> Onar suggests, if I understand him correctly, that hyper-set theory resolves
> the paradoxes that only appear to be present with using dual worldviews. He
> writes:
>
>>...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 lo
ng
> 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 objectiv
e
> world, then the Moebius strip metaphor (and hyper-set theory) is not applicabl
e.
>
> 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 th
e
> 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 cru
se
> 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 expressi
on
> 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 Objectiv
e
> world? I have my doubts.
>
> Jeff Prideaux
The way out of this, it would seem, is to not discuss these issues without
staying in touch with the modeling relation. If it is rejected, the
discussion fails for obvious reasons and probably can't be salvaged.
The relation between the "natural system" (on the left of the diagram)
and the "formal system" (on the right of the diagram) is only complete when
an encoding(left to right arrow) and decoding (right to left arrow)
cause a
causal event (on the natural system) to result in a commutative diagram
with respect to an implication in the formal system. That's a mess
so lets follow around the diagram when it commutes. Causal event:arrow from
NS(Natural system) to itself......then encoding:arrow from NS to FS (formal
system)....then implication: Arrow from FS to FS mimicing causal event....
then decoding:arrow from FS to NS completing the diagram. Our view, growing
out of Rosen's is that unless such a commutative diagram exists, we
have no efective way to link our minds to the "outside" (in Onar's sense???).
Not only that, but the encoding and decoding must be supplied INDEPENDENTLY
from the formal system. This is much more complicated a concept than can
be adequately described by speaking of sets and subsets. Perhaps hypersets
are more effective? We need to look at this.
Best wishes, Don Mikulecky