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We use in e) the fact th
possible worlds satisfying
that I add to my set of belie
will be also added, items th
case, for example, of 'John
brave', and so on). On the
'John is at the beach' the ad
smaller (observe for instan
this kind of expeditions to t
go to the beach). It seems th
adds, and thus the smaller
using here. So if X = {'Joh
we should expect to get is
beliefs at the moment.
(·,·) is of special impor
deficit of a belief
given
Definition 4., will play an im
to which we devoted this s
belief is justified?
hat the more the conditions we add, the smaller the set
the conditions is. Let us explain how we use it. Imag
efs 'John is in Antarctica', then together with it other ite
hat somehow were implied by the previous one (this is
n must have access to this kind of expeditions', 'John
other hand, if I rather decide to add to my set of bel
dditional set of items that I will also need to include will
nce, that I already believed before that 'John has access
the beach', and that John does not really need to be brav
hen that the less plausible a belief is, the more condition
the set of possible worlds will be, and this is what we
hn is at the beach'} and Y = {'John is in Antarctica'}, w
that e(
||
|Y|)
e(
||
|X|), where
is my salient se
t of
gine
ems
the
n is
liefs
l be
s to
e to
ns it
are
what
et of
rtance in order to introduce, in Definition 3., our so cal
the salient set of beliefs
related to it
, which in its tu
mportant role to give an answer to the first of the questi
section: When would a person having a belief say that
lled
urn,
ions
the
Γ
,
,
⊆ Γ
, not-empty salient sets of beliefs rela
ectively,
and
, and
S
a system of Grove spheres.
f
given
. We establish the following relation betw
Definition 3.
Let be
,
to but not containing, respe
call
d
(
,
) the
deficit of
deficits:
a)
If
and
are
acceptab
d
(
,
)
ated
We
ween
ble
beliefs, then:
d
(
,
,
) iff
Y s.t.
(X,
)
(Y,
), where
X
X is a
witness
of the a
acceptability of
relativ
b)
If
is a not an
acceptab
acceptability of
relative to
, and Y is a witness of
ve to
'.
ble
belief, then:
the
d
(
,
)
d
(
,
)
Definition 4.
Let be
does not include
, and
S
if
is
acceptable
for
A
a
justified', if
is justified fo
Intuitively, the deficit of
one's salient set of beliefs
below when we discuss the
just see how this definition
of the section. In it,
is th
set {'ten boys (
b
1
, ...,
b
10
) an
the children fell down'},
an
Γ
,
⊆ Γ
the salient set of beliefs related to
wh
a system of Grove spheres.
.
is
justified
for
A
at
t
, and
d
(
,
) <
d
(¬
,
). We will say at
t
that '
or us at
t
.
f
is the amount of credulity one needs to infer
fr
s related to
,
. We will come back again to this i
e third person perspective on knowledge. For now, let
n works given the example we introduced at the beginn
e belief that 'one of the boys has fallen down'. Let
be
nd one girl were running', 'now someone is crying', 'one
nd let
S
be a system of Grove spheres. Observe that gi
hich
at
t
is
rom
idea
t us
ning
the
e of
iven
