--- /dev/null
+Motivating types; motivating the Maybe monad
+============================================
+
+In [[a long footnote discussing Russell|readings/kaplan-plexy.pdf]],
+Kaplan 1989:496 poses a problem for the interaction of structured
+meanings with direct reference, and then offers a solution based on
+types.
+
+To grasp the problem, consider a structured-meaning theory of meaning,
+on which the meaning of natural language expressions are represented
+by objects that can have internal structure.
+
+ 1. The center of mass of the solar system is a point.
+
+Further suppose that the meaning of the DP in subject position in (1),
+namely, *the center of mass of the solar system*, has internal
+structure. For instance, suppose that the meaning of this DP is a
+structure that contains within it an object representing the meaning
+of *the solar system*, an object representing the relational concept
+denoted by *center*, and so on. It doesn't matter precisely what that
+structure is, as long as it has distinct internal parts.
+
+Kaplan names this complex object "Plexy". On Kaplan's assumptions,
+the name *Plexy* is directly referential, and refers to the complex
+object that represents the meaning of *the center of mass of the solar
+system*.
+
+ 2. Plexy is a point.
+
+Kaplan observes that sentences (1) and (2) have very different
+meanings. The sentence in (1) attributes a property to a location in
+space, and the setence in (2) attributes the same property to the
+referent of *Plexy*, which is a structured meaning. Since meanings
+need not be locations in space, it is easy to imagine judging (1) true
+and (2) false. As Kaplan puts it, the two sentences "speak about
+radically different objects".
+
+The problem is that on a structured meaning theory, the meaning of the
+sentence contains Plexy in the position corresponding to the argument
+of the predicate. Likewise, we might suppose that the contribution of
+a directly referential term is simply the object it refers to.
+Combining these two assumptions, we incorrectly predict that (1) and
+(2) denote the same structure, and therefore have exactly the same
+meaning.
+
+(Instead of using a sentence like (2), Kaplan constructs a different,
+more complicated expression that, he argues, refers to Plexy, but this
+nicety is not crucial to our discussion here.)
+
+Kaplan's solution is, in effect, to impose a type system on his
+grammar in such a way that structured meanings cannot be confused with
+the referent of a directly-referential term. He suggests that the
+meaning of a directly referential term always be marked by a special
+bit of structure that is unique to direct reference. More concretely,
+Kaplan suggets that instead of inserting the referent of a directly
+referential term directly into the structure of the sentence in which
+it occurs, we insert the singleton set containing that referent. As
+long as no complex structured meaning (that is not the meaning of a
+directly referential term) happens to be a singleton set, we have a
+solution. If *P* is Plexy, the meaning of (1) is `<P, point>`, and
+the meaning of (2) is `<{P}, point>`: radically different, as desired.
+
+In terms of the type systems we'll be developing over the next few
+weeks, the type of a DP will be a sum type: the disjoint union of the
+class of objects that a directly referential term can refer to, and
+the class of objects that can serve as the complex structure
+corresponding to a DP that is not directly referential.
+
+Kaplan goes on to use this solution to attack a different problem, the
+problem of non-referring names. Russell supposed that if a name had
+no referent (e.g., *Santa*), a sentence containing that name would
+have no meaning, since there would be no object to insert into the
+structure representing the meaning of that sentence. But on Kaplan's
+scheme, there is no problem: *Santa is hungy* would denote `<{},
+hungry>`.
+
+This second idea has some obvious flaws. For instance, it predicts
+that sentences that differ only in the choice of a non-referring name
+will have the same meaning. But it does not seem obvious that the
+sentence *Santa is hungry* does not mean the same thing as *Cupid is
+hungry*.
+
+Setting aside such objections, we will see over and over again the
+utility of Kaplan's strategy for representing the meaning of
+directly-referential expressions:
+
+ Kaplan's rule for directly-referential expressions:
+ a directly referential expression E contributes either
+
+ {} if there is no object that E refers to, or else
+ {P} if E refers to P
+
+In later weeks, we will call this technique the Maybe monad.
+
+
+Kaplan, D. 1989. "Demonstratives. InJ. Almog, J. Perry, & H. Wettstein
+(Eds.), Themes from Kaplan (pp. 481-563)."