# Re: Numbers, Machine and Father Ted

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."

> 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

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