Topological Ontology and Logic of Qualitative quantity

of Leonard Euler and later with the works of Henri Poincare, springs the fluid of one
postmodern science, the science of topology.
Topology challenged and changed the conditions and the grounds of “hard” sciences by
redefining the means of construct, suggesting that intrinsic properties were no longer
sufficient to describe a figure. In topology geometrical figures like circle, triangle and
square are the same.
This character and role of “Analysis situs” is the reason to define topology as postmodern
science. The last development of topology and its applications has proved her role to make
meaningful, qualitative statements and analysis not only to the mathematical objects but
also to the cultural and social dynamics.
Social Topology and Philosophical Topologies are the fruits of this postmodern mathematics.
Topology stems from the need to overcome the traditional, “solid” division of knowledge,
typical of Western culture, which goes back to the contrast between philosophy seen as
episteme (Plato, Aristotle), and philosophy seen as rethoric (Isocrates), right to the Hegelean
and later Diltheyan distinction between the sciences of nature and those of the spirit.
The phenomenom of understanding is the domain of hermeneutics. In the sense of Bauman,
Sociological Hermeneutics is about the understanding and interpretation of sociality in the
liquid times and places as toposes of Liquid modernity. Bauman’s model of Liquid Modernity
and his sociological hermeneutics could be integrated with the tools of topology and
topological approach to cultrual dynamics and social understanding.
Urgen Klüver and Christina Klüver with their book “Social Understanding: On
Hermeneutics, Geometrical Models and Artificial Intelligence” (2010) proposed an analysis
of hermeneutical problems by mathematical models (in what they defined as Hermeneutical
AI, something more than metaphor) aiming to bridge the gulf between the science and the
humanities. According to Klüver and Klüver, topology is the most influetial factor to the
dynamical beheviour of the complex system. (p.120)
The topological approach to social science could be traced back to Kurt Lewin’s study
“Principles of Topological Psychology” (1936) and followed trough the era of
postmodernity in the works of philosophical topologies (Arkady Plotinsky). In sociology, the
so called topological sociology or social topology was developed by Gregory Bateson, and
also evident in works of anthropology Levi-Strauss and Edmund Leach.
John Law and Annemarie Mol’s study “Regions, Networks and Fluids: Anaemia and Social
Topology” (2010) discusses the opportunity to add to the well known types of social space
or topological forms of spatiality – “regions” and “networks”, mobilized in social theory, the
third kind or form of social space called “fluid spatiality”.
Law and Mol establishes that “sometimes social space behaves like a fluid…and flow...the
space with which we are dealing is fluid.”
Bauman himself underlined the network characteristic of sociality.
Spatial or Topological thinking of Modernity – Fluid Modernity – presupposes the concept
of Relational Space. The relational thinking about space and time originated with Leibnitz’s
works in the non-Eucledean geometry. Space is always in a process of becoming. Space
could be seen as a verb, rather than a noun. Space is doing. Space is practiced, space is
experiencing. Verb-a-tizing time and space is timing and spacing.
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