edits

diff --git a/week3.mdwn b/week3.mdwn
index a55659c..88b1c4f 100644 (file)
--- a/week3.mdwn
+++ b/week3.mdwn
@@ -585,9 +585,10 @@ rather than recursive functions.
 
 HOWEVER, you should be cautious about feeling too comfortable with
 these results.  Thinking again of the truth-teller paradox, yes,
-<code>&omega;</code> is *a* fixed point for `I`, and perhaps it has
+<code>&Omega;</code> is *a* fixed point for `I`, and perhaps it has
 some a privileged status among all the fixed points for `I`, being the
-one delivered by Y and all.
+one delivered by Y and all (though it is not obvious why Y should have
+any special status).
 
 But one could ask: look, literally every formula is a fixed point for
 `I`, since
@@ -600,7 +601,8 @@ So the Y combinator is only guaranteed to give us one fixed point out
 of infinitely many---and not always the intuitively most useful
 one. (For instance, the squaring function has zero as a fixed point,
 since 0 * 0 = 0, and 1 as a fixed point, since 1 * 1 = 1, but `Y
-(\x. mul x x)` doesn't give us 0 or 1.) So why in the reasoning we've
+(\x. mul x x)` doesn't give us 0 or 1.) So with respect to the
+truth-teller paradox, why in the reasoning we've
 just gone through should we be reaching for just this fixed point at
 just this juncture?
 
@@ -616,6 +618,12 @@ fixed point for this referential function: if this pen cap is the
 referent of *this noun phrase*, then it is the referent of (3), and so
 for any object.
 
+The chameleon nature of (3), by the way (a description that is equally
+good at describing any object), makes it particularly well suited as a
+gloss on pronouns such as *it*.  In the system of [Jacobson 1999] 
+(http://www.zas.gwz-berlin.de/mitarb/homepage/sauerland/jacobson99.pdf)
+pronouns denote (you guessed it!) identity functions...
+
 Ultimately, in the context of this course, these paradoxes are more
 useful as a way of gaining leverage on the concepts of fixed points
 and recursion, rather than the other way around.