Re: SUO: Re: Proposed SUO Content Outline
John,
If you'd be willing to restate the axioms in your section 2 in KIF, and
either consistent with, or, with mention of inconsistencies with, the
current proposed "merged ontology" I think that would be a great aid to
communication.
Adam
At 12:14 PM 3/4/2001 -0400, John F. Sowa wrote:
>Pat,
>
>It is much easier to state axioms that are independent of any
>coordinate system than to state axioms for any particular
>system.
>
> >>.... We will need to write axioms which say that spatial
> >> coordinate systems exist, without saying anything in particular about
> >> any spatial coordinate system.
>
>Writing such axioms is a trivial exercise:
>
>A coordinate system is nothing more nor less than a set C
>called the coordinates, a designated region R of space-time,
>and a function that maps C into points of R. This is true
>of coordinate systems tied to the earth, to the sun, to the
>center of gravity of the universe, or whatever. It is true
>of 4D systems and 3D+time systems. It is true of inertial
>coordinate systems and arbitrarily accelerated systems.
>
>For an example, see Section 2 of my paper on processes
>and causality:
>
> http://www.bestweb.net/~sowa/ontology/causal.htm#s2
>
>In that section, I assume that C is an open subset of Euclidean
>4-space, which is general enough to include nonEuclidean
>spaces that are locally Euclidean (which includes spherical
>coordinate systems, such as the lattitude, longitude, and
>altitude on the earth.)
>
>The only thing that the axioms have to say is that the set C
>and the set of points of R exist and there is a mapping from
>C to R that is (locally at least) one-to-one, continuous,
>and differentiable. A total of less than one page of axioms
>will cover any and all coordinate systems that physicists,
>engineers, mapmakers, ship captains, and NASA ever use.
>
>Recommendation: State all axioms about space, time, and
>space-time in terms of arbitrary sets C, R, and functions
>from C to R. Then for any particular coordinate system,
>you give a separate set of axioms that define the mapping
>from C to R. But all the basic axioms (which include all
>versions of Euclidean and various nonEuclidean geometries)
>remain unchanged.
>
>Furthermore, the axioms are completely independent of anybody's
>notions about continuant, occurrent, endurantist, perdurantist,
>obdurantist, or any other philosophy of space and/or time.
>
>And if you want to define time in an arbitrary coordinate
>system, I suggest Eddington's "arrow of time", which at any
>point is the direction of the maximum gradient of entropy.
>
>This arrow may be undefined in certain regions, such as black
>holes -- and that is as it should be. But for ordinary regions
>of the universe, it is well defined. For those people who want
>a "plug & play" ontology, certain predefined modules can be
>specified for the most common systems. (But then, of course,
>we have to face the question about specifying modules in KIF,
>which I believe is essential for many other reasons as well.)
>
>John
-----------------
Adam Pease
Teknowledge
(650) 424-0500 x571