Topological Ontology and Logic of Qualitative quantity

Kairos, Chora and Topos as follow: "Chronochora", "Chronotopos", "Kairochora" and
"Kairotopos".
There are two notions of Time and two notion of Space in the Ancient Greek concepts of
time and space. The two temporal notion of Time are Chronos and Kairos. Chronos is the
quantitative Time and Kairos is the qualitative Time. And there are two spatial notion of
Space – Chora and Topos. Chora is the quantitative abstract notion of space and Topos is the
qualitative notion of space. The abstract space is Chora and the concrete place is Topos.
Aristotle defined Chronos quantitatively as the “number of motion with respect to the before
and the after”, which is a classical expression of the concept of (chronos) time as change,
measure, and serial order. The definition of Chronos is focused on an exact quantification of
time.
Following Aristotele analysis there are temporal and spatial pairs of chronos/kairos and
chora/topos, relationships. Kairos is the time that gives value thus quality. Kairos is
qualitatively defined. The result would produce the following:
- quantitative quantity - /in the domain of Chronochora – Abstract
Space and Abstract Time/;
- quantitative quality - /in the domain of Chronotopos -Meaningful
Place and Abstract Time/;
- qualitative quantity - /in the domain of Kairochora – Abstract Space
and Meaningful Time/;
- qualitative quality - /in the domain of Kairotopos – Meaningful Place
and Meaningful Time/.
This fourfold of infinities (in Hegel) could be expressed by the term or category of
COBORDISM - A cobordism between a single circle (at the top) and a pair of disjoint circles
(at the bottom).
In topological terms, the category of Qualitative quantity is a cobordism between a single
circle (at the top) and a pair of disjoint circles (at the bottom).
Cobordisms form a category whose objects are closed manifolds and whose morphisms are
cobordisms.
Cobordism had its roots in the attempt by Henri Poincare in 1895 to define homology
purely in terms of manifolds. Poincaré simultaneously defined both homology and
cobordism, which are not the same, in general. In mathematics, cobordism is a fundamental
equivalence relation on the class of compact manifolds of the same dimension, set up using
the concept of the boundary of a manifold. Two manifolds are cobordant if their disjoint
union is the boundary of a manifold one dimension higher. The name comes from the
French word bord for boundary.
The notion of cobordism is simple - two manifolds M and N are said to be cobordant if their
disjoint union is the boundary of some other manifold. 63
Given the extreme difculty of the classifcation of manifolds it would seem very unlikely that
much progress could be made in classifying manifolds up to cobordism.
63 See: Borislav Dimitrov, Logic and Hermeneutics Topo (logic) ally Approached - From Hans-Georg
Gadamer’s essay “The Idea of Hegel’s Logic” to the Topological Approach in-to Hermeneutics -
http://ariadnetopology.org/Gadamer.pdf
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