dependence of A and -A upon each other
for their unique identity features, and which therefore
renders the "A = -A" statement true with respect to
the degree of dependence for identity existence.
A = A if, and only if, A =/= -A, which means that for
A to exist A must be differentiated from -A, which means
that A requires -A as much as A (itself), and the degree
to which A requires -A = the degree to which A requires A.
So when we say "A =/= -A" we say that A has features that
are different than the features of -A, and when we say
that "A = -A" we say that the degree to which A requires
-A for its identity is equal to the degree A requires A.
Hence the identity structure of A contains both A and -A,
and the identity of A spreads out beyond the limits of A.
We can express this via the holistic set theory I've
proposed, which defines the "A = -A" context of A as
(super)A. (super)A is the superstructure of the iden-
tity of A that contains all the features that are re-
quired for the existence of (in)A. (in)A is the in-
terior region of the entity called "A." (super)A
contains both (in)A and (out)A, and (out)A is
simply the external area of (in)A. So:
(super)A = {(in)A, (out)A}
and (in)A =/= (out)A
which states that (in)A is different than (out)A.
When we add entities to (out)A, we have overlapping
identity mappings, which my upcoming pages cover.
**************************************************************
VISIT IAN WILLIAMS GODDARD --------> http://Ian.Goddard.net
______________________________________________________________
"A new scientific truth does not triumph by convincing its
opponents and making them see the light, but rather because
its opponents eventually die, and a new generation grows
up that is familiar with the idea from the beginning."
Max Plank - Nobel physicist
"The smallest minority on earth is the individual.
Those who deny individual rights cannot claim
to be defenders of minorities." Ayn Rand