+ in fun r -> exists (shifted'' r)
+
+ fun bool_reader ->
+ let shifted'' r new_value =
+ let r' = fun var -> if var = 'x' then new_value else r var
+ in bool_reader r'
+ in fun r -> exists (shifted'' r)
+
+ This gives us a value for \[[∃x]], which we use like this:
+
+ <pre><code>\[[∃x]]<sub>reader</sub> ( \[[Qx]] )
+ </code></pre>
+
+ Contrast the way we use \[[∃x]] in GS&V's system. Here we don't have a function that takes \[[Qx]] as an argument. Instead we have a operation that gets bound in a discourse chain:
+
+ <pre><code>u >>= \[[∃x]] >>= \[[Qx]]
+ </code></pre>
+
+ The crucial difference in GS&V's system is that the distinctive effect of the \[[∃x]]---to allocate new pegs in the store and associate variable `x` with the objects stored there---doesn't last only while interpreting clauses supplied as arguments to \[[∃x]]. Instead, it persists through the discourse, possibly affecting the interpretation of claims outside the logical scope of the quantifier. This is how we're able to interpret claims like:
+
+ > If ∃y (farmer y and ∃x y owns x) then (y beats x).