Topological Ontology and Logic of Qualitative quantity

David Gray Carlson’s “A Commentary on Hegel's Science of Logic” is not only the first
English language full commentary on the monumental The Science of Logic, but it is
considered a major advancement in the study of Hegelian philosophy. Carlson has devised a
system for diagramming every single logical transition that Hegel makes, many of which
have never before been explored in English. The topological approach in Hegel’s Science of
Logic is evident in Carlson’s diagrams for clarifying the argumentative structure of each
move of the text in the fashion of complicated Venn diagram called a Borromean Knot
/Lacan’s famous Borromean knots/. The “inapparent” Hegel and topological notion of his
philosophy is revealed by Carlson as we read in the publisher’s review of the book: “The
author has devised a system for diagramming every single logical transition that Hegel
makes, many of which have never before been explored in English. This reveals a startling
organizational subtlety in Hegel's work which heretofore has gone unnoticed.
In the course of charting Hegel's logical progress, the author provides a vigorous defence
and thorough explication of unparalleled scale and scope.” Carlson’s diagrams are really
evoking the topological qualitative quantity of the Lacan’s famous Borromean knot, where
no one of the rings is directly tied to the other, but if you cut one of the rings the other two
slip away. The qualitative quantity is the third ring linked with quality and quantity in the
measure and if one cut off the qualitative quantity, the notion of the two – quality and
quantity will remain uncomplete and non-topological.
In his “Hegel’s Dialectic” /1976/, Gadamer asserts that Hegel’s approach to logic and indeed
his whole style of writing is ‘‘tautological’’. In the essay “Hegel and the Dialectic of the
Ancient Philosophers” in his “Hegel's Dialectic”, Gadamer maintains that a philosophical
statement is very different from ordinary empirical statements. In the empirical statements,
the predicate always leads us to ‘‘something new or different’’, but in a philosophical
statement, the predicate always leads us back to a deeper reflection of the subject itself, such
that ‘‘to ordinary ‘representative’ thinking a philosophical statement is always something like
a tautology; the philosophical statement expresses an identity’’.
8. Towards the merger between the categories of quality and quantity in the
Hegelian Concepts, and the category theory as an area of study in
mathematics and its branch categorical logic
The debate over human infinity between Alain Badiuo and Gadamerean hermeneutics could
be seen as debate over conceptual infinity and rise the question:
Are there grounds towards this merger between the categories of quality and quantity in the
Hegelian Concepts, and the category theory as an area of study in mathematics and its
branch categorical logic
Category theory is an area of study in mathematics that examines in an abstract way the
properties of particular mathematical concepts, by formalising them as collections of objects
and arrows (also called morphisms), where these collections satisfy some basic conditions.
Many significant areas of mathematics can be formalised as categories, and the use of
category theory allows many intricate and subtle mathematical results in these fields to be
stated, and proved, in a much simpler way than without the use of categories. In 1942–45,
Samuel Eilenberg and Saunders Mac Lane introduced categories, functors, and natural
transformations as part of their work in topology, especially algebraic topology. Their work
was an important part of the transition from intuitive and geometric homology to axiomatic
Cardozo School of Law, 2004, Working Paper No. 84
42 David Gray Carlson, A Commentary on Hegel's Science of Logic, Palgrave Macmillan,
February 2007
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