--------------- ---------------
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
-- 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
{(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
= {(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 possible
-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 have
+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