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
it is possible to have several universes which are consistent with each
other , but mutually inconsistent. That is in fact
the situation with contemporary mathematics.
> 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. This is exactly the reasoning
> they are using in analyzing the WIMP observations. 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.
I hardly follows from that, that all maths is physically
true. The point of making observations is to
exclude un-physical maths (ie falsify theories).
> 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.
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