Re: lattice of ontology
On Thu, Dec 22, 2005 at 10:45:53PM +0200, Azamat wrote:
> John wrote:
> ''In a previous note, I compared it to the integers, but that led to too
> many confusing associations. Therefore, I'll give another analogy: the
> coordinates of latitude and longitude on the earth.''
>
> In making a poem, ''the command of metaphor is the mark of genius'', and I
> know here nobody who can overpass John in this ability. But we are trying
> to make the science asking for a strict language and precise description
> and prediction.
>
> There is the world and its abstract, ontological representation,
> intermediated with mathematical theories and logical formalisms and
> theoretical sciences, all operating such conceptual tools as models and
> schemas, diagrams and graphs, theoretical models and generic theories, and
> all distinguished by the definiteness of the sense and scope of the
> conceptual representations. Depending on the starting point of analysis of
> thing, from abstract structures to factual realities, or vice versa, we
> choose either semiotic or ontological interpretations along the general
> way: The Real World < Ontology < Mathematics < Logic < Theoretical Science
> < Empirical Science < Engineering and Technology < Applications.
>
> We are not at opposite poles. It is plain that you are looking for some
> sort of an open-ended reference frame for theories to be functioning like
> as a general context for determining the meaning of a construct, or the
> space-time frame for measuring the position of a physical object. Extending
> your analogy of the globe grid, to determine the location of some place on
> the Earth's surface, your need the Poles (North and South), the prime
> meridian (at Greenwich) and the prime parallel (the Equator). So what all
Sorry to jump into the middle of this, I may have missed something in
previous messages, but here goes:
It's not clear to me that John is looking for a "reference frame" in this
sense. A lattice only needs to be a poset with meet and join. I.e., it
needs a sense of direction, and ... (but I don't want to push this
metaphore to the limit (pun intended)).
Somehow the following annecdote seems relevant: I was once (long long ago)
at an after hours seminar given by E.T. Bell on some aspect of number
theory. Prof. Bell had a minor reputation as a science fiction writer as
well as a mathematician. One of the grad students asked him "Do the
Martians know about prime numbers?" After a moment, Prof. Bell answered --
"They certainly have radar, but I doubt that they have prime numbers."
> the constructs, generic, specific and particular, require is the Entity
> Reference Frame in which all things are located as much as the space-time
> continuum determines all the physical events.
> At the first place, it is required to put up a comprehensive lattice of the
> classes of entities and relationships, logically followed with a lattice of
> constructs (concepts, predicates or theories) and well-founded with a
> consistent set of ontological, factual and semantic axioms.
This sounds like a pretty thorough ontology. Seems to me what is needed is
the partial order relation, a way to determine joins and meets, and maybe
algorithims for upward and downward movements.
>
> Regards,
> Azamat
>
[snip]
Best,
John Velman