Any experiments to back up these ideas?
On Wed, Mar 13, 2013 at 3:07 AM, YKY (Yan King Yin, 甄景贤) < [email protected]> wrote: > 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* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/3701026-786a0853> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- -- Matt Mahoney, [email protected] ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
