1. {(w,g)}[∃x.man(x)]
- = {(w,g[n->a])}[man(x)] ++ {(w,g[n->b])}[man(x)]
- ++ {(w,g[n->c])}[man(x)]
- = {} ++ {(w,g[n->b])} ++ {(w,g[n->c])}
- = {(w,g[n->a]),(w,g[n->b]),(w,g[n->c])}
+ = {(w,g[x->a])}[man(x)] ++ {(w,g[x->b])}[man(x)]
+ ++ {(w,g[x->c])}[man(x)]
+ = {} ++ {(w,g[x->b])} ++ {(w,g[x->c])}
+ = {(w,g[x->a]),(w,g[x->b]),(w,g[x->c])}
-- Bob and Carl are men
2. {(w,g)}[∃x.woman(x)]
3. {(w,g)}[∃x∃y.man(x) and man(y)]
- 4. {(w,n,r,g)}[∃x∃y.x=y]
+ 4. {(w,g)}[∃x∃y.x=y]
Running the [[code|code/gsv.ml]] gives the answers.
--------------- ---------------
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