Saturday, January 2, 2016

2015 year in review

Within the year 2015 it was realized that it can be useful to study pure set theory. By studying pure set theory we are also dealing with pure ontology. We are classifying sets entirely in terms of their own properties as sets. We can use set systems in order to define preorder containment families and alexandrov families which correspond to one another. We can also define dependency families in accordance with this process. Dependency families can be defined as the join representations of certain preorder containment families. Though we can deal with sets of sets as a particular case we can also deal with sets of sets of sets. These allows us to deal with structures which we could not effectively define simply with sets of sets. In this way we are still dealing with pure ontology as we are defining sets entirely in terms of sets. As we create a pure ontology dealing with sets and classes defined entirely in terms of themselves we can later extend this ontology to deal with particulars but in the end the pure ontology is the foundation of this.

No comments:

Post a Comment