FIGURE 22 (S1503F): Pseudoconceptual reasoning in an elaborate diffuse complex

The fifteen-year-old participant in Figure 22 (S1503F) picked up a cev triangle (same shape as the mur exemplar) and immediately turned it over. Her next approach was a consideration of height (where she physically measured some of the blocks against others); then, a consideration of the number of corners of the blocks; and then she moved on to the solution presented here which involved combinations of flat trapezoids and triangles (bottom left), and tall triangles and squares (top left), but the other groups did not conform to this combination of characteristics.

The photograph in Figure 22 depicted a problem that this participant had with where to place the lag trapezoid that was left in the middle of the board. Even though inconsistent principles applied to the groups, the group of trapezoids and triangles at bottom left was consistent in that all of them were flat and had a similar shape. Yet, the group of possible mur candidates (top left), which had started with all the tall triangles and squares, also contained a flat square. The differentiation of height corresponding with shape further broke down with the group at top right, where the circles were placed, irrespective of height, and then the two hexagons had been put into a group of their own because they were different shapes from any other on the board. Why this participant had a problem with where to place the lag trapezoid was not clear (although to some extent I appreciated it): one would have imagined that the inconsistency in the inclusion of the flat square with the mur group (top left), coupled with a single idea of height (for the group at bottom left), in addition to the inclusion of only one shape in the group of circles (at top right) irrespective of height and where the two semi-circles had been put together to form a “circle” would have presented more of a problem to a logical approach to the problem of the blocks than did the lone trapezoid.

Further evidence of this participant’s insensitivity to contradiction and to inconsistent principles was demonstrated when she advanced yet another solution: she placed the semi-circles and trapezoids into a group which was described as containing the incomplete versions of the next group, which contained hexagons and circles (elegant). However, although the two remaining groups were described as groups of squares and of triangles, these were not considered to be incomplete and complete versions of one another, which could have completed the symmetry of her solution (my objections to this approach with the next participant notwithstanding).