Chinese Ontology

An Aperçu

Chinese ontology (cosmology) can be put into two main statements:

A. Everything in the world is changing.

B. The world, in which everything is changing, doesn't change.

This two main statements are designing a paradoxical constellation.


Hence,

1. The finiteness of the world is not closed but open.
Because of the changing statement (A) the finiteness (B) is not static.
"In a closed world, which consists of many worlds, there is no narrowness. In such a world, which is open and closed at once, there is profoundness of reflection and broadness of interaction." (The Book of Diamonds, Intro)

2. Everything in the world is connectable.
Because of the finite structure of the world, entities are accessible in many ways.

3. Connections are bi-directional.
Because of the finiteness there is no uni-directionality in linear time.

4. Bi-directionality is chiastic.
Because the world is changing, the way back is not exactly the same as the way forwards. This is defining the heterarchic grid structure of the world.

5. The modeling process of Chinese ontology is not phono-logocentric.
Because of the paradoxical character of the "ontology" it can not be represented by phono-logical statements of identity-based mathematics and logic.

Therefore,

6. Because it is written in logical sentences, this aperçu of a definition of Chinese ontology is a paradox metaphor.

7. A first operative description and formalization of Chinese ontology is proposed by the Diamond Theory, which is in a trans-phonological sense a paradox.

8. Diamond theoretic paradoxy is positively inscribed in Diamond Theory as the interplay, i.e., chiasm, between categories and saltatories. Saltatories are complementary to categories. Complementarity is not duality.

9. The structure of the interplay (chiasm) of categories and saltatories in Diamond Theory is defined by the proemial relationship.

10. The proemiality of the proemial relationship is inscribed as an interplay between order-, exchange- and coincidence relations, distributed over different loci.

11. Because of the finiteness of the world Diamonds have a location in it. The location (position) of Diamonds is inscribed by their place-designators.

Thus,

12. The self-referential paradoxy/parallaxy of the metaphor of Chinese ontology is realized by the operative calculus of Diamonds as an interplay between categories and saltatories of Diamond Theory.

The Complementary Blog: Diamond Strategies

Have a look at the complementary Blog to the Chinese Challenge Blog:

Rudy's Diamond Strategies.

The new Blog is presenting, step by step, new insights into the mathematical theory of Diamonds.


Chiasm (Categorification, Diamondization)

Diamond: 2-graphs with 2-structures

i) Data: 2-diagram C1–s,t––>Co/Co<–diff–C1 in 2-Set Objects in diamonds are involved into 2 operations: coincidence and difference. Coincidence is producing composition and therefore commutativity.
Differences are producing hetero-morphisms and therefore jumpoids.

ii) Structure: composition, identities + complement, differences

iii) Properties: unit, associativity + diversity, jump law

iv) Interaction: Chiasm between category and saltatory.

"In ordinary category theory we have 1-dimensional arrows ––>; in higher-dimension category theory we have higher-dimension arrows."

"...n-categories are studying morphisms between morphisms." Tom Leinster

Hence, Diamond theory is neither studying linear ordered arrows nor morphisms between linear ordered arrows but the complementarity of morphisms and hetero-morphisms, acceptional and rejectional morphisms, i.e., the relations between the operation of composition and its complementary morphisms.

In this sense, diamond theory is studying 2-dimensional, i.e., tabular categories, independent from the questions of n-categories or others.

Thus, diamond theory is the study of tabular categories as an interaction of categories and saltatories. Saltatories are the complementary diamond structures of categories.

The term interaction is correct because the interplay between categories and saltatories happens inside the diamond definition and is not only a meta-theoretical fact like the duality of categories in category theory.

Compositions as operations are not thematized in Category theory but only their result, which are new morphisms.

Diamond theory is thematizing the activity of the composition operator not as a morphogram but as a complementarity to the operator, implemented as a hetero-morphism.

Diamonds are thematizing the basic operation of category theory as such: the operation of composition. The thematization is modeled into the hetero-morphisms.

In a general setting of graphematic analysis of composition the morphogrammatics of the operator "composition" has to be taken into account, too. That is, the neither-nor gesture of categorical object and morphism has a double face: hetero-morphism and morphogram of composition.

As Categories can be generalized to n-Categories, Diamonds can be generalized to n-Diamonds.

Topics
Category Theory: object/morphism
n-Category: morphism/morphism
Diamond Theory: categories/saltatories.