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Richard raises some important issues.?Where are we with Inhelder and Piaget 50 years later??Les Smith may want to correct me in some of these details, but what seems to have happened is that stage became very controversial.? This is too bad because people confuse the notion of stage with the particular model of stage provided by Inhelder and Piaget.?The reject came about because the Inhelder and Piaget stage theory based on the groupments made predictions that were not supported by data.?This was clear from the use of the Wason Laird instrument. One of the more critical aspects of reasoning is the detection of causality.?As long as an organism is the actor, the difference between sufficient cause and necessary cause is probably not very important.?Le me illustrate.?When a bird sees a seed, it pecks at it and the result is that it consumes it.?So the seeing the food and then pecking it and its consumption provided it with calories to survive.?What if it were not a seed but a little stone that looked like a seed??Sufficiencies would suggest that as long as most of the time, if the bird correctly identified seeds from non seeds, the outcome would be fine.?But what if it were not a seed and there were no calories obtained??Should the bird reject causality??No.?We live in a probabilistic world.?What we have come to understand is that the mechanism that animals use to determine causality is correlational not causal.?As long as one is the actor, this does not cause too many problems.?But if one is using backward inference and does not understand necessity, and one is not the actor, there are real problems.?There have been a huge number of studies of necessity.?The outcomes seem to depend on “bias?.?With changes in the plausibility of outcomes, people have no trouble doing the Wason Laird problem correctly.?There was a dissertation done at Harvard in the 1980's showing this. There are other problems with Inhelder and Piaget.?As Pascual-Leone showed, the half stages were actually stages.?This also presented a logical problem for the groupments model.?Most neo-Piagetians have half stages (e.g. Case, Commons, Fischer, Pascual-Leone, etc ).?For a review, look at the table in Commons, Richards and Armon, 1984.? The real issue is not whether or not there are stages because there is overwhelming evidence that there are.?The issue is what models best account for what we find to be stages and how do organism solve the tasks that require those stages?? In a very simple minded way, let me set forth some very simple criteria for choosing a model.?First, it must fit the data.?As far as I know, Pascual-Leone’s account of the psychology of performance has held up.?Something like working memory seems to limit what stage an organism reaches or a child or adult at a given time can do.?One of the most serious and innovative models has been Fischer’s (1980) skill theory.?It is packed with insights and predictions that were not made by Inhelder and Piaget.?These include that there were postformal levels that were not reducible to formal operations.?Fischer himself, suggested to me that there could be problems.?He said that Biggs and Biggs found a stage in preoperations that was not in Inhelder & Piaget nor in his theory.?Also, stages beyond the metasystematic, while possible would require a new tier, something he was not supportive of if I remember correctly.?Although there is only one stage missing and the evidence is striking and important for the Sentential stage, it suggests that a less rigid theory of the sequence was necessary.? Contemporaneous and with Fischer’s help, Commons and Richards developed what would be come to be called the Model of Hierarchical Complexity.?It made many fewer assumptions than Inhelder and Piaget and some fewer than Fischer.?We are waiting for someone to come up with additional stages.?The chance that there are too many is not supported by the data. Now most directly to Richard’s point about the operatory structure.?In the later 19th century, physical had posited an ether in which light traveled.?The inference that this was necessary turned out not to be true.?There are many cases like this all throughout science.?An other example, is that were was a life force that was vesting in all living things.?That force gave rise to life of an organism. What the Model of Hierarchical Complexity proposed is that the structure that Inhelder posited was in the mind, was really in the structure of the tasks. See the attached PowerPoints.?Fischer pointed out that stage change on a task appeared to be relatively sudden especially when tested under conditions of support.?Also, Theo Dawson, Sara Ross and I have discussed at length whether or not there are gaps between stages as Inhelder and Piaget suggested.?It turns out that there are when all extraneous variables are controlled for as was the case in our Laundry series studies.?We posit that the ordinal structure of tasks leads there to be a correspond order nature to stages, but the direction of causality is clear, task ordinality causing stage of performance gaps.? In fact the stage part of?Model of Hierarchical Complexity is somewhat silent on the psychology of how problems are actually solved.?But the stage transition part suggest some processes.?These are completely consistent with Pascual-Leone’s notion of m-space. No one disputes that organisms plan their actions and many animals have representations.?The plans and representations should change with stage.?But the Group theoretical account based on operations did not hold up.? Lastly in comparing the adequacy of models, we should use Occam’s razor, models with fewer assumptions should be chosen over those with more assumption given that they each account for the data equally well.