Simulating Belief and Action - Natural and Artificial Reasoning - page 89

Table 7.2 Initial position of subject A. The table relates the constructs (hypotheses) to the observa-
tions (data) via the probability of observing (say) a triangle if the box contains (say) a cone. Each of
the three constructs is compatible with the only available data, so each datum is assigned an equal
probability of 1.0
Hypothesis:
Observed shape:

2D: triangular card 3D: cone 3D: triangular

section bar

Triangle p = 1.0 p = 1.0 p = 1.0

Circle Not envisaged Not envisaged Not envisaged

Cross Not envisaged Not envisaged Not envisaged

Table 7.3 Position of subject A after consulting subject B, who reports seeing a circle. There is now
some ambiguity, e.g. if there is a cone in the box, observation of a triangle or a circle are equally
probable
Hypothesis:
observed
shape:

2D: triang.
card

3D: cone 3D: triang. bar 2D: disc 3D: sphere 3D: rod

Triangle 1.0 0.5 1.0 0.0 0.0 0.0

Circle 0.0 0.5 0.0 1 1 1

Cross Not seen Not seen Not seen Not seen Not seen Not seen

Table 7.4 Position of subject A after first consulting subject C who reports seeing a cross
Hypothesis:
observed
shape

2D: triang. card 3D: cone 3D: triang. bar 2D: flat cross 3D: intersecting

sheets

Triangle 1.0 1.0 1.0 0.0 0.0

Cross 0.0 0.0 0.0 1.0 1.0

Circle Not seen Not seen Not seen Not seen Not seen

In Gruber's experiments, if a subject interprets a triangular shadow as being
compatible with (say) 'the existence of a solid cone in the box' then this hypothesis
would be ruled out by a second subject's report of a circular image. Consider the
situation of one of three subjects, A , as shown in Table 7.2 . A has postulated three
objects compatible with the evidence. The observations of subjects B and C are not
yet known. On the basis of this one observation A could postulate a 2-D object (a flat
triangular card) or two 3-D objects (an opaque cone and a triangular bar).
New objects are postulated to explain new kinds of observation. Suppose A first
consults B, who reports seeing a circle. A could postulate or negotiate with B the
construction of three further objects (a disc, a sphere, and a rod). A's situation at this
point is shown in Table 7.3 .
Suppose A first consults C, who reports seeing a cross. Then, as indicated in
Table 7.4 , A invokes a different set of hypotheses and phenomena than if B is consulted
first.