complete. This is shown by a special set of transformations that permits
the thinker to return to an original starting point.
This set of transformations makes use of four operations. These are
the I (or identity ) operation which changes nothing in any proposition.
If the I operation is performed on A (“it is raining and I shall put up an
umbrella”), nothing alters. The N (or negation ) operation changes every-
thing in the proposition on which it bears. Thus if N is applied to A it
becomes “it is not raining or I shall not put up an umbrella.” The R (or
reciprocal ) operation changes assertions and negations but leaves conjunc-
tions and disjunctions unchanged. So R applied to “it is not raining and
I shall not put up an umbrella” becomes “it is raining and I shall put up
an umbrella.” The C (or correlative ) operation changes conjunctions and
disjunctions but leaves assertions and negations untouched. So R applied
to “it is raining and I shall put up an umbrella” becomes “it is raining or I
shall put up an umbrella.” In short, I=NRC, IRC=N, CR=N, NR=C and
so on. 8
THE INTERPRETATION OF TEXTS
The work of Piaget and his collaborators has been given its due attention
by other psychologists and educationalists and, sometimes, by linguists.
But there has been little exchange between this group of scholars and
those who have been engaged in theorizing the tasks of biblical herme-
neutics 9 or Pentecostal hermeneutics. 10
We can posit a relationship between the child’s mind and the child’s
interpretation of the physical or moral world and the same child’s interpre-
tation of the world within texts. We could argue that the child’s understand-
ing of the physical world is repeated at one remove in the understanding of
the text so that the understanding of the text follows in step with an under-
standing of the physical worlds. This parallel development between the
physical or moral world and the world of story will lead to a range of pos-
sibilities. For instance, the two worlds are synchronized so that the world
of one is interpreted as if it is the world of the other—if there is magic in
one, there will be magic in the other; if there are miracles in one, there will
be miracles in the other. Or there is a mismatch whereby the child’s physi-
cal world is grey and dull while the story world is full of fabulous events.
And other mixed relationships are obviously also possible including, as we
suggest below, a single understanding of a story that can be interpreted—
indeed is intended to be interpreted—in more than one way.
272 W.K. KAY