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author
Chris
<chris.barker@nyu.edu>
Thu, 23 Apr 2015 00:28:55 +0000
(20:28 -0400)
committer
Chris
<chris.barker@nyu.edu>
Thu, 23 Apr 2015 00:28:55 +0000
(20:28 -0400)
topics/week10_gsv.mdwn
patch
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diff --git
a/topics/week10_gsv.mdwn
b/topics/week10_gsv.mdwn
index
0775ae2
..
8afe744
100644
(file)
--- a/
topics/week10_gsv.mdwn
+++ b/
topics/week10_gsv.mdwn
@@
-391,7
+391,7
@@
two worlds.
--------------- ---------------
w: a true a false
b false b true
--------------- ---------------
w: a true a false
b false b true
- c
true
c false
+ c
false
c false
w': a false a false
b false b false
w': a false a false
b false b false
@@
-412,12
+412,10
@@
Let's see how this works out in detail.
-- existential introduces new peg
-- existential introduces new peg
- = ( {(w,g[x->a])}[closet(x)]
- ++ {(w,g[x->b])}[closet(x)]
- ++ {(w,g[x->c])}[closet(x)]
- ++ {(w',g[x->a])}[closet(x)]
- ++ {(w',g[x->b])}[closet(x)]
- ++ {(w',g[x->c])}[closet(x)])[◊guilty(x)]
+ = ( {(w,g[x->a]), (w',g[x->a])}[closet(x)]
+ ++ {(w,g[x->b]), (w',g[x->b])}[closet(x)]
+ ++ {(w,g[x->c]), (w',g[x->c])}[closet(x)]
+ )[◊guilty(x)]
-- only possibilities in which x is in the closet survive
-- the first update
-- only possibilities in which x is in the closet survive
-- the first update
@@
-437,12
+435,9
@@
Now we consider the second half:
{(w,g), (w',g)}[∃x(closet(x) & ◊guilty(x))]
{(w,g), (w',g)}[∃x(closet(x) & ◊guilty(x))]
- = {(w,g[x->a])}[closet(x)][◊guilty(x)]
- ++ {(w,g[x->b])}[closet(x)][◊guilty(x)]
- ++ {(w,g[x->c])}[closet(x)][◊guilty(x)]
- ++ {(w',g[x->a])}[closet(x)][◊guilty(x)]
- ++ {(w',g[x->b])}[closet(x)][◊guilty(x)]
- ++ {(w',g[x->c])}[closet(x)][◊guilty(x)]
+ = {(w,g[x->a]), (w',g[x->a])}[closet(x)][◊guilty(x)]
+ ++ {(w,g[x->b]), (w',g[x->b])}[closet(x)][◊guilty(x)]
+ ++ {(w,g[x->c]), (w',g[x->c])}[closet(x)][◊guilty(x)]
-- filter out possibilities in which x is not in the closet
-- and filter out possibilities in which x is not guilty
-- filter out possibilities in which x is not in the closet
-- and filter out possibilities in which x is not guilty
@@
-451,10
+446,10
@@
Now we consider the second half:
= {(w',g[x->c])}
= {(w',g[x->c])}
-The result is different. Fewer possibilities remain. We have
one of
-
the possible worlds (w is ruled out), and we have ruled out possibl
e
-discourses (x cannot refer to Alice). So the second formula is more
-informative.
+The result is different. Fewer possibilities remain. We have
+
eliminated one of the possible worlds (w is ruled out), and we hav
e
+eliminated one of the possible discourses (x cannot refer to Alice).
+
So the second formula is more
informative.
One of main conclusions of GSV is that in the presence of modality,
the hallmark of dynamic treatments--that existentials bind outside of
One of main conclusions of GSV is that in the presence of modality,
the hallmark of dynamic treatments--that existentials bind outside of