Rosen's concepts, as you present it, sound very familiar. The trick that
paradoxes dedudes from division was, however, new to me. I will have to think
more about that. In my school of thought I am not used to thinking about
paradoxes as a problem. I've come to find that paradoxes easily resolve with
hyper-set theory. What is particularly neat is that they have an exact
geometrical interpretation. When Russell constructed his famous "Principia
Mathematica" he for some reason he disallowed a set X to be and element in its
own set. This was completely based on aesthetics and the limitations of the
mathematical tools at that time. In the 50s or 60s, however, a mathematician
(I can't recall his name) developed the obscure mathematics known as hyper-set
theory. I believe he used a proof stating that all sets can be drawn as graphs
(from graph theory). He then went on to show that it is fully possible to draw
graphs of sets which contain themselves as elements and thereby rendered
Russell's aesthetic judgement wrong. As a result 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. But it is also completely possible to argue that the real, objective
world "out there" is an illusion of the mind, a staggeringly real virtual
reality spanned by the mind. In this view the objective world "out there" is a
subset of the subjective world. With hyperset theory both these views are
correct, simultaniously. A geometrical interpretation of this particular
hyperset could be an object where the subjective world is the world seen from
the inside while the objective world is the world seen from the outside (on the
surface of things).
>The
>paradox prevents Cartesian science from saying anything about the mind or
>consciousness. It also probably prevents us from really knowing anything
>fundamental about objects.
I react to this. What's so paradoxical about this? Suppose that the objective
world is the world seen from the outside. *Of course* the inside of things is
out of reach. That's a limitation with Cartesian science which makes it
extremely unsatisfactory, but not a paradox as I see it.
While a working dual worldview is unsatisfactory it is even more unsatisfactory
that there is a higher level splitting of the world, namely the split between a
dual and a non-dual worldview. It is not good that there is a dual way of seeing
the world: either as DUAL or as NON-DUAL. Fortunately hyperset theory allows
this seeming paradox to be solved. There exists a kind of hyper-geometrical
figures which describes exactly such dual dualities, namely the "Escher"
objects. (i.e. the Escher triangle, the Moebius strip, the Kleinian bottle etc.)
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.
I use this method myself in my theory of social consciousness which I model with
the magic mirrorhouse ("The Magic Mirrorhouse" and "Illusory Illusions" on my ww
w
homepage). The mirrorhouse is essentially ONE world pretending to be two, while
the magic mirrorhouse is really TWO worlds pretending to be one. Since these are
indistinguishable both are valid worldviews and they may be joined into a single
worldview using the moebius strip. Personally I think this is a very aesthetic
model because it outlines the *Geometry* of consciousness. That's very pleasing.
Onar.