Topological Ontology and Logic of Qualitative quantity

Name:
Firstness.
Secondness.
Thirdness.
Typical
characterizato
n:
Quality of feeling.
Reaction,
resistance,
(dyadic) relation.
Representation,
mediation.
As
universe
of
experienc
e:
Ideas,
chance,
possibility.
Brute facts,
actuality.
Habits,
laws,
necessity.
As
quantity:
Vagueness,
"some".
Singularity,
discreteness,
“this”.
Generality,
continuity,
"all".
Technical
definition:
Reference to a
ground (a
ground is a
pure
abstraction of a
quality).
Reference to a
correlate (by its
relate).
Reference to an
interpretant*.
Valence,
"adicity":
Essentially
monadic (the
quale, in the
sense of the such,
which has the
quality).
Essentially dyadic
(the relate and
the correlate).
Essentially triadic
(sign, object,
interpretant*).
*Note: An interpretant is an interpretation (human or otherwise) in the sense of the product
of an interpretive process. (The context for interpretants is not psychology or sociology, but
instead philosophical logic. In a sense, an interpretant is whatever can be understood as a
conclusion of an inference. The context for the categories as categories is phenomenology,
which Peirce also called phaneroscopy and categorics.) 79
Same as the the Topological Hegel’s Qualitative quantity, Charles Sanders Peirce’s
Contributions seems ignored by both the analytic philosophers and the so-called
Continental philosophers. Rediscovering the topological forfold of quality and quantity in
Peirce could be an promising direction for the 21st century in establishing a foundation for
unifying and relating the insights of multiple branches of cognitive science (linguistics,
philosophy, psychology, and artificial intelligence).
Yu, Chong Ho, in his research paper – “Abduction Deductio Induction Is there a Logic of
Exploratory Data Analysis” 80 directed the philosophical notions introduced by Charles
Sanders Peirce as helpful for researchers in understanding the nature of knowledge and
reality:
“In Peircean logical system, the logic of abduction and deduction contribute to our
conceptual understanding of a phenomenon, while the logic of induction adds quantitative
details to our conceptual knowledge. Although Peirce justified the validity of induction as a
self-corrective process, he asserted that neither induction nor deduction can help us to
unveil the internal structure of meaning. As exploratory data analysis performs the function
as a model builder for confirmatory data analysis, abduction plays a role of explorer of
viable paths to further inquiry. Thus, the logic of abduction fits well into exploratory data
analysis. At the stage of abduction, the goal is to explore the data, find a pattern, and suggest
a plausible hypothesis; deduction is to refine the hypothesis based upon other plausible
premises; and induction is the empirical substantiation.” 81
I will summarize paraphrasing the conclusion of Alex Yu /Yu Chong Ho/ that both
qualitative and quantitative research methods have different merits and shortcomings such
79 http://en.wikipedia.org/wiki/Categories_(Peirce)#cite_note-cenopythagorean-7
80 Yu, Chong Ho, “Abduction Deductio Induction Is there a Logic of Exploratory Data Analysis, presented
at the Annual Meeting of American Educational Research Association, New Orleans, Louisiana, April, 1994 -
http://www.creative-wisdom.com/pub/Peirce/Logic_of_EDA.html
81
Ibid.
37