>...As a result (of hyper-set theory) it is completely consistent to
>construct a set where A is a subset of B and B is a subset of A. Suppose now
>that we divide the world into a subjective world and an objective world.
>According to standard theory, subjective worlds are subsets of the objective
>world....
and
>The Moebius strip has the dual duality embedded into it in a very natural way.
>Locally the strip is TWO-sided (corresponding to a dual worldview) but
>globally only has ONE side (corresponding to a non-dual worldview). This
>means that hyperset theory not only removes the paradoxes of Cartesian
>worldview, it unifies the monistic and dualistic worldview into one, using the
>moebius strip.
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...that if you cruise along the "objective side" of the Moebius strip long
enough, you will eventually get to the "subjective side" (without ever really
leaving the "objective side").
All of this hyper-set theory stuff (as applied to consciousness) appears to be
based on the assumption that subjective worlds are subsets of the objective
world (or visa versa). If subjective worlds are not subsets of the objective
world, then the Moebius strip metaphor (and hyper-set theory) is not applicable.
If you have a property that doesn't actually discriminate, then the paradox
Rosen referred to doesn't happen.
Again Rosen said
"Most, if not all, (of) the known paradoxes arise from an attempt to divide a
universe into two parts on the basis of satisfying some property or not (e.g., a
property like objectivity). Trouble arises whenever this property can be
turned back on itself; in particular, when we try to put some consequent of the
property back into one or the other class defined by the property."
For example, consider a property like truth. It discriminates statements into
those that are true and those that are false. One couldnt say that the true
statements are a subset of the false ones (or visa versa)...or that if you cruse
along the "true statement side" long enough, you will get to the "false
statement side".
The following is a quick example of the paradox.
Consider evaluating the truth of the following statement:
"This statement is false."
The statement cannot be true because, as stated, it says that the statement is
false. The statement cannot be false, because, if it were false, the expression
this would be true, which would contradict the fact that it says
that it is false.
It seems to me that the Moebius strip metaphor (and hyper-set theory) doesn't
resolve true paradoxes...only apparent paradoxes. A true paradox can occur
with an actual real discrimination. An apparent paradox can be resolved when
the discrimination is shown not to really exist.
The BIG QUESTION is whether objectivity truly discriminates (between
subjective and objective). Is the subjective world a subset of the Objective
world? I have my doubts.
Jeff Prideaux