Le 05-avr.-06, à 23:14, daddycaylor.domain.name.hidden (Tom) wrote :
>
> Another categorization of this dichotomy could be the Plato universals
> corresponding to Intensional definitions and the possible, vs. the
> Aristotle particulars corresponding to the Extensional definitions and
> the actual. The Intensional can also be associated with mathematical
> descriptions and algorithmic complexity, whereas Extensional is when
> something is defined by listing all of its components without assigning
> any order to it or doing any information compression. I think that it
> takes a person to do the Intensional, to assign order, beauty or
> meaning. My belief is that we as finite persons cannot reduce that to
> numbers, fully understanding it in a reductionist way. I think this is
> what Stephen was getting at with Intensionality, and perhaps what is
> also called simple apprehension, intuition. I guess this could be
> Bruno's distinction between the inside view (G) of only the world that
> is accessible to us through proof, versus being able to somehow
> comprehend truth, beauty and order directly (G*).
Careful. Both G and G* gives third person, and thus objective,
intellectual, outside, ... views. G is terrestrial or effective, and G*
is divine (still effective, but not from the machine's point of view).
The inside view are given by defining the new boxes (corresponding to
hypostases in Plotinus).
The first person inside view (soul) is given by "Bp & p", the sensible
soul is given by Bp & Dp & p.
I will come back on this soon or later. Many (including myself times
ago) got that wrong. I agree it is a bit confusing.
>
> I think there might be some confusion sometimes with what math and
> numbers are about. I think that math is about Intensionality, seeing
> truth, beauty and order. By definition, this is saying that we are
> leaving out a lot of the particulars, we are compressing information.
Yes but almost like Plotinus, I do believe that matter is already
compressed information, and that there is no real particular. Comp
leads naturally to a "Many Types No Token" interpretation of
arithmetic.
> Some people (particularly the reductionist view) say that math brings
> us closer to understanding everything about the universe.
Before Godel, you can think like that. Since Godel we know that any
mathematical theory is just a tool to open doors on bigger mysteries
and Unknown. About numbers, we know really nothing, but after Godel we
know, at least ,that we know nothing (assuming we are consistent, in
some way).
> They look at
> numbers and say wow numbers are very precise, so this means we can do
> the same thing with the universe.
But numbers are not so precise. If this is counterintuitive wait for my
post 'the herat of the matter" to George Levy. I will explain where
does the Universal Dovetailer (UD) comes from and why does the UD needs
necessarily to dovetail, and this is related with the fact that numbers
are not so precise, and that there is an infinity of information hidden
there.
> Perhaps in a way math does bring us
> closer or give us a better understanding, but I think it is wrong to
> believe that "closer" means that we can have a goal of actually
> understanding everything.
Right, but "modern" (post-Godel) math shows the contrary. The more we
know, the less we know!
The *learning* machine ignorance can be described by the corona G*
minus G. But as the machine learns new information, G get bigger, but
G* get still bigger, and consequently, the corona get itself still
bigger too. We have to be modest.
> It is like Zeno's paradox, yes we are
> getting closer, but what does that mean? I think that we have to
> always take the humble stance that there will always be something that
> we don't understand.
I think you are right, but more can be said. You are right from purely
logico-arithmetical reason.This provides effective information for
finding mathematical structure bearing on what we don't understand, a
little bit like physicists talking about the "universe".
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Apr 07 2006 - 11:04:57 PDT