202 11 Stages of Cognitive Development

202 11 Stages of Cognitive Development A problem commonly used to illustrate the difference between the Piagetan concrete opera- tional and formal stages is that of figuring out the rules for making pendulums swing quickly versus slowly [P58]. If you ask a child in the formal stage to solve this problem, she may pro- ceed to do a number of experiments, e.g. build a long string with a light weight, a long string with a heavy weight, a short string with a light weight and a short string with a heavy weight. Through these experiments she may determine that a short string leads to a fast swing, a long string leads to a slow swing, and the weight doesn’t matter at all. The role of experiments like this, which test “extreme cases,” is to make cognition easier. The formal-stage mind tries to map a concrete situation onto a maximally simple and manipulable set of abstract propositions, and then reason based on these. Doing this, however, requires an automated and instinctive understanding of the reasoning process itself. The above-described experiments are good ones for solving the pendulum problem because they provide data that is very easy to reason about. From the perspective of uncertain inference systems, this is the key characteristic of the formal stage: formal cognition approaches problems in a way explicitly calculated to yield tractable inferences. Note that this is quite different from saying that formal cognition involves abstractions and advanced logic. In an uncertain logic-based AGI system, even infantile cognition may involve these — the difference lies in the level of inference control, which in the infantile stage is simplistic and hard-wired, but in the formal stage is based on an understanding of what sorts of inputs lead to tractable inference in a given context. 11.4.4 The Reflexive Stage In the reflexive stage (Figure 11.8), an intelligent agent is broadly capable of selfmodifying its internal structures and dynamics. As an example in the human domain: highly intelligent and self-aware adult humans may carry out reflexive cognition by explicitly reflecting upon their own inference processes and trying to improve them. An example is the intelligent improvement of uncertain-truth-value- manipulation formulas. It is well demonstrated that even educated humans typically make numerous errors in probabilistic reasoning [GGIK02]. Most people don’t realize it and continue to systematically make these errors throughout their lives. However, a small percentage of individuals make an explicit effort to increase their accuracy in making probabilistic judgments by consciously endeavoring to internalize the rules of probabilistic inference into their automated cognition processes. In the uncertain inference based AGI context, what this means is: In the reflexive stage an entity is able to include inference control itself as an explicit subject of abstract learning (i.e. the ability to reason about one’s own tactical and strategic approach to modifying one’s own learning and thinking), and modify these inference control strategies based on analysis of experience with various cognitive approaches. Ultimately, the entity can self-modify its internal cognitive structures. Any knowledge or heuristics can be revised, including metatheoretical and metasystemic thought itself. Initially this is done indirectly, but at least in the case of AGI systems it is theoretically possible to also do so directly. This might be considered as a separate stage of Full Self Modification, or else as the end phase of the reflexive stage. In the context of logical reasoning, self modification of inference control itself is the primary task in this stage. In terms of inference control this HOUSE_OVERSIGHT_013118