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definability of concepts
says that something is a member of, say, category
C
if it
possesses “a set of defining features to meet the nature or essence of C-hood.” To
distinguish
classical
and
nonclassical
concepts he gave the following definition:
Definition 20.
“A concept is said to be:
1. a reducible or classical one iff it denotes a reducible category [...] and
2. an irreducible or nonclassical one iff it denotes an irreducible category, for
example our concept of disease [...]. ” [70, 114]
It is well-known that ancient philosophers characterized categories as reducible con-
cepts and refering back to Bunge's
Iatrophilosophy
(see section 3.2.1) we notice that
also his approach tried to define the concept of disease by a finite number of proper-
ties. However, Sadegh-Zadeh emphasizes that “nearly all real-world categories are
irreducible ones and, according to our terminology introduced above, all concepts
denoting such categories are nonclassical concepts.”
Moreover, “in an irreducible category, there are no comon-to-all features because
both regarding their number as well as their intensity the features are unequally dis-
tributed over the category members to the effect that some members appear more
typical than other ones.” [70, 119] Again using his favorite example he asked to
“propose a defining set of features that are common-to-all members of the category
bird
embracing such diverse subcategoriesa as robin, sparrow, nightingale, crow,
bird of paradise, bird of prey, albatros, ostrich, emu, penguin, etc. You will not suc-
ceed because these innumerable bird types do not share a birdhood-estblishing fea-
ture set such as, for instance,
}
that would uniformly recur in all of them to define the nature of birdhood. Rather
they are characterized by only partially overlapping feature sets such as
{
has-feathers, has-a-beak, flies, chirps, lays-eggs, ...
{
A, B, C
}
,
{
B, C, D
}
,
{
C, D, E
}
,
{
D, E, F
}
,
{
E, F, G
}
and other ones in the folowing fashion:
Ta b l e 3 . 1
Some birds and their features
Robin
A B C
crow
BCD
eagle
C D E
ostrich
D E F
penguin
E F G
...
...
Although neighboring bird types in this chain have something in common, two
distant ones such as robin and penguin evidently have nothing in common. and most
interestingly, there is nothing common to all.” [70, 116]
It is understood that Sadegh-Zadeh linked these irreducible categories to Wittgen-
stein's concept of “familiy resemblances” that he suggested in the
Philosophical
Investigations
finally writing that we:
