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Thanks: I will read eg Fischer(1980). I see that he has some of the detailed arguments for specific stages: the details that I am looking for. You say (in your Laundry paper) that you long ago added the Sentential Order 5 compared with Fischer.? Where in the literature do you argue for this? MLC:?Biggs, J. & Collis, K.?(1982).?A system for evaluating learning outcomes:?The SOLO Taxonomy. New York: Academic Press. Note still, that the FORMAL theory does not forbid empirical arguments to add or delete an order of complexity. MLC:?That is correct.?If there were a problem where we met the axioms and controlled for variables other than hierarchical complexity, and there still was an overlap, there would be a problem.?This has not happened in 30 years. If order 5 were not supposed to be there, say, then present orders 6-14 would simply be renamed 5-13, and the formalism would still be valid. Similarly, if a new order between 4 & 5 were needed, say, then it would be called order 5, and the present orders 5-14 would be renumbered 6-15, and the formalism would still be valid. This is exactly what you did to Fischer when you added Order 5. MLC:?So far we agree I conclude that it is empirical arguments that are needed to justify each order: these are more than purely formal considerations. MLC:?We have spent 30 years constructing instruments to increase our certainty on these issues You say (below) that you have empirical arguments for “no extra ones? Exactly these are the arguments I am looking for! Have you been keeping a record of which empirical investigations have yielded conclusions concerning which order of complexity? MLC:?Yes.? If you have been, then such a compendium ought to be published, since it would enormously strengthen the case for your model. If this is not been done, then, really, each order of complexity has to be looked at individually to see whether it is empirically supported. MLC:?We are going to try to publish the Laundry series and it variants now. My overall conclusion is that we are not logically forced to accept the whole structure of 0-14 orders in toto. Instead, there need to be empirical arguments for each order. Of course, if the are LOGICAL arguments to connect one order to another, then so much the better, as then you are on even stronger ground. This is from the scoring manual Stages of Development The MHC specifies 15 order of hierarchical complexity and their corresponding stages, showing that each of Piaget’s substages, in fact, are hard stages.?Commons also adds three postformal stages. The sequence is as follows: (0) computory, (1) sensory & motor, (2) circular sensory-motor, (3) sensory-motor, (4) nominal, (5) sentential, (6) preoperational, (7) primary, (8) concrete, (9) abstract, (10) formal, (11) systematic, (12) metasystematic, (13) paradigmatic, and (14) cross-paradigmatic.?The first four stages (0-3) correspond to Piaget’s sensorimotor stage at which infants and very young children perform.?The sentential stage was added at Fischer’s suggestion.?Adolescents and adults can perform at any of the subsequent stages.?MHC stages 4-6 correspond to Piaget’s?pre-operational stage; 6-8 correspond to his concrete operational stage; and 9-11 correspond to his formal operational stage.?The three highest stages in the MHC are not represented in Piaget’s model.?Because MHC stages are conceptualized in terms of the hierarchical complexity of tasks rather than in terms of mental representations (as are Piaget’s stages), the highest stage represents successful performances on the most hierarchically complex tasks rather than intellectual maturity. Stages 0-5 normally develop during infancy and early childhood in people. At the calculatory stage (0), machines can do simple arithmetic on 0s and 1s. At the sensory and motor stage (1), infants may see or touch shapes, make generalized discriminations, as well as babbling vocalizations. At the circular sensory and motor stage (2), reaching and grasping actions occurs.?These actions generate simple gestures. At the sensory-motor stage (3), the actions become associated with vocalizations.?For instance, an infant may hold up an object and make sounds while doing so.? At the nominal stage (4), first single words are formed.?These words such as “cup?or “water?relate concepts to others. At the sentential stage (5), toddlers form short sentences and phrases.?The use pronouns, and say numbers and letters in order as well.?Sentences might be “want water,?“cup of water,?etc. At the preoperational stage (6), these sentences are organized into paragraph long utterances.? At the primary stage (7), these paragraph long utterances are organized into stories which may be matched to reality. At the concrete stage (8), two primary stage operations may be coordinated.?For example, children think that a deal is fair after looking at from the perspective of simple outcomes for each person who is entering the deal.?Negotiations make sense but there are not social norms for setting prices or values.? At the abstract stage (9), variables, stereotypes, personalities, traits, etc are introduced.?Quantification words like “everyone in my group,?What would other’s think??appear.?The dimensionalized qualities may be used to express preferences. At the formal stage (10), discussions are logical and empirical support is logical brought.?Words like “if ...then,?