Topological Ontology and Logic of Qualitative quantity

The true resurgence of Hegel’s Qualitative quantity can be unfolded in the works of Charles
Sanders Peirce. The notion of Qualitative quantity and the presence of the Topological Peirce
could be discovered in Peirce’s Abduction, Peirce’s Theory of the Continuum and his
concept of Hypostatic abstraction. The Topological approach of Charles Sanders Peirce’s
qualitative-ness is recognized by recent research works 56 and giving us the ground to speak
about The Topological Peirce. The proposed qualitative quantity method of research is
relativistic approach based on the The Topological Hegel /after Arkady Plotinsky/, but not
opposing the pragmatism of Charles Sanders Peirce, positivism and postpositivism. Charles
Peirce is the Semiotical Partner for Qualitative quantity methods research due to the
topological notion of the category - qualitative quantity.
Topological approaches penetrated cybernetics and AI, after Warren McCulloch’s work “A
Heterarchy of Values Determined by the Topology of Nervous Nets".The interdisciplinary
amalgam of dialectics and cybernetics is recognized in the works of Gotthard Günther
(Gotthard Günther, “Cybernetics and the Dialectic Materialism of Marx and Lenin”,
published at http://www.thinkartlab.com) as an enlarged representation of a lecture
Gotthard Günther did deliver at the University of Cologne (Köln, Germany) July 17, 1964.)
The topological approaches are used widely in psychology after Kurt Lewin work
“Principles of topological psychology” 57 The topology of qualitative quantity could be found
in Jean Piaget’s Genetic Epistemology, especially in the known Piaget’s “topological primacy
thesis”. Piaget and Inhelder /1959/ claimed that the young child’s intristic geometry was
first of all topological and then, later, projective Euclidean. The term “topology of meaning”
emerged at the proceedings of the “Einstein meets Magritte” Conference, Brussels,
Belgium /1995/, introduced by R. Ian Flett and Donald H. McNeil in their paper “What’s
Wrong with this Picture Towards a Systemological Philosophy of Science with Practice.”
4. Topology and Qualitative quantity
Topology is a logico-mathematical theory that treats the scriptural aspects of place – a trait
– on the basis of the differential of continuous/discontinuous. This revision (given by Robert
Groome) is nothing other than a literal interpretation of Poicare’s description of topology as
a theory of “badly drawn figure”.
Robert Groome, from P.L.A.C.E., Santa Monica 58 , is the author of the original study
“Formalization of Hegel’s Phenomenology of the Spirit”. 59 3 In his study Groome proposed
and developed the thesis of topological Hegel, establishing that Hegel’s The Phenomenology
of the Spirit [Phänomenologie des Geistes] first appeared in 1807 under the title System of
Science. According to Groome, “Here, Knowledge [Wissen/Savoir] or Science [Wissenshaft]
has been called by Hegel a System or Manifold (Mannigfaltigkeit), which has both a
topological and philosophical sense.” Countering “the standard procedures that view the
notion of a Manifold philosophically, if not metaphorically”, Groome’s aim is to read and
construct its place topologically, both globally and locally, in a Theory. In proceeding in
56 See:
- Robert W. Burch, "A Peircean Reduction Thesis: The Foundations of Topological Logic". Texas Tech University
Press,Lubbock, TX, 1991;
- Helmut Pape, "Abduction and the Topology of Human Cognition" – http://user.unifrankfurt.
de/~wirth/texte/pape.html;
- Arnold Johanson, "Modern Topology and Peirce's Theory of the Continuum", Transactions of the Charles S.
Peirce Society, Vol.37, No..1, Indiana University Press, 2001,pp.1-12 http://www.jstor.org/pss/40320822.
57 Kurt Lewin work (1936) Principles of topological psychology. New York: McGraw-Hill.
58 http://lacanlosangelespsychoanalysis.com/
59 Robert Groome, “Formalization of Hegel’s Phenomenology of the Spirit”
http://www.lacanlosangelespsychoanalysis.com/classes/course/info.phpid=21
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