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. 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.
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.
> > Another example would be an electric circuit: Given the structure of
> > an electric circuit, and axioms and rules about electricity, we can
> > predict what the output of the circuit will be. If we go through a
> > different sequence of contortions/calculations with that same
> > structure, axioms and rules, and get a different output value, then the
> > axioms, rules *together with the structure* are inconsistent.
> The structure can't be inconsistent - it's not a statement or proposition.
> Brent Meeker
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