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If
there exist
H ,{
D
1
,...,
D
n
},H ,
similar
and West Europeans
such that
the
H ,{
,...,
},H ,
,
structure
D
1
D
n
similar
West Europeans
is a fuzzy prototype re-
D
H
semblance frame,
then
the family
of fuzzy sets in
is a fuzzy prototype resem-
blance category.
From this result and
Hypothesis 2
it follows
Hypothesis 1
!
3.9
Outlook: A Fuzzy Structuralist View on Scientific Theories
In order to give an introduction to Kazem Sadegh-Zadeh's work as a philosopher
of medicine I have often and interchangeably employed the so-called “structuralist
approach” or “Metastructuralism” to define important concepts in Analytical Phi-
losophy of Medicine. In this vein I quoted already in section 3.5.1 Sadegh-Zadeh's
definitions of a
(basic) fuzzy structure
,a
fuzzy structure
,a
metric space
,a
Zadeh
structure
and a
Zadeh space
and in section and in section 3.8 I continued with the
definitions of a
fuzzy prototype resemblance frame
and a
fuzzy prototype resem-
blance category
. The reader may have a look to the preface in this volume to have
more details on the framework of this approach to philosophy of science!
With this “structuralist view” we are able to axiomatize scientific theories in a
precise way without recurring to formal languages. This approach, also called nowa-
days “Metastructuralism”, uses only informal logic and informal set theory. When
I wrote my Ph.D thesis on “Probabilistic Structures in Quantum Mechanics” [75]
using this structuralist approach, I already thought about the possibility of “fuzzify-
ing” this approach. In the nineties I did not know that Kazem Sadegh-Zadeh, already
a well-known philosopher of medicine then, used this structuralist approach, Later,
when I started my work on history and philosophy of the theory of Fuzzy Sets, I
also considered the developments of the first Fuzzy systems in medicine [76, 77].
In 2006 I visited Kazem Sadegh-Zadeh at home in Tecklenburg, Germany and
during our discussions we also thought on the fuzzification of the “structuralist
view” in philosophy of science into a “Fuzzy structuralism”. We wondered why no-
body ever used fuzzy sets and fuzzy relations instead of usual sets and set relations
to reconstruct scientific theories! Then we started thinking on fuzzifications of (par-
tial (potential)) models of scientific theory elements and some of Sadegh-Zadeh's
considerations to this subject found their place in his
Handbook on Analytical
Philosophy of Medicine
[71].
Acknowledgement.
The author warmly thanks Prof. Dr. Kazem Sadegh-Zadeh and his wife
Maria Klein for help during writing this chapter. He also thanks Marco Elio Tabacchi for
discussions and valuable comments and for making figure 3.11 (a) available. Work leading to
this paper was partially supported by the Foundation for the Advancement of Soft Computing
Mieres, Asturias (Spain).
