On Sun, Mar 10, 2013 at 8:29 AM, Jim Bromer <[email protected]> wrote:
> Let me speak about something that (I can delude myself into thinking) I
> know something about. The section, "Geometrization of Inference," is based
> on an primitive theory that semantics might be based on 'ontological
> subsumption'. The problem with this, from the viewpoint that conceptual
> relativism dominates conceptualization is that the supposed semantic space
> has to be relativistic. You can realize this in a number of ways.
> Definitions of generalizations are specifications. You can generalize
> across any group of things. The fact that you have to use concepts in
> order to define or analyze concepts shows that no concept could be
> considered without affecting it with the meanings or frames of the other
> concepts. So, for example, you can not view semantic space from a
> different vantage without reshaping the arrangement space. Although you
> might record statistics on how words or even concepts are used there is
> just no natural occurrence of semantic space that you can draw on.
>
> Since you need to use concepts in order to analyze concepts and since
> concepts typically affect other concepts when they are used together there
> is no such thing as a stable semantic space.
>
Thanks, I completely agree that the arrangement of semantic space is not
constant. The ontology is arranged like a set of basis vectors, but these
bases can move according to new conceptions. For example, we used to think
of humans as distinct from animals, but after evolution theory the concept
of "human" is brought closer to that of "animal". So there is always an
on-going interaction between the body of knowledge and the ontology upon
which we classify / organize the knowledge.
Of course, we hope that over time, our conceptual organization will
stabilize, punctuated by some revolutions of ideas =)
I was wondering if you could explain Cayley's diagram. Can you tell me
> what is meant by, "A sum of products is just the set union of such points,"?
>
Sorry I didn't explain sufficiently -- the Cayley diagram can represent any
products of the form a*b*c... etc. But it cannot represent terms like
a*b*c + d*e*f + .... So we need to find a way to represent 2 or more
points added together. I figured that it would be the set union of the
points. So they would appear on the diagram as *multiple* points.
For example, I want to represent:
john is paul's father, AND
paul is pete's father
so these would be 2 points in the diagram.
Now these 2 points would imply:
john is pete's grandfather.
which is yet another point in the diagram.
The implication order is:
point #1 + point #2 > point #3.
But so far I only have the geometric picture of one point > another point.
It's not clear what's the geometric picture of "a sum of points > another
point".... I'm still thinking about that =)
YKY
-------------------------------------------
AGI
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