resolves in hyperset theory as
A = {not A}
The above is a hyper-function. "not A" is not the set A itself (by definition!)
but it is a *function* of A. That is, it depends on the truth variable of A. The
contention that hyperset theories does not solve real paradoxes is false.
Hyperset theory was constructed _precisely_ to solve paradoxes. The motivation
was to resolve Russell's famous paradox: "Let X be the set of all sets which do
not contain itself." Obviously X is itself a set which does not contain itself
which in turn means that it contains itself. This is easily resoved in hyperset
theory.
>The Moebius strip metaphor (used as above) suggests that if you try to divide
>the world up into subjective and objective parts, everything will go to one
>side...that the objectivity property does not really globally discriminate.
>This suggests that the subjective world doesn't really exist as an independent
>entity...
This is a very important point. If you substitute "doesn't really exist" with
"is illusory" then you are very much closer to the true picture. There is a
great debate among cognitive scientists and philosophers how consciousness
emerges, but they all agree on one thing: it is illusory in nature. That of
course, doesn't mean that it "doesn't really exist". Consciousness has structure
.
This is what Gestalt psychology is all about: the structure of illusions.
Now, the division of the world arises from the limitation of
consciousness: consciousness cannot perceive _everything_ at once, it is at all
times restricted to only seeing a local, limited section of reality. While
consciousness is illusory these limitations on consciousness are highly real. An
d
when we look at the moebius strip with the same limitations as consciousness
(locally) it has two sides.
That the Self doesn't really exist as a real entity is, BTW, not a new
thought. If I'm not totally mistaken this is the central thesis of Buddhist
philosophy.
If you take the time to read my "Illusory Illusions" I describe the structure of
social consciousness and show that it emerges from the ability to see second
order illusions. In hyperset theory a hologram is defined as follows:
Let M be a hyper-set such that M = {C1,C2,C3...Cn} where all components
themselves are hyper-sets such that Cr = {M}, r = {1,2,3...n}. M is then said to
be holographic.
By lucky chance this is precisely the structure of a mirrorhouse. Let M be the
mirrorhouse and each component, C, be a mirror in the mirrorhouse. Note that the
set is finite, but it creates an illusory infinite regress.
Onar.