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.require "memo.pub[let,jmc]" source;
.cb A DIFFICULT HYPOTHESIS ABOUT MEANING IN NATURAL LANGUAGE


	The object of this note is to advance a certain hypothesis
about the what is the "true" meaning of a term or sentence in
a natural language or in artificial languages having expressiveness
like that of natural language.  If this hypothesis is true, then
theories of meaning will be quite complex, and the "true" meaning
of a sentence may be unstatable in finite terms and will be something
like an inverse limit of partial meanings.

	Start with the sentence, %2"Pat tried to dial Mike's telephone
number%1.  Let us parse it into

!!a1:	%2tried(Pat,dial(telephone(Mike)))%1.

Let us further suppose that Mike's telephone number is 497-4444.  The
simplest logical situation would be one in which all contexts are
transparent, %2compositionality%1 reigns, and we can use the equality

!!a2:	%2telephone(Mike) = 497-4444%1

to get

!!a3:	%2tried(Pat,dial(497-4444))%1.

There are many contexts of English usage in which this interpretation
would be correct.
However, there is another common interpretation.  Suppose that Mike
mistakenly believed Pat's telephone number to be 497-3333 and dialed
that number. In this case, it would seem that %2dial(telephone(Mike))%1 is
not to be regarded as the result of applying the function %2dial%1 to
an object %2telephone(Mike)%1.

	We have two observations:

.item←0
	#. Consider a person who took the sentence in the first sense
and never noticed the second possible interpretation.  Did he misunderstand
the sentence?  Certainly if the sentence was uttered with the first
meaning in a certain context and he understood it that way, especially
if neither the speaker nor the listener noticed the additional
interpretation.  But what if the sentence was not uttered with the
intent of asserting something but merely as a linguistic exercise or example?
Then we are inclined to say that understanding the sentence would
require awareness of both interpretations.
For this reason we will distinguish between understanding an
utterance of a sentence (or phrase) and understanding the
sentence itself.

	Our exotic hypothesis is that people often understand
utterances of sentences and maybe never understand the sentences
themselves.  The idea is that understanding the sentence might
involve aareness of its meaning in any context in which it
might meaningfully be uttered and there might be an infinity
of them.

	Let's concoct a more fanciful situation in which
({eq a1}) might be uttered.

	Supposed that Pat wished to speak to Clancy
and mistakenly believed that Clancy's telephone number was 497-4444,
and further assume that Pat has never even heard of Mike.
Suppose that the speaker of the sentence doesn't know the
number, but does know that the the number Pat attempted to
dial was Mike's.  He is recounting Mike's narrow escape
from being awakened at 3am by Pat who was drunk.

	Suppose Pat who was drunk at 3am and never heard of
Mike wished to speak to his friend Clancy and mistakenly
believed that Clancy's telephone number was 497-4444 and
attempted to dial it, but Mike was saved from being awakened
by a drunk at 3am by a malfunction of the telephone system.
Suppose that the story is being recounted by someone who
knows the people involved but doesn't know the telephone
numbers.  Then he might utter ({eq a1}) without asserting
that Pat wished to communicate with Mike.

	Do me the favor for the moment of accepting this
interpretation as a legitimate but farfetched possibility.
It is certainly unreasonable to expect that every hearer of
the sentence would immediately think of it, even though
he would give that interpretation if he heard the sentence
under appropriate circumstances.

	If you grant all this, then the question arises of
how a person can understand any utterance of a sentence
without being aware of all the possible meanings of the
sentence so as to choose the right one.  Our idea is that
humans use (and computers had better use) the ability to
jump to conclusions discussed in (McCarthy 1976a).
Specifically, people assume that the facts and objects
they know about are all the relevant facts, i.e. they
make an appropriate %2minimal inference%1.  After such
a minimal inference is made, the appropriate interpretation
of the sentence follows.  (We have not worked out the
details of this yet).

	#. There may be an advantage in preserving
extensionality, i.e. in redefining meanings so that
the meaning of %2dial(telephone(Mike))%1 is otained
by a∨plying the meaning o %2dial%1 to the meaning
of %2telephone(Mike)%1 which in turn is obtained by
applying the meaning of %2telephone%1 to the meaning
of %2Mike%1.  It seems that this can be done in several ways.

	The first involves introducing concepts as objects
as in (McCarthy 1976b).  The second involves making the meaning
of each constituent a higher order object, namely a
λ-expression abstracting over contexts or environments
in the manner of (Gordon 1973) defining the semantics
of LISP.
.skip 2
.begin verbatim
John McCarthy
Artificial Intelligence Laboratory
Computer Science Department
Stanford University
Stanford, California 94305

ARPANET: MCCARTHY@SU-AI
.end

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