ABSTRACT
Grize’s formalism will be the backbone of a model that attempts to explain children’s understanding of the length and class-inclusion principles exemplified in the tasks of Chapters 3 and 4. How the formalism serves this purpose will be elucidated as we progress. For now, the following general characterization may be offered. By looking at purely logical relationships between formulas in Grize’s system, we shall attempt to illuminate the psychological relationships between the abilities underlying the corresponding tasks. The merit of the model may be assessed by comparing its predictions about children’s performance on the length and class-inclusion tasks with the children’s actual performance. The model predicts the pattern of passes and failures of each child. It specifies which tasks each child will pass or fail, given that he has passed or failed other tasks. The model does not predict the absolute level of difficulty of tasks for any age level.
