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C00002 00002	.require "memo.pub[let,jmc]" source
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.require "memo.pub[let,jmc]" source;
.cb HOW DOES A CHILD CHANGE THE WORD "MOTHER" FROM ONE ARGUMENT TO TWO?


	The word "mother" is learned early and presumably plays an
important role in a child's life.  Children often have a misconception
about its use that from the point of view of mathematical logic
amounts to using it as a one argument predicate rather than a two
argument predicate.  The misconception shows itself when the
child refers to Mr. Jones's wife by saying "Mr. Jones's mother".
We suppose that the child regards a mother as a kind of person
and says "Mr. Jones's mother" in order to refer to the mother
closely associated with Mr. Jones.  Expressing this in logic,
we suppose the child (or our program imitating a child as advocated
by Turing) would have a predicate ⊗mother(x) applicable to those
entities that are mothers.

	A child who makes this mistake is readily corrected and
subsequently refers to Mr. Jones's wife properly and is also prepared
to refer to an occasionally seen old lady as "Mr. Jones's mother"
if the relationship is pointed out.
While the facts of motherhood may be pointed out, the biology seems irrelevant
to the child's ability to readjust his use of language.
Logically this corresponds to now regarding motherhood as a relation
%2mother(x,_y)%1.

	This phenomenon exposes some problems in making an AI program
with the flexibility of a child.  Namely, the program should be
able to accept correction as readily as a child does.  However, if
the program expresses its knowledge as sentences in first order logic
or in many other systems, it doesn't seem to be trivial to change
all sentences using a predicate ⊗mother(x) to sentences
using ⊗mother(x,y).  After all, there is no evidence that when a
child receives this or any other such correction, it spends a day
massaging its data base.

	There are several possibilities.

	1. Perhaps there is an external language used for communication
and a ⊗mentalese used for thinking.  The database is in mentalese including
all the common sense facts.  Language is just an epiphenomenon, so
the problem of merely changing the output routines isn't substantial.
In the mentalese there are already distinct names for the relation
between a mother and child and for the property of being a mother,
so the correction is merely a matter of changing a few table entries
associated with the word "mother".  Introspectively it seems that this
is a part of the truth.

	An adult example is learning the distinction between a
disease (a malfunction of a part of the body, usually taking the
form of a physical defect of some part) and a syndrome (a collection
of signs and symptoms).  I suppose the distinction is taught early
to medical students to some of whom it may be new.  I also suppose
that making the distinction explicit is relatively new in medicine
- perhaps a nineteenth century idea.  In any case, the distinction
is made relatively smoothly.

	2. A second possibility is to make a language in which
the word mother can be applied to an arbitrary number of arguments.
It might be supposed that this must take us out of first order logic,
but this isn't so.  We could assume that ⊗mother takes a set as an argument
or that ⊗mother is an object not a predicate, and we can write
⊗app1(mother,_x) or ⊗app2(mother,_x,_y).  When the child learns the
distinction, he learns something like

	%2app1(mother, x) ≡ ∃y.app2(mother x, y)%1,

and he would not have substantial difficulty with a further discovery
that ⊗app3(mother,_x,_y,_z) was sometimes called for.

	Most likely, there are even more possibilities for reformulating
the assertions, but it isn't obvious how one would make a system that
could accept surprises easily.