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∂AIL Professor Barbara Partee↓Department of Linguistics
↓University of Massachusetts↓Amherst, MA 01003∞
.<<(413) 545-0885>>
Dear Barbara:

Here are some more thoughts suggested by your "Semantics - Mathematics or
Psychology?

1.  The word "psychology" requires clarification.  Does it apply only to
people or to machines also?
  Your main example of a
psychological limitation - non-substitutability of logical equivalents -
applies to machines as well as people, so long as we require that what is
known be sayable.  This is a consequence of the undecidability of logical
equivalence, but practically buildable machines have limitation far tighter
than those imposed by these theorems.

2.  I think it %2may%1 be fruitful to extend psychological considerations
to machines, i.e. to have a "generalized psychology".

3.  As far as I know, the Chomskyans don't distinguish performance limitations
imposed by the fact that a human is a material system - further limited in
speed and memory performance - from evolutionary accidents.  To put the
matter positively, it seems that allowing phrases rather than just single
words in certain sentence positions is required for communication between any
physical systems with limited ability to see through each others eyes.

It may be very difficult to decide whether a feature of human linguistic
behavior is functionally required before we can build programs that
communicate well without the feature.  For this to be a good test, we
must subject the programs to corresponding speed and memory limitations.

4.  I believe that linguistics can and should become less theological just
as metamathematics has made the foundations of mathematics less theological.
Namely, we will need to study for many years the characteristics of different
formalizations before we can discard all but one kind of system (if ever).
In particular formalizations of propositional expressions in which expressions
equivalent under many kinds of equivalence relations are intersubstitutable
will be useful.  Sometimes the relations will be logical extensional, sometimes
intensional in varous ways, and sometimes psychological or computational
in various ways.

5.  One reason why I believe that many theories will be found useful is my idea
that they are ascriptive anyway.
[See my %2Ascribing Mental Qualities to Machines%1.]
If that be granted, it seems likely that different systems for ascribing belief
would be useful depending on circumstances.  To put this idea as a bold
contention:  Humans could be brought up to use different systems in natural
language comfortably in conversation with similarly brought up people.  They could
probably switch from one system to another especially if different vocabularies
were used.

6.  I have on major difference in taste from Montague.  He likes to regard a
proposition as a function from possible worlds to truth values.  I would
prefer to regard propositions as abstract entities and have a function
%2holds(proposition,world)%1 - assuming I were using possible worlds.  My approach
reduces to Montague's if I have an extensionality axiom

(1) %2∀w.holds(prop1,w)≡holds(prop2,w) ⊃ prop1=prop2%1

and

(2) means establishing the existence of a proposition corresponding to every
Montague predicate.

	As you see, I found your paper very stimulating.

	Many thanks for your hospitality in Amherst, and I am looking forward
to March.

.reg

P.S. Consider %2"He took a spoonful of soup and found a fly in it"%1.  It is
not at all suggested that he only took one spoonful of soup.  It is suggested
that he only found one fly.  It seems to me that %2"John took a spoonful
of soup.  He found a fly in it".%1  has the same property.  The uniqueness
is provided by the sentence containing %2"it"%1.