Wording improvements.halt3-1.6

1 files changed, 14 insertions, 12 deletions

diff --git a/proof-sketch.txt b/proof-sketch.txt
index 4a79e07..73c2bf5 100644
--- a/proof-sketch.txt
+++ b/proof-sketch.txt
@@ -84,23 +84,25 @@ Background:
 
 Motivation:
 
-  Some researchers disbelieve the proof of the halting problem, claiming
-  that it is a contrived trick and that the test cases which are generated
-  by that trick are somehow invalid, the implication being that deciders
-  may be legitimately excused for not being able to to determine whether or not
-  these cases halt.
+  Some researchers take issue with the proof of the halting problem, claiming
+  that even though it is true, it is a contrived trick and that the test cases
+  which are generated by that trick are somehow invalid, the implication being
+  that deciders may be legitimately excused for not being able to to determine
+  whether or not these cases halt, and that these cases do not represent
+  a true, palpable limit on computability.
 
   It has been proposed that a three-valued version of the halting problem
-  can provide the necessary framework. Under this notion, the halting function
-  is augmented to have a third possible return value, so that for each
-  <program, input> pair, it assigns the value true, false or error.  The new
-  error value has some meaning such as that <program, input> test case
-  constitutes a test case which is trying to break the decider through some
-  self-referential trick.
+  can provide the necessary framework which allows halting deciders to
+  effectively diagnose situations when they are subject to "unfair"
+  test cases.  Under this notion, the halting function is augmented to have a
+  third possible return value, so that for each <program, input> pair, it
+  assigns the value true, false or error.  The new error value has some meaning
+  such as that <program, input> test case constitutes a test case which is
+  trying to break the decider through some self-referential trick.
 
   This paper presents a proof sketch which suggests that the three-valued
   halting function is also not total computable. Using a more refined trick,
-  three-valued halting deciders can be shown to be incorrect. For any
+  three-valued halting deciders can be shown to fail. That is to say, for any
   halting decider, a test case can be found such that it incorrectly returns
   error in a situation when no trick is going on: a situation when that decider
   could be altered to return true or false without being contradicted.