Would you agree with the following?
First, a definition of Cartesian dualism:
In set theory, the "universe" can be depicted as drawing a big circle (infinite
in extent if you like). The "subjective world" can be depicted as drawing a
smaller circle (also possibly infinite) within the larger "universe" circle...so
therefor the "subjective" world is a subset of the "universe". The "objective"
world is what falls outside the "subjective" world circle and still lies inside
the "universe" circle. So the "universe" equals the union of "subjective" and
"objective"... and the intersection of "subjective" and "objective" equals the
"null" set. Therefor the "subjective" world is not a subset of the "objective"
world.
Empirical Science (operating within Cartesian dualism) has been a science of
the "objective" world (as defined from above). Therefor, that science cannot
address issues of the "subjective" world like consciousness.... if you try to,
you get a logical paradox.
Now, what "hyper-set" theory is saying is that the "paradox" is a product of
how we are viewing the "universe". If we view it in a different way, the
paradox goes away.
The above pictorial description of the "universe" is basically to divide a whole
(the "universe") into two parts. This could also be represented as the
"subjective" being on one side of a piece of paper (possibly infinite in
extent), and the "objective" being on the other side of the same piece of paper
(where the "universe" consists of both sides of the piece of paper. So far
nothing is different than the earlier circle depiction of Cartesian dualism.
You could also represent this by a hollow cylinder (possibly infinite in both
height and diameter) where the "subjective" world is on the inside, and the
"objective" world is on the outside.
Hyper-set theory suggests that if you consider the above depiction as a
cylinder (or so connected piece of paper) of finite height (possibly still
infinite in diameter) and cut the cylinder (or paper) at a particular place,
give a half twist, and reconnect the cylinder (or paper) you get the
geometrical depiction of a "hyper-set"...where you can identify (locally)
a "subjective" side and an "objective" side....but if you travel long
enough on one side, you get to (what was once viewed as) the other side.
Here the "subjective" side is globally a subset of the "objective" side
(and visa versa)...and both are globally equivalent to the "universe".
I have four questions:
(1) In the human mental process from going from a Cartesian dualism
perspective to a hyper-set perspective, is there any significance to
where the "cut-twist-reconnect" is made?
(2) Is there any significance as to how the cut is made (like what
angle)?
(3) Is there any significance (in the construciton process) to the
requirement that the piece of paper (or "universe") be finite in the
hight demension order to make the Moebius strip.
(4) If you consider an infinite Moebius strip that has always existed
(doesn't need to be constructed), doesn't this suggest a problem in
getting to the other side (if you have to travel an infinite distance)?
Jeff Prideaux