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C00002 00002		When my understander  has digested the  story of Mr.  Hug, it
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	When my understander  has digested the  story of Mr.  Hug, it
will have added  one or more predicate calculus sentences to its data
base.  One sentence will do if it has the form

	∃ e p1 p2 g1 g2 e1 e2 ...  . event(e) ∧ person(p1) ∧ name(p1)
= "John. J. Hug" ∧ g1 ⊂ Robbers ∧ ... etc.


In this form,  all the entities  involved in expressing the  facts of
the story are existentially quantified variables.  The only constants
in the  formula would  have been  present in  the system  previously.
However,  it is  probably better  to  use a  collection of  sentences
introducing  a collection  of  individual constants.   In  this case,
there will be 20 or so new individual  constants representing people,
groups  of  people,  the  main  event  and  its  sub-events,  places,
organizations, etc.

	1. In representing  the robbers, the  system has a  choice of
representing them by three individual constants, R1, R2, and R3 or by
using a single symbol G1 to  represent the group of robbers.  A  good
system will  probably use  both. If  the number  of robbers  were not
specified, we would have to use a constant for the group.  We have to
identify the robber who operated the elevator while the others pushed
Mr. Hug into the shaft.  We shall call him R1.  The other two are not
discriminated in the story, but there is no harm in our calling  them
R2 and R3, even if there is no information  to discriminate them.  If
there  were  20 robbers,  it  would be  a  mistake to  give  them all
individual names.  Suppose it  had further  been stated  that as  the
robbers left one of them threatened  to return and kill Mr. Hug later
but  that it was not stated whether this  robber was the same one who
operated the elevator.  We could designate this robber  by R4, but we
would not have  sentences asserting that R4 was  distinct from R1, R2
and R3; instead we would have a sentence asserting that R4 was one of
these.  It is tempting to identify the group  of robbers with the set
{R1,R2,R3},  but we may  want to give  the group  some properties not
enjoyed by the set  of its members.   Sentences with plural  subjects
express  some rather  tricky concepts.   Thus,  the group  robbed the
store,  and this  is  not an  assertion that  each member  robbed the
store.

	The  "members  of  the police  emergency  squad"  presents  a
similar  problem. We don't  want to assert  how many there  were.  In
this connection,  it may be  worthwhile to  distinguish between  what
happened and what we wish to  assert about what happened.  A language
adequate to describe what happened would not have to leave the number
of policemen present vague  and could give them  each a name.   In my
old jargon,  such a language would be  metaphysically adequate though
not epistemologically adequate.   Devising  a language  that is  only
metaphysically adequate may  be a worthwhile  stage on the way  to an
epistemologically adequate  system.  By "devising  a language" I mean
defining  a  collection  of   predicate  and  constant  symbols   and
axiomatizing their general  properties.  This language  should not be
peculiar  to the story of Mr. Hug, but  we should not require that it
be completely general in the present state of the science.

	2. It is not obvious how to express what we  know when we are
told that Mr.  Hug is a furniture salesman.   A direct approach is to
define an  abstract entity  called Furniture  and a  function  called
salesmen and to assert

	Hug ε salesmen(Furniture).

This will probably  work although the logical connection  between the
abstract entity Furniture  and concrete chairs and tables needs to be
worked out.  It would  be over-simplified to identify Furniture  with
the set of furniture in existence  at that time, because one could be
a  salesman of space shuttles even though  there don't exist any yet.
In my opinion,  one should resist a  tendency to apply Occam's  razor
prematurely.  Perhaps we can identify the abstract Furniture with the
an extension of the predicate that tells us whether an object  should
be regarded as a piece of furniture, perhaps not.  It does no harm to
keep  them separate  for the  time being.   This  case looks  like an
argument for  using  second  order  logic so  that  the  argument  of
\F1salesmen\F0  could be  the  predicate  \F1furniture\F0 that  tells
whether  an  object is  a  piece of  furniture.   However,  there are
various techniques  for getting the  same result  without the use  of
second order logic.

	3. Occam's razor.   After reading the story, one  is prepared
to answer  negatively the question of whether  there was someone else
besides  Mr.  Hug  and  the  robbers  present.    However,  sentences
describing such  another person could  be added to the  story without
contradiction.  Our  basis for  the negative  answer  is that  we can
construct a model  of the facts  stated in the  story without such  a
person, and we are applying Occam's razor in order to not \F1multiply
entities beyond necessity\F0.  This could be  attributed to the  fact
that the \F1New York Times\F0 tells the whole  story when it can, but
I  think that by  putting Occam's razor  into the system,  we can get
this result without having to formalize the \F1New York Times\F0.

	This  suggests   introducing  the   notion  of  the   minimal
completion  of a  story  expressed in  the predicate  calculus.   The
minimal completion of  the story is  also a set  of sentences in  the
predicate calculus,  but it contains sentences  asserting things like
"The  set of  people in the  store while  the robbers  were trying to
crush Mr. Hug consists of Mr. Hug and the  robbers".  These sentences
are  to be obtained  from the  original set by  the application  of a
process formalizing Occam's razor.  This process works from a set  of
sentences  and  is  not  logical  deduction   although  it  might  be
accomplished  by   deduction  in  a  meta-  language  that  contained
sentences about sets of sentences.  As I have pointed  out elsewhere,
the process cannot be deduction,  because it generates sentences that
contradict  sentences that  are consistent  with the original  set of
sentences.

	A number of the questions given in  the previous section have
answers that can  be formally deduced from the minimal completion but
not from the original list.

	It has been suggested that  probabilistic reasoning should be
used  to exclude  the presence  of other  people rather  than Occam's
razor. The  problem  with  this  is that  the  number  of  additional
entities that  are not  logically excluded is  limited only  by one's
imagination  so  that  it is  not  clear how  one  could  construct a
probabilistic model that  took these possibilities into  account only
to   exclude  them  as   improbable.  If   one  wants   to  introduce
probabilities, it might make  more sense to  assign a probability  to
the correctness of the  minimal completion of a \F1New  York Times\F0
story  based on  its past  record  in finding  the relevant  facts of
robberies.

	Another  problem  in  constructing  the  completion  is   the
isolation of the  story from the rest  of the world.   The members of
the Police  Emergency Squad all have mothers (living or dead), but we
don't want to bring them in to the completion.

	To  recapitulate: The  original  set  of  predicate  calculus
sentences can  be generated from the  story as one goes  along.  Each
sentence is generated approximately from a sentence of the story with
the aid  of general knowledge  and what has  been generated  from the
previous sentences.   (This will usually be the  case if the story is
well told although there are sometimes cases in which the correct way
to express a sentence  will depend on what follows -  but this is not
good writing).   The completion, however, will depend on the whole of
the story.

	It might be interesting to consider what can be determined
from a partial reading of the story - even stopping the reading
in the middle of a sentence since what has appeared so far in a
sentence often must be understood in order to even parse the rest of
the sentence.