Hi Stephen,
OK, did you make sense of the idea of representing
Integer with a sort of equivalence class that have members that are
the arithmetic generators or creators or acts that equal examples of
the number? We can think of 1 in the Platonic sense as the class of
all arithmetic operations that are equal to 1, 2 as the class of all
arithmetic operations that equal 2, etc. OK, given that then it
seems to follow that, say a 2 in the operation that equals some
other number is in a sense a mapping of the entire class of 2 into
that other class. Does this make sense so far?
With a lot of effort!
Why introduce impredicativity for the numbers? It does not make a lot
of sense: it introduces complexity. It seems to me like doing alpinism
with a microscope. It is akin to the 1004 fallacy.
[BM]
But this has been shown not working. You cannot both capture
consciousness by Turing machine states, and at the same time to invoke
a notion of physical resource. It is the whole point of most of my
posts. Physical resource including space and time have to be recovered
from the math of (abstract) computer science.
[SPK]
No no no! I am not "capturing consciousness by Turing
machine"! I am
pointing at the content, using Descartes' brain in a vat and related
gedankenexperiments to show how there is an equivalence relation
between the
content of experience (minus "agency" notions, self-awareness,
etc.) and
the content of what can be generated by universal Virtual reality
machines,
as explained by D. Deutsch in Fabric of Reality, that can be used. The
notion of a physical resource is allowed because I am assuming that
both
mind (crudely an information structure, like a Boolean algebra) and
matter
(crudely as a Cantor dust or completely disconnected Hausdorff
space) are
both equally existent and "real". The idea in Pratt's work is that
Logic and
Time (the evolution of physical systems) form a duality see:
http://boole.stanford.edu/pub/dti.pdf
[BM]
This pleads for no fundamental matter, nor time.
[SPK]
Yes, but bOnly in the limit of the totality of
Existence, there is no measure or differentiation, thus no matter or
time in that fundamental sense. That’s why the dualism that I am
advocating is one that degenerates to a neutral monism in that
limit. But the Totality includes the finite and in that finite case
we have matter and time.
snip
[SPK] Your modelization so far seems to only consider a "frozen"
perspective and there is scant mention of how the model is extended
to cover
a plurality of entities, except for the diamond^alpha aspect mentioned
below. As far as I can tell, your Model offers a logical structure
to a new
version of the individual Leibnizian Monad (
http://www.iep.utm.edu/leib-met/#H8 ) that I am trying to develop,
but only in the static sense. There is no dynamic in it.
[BM]
The 'sensible' modalities, like Bp & p, and Bp & Dp & p, introduces an
internal dynamic. S4Grz is not just a logic of knowledge, it is a
logic of evolving knowledge, or time. It is due to the "& p". It makes
the first person intuitionist, the builder of its mental reality.
[SPK]
It may exist there Bruno, but it is by no means
explicit. The fact
that we can map Bp & p, etc. to some abstract structure and use the
orderings of those relations to act as a quotienting does nothing to
obtain
the experiential transitivity that is explicit in the 1st person.
[BM]
Why? The experiential logic is typically transitive, and anti-
symmetrical.
[SPK] Yes, that is true but in a static Platonic Idea sense. The
main problem, I suspect, obtains from the enumerability of the
content of experiential logic as I see in your Model.
It is enumerable, but not recursively enumerable.
This makes a computation of logical sentence something that has
properties in-it-self independent of any notion of interaction;
Well, yes. At least in the third person global view.
therefore it is, in a deep sense, solipsistic.
It is platonistic. Why solispsist. You lost me again I' afraid.
To boil this down, we need to start with the existence of a
plurality of minds, explaining why it is necessary that there is
more than just the One. You move toward this in SIENA.pdf but not
sufficiently to nail down the reasoning.
What is missing?
[BM]
Nobody said that. I said only that the natural numbers does provide
a kind of computational time, but the subjective time (and space
time) comes from the first person logic S4Grz (and S4Grz1), in the
ideal case under scrutiny.
[SPK]
A Liebnitzian "order of succession" aspect of time, certainly obtain
in what you point out here, but that is cheap, for there are no a
priori alternatives in the notion of the number that is subsequent
to n, for example n +1 or n+2 have only a single and unique
property. We do not see this kind of singular one- to one and onto
like map of determination in our notions of free-will and
responsibility. We see a selection process from a menu of
alternatives, alternatives that are all given concurrently. This is
a very different notion than what we see in natural numbers.
That would be the case if all the hypostases (modal points of view, Bp
& p, Bp & Dp, etc.) were obeying classical logic, but S4Grz gives an
intuitionist logic, Z1 and X1 give quantum logics, etc. What you say
don't follow.
Snip
Let us deal with the rest of my critique of Plotinus's
model some other time. It is of great interest to me as it helps me
understand details that are absent in Leibnitz' Monadology and need
to be considered, but I need to focus on developing a mutual
understanding of the ideas here so far.
All what I say is that we cannot have both mechanism and materialism,
and that mechanism explain the perception of physical laws, were
materialism has to postulate those laws, and use an identity thesis
not capable of being sustained by digital machine. So materialist have
to be non mechanist dualist, or have to eliminate the first person out
of the picture.
Bruno Marchal
http://iridia.ulb.ac.be/~marchal/
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