Topological Ontology and Logic of Qualitative quantity

The roots of Hegel’s Qualitative quantity and the presence of the modern category of
Qualitative quantity can be unfolded in the works of Charles Sanders Peirce. Peirce arrived
at his own system of three categories after a thoroughgoing study of his predecessors, with
special reference to the categories of Aristotle, Kant, and Hegel. The names that Peirce used
for his own categories varied with context and occasion, but ranged from reasonably
intuitive terms like quality, reaction, and representation to maximally abstract terms like
firstness, secondness, and thirdness, respectively.
The influence of German tradition and especially of Hegel in Peirce categorical system is
widly recognized. 67 The prevalence in Peirce’s thinking of Kantian and Hegelian resources
are well illustrated in his early essay “On a New List of Categories”. Peirce’s argument here
patently draws on Kantian concepts of categorial analysis as a means of distinguishing
ontological realms, although the categories he proposes, here denominated Quality,
Relation, and Representation, are of very different character from Kant’s. Instead, this triadic
scheme of categories seems clearly, if roughly, correlate with the three movements of the
Hegelian dialectic (considered as Being, Negation, and Mediation); in later formulations,
Peirce even identifies his third category (in one of its aspects) with mediation (e.g., EP
2.183, in the fourth Harvard Lecture [1903]).
The category of Qualitative quantity is a sign, a sign of gradualness, a topological sign. The
aspects of the Qualitative quantity involve not the dyadic relations typical for the physical
sciences, but the triadic relations of the semiotic sciences. The interplay of qualitative
andquantitative in the qualitative quantity is the interplay of the predicates of predicates.
As Peirce asserted:
“I will now say a few words about what you have called Categories, but for which I prefer
the designation Predicaments, and which you have explained as predicates of predicates.” 68
I will direct to the Qualitative quantity with the known Peirce’s expression – “That
wonderful operation of hypostatic abstraction”:
“That wonderful operation of hypostatic abstraction by which we seem to create entia
rationis that are, nevertheless, sometimes real, furnishes us the means of turning predicates
from being signs that we think or think through, into being subjects thought of. We thus
think of the thought-sign itself, making it the object of another thought-sign.” 69
66 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
67 See: Richard S. Beth, “On the Recent German reception of Peirce, with emphasis on Habermas”,
Congressional Research Service (U.S.A.), paper prepared for delivery at the Sixth Pan-European International
Relations Conference of the Standing Group on International Relations of the European Consortium for
Political Research, Turin, Italy, September 12-15, 2007
68 Charles Sanders Peirce, p. 522, "Prolegomena to an Apology for Pragmaticism", The Monist, vol.XVI, no.4,
Oct. 1906, pp. 492-546, reprinted in the Collected Papers vol 4, paragraphs 530–572, see paragraph 549.
69 Charles Sanders Peirce, p. 522, "Prolegomena to an Apology for Pragmaticism", The Monist, vol.XVI, no.4,
Oct. 1906, pp. 492-546, reprinted in the Collected Papers vol 4, paragraphs 530–572, see paragraph 549.
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