“in every case, it turned out the same,?“the reasons were?occur.?This is the stage with univariate and linear explanations.?There can be multiple outcomes however.?The different outcomes are generally unrelated so they do not form systems. Few individuals perform at stages above formal operations. More complex behaviors characterize multiple system models ( Kallio, 1995;?Kallio & Helkama, 1991) at the metasystematic stage.?Some adults are said to develop alternative to, and perspectives on, formal operations. They use formal operations within a “higher?system of operations and transcend the limitations of formal operations. In any case, these are all ways in which these theories argue and present converging evidence that adults are using forms of reasoning that are move complex than formal operations. At the systematic stage (11), the new concepts are referred to as 3rd order abstractions. These coordinate elements of abstract systems. Words like bureaucratic, capitalist, functional, and structural?are common. The systematic stage concept, structure, for example, can be employed to ask whether the structure of camp helps instill the qualities we want in future citizens. The logical structure of this stage coordinates multiple aspects of two or more abstractions, as in: “relationships are built on trust and though we can’t always keep them, making promises is one way we build trust, so it’s generally better to make promises than not to make them.? Here, the importance of trust to relationships, building trust, and the possibility that promises can be broken,?are all taken into account while formulating the conclusion that promises are desirable.?Each system consists of multivariate inputs or multiple relations.?For example A or B causes C can be decomposed into two causal relations, A causes C or B causes C.?A and B causes C is the cross product of two independent variables.?Think of systems as a two or more way Anova or a regression equation with cross products and multiple inputs. At the metasystematic stage (12), the new concepts are referred to as 1st order principles. These coordinate formal systems. Words like autonomy, parallelism, heteronomy, and proportionality?are common. The metasystematic stage concept of parallelism, for example, can be employed to compare the structures of the military and of camp as institutions. The logical structure of this stage identifies one aspect of a principle or an axiom that coordinates several systems, as in: “contracts and promises are articulations of a unique human quality, mutual trust, which coordinates human relations.?Here, contracts and promises are seen as the instantiation of a broader principle coordinating human interactions.? At the paradigmatic stage (13), people create new fields out of multiple metasystems.?The objects of paradigmatic acts are metasystems.?When there are metasystems that are incomplete and adding to them would create inconsistencies, quite often a new paradigm is developed.?Usually, the paradigm develops out of a recognition of a poorly understood phenomenon.?The actions in paradigmatic thought form new paradigms from metasystems (metasystems).?? Paradigmatic actions often affect fields of knowledge that appear unrelated to the original field of the thinkers. Individuals reasoning at the paradigmatic order have to see the relationship between very large and often disparate bodies of knowledge, and co-ordinate the metasystematic metasystems.?Paradigmatic action requires a tremendous degree of decentration.?One has to transcend tradition and recognize one's actions as distinct and possible troubling to those in one's environment.?But at the same time one has to understand that the laws of nature operate both on oneself and one’s environment—a unity.?This suggests that learning in one realm can be generalized to others. ?????? At the cross-paradigmatic, paradigms and coordinated.?This is the fourth postformal stage.?Cross-paradigmatic actions integrate paradigms into a new field or profoundly transform an old one.?A field contains more than one paradigm and cannot be reduced to a single paradigm.?One might ask whether all interdisciplinary studies are therefore cross-paradigmatic??Is psycho biology cross-paradigmatic??The answer to both questions is ‘no??Such interdisciplinary studies might create new paradigms, such as psychophysics, but not new fields. This order has not been examined in much detail because there are very few people who can solve tasks of this complexity.?It may also take a certain amount of time and perspective to realize that behavior or findings were cross-paradigmatic.?All that can be done at this time is to identify and analyze historical examples.