From 1c16fa54d8d79a3f77d166cab7094bf894013f1b Mon Sep 17 00:00:00 2001 From: Chris Date: Mon, 16 Mar 2015 10:08:32 -0400 Subject: [PATCH] plexy --- topics/_week6_plexy.mdwn | 97 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 97 insertions(+) create mode 100644 topics/_week6_plexy.mdwn diff --git a/topics/_week6_plexy.mdwn b/topics/_week6_plexy.mdwn new file mode 100644 index 00000000..b1f94eaa --- /dev/null +++ b/topics/_week6_plexy.mdwn @@ -0,0 +1,97 @@ +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 ``, 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)." -- 2.11.0