A similar point is familiar from discussions in the lingusitics
literature concerning discourse anaphora.
- 1. a. A woman arrived.
+ 1. a. A woman arrived.
b. She spoke.
c. "a woman" == "she": OK
- 2. a. She spoke.
+ 2. a. She spoke.
b. A woman arrived.
c. "a woman" == "she": nearly impossible
describing a situation in which the same woman who entered spoke. In
contrast, in discourse (2), it is much more difficult---in fact,
barring time travel, nearly impossible---to interpret the situation as
-describing two events involving a single person.
+describing two events involving a single person.
The standard explanation is that the use of an indefinite such as "a
woman" creates a new discourse referent, which a pronoun such as "she"
natural language meanings are isomorphic to computer programs. A
closely related version of this claim is the Curry-Howard isomorphism,
which establishes a parallel correspondence between logical
-derivations and programs.
+derivations and programs.
One consequence of this correspondence is that it makes sense to think
of interpreting an expression in natural language in the same terms as
logical connectives of classical logic, expressed in the form of a
standard truth table:
- A B A&B
- -----------
+ A B A and B
+ --------------
T T T
T F F
F T F
they are neither true nor false. Certainly (5) is not true, and
saying that it is false appears to commit you to believing that its
negation is true, which is not a commitment that everyone is willing
-to make.
+to make.
Given that a partial-function approach to presupposition failure is
coherent, let's consider one way to extend classical conjunction:
- p q p&q
- --------------
+ p q p and q
+ -----------------
a. T T T
b. T F F
c. F T F
So far, so good. Nothing so far undermines the static view. But now
consider the two remaining possibilities, one by one, starting with
line (h). Here is a concrete sentence fitting the pattern addressed
-by line (h), `F&#`:
+by line (h), `F and #`:
6. The sun is green and the King of France is bald.
realizes that the first conjunct is false. In fact, she can simply
stop listening as soon as she hears "The sun is green and...". No
matter whether the second conjunct is well defined, the conjunction as
-a whole must be false.
+a whole must be false.
7. The King of France is bald and the sun is green.
embodies the following processing strategy: if the status of the first
conjunct reliably determines some aspect of the status of the
conjunction as a whole, let the value of the left conjunct control the
-outcome.
+outcome.
To be sure, it would also be coherent to choose a fully symmetric
-truth table by replacing line (h) with one that maps `F&#` to `#`, or
-by replacing line (i) with one that maps `#&F` to `F`. With respect
+truth table by replacing line (h) with one that maps `F and #` to `#`, or
+by replacing line (i) with one that maps `# and F` to `F`. With respect
to natural language, of course, which truth table is a better match
for a given natural language is an empirical question, and not one
that can be settled by logical argument. If native speakers behave as
but in the material implication `F --> ?`, the outcome is `T` no
matter what the value of `X` turns out to be.
-[to be added: citation details; reasoning about order sensitivity in
-an order-independent way]
+(To be added: citation details; reasoning about order sensitivity in
+an order-independent way.)
+
+The preceding discussion has endeavored to bring out some *similarities*
+between the kind of order-dependence in our three-valued truth-table, and the
+kinds of order-dependence exhibited by "dynamic semantics." But there are also
+of course substantial *differences* between them, and these are also, perhaps
+even more interesting. Over the course of this semester we hope to clarify and
+help you to think more carefully about both the similarities and the
+differences.
+