and epistemic possibility).
An implementation in OCaml is available [[here|code/gsv.ml]]; consult
-that code for details of syntax, types, and values.
+that code for details of syntax, types, and values. [[An implementation
+in Haskell|code/gsv.hs]] is available as well, if you prefer.
Terms in this language are either individuals such as Alice or Bob, or
else variables. So in general, the referent of a term can depend on a
from the domain of discourse. Construct a modified infostate s' by
adjusting the assignment function of each possibility so as to map the variable x to a.
Then update s' with φ. Finally, take the union over the results of
-doing this for every object a in the domain of discourse.
+doing this for every object a in the domain of discourse. If you're
+unsure about this, examine the [[code|code/gsv.ml]].
Negation is natural enough:
We have elminated both possible worlds and possible discourses.
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
+their syntactic scope--needs to refined into a more nuanced understanding.
+Binding still occurs, but the extent of the syntactic scope of an existential
+has a detectable effect on truth conditions.
+
As we discovered in class, there is considerable work to be done to
decide which expressions in natural language (if any) are capable of
expressing which of the two translations into the GSV fragment. We
variable is assigned a discourse referent distinct from all previous
discourse referents.
-End of digression on pegs.
-
+The addition of pegs tracks an active discussion in the dynamic
+literature around the time of publication of the paper. Groenendijk
+and Stokhof (Two theories of dynamic semantics, 1989) noted that it
+was possible in DPL for information to be "lost".
+
+ 18. (∃x.P(x)) & (∃x.Q(x)) & R(x)
+
+If the two existentials happen to bind the same variable (here, "x"),
+then the second existential occludes the first. That is, at the point
+at which we evalute R(x), all of the assignment functions will be
+mapping the variable "x" to objects that have property Q. The
+information that there exist objects with property P has been lost.
+If you want your dynamic system to be eliminative---or in more general
+terms, if you want the amount of information embodied by an updated
+information state to be monotonically increasing---then this is a
+problem.
+
+A syntactic solution is to require that the variable bound
+by an existential to be chosen fresh.
+
+Vermeulen, Cees FM. "Merging without mystery or: Variables in dynamics
+semantics." Journal of Philosophical Logic 24.4 (1995): 405-450 offers
+a different approach, one based on *referent systems*. GSV's pegs are
+a referent system. In the pegs system, when (18) is processed, the
+information that there is an object that has property P is maintained
+in the information state. Curiously, however, there is still no way
+to refer to that object, at least, not with a variable, since there is
+no variable that is associated with the peg that points to the
+relevant object. So the information is present, but not accessible.
+
+That does not mean that there aren't other expression types that are
+able to latch onto peg. An intriguing suggestion based on an example
+in Vermeulen is that "former" might be able to provide access to a
+hidden peg:
+
+ 19. Someone entered. Someone spoke. The former was a woman.
+
+Presumably we want *the former* to be able to pick out the person who
+entered, whether or not the two existentials bind the same variable or
+not. If we allow "former" to latch onto the second most recently
+established peg, no matter whether there is a variable still pointing
+to that peg, the desired effect is achieved.
+
+But none of this is relevant for any of the explanations or analyses
+provide by the GSV fragment, and it is considerably simpler to see
+what their fragment is about if we leave referent systems out of it.