John takes his pessimistic assumption that the world may be
fundamentally inexplicable to imply that it will be a very small
upper level ontology upon which we all can agree. From this he infers
that we should strive to keep it very small. I, in contrast, think
that our job should be to maximize as far as possible the number of
axioms on which we can agree, and work from there. (01)
Here some proposals, which would be in addition to the many axioms
governing dimensionality and before/after which John himself allows: (02)
The upper ontology should contain at least the following top-level categories: (03)
Independent Continuant
Dependent Continuant
Process (aka Occurrent) (04)
We then have axioms unpacking: (05)
Independent Continuant is_a 3 D entity (e.g. me)
Dependent Continuant is_a 0,1,2 or 3 D entity (e.g. the color of this bruise)
Boundary of Independent Continuant is_a 0,1 or 2 D entity (e.g. my
outer surface)
Extended Process is a (1,2 or 3)+t D entity (e.g. my life)
Boundary of Process is a (0, 1 or 2)+t D entity (e.g. my death) (06)
where t stands for the dimension of time. (07)
Note that the fact that the ontology contains these three categories,
does not mean that everyone who uses it must be committed to using
all three. Thus 4-dimensionalists would just use the Process category
(and reclassify the examples above accordingly; thus they would not
talk about Bill Clinton, but rather about a very slow
BillClintonizing process). (08)
We would also have axioms such as: (09)
No part of an independent continuant is part of a dependent continuant
No part of a dependent continuant is part of an independent continuant
No part of a process is ever part of a continuant
No part of a continuant is ever part of a process
Every dependent continuant depends on one or more independent continuants (010)
In addition the ontology would distinguish between types (aka
universals, classes) (among which the categories mentioned above
would be included at the highest level) and instances (aka
individuals, particulars), with corresponding axioms formulated for
the different <instance, instance>, <instance, type>, and <type,
type> relations defined in the OBO Relation Ontology at
http://genomebiology.com/2005/6/5/R46. Thus for example that, (011)
for all instances a, b of independent continuants then (012)
a adjacent_to b implies b adjacent_to a (013)
Many of the mentioned axioms (and the many which can be formulated in
a similar vein) are, of course, trivial, to human beings. But not
all. (Thus, for example, an axiom asserting the symmetry of the
adjacency relation does not hold on the level of types, and the same
holds e.g. for the relation of simultaneity in the dimension of time.) (014)
For computers, though, we need to write down even trivial axioms.
Let's do that, shall we? Anyone who objects to a specific axiom
should then speak up, but perhaps we might all agree to refrain from
formulating general embargoes on the very activity of formulating axioms. (015)
BS (016)
At 05:36 AM 1/5/2006, you wrote:
>I received the following offline comment, and I gave
>the same response I've been giving for the past
>several years.
>
>John Sowa
>
>-------- Original Message --------
>
>Nobody knows exactly how many theories will be needed:
>
>>But I don't have any good idea **how many** logically
>>different theories will in fact be required. I do have
>>a strong suspicion that it will not be as many as one
>>would suppose after a casual glance at the different
>>upper ontologies that people have proposed.
>
>But there are certain things that are pretty safe bets:
>
> 1. There will be categories called Time, Space, Object,
> Process, etc.
>
> 2. There will be some assumptions common to all the
> axiomatizations: time will have a before and
> after, and space will have 3 dimensions.
>
> 3. But beyond that, all bets are off. It would be
> a mistake to adopt situation calculus instead of
> pi calculus for reasoning about time; it would be
> a mistake to insist on either 3D or 4D treatments
> of space-time; it would be a mistake to insist
> that objects are "ontologically prior" to processes;
> it would be a mistake to say that a vase and the
> lump of clay from which it is made must be or must
> not be considered different entities.
>
>That's why the only thing you can insist on is a very
>sparse, very limited set of common axioms. At that
>level, you can't do much problem-oriented reasoning.
>
>For more detailed reasoning in specific applications,
>you need the problem-oriented modules or microtheories.
>
>John
>
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