How & When A = -A

Ian Goddard (
Thu, 18 Jun 1998 15:18:39 -0400

Gerhard contends that the "A = -A" statement is
false, as it would be if we say that A is 100%
the same as -A, but it is not false in an im-
portant context. Let's see how A can = -A.

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.


"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