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intrinsically recursive, due to its ability to generate two contrary statements, P and
not-P, that is, Statements 5.16 and 5.17.
Finally, it should be pointed out that, if not all contraries are complementary (as I
originally thought in contrast to the views of Kelso and EngstrØm (2006) and Barab
(2010)), there must be at least one other relation operating between contraries. In
fact, there may be at least three noncomplementary relations operating between
contraries:
1. SUPPLEMENTARITY ¼ C is the sum of A and B (e.g., energy and matter).
2. DUALITY
A and B are separate entities on an equal footing (e.g., Descartes'
res cogitans and res extensa ).
3. SYNONYMY
¼
A and B are the same entity with two different labels or names
(e.g., Substance and God in Spinoza's philosophy; the Tao and the Supreme
Ultimate in Lao-Tzu's philosophy).
¼
5.2.5 Fuzzy Logic
There are two kinds of logic - classical (also called Aristotelian, binary, or
Boolean) logic where the truth value of a statement can only be either crisp yes
(1) or no (0), and multivalued logic where the degree of truthfulness of a statement
can be vague or fuzzy and assume three or more values (e.g., 0, 0.5, and 1). Fuzzy
logic is a form of multivalued logic based on fuzzy set theory and deals with
approximate and imprecise reasoning. In fuzzy set theory, the set membership
values (i.e., the degree to which an object belongs to a given set) can range between
0 and 1 unlike in crisp set where the membership value is either 0 or 1. In fuzzy
logic, the truth value of a statement can range continuously between 0 and 1. The
concept of fuzziness in human reasoning can be traced back to Buddha, Lao-tze,
Peirce, Russell, Lukasiewicz, Black, Wilkinson (1963), and others (Kosko 1993;
McNeill and Freiberger 1993), but it was Lotfi Zadeh who axiomatized fuzzy logic
in the mid-1960s (Zadeh 1965, 1995, 1996a).
Variables in mathematics usually take numerical values, but, in fuzzy logic, the
non-numeric linguistic variables are often used to express rules and facts (Zadeh
1996b). Linguistic variables such as age (or temperature) can have a value such as
young (warm) or old (cold). A typical example of how a linguistic variable is used
in fuzzy logic is diagrammatically illustrated in Fig. 5.6 .
5.2.6 Fuzzy Logic and Bohr's Complementarity
In Sect. 5.2.4 , it was shown that the principle of Bohr's complementarity embodies
the principle of recursivity as well, which may be seen as an example of the
intertwining among principles as symbolized by the dark and white objects in the
Yin-Yang diagram (Fig. 5.4 ). Bohr's complementarity exhibits
fuzziness.
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