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In-Depth Information
In this domain of human perception it helps to think of subjective probabilities as
expectations of particularly simple random variables called “indicators” [5]. Then,
the indicator of a hypothesis
H
is a constant,
I
H
,whichis1if
H
is true and 0 if
H
is
false. Now we can write:
I
H
)
In our case, and as said previously, the indicator
I
H
= “wealthy parents having a
healthy child” usually has an expectation
Ex
P
S
(
H
)=
Ex
(
(
I
H
)=
1, so the subjective probability
will be
P
S
(
1. On the other hand, when dealing with an autosomal recessive
disease, the indicator
I
H
= “carrier parents having a child that will enjoy a good
quality of life”, the expectation becomes
Ex
H
)=
(
I
H
)=
P
S
(
H
)
≤
1, although the real
probability
P
of this hypothesis equals exactly 0
75, as stated previously.
Subjective probabilities deserve another important remark: they differ from per-
son to person and some carrier parents will experience a
P
S
(
.
H
)=
0
.
9, while for
others it will be, for example,
P
S
(
2 or maybe less. Because now the prob-
ability is subjective, it contains a high degree of personal bias, so the expectation
of a physician about a given condition or disease can be, and usually it is, different
from the patient, patient's relatives or even the society, so we can see that subjective
probability is a personal perception, but plays and important role in medicine since
many human decisions rest on such type of information. We shall tackle again this
concept from another point of view in section 20.3 of this work.
H
)=
0
.
20.2
From Aristotle to Plato and Then Zadeh
There is no doubt about the influence that Aristotle has had not only in philosophy
but also in science, including health sciences and medicine along the history of the
western culture. Such an authority in the established way of thinking has brought
as a result the use of sharp classifications in every branch of science, that is, classi-
fications where the law of excluded middle holds. We can read an example of sharp
classification for the concept of “being a man” by Aristotle himself:
“It is impossible, then, that “being a man” should mean precisely “not being
a man”, if “man” not only signifies something about one subject but also
has one significance. ... And it will not be possible to be and not to be the
same thing, except in virtue of an ambiguity, just as if one whom we call
“man”, and others were to call “not-man”; but the point in question is not
this, whether the same thing can at the same time be and not be a man in
name, but whether it can be in fact.” [1]
In medicine, every type of symptom, state of the organism, disease, or therapy,
for naming just a few families of concepts used everyday by physicians, is catego-
rized into a sharp, clearly defined and bounded group, partition or classification. In
essence, an observable magnitude
x
belongs to a traditional set
S
of symptoms and
diseases, while a knowledge-based element
y
belongs to a traditional set
T
of treat-
ments. In this simple but conceptually significant model, medicine can be seen as a
function
f
that relates
x
i
symptoms and diseases to
y
j
treatments:
