>> I am
>>presently struggling to understand and evaluate Rosens work. Onar may find it
>>worth considering, also, in his attempt to "do better" than Dawkins.
>
>
> 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 t
o
> 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 th
e
> surface of things).
Rosen uses category theory which involves sets of sets and sets of
mappings, mappings on mappings, etc. How does this relate to hypersets?
I start to sense a convergence may be lurking in the shadows????
Your use of "inside" and "outside" is making it hard to know
what your meaning is. Is there another metaphor you can add to help
me see? Is Dennets "Cartesian Theatre" vs "Multiple Drafts" attempt
to make a distinction of any help?
>
>
>>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.
>
Still having difficulty with "outside". I agree that any apparent
paradox is
probably the result of the inadequacy of our worldview as inherited from
Descartes.
>
>
>
> While a working dual worldview is unsatisfactory it is even more unsatisfactor
y
> 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 seei
ng
> 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 globall
y
> 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 wi
th
> the magic mirrorhouse ("The Magic Mirrorhouse" and "Illusory Illusions" on my
ww
> w
> homepage). The mirrorhouse is essentially ONE world pretending to be two, whil
e
> the magic mirrorhouse is really TWO worlds pretending to be one. Since these a
re
> indistinguishable both are valid worldviews and they may be joined into a sing
le
> worldview using the moebius strip. Personally I think this is a very aesthetic
> model because it outlines the *Geometry* of consciousness. That's very pleasin
g.
>
>
>
>
>
>
> Onar.
It sounds, from your reference to Escher, etc. that hypersets
accomplish the same thing that Rosen does with category theory. What's
a good place to look for more on hypersets. These both seem ways to
get gid of the apparant paradoxes arising from self-reference, etc.
Best, Don Mikulecky