SUO: Re: Proposed SUO Content Outline
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John Sowa wrote:
>
> I agree with Jon's point:
>
> > The problem is not writing the axioms --
> > the problem is drawing the consequences.
>
> But I would add the more difficult problem of trying to decide
> which axioms have consequences that can peacefully coexist with
> the consequences of all the other axioms in the very big SUO pot.
Exactly. This is what makes ontology-building an iterative process,
at any rate, once it gets going at all. You deduce the consequences
of your initial trial axiom set, at which point you will typically
find that your "system of belief" (SOB, yes, in the sobering sense)
crashes in either one of two ways:
0. Into the Ground -- which means that you never quite get around
to being able to derive any theorems that were not already as
evident and as obvious as the axioms themselves, or as little.
1. Into the Sky -- which means that all statements are theorems now,
that the axiom set hides a contradiction and is thus inconsistent.
It is the possibility of this higher way of crashing, and the fact
that it is in practice the most prevalent way to go, that renders
most of what you hear about "non-monotonic reasoning" utter jive.
What all of this rap really means is that people typically respond
to the threat of inconsistency, in the way that most varieties of
religion have always done, by weakening their inference rules to
the point where almost no contradiction can actually be derived.
And here, at the outset of this prospectively recurring cycle,
is where we discover that we are not likely to get very far
without the utility of some very powerful theorem provers.
> By the phrase "peacefully coexist", I would include
> an enormous number of related problems:
>
> 1. Do they make the same or somehow reconcilable assumptions?
>
> 2. Among those assumptions are the basic coordinate systems,
> such as spherical for the earth as a whole, but rectangular
> for any reasonably small piece of the earth. (And who decides
> what is reasonable?)
>
> 3. And while we are talking about coordinate systems,
> should we choose the center of the earth as the origin?
> Or should we use the average sea level as the zero point?
It is my observation that everybody initially starts out with their origin
located at the "center of the interesting and knowable universe" (COTIAKU),
so it is practically unavoidable that we find flexible ways to translate
among highly diverse "reference frames" and styles of representation.
It leads to the notion of, not a "universe", not a "multiverse",
but a genuine "transverse".
> 4. But anything relative to the earth is definitely not
> an "inertial coordinate system" in Einstein's terms.
> Why not do everything relative to the sun? Or to the
> center of the Milky Way galaxy? Or to the center of
> gravity of the universe as a whole (as Ernst Mach
> suggested)?
>
> 5. Or should we state our axioms in a way that is
> independent of any coordinate system whatever?
My vote is for this, modulo the proper definition of "independent",
and not to mention the proper hedges around "whatever", of course.
> 6. Or perhaps we should make them easily tailorable
> to any particular coordinate system that is
> relative to the object of interest?
Yes, but I would spell it "Taylorable".
> 7. Or maybe all of the above?
Y0 (Why Nought!?)
Jon Awbrey
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