From 3ed0f65ba08e4e5e95eb0e6175e4854859ce609c Mon Sep 17 00:00:00 2001 From: Chris Date: Wed, 22 Apr 2015 20:28:55 -0400 Subject: [PATCH] edits --- topics/week10_gsv.mdwn | 29 ++++++++++++----------------- 1 file changed, 12 insertions(+), 17 deletions(-) diff --git a/topics/week10_gsv.mdwn b/topics/week10_gsv.mdwn index 0775ae2e..8afe744e 100644 --- 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 - c true c false + c false c 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 - = ( {(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 @@ -437,12 +435,9 @@ Now we consider the second half: {(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 @@ -451,10 +446,10 @@ Now we consider the second half: = {(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 -- 2.11.0