Topological Ontology and Logic of Qualitative quantity

3. The Topological Notion of Qualitative quantity
Back in 1989, as a Research Associate at Institute for Philosophical Research at Bulgarian
Academy of Science, I have established the qualitative quantity as vocamen of my research
interests in philosophy or topological philosophy. In two papers “Quality of quantity”
(1989) 39 and “Quality and Time” (1990) 40 , I have focused on the resurgence of G.F.W.
Hegel’s category “qualitative quantity” historically left “inapparent” arguing that this
category is the real breakthrough from the cliche of the known law of dialectics – the the
law of transformation of quantity to quality and the appearance of the new quality as
qualitative leap.
Due to the gradual and continuous notion of qualitative quantity, linking Henri Poincare’s
Analysis Situs with Hegel’s qualitative quantity, I proposed the argument that the exhibit
form and notion of the Qualitative quantity is Topology and topological homeomorphism.
Today in the recent work on my PhD thesis I tend to link the exhibit form of Hegel’s
qualitative quantity with the topological cobordism. 41
Back in 1989, in my first article, based on the exploration of D'Arcy W. Thompson’s
(“Growth and Form”,1917) findings and examples, extracted from Hermann Haken 42 , who
is illustrating the qualitative quantity notion in the structural stability, I have argued that
topology is the field of qualitative quantity and topological homeomorphism is exhibit form
of this category. The Qualitative quantity is applicable to the complex dynamic systems as
complimentary method to the qualitative and quantitative approaches and methods in the
paradigm shift from Typological to Topological thinking (Jay Lemke).
From his reading of Hegel, Engels elucidated the three laws of dialectics in his “Dialectic of
Nature”. The second law of dialectics, the law of transformation, established by Engels is the
law of the passage of quantitative changes into qualitative changes. This law states that
continuous quantitative development results in qualitative "leaps" in nature whereby a
completely new form or entity is produced. This is how "quantitative development becomes
qualitative change". The new quality develops quantitatively through a step-by-step process
of quantitative changes, qualitative changes begin with the quantitative introduction of the
new quality into the quantitative development of the old measure. Qualitative changes
occur as leaps. This Engels’s law of transformation and the passage of quantitative changes
into qualitative changes, as all of the three laws of Engels’s dialectics become cliché in the
mode of thinking of quality and quantity. The three laws of dialectics are not only
oversimplified, but also misleading at best, establishing something quite self-evident, trivial
and commonplace. Gradualness and gradual changes which are not leading to turning
points, where one force overcomes the other and quantitative change leads to qualitative
change, remained inapparent just like Hegel’s dialectics of Qualitative quantity.
Approaching the domain of topology from the standpoint of the dialectics of qualitative
quantity, we should conclude that the interplay of quality and quality is associated with the
39 Borislav Dimitrov, “Quality of the Quantity”,“Philosophic Thought Magazine”, March, 1989, Institute of
Philosophical Sciences, Bulgarian Academy of Science
40 Borislav Dimitrov, “Quality and Time”, presented at the conference “The Fundamental Knowledge between
Ontology Dilemma and Cognitive Problems”, 1990, Institute of Philosophical Sciences, Bulgarian Academy of
Science
41 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 (2012):
http://ariadnetopology.org/Gadamer.pdf, Borislav Dimitrov, Cultural Phenomenology of Law and Topological
Approach to Law,(2012): http://ariadnetopology.org/1PDF.pdf
42
Hermann Haken, “Synergetics: Introduction and Advanced Topics”, 1983, Springer (Chapter 1.13.
Qualitative Changes: General approach, p. 434-435)
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