Pearl, J. (1996) Structural and Probabilistic Causality
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Similar problems affect psychological theories that use statistical relevance to explain how children extract causal information from experience. The proponents of such theories cannot ignore the fact that the child never operates in a closed, isolated environment. Unnoticed external conditions govern the operation of every learning environment, and these conditions often have the potential to confound cause and effect in unexpected and clandestine ways.
Fortunately, that children do not grow in closed, sterile environments like those in statis tical textbooks has its advantages too. Aside from passive observations, a child possesses two valuable sources of causal information which are not available to the ordinary statistician: manipulative experimentation and linguistic advice. Manipulation subjugates the putative causal event to the sole influence of a known mechanism, thus overruling the influence of uncontrolled factors which might also produce the putative effect. “The beauty of indepen dent manipulation is, of course, that other factors can be kept constant without their being identified'’ [Cheng, 1992]. The independence is accomplished by subjecting the object of interest to the whims of one’s volition, to ensure that the manipulation is not influenced by any environmental factor likely to produce the putative effect. Thus, for example, a child can infer that shaking a toy can produce a rattling sound, because it is the child’s hand, governed solely by the child’s volition, that brings about the shaking of the toy and the subsequent rattling sound. The whimsical nature of free manipulation replaces the statistical notion of randomized experimentation and serves to filter sounds produced by the child’s actions from those produced by uncontrolled environmental factors.
But manipulative experimentation cannot explain all of the causal knowledge that hu mans acquire and possess, simply because most variables in our environment are not subject to direct manipulation. The second valuable source of causal knowledge is linguistic advice, namely, explicit causal sentences about the workings of things which we obtain from parents, friends, teachers, and books, and which encodes manipulative experience of past generations. As obvious and uninteresting as this source of causal information might appear, it probably accounts for the bulk of our causal knowledge, and understanding how this transference of knowledge works is far from trivial. In order to comprehend and absorb causal sentences such as “The glass broke because you pushed it,'’ the child must already possess a causal schema within which such inputs make sense. To further infer that pushing the glass will make someone angry at you and not at your brother, even though he was responsible for all previous breakage, requires a truly sophisticated inferential machinery. In most children, this machinery is probably innate.
Note, however, that linguistic input is by and large qualitative; we rarely hear parents explaining to children that placing the glass at the edge of the table increases the probability of breakage by a factor of 2. Yet, quantitative assessments of the effects of one’s actions must be made in any decisionmaking situation, and the question arises, How does one combine quantitative empirical data with qualitative causal relations to deduce quantitative causal assessments? The problem is especially critical in situations in which empirical data is available on only a small part of the causal field, while the bulk of that field is represented as rudimentary statements of what affects what in the domain. By analogy, this resembles the task of figuring out how to fix a TV set when given only a general understanding of the principles of television electronics combined with empirical data on five knobs and one screen. This problem will be dealt with in Section 4.
Pearl, J., “Structural and Probabilistic Causality,'’
In D.R. Shanks, K.J. Holyoak, and D.L. Medin (Eds.), The Psychology of Learning and Motivation, Vol. 34 Academic Press, San Diego, CA, 393–435, 1996.
2June2003
Pearl’s following quote suggest an interesting new direction to study children’s reasoning — a more complex framework than existing ones. How to put them into a psychological thoery is the challenge. What task domain is a good example?- Language learning?
- Physical problem solving?
- Infant toy playing?
- Theory of Mind?
Quote:
Similar problems affect psychological theories that use statistical relevance to explain how children extract causal information from experience. The proponents of such theories cannot ignore the fact that the child never operates in a closed, isolated environment. Unnoticed external conditions govern the operation of every learning environment, and these conditions often have the potential to confound cause and effect in unexpected and clandestine ways.
Fortunately, that children do not grow in closed, sterile environments like those in statis tical textbooks has its advantages too. Aside from passive observations, a child possesses two valuable sources of causal information which are not available to the ordinary statistician: manipulative experimentation and linguistic advice. Manipulation subjugates the putative causal event to the sole influence of a known mechanism, thus overruling the influence of uncontrolled factors which might also produce the putative effect. “The beauty of indepen dent manipulation is, of course, that other factors can be kept constant without their being identified'’ [Cheng, 1992]. The independence is accomplished by subjecting the object of interest to the whims of one’s volition, to ensure that the manipulation is not influenced by any environmental factor likely to produce the putative effect. Thus, for example, a child can infer that shaking a toy can produce a rattling sound, because it is the child’s hand, governed solely by the child’s volition, that brings about the shaking of the toy and the subsequent rattling sound. The whimsical nature of free manipulation replaces the statistical notion of randomized experimentation and serves to filter sounds produced by the child’s actions from those produced by uncontrolled environmental factors.
But manipulative experimentation cannot explain all of the causal knowledge that hu mans acquire and possess, simply because most variables in our environment are not subject to direct manipulation. The second valuable source of causal knowledge is linguistic advice, namely, explicit causal sentences about the workings of things which we obtain from parents, friends, teachers, and books, and which encodes manipulative experience of past generations. As obvious and uninteresting as this source of causal information might appear, it probably accounts for the bulk of our causal knowledge, and understanding how this transference of knowledge works is far from trivial. In order to comprehend and absorb causal sentences such as “The glass broke because you pushed it,'’ the child must already possess a causal schema within which such inputs make sense. To further infer that pushing the glass will make someone angry at you and not at your brother, even though he was responsible for all previous breakage, requires a truly sophisticated inferential machinery. In most children, this machinery is probably innate.
Note, however, that linguistic input is by and large qualitative; we rarely hear parents explaining to children that placing the glass at the edge of the table increases the probability of breakage by a factor of 2. Yet, quantitative assessments of the effects of one’s actions must be made in any decisionmaking situation, and the question arises, How does one combine quantitative empirical data with qualitative causal relations to deduce quantitative causal assessments? The problem is especially critical in situations in which empirical data is available on only a small part of the causal field, while the bulk of that field is represented as rudimentary statements of what affects what in the domain. By analogy, this resembles the task of figuring out how to fix a TV set when given only a general understanding of the principles of television electronics combined with empirical data on five knobs and one screen. This problem will be dealt with in Section 4.