192 11 Stages of Cognitive Development
Finally, another limiting aspect of Piaget’s model is that it did not recognize any stages beyond formal operations, and included no provisions for exploring this possibility. A mumber of researchers [Bic88, Arl75, CRK82, Rie73, Mar01| have described one or more postformal stages. Commons and colleagues have also proposed a task-based model which provides a framework for explaining stage discrepancies across tasks and for generating new stages based on classification of observed logical behaviors. [K1<90] promotes a statistical conception of stage, which provides a good bridge between task-based and stage-based models of development, as statistical modeling allows for stages to be roughly defined and analyzed based on collections of task behaviors.
[CRK&82] postulates the existence of a postformal stage by observing elevated levels of abstrac- tion which, they argue, are not manifested in formal thought. [CTS~ 98] observes a postformal stage when subjects become capable of analyzing and coordinating complex logical systems with each other, creating metatheoretical supersystems. In our model, with the reflexive stage of development, we expand this definition of metasystemic thinking to include the ability to consciously refine one’s own mental states and formalisms of thinking. Such self-reflexive re- finement is necessary for learning which would allow a mind to analytically devise entirely new structures and methodologies for both formal and postformal thinking.
In spite of these various critiques and limitations, however, we have found Piaget’s ideas very useful, and in Section 11.4 we will explore ways of defining them rigorously in the specific context of CogPrime’s declarative knowledge store and probabilistic logic engine.
11.3.1 Perry’s Stages
Also relevant is William Perry’s [Per70, Per81] theory of the stages (“positions” in his terminol- ogy) of intellectual and ethical development, which constitutes a model of iterative refinement of approach in the developmental process of coming to intellectual and ethical maturity. These stages, depicted in Table 11.2 form an analytical tool for discerning the modality of belief of an intelligence by describing common cognitive approaches to handling the complexities of real world ethical considerations.
11.3.2 Keeping Continuity in Mind
Continuity of mental stages, and the fact that a mind may appear to be in multiple stages of development simultaneously (depending upon the tasks being tested), are crucial to our theoretical formulations and we will touch upon them again here. Piaget attempted to address continuity with the creation of transitional “half stages”. We prefer to observe that each stage feeds into the other and the end of one stage and the beginning of the next blend together.
The distinction between formal and post-formal, for example, seems to “merely” be the application of formal thought to oneself. However, the distinction between concrete and formal is “merely” the buildup to higher levels of complexity of the classification, task decomposition, and abstraction capabilities of the concrete stage. The stages represent general trends in ability on a continuous curve of development, not discrete states of mind which are jumped-into quantum style after enough “knowledge energy” builds-up to cause the transition.
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