Tuesday, November 08, 2005
First bead from the Lajitas Studio [57] ß
BCNGroup Glass Bead Game Index [index]
Outline of Work to be done on
Learning Theory and the Core Liberal Arts Curriculum
Home
Overview,
the use of an ontological model
The outline of an alternative curriculum in mathematics is given at { [1] }.
This alternative curriculum supports the extension of contemporary mathematics to the ontological sciences [2].
The basic formalism for ontological science is the graph, represented as a set of triples
{ < a , r , b > }
where the referent “a” and “b” are “topics of discourse” and “r” is a relational category.
Our proposed core liberal arts curriculum assumes that ontological models are to be adopted to supplement classical models of physics, chemistry and biology. Ontological models may provide additional foundation for the study of complexity in living systems. Classical mathematics provides the foundation to this extension of formalism.
A Core Liberal Arts Curriculum in the mathematical and ontological sciences is introduced with the help of a theory of learning. (next bead [1] )
[1] http://www.ontologystream.com/beads/QuestionOfAccess/AQA.htm
[2] The ontological sciences are based on set theory and category theory. Some scholars suggest that ontological sciences allow a useful representation of human knowledge. The issues are subtle and interesting. For example, foundational elements to the philosophy of mathematics can be exposed and discussed. The way that the exposure occurs can be “from a member of the class” rather than “from the textbook”. These elements expose to the student issues related to human cognition and reasoning behavior. Ontological modeling is now used in business and government. Over the past decade, ontological modeling has become more important in social, biological and other soft sciences. Library science and computer science are merging in a way that promises to help index and validate the information that is available due to the World Wide Web. The ontology standards developed by DARPA (Defense Advanced Research Project Agency) science support the development and wide use of ontological models. A public model for “semantic technology” adoption by US Customs on commodity transport, is available at { [2] }.