Information Technology Reference
In-Depth Information
To sum up, the belief that of an agent A at a time t is knowledge at t for some
agent B from the second person perspective if, and only if, B is convinced at t that A
will behave according to .
2.3
The Third Person Perspective
The third person perspective is that of an observer who draws attention to the
dynamic of an individual A 's belief-system (i.e. what the salient set of beliefs related
to a belief are at any time) given the evolution of the situation in which the particular
belief is elicited. In particular, we have in mind two sort of contexts: one in which the
observer has actually witnessed the evolution of the situation and the reactions of A
(witness-case), and another in which the observer predicts what is going to happen
(prediction-case). We say that A 's belief that
shows a successful behavior for B from
the third person perspective at a time t if A 's belief that
˕
is successful for B at t from
the first person perspective (given the idea held by B of A 's belief-system), and the
evolution (witness-case) or natural evolution (prediction-case) of the situation does
not present a challenge to it, that is, the situation evolves in a way in which none of
the new items added to the set of salient beliefs undermines A 's belief that
˕
˕
.
Let us introduce an example in order to clarify our proposal:
A is a teacher in a school. He witnesses the following situation in the playground:
At the corner of the main building is student S1 . Running towards him is S2 . After a
couple of minutes S1 and S2 have moved out from the sight of the teacher who then
hears someone crying. The teacher believes that ' S1 is crying' (
˕
).
Suppose that the salient set of beliefs of A related to
˕
at the time the teacher sees
the scene t 0 is:
= {' S2 was running towards S1 ', 'Someone is crying', ' S2 hates S1 ', ' S2
is a violent boy', ' S1 has reported S2 's bad behavior', 'if S2 heard about the report, he
would hit S1 ', 'if S1 were hit, he would cry'}. In this case, on the one hand γ {' S2
has heard about the report'} ϕ, and hence ˕ is acceptable (see section 2.1), and on
the other hand, ¬
ʳ
˕
is not acceptable for A at the same time t 0 given
ʳ
. Thus the belief
˕
is knowledge for A at t 0 from the first person perspective. But is A 's belief also
knowledge for A at t 0 from the third person perspective?
The situation evolves in such a way that, when A hears the cry, he runs towards it.
Once there, at t 1 , A observes that S1 lies on the ground crying, while S2 is calmly
talking to someone else. A is puzzled. The fact that S2 is calmly talking to another
student causes the introduction into
' = γ {' S2
seems to be calmly talking to another student', 'after hitting a person one is excited'}.
The teacher would have needed more credulity at t 0 in order to get
ʳ
at t 1 of at least two new beliefs:
ʳ
out of the new
salient set of beliefs: γ {'S2 has heard about the report', 'S2 is pretending to be
calm'} ϕ. That is, d (˕, ʳ) < d (˕, γ ). In this case (witness-case) the belief that ˕ ,
was not knowledge at t 0 for the teacher from the third person perspective. The teacher
would not say at t 1 that he knew at t 0 that S1 was crying.
The previous example is, as we have just pointed out, a witness-case example. Let
us talk now for a while about the prediction-cases. In these cases the observer, the
evaluator of the belief, predicts the evolution of the situation. So the question to raise
is: What is the evolution which the observer will predict? When is a situation said to
˕
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