Brent Meeker wrote:
> Tom Caylor wrote:
> > Brent Meeker wrote:
> >> Tom Caylor wrote:
> >>> Bruno has tried to introduce us before to the concept of universes or
> >>> worlds made from logic, bottom up (a la constructing elephants).  These
> >>> universes can be consistent or inconsistent.
> >>>
> >>> But approaching it from the empirical side (top down rather bottom up),
> >>> here is an example of a consistent structure:  I think you assume that
> >>> you as a person are a structure, or that you can assume that
> >>> temporarily for the purpose of argument.  You as a person can be
> >>> consistent in what you say, can you not?  Given certain assumptions
> >>> (axioms) and inference rules you can be consistent or inconsistent in
> >>> what you say.
> >> Depending on your definition of consistent and inconsistent, there need 
> >> not be any axioms or inference rules at all.  If I say "I'm married and 
> >> I'm not married." then I've said something inconsistent - regardless of 
> >> axioms or rules.  But *I'm* not inconsistent - just what I've said is.
> >>
> >>> I'm not saying the what you say is all there is to who
> >>> you are.  Actually this illustrates what I was saying before about the
> >>> need for a "reference frame" to talk about consistency, e.g. "what you
> >>> say, given your currently held axioms and rules".
> >> If you have axioms and rules and you can infer "X and not-X" then the 
> >> axioms+rules are inconsistent - but so what?  Nothing of import about the 
> >> universe follows.
> >>
> >
> > Yes, but if you see that one set of axioms/rules is inconsistent with
> > another set of axioms/rules, then you can deduce something about the
> > possible configurations of the universe, but only if you assume that
> > the universe is consistent (which you apparently are calling a category
> > error).  A case in point is Euclid's fifth postulate in fact.  By
> > observing that Euclidean geometry is inconsistent with non-Euclidean
> > geometry (the word "observe" here is not a pun or even a metaphor!),
> > you can conclude that the local geometry of the universe should follow
> > one or the other of these geometries.
> No, you are mistaken.  You can only conclude that, based on my methods of 
> measurement, a non-Euclidean model of the universe is simpler and more 
> convenient than an Euclidean one.
> >This is exactly the reasoning
> > they are using in analyzing the WIMP observations.
> The WIMP observations are consistent with a Euclidean model...provided you 
> change a lot of other physics.
> >Time and again in
> > history, math has been the guide for what to look for in the universe.
> > Not just provability (as Bruno pointed out) inside one set of
> > axioms/rules (paradigm), but the most powerful tool is generating
> > multiple consistent paradigms, and playing them against one another,
> > and against the observed structure of the universe.
> Right.  As my mathematician friend Norm Levitt put it,"The duty of abstract 
> mathematics, as I see it, is precisely to expand our capacity for 
> hypothesizing possible ontologies."

This quote is basically what I've been trying to get at.  The possible
ontologies are the multiple self-consistent paradigms that I was
referring to.  When we keep finding that "using abstract math to
hypothesize" actually works in guiding us correctly to what to look
for, then we have to start believing that there's got to be some kind
of truth to math that is greater than trivial self-consistent logical
inference.  I think this is what Bruno is getting at with the border
between G (provable truth) and G* (provable and unprovable truth).
Math helps us find not just G, but we can also explore the border of G
and G*.

> > On the other hand, I think that the real proof of the pudding of
> > Bruno's approach would be, not does his approach agree with empirical
> > evidence at the quantum/atomic level, but does it agree at the global
> > level, e.g. by make correct predictions about the spacial curvature,
> > compactness, finitude/infinitude, connectedness, etc. of the observed
> > universe.  Of course the quantum vs. global agreement would be the real
> > "proof" of any TOE.
> Agreement would be great.  But the proof of scientific pudding is predicting 
> something suprising that is subsequently confirmed.
> Brent Meeker

I would like to hear Bruno's thoughts on comp with respect to
prediction of global aspects such as geometry, as I brought up in the
above paragraph from a previous post.

Also, a thought comes to mind that Bruno once said something about
reality (physics, sensations?) arising from our ignorance of the
absolute border between G and G*.  This brings me back to the analogy
of the Mandelbrot set.  We can never know the actual absolute border of
the Mandelbrot set.  If we were asked to point out even one
(non-trivial) point on the complex plain that is exactly on the border,
we wouldn't be able to do it.  However, if we take a finite number of
iterations of the recursive equation, we get a definite border, which
is an approximation.  We get an actual instantiation/shape we can
interact with, something that kicks back, something akin to reality.
Again, as I originally proprosed, perhaps this is like the measurement
process in physics, or even the process of setting your coffee cup on
the table...  In my view the table doesn't kick back any more than the
Mandelbrot set.


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