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I have read through the Commons & Pekker article on the formal structure of MHC. That does seem straightforward from the formal point of view. Higher-order actions are defined by means of rules for the coordination of some lower-order actions. However, when I look at the detailed MHC stages that this formalism is supposed to cover, I see much more complexity than is available within the formal structure by itself.? The detailed MHC claims about humans are: >From pre-operational down (MHC levels 6 to 1), we have?deductions / sequences / relations-among-concepts / concepts / open-ended classes / stimulus discrimination. My queries:? Are deductions not more than rules and coordination of sequences? MLC:?These are not definitions but examples.?The are co-ordinations of sequences of rules.? A implies B? is a rule statement A is the a statement Together one gets B. Are sequences not more than rules and coordination of relations-among-concepts? Are relations-among-concepts not more than rules and coordination of concepts?? Etc. Certainly, deductions involve rules and coordination of sequences (etc.), but they do much more than that! MLC:?That is why getting to that stage make such a difference What I see, is that there is enormous AMOUNT of empirical content in the 14 ‘Orders of Hierarchical Complexity?that Michael and others have formulated!?Much MORE empirical content than described by the formal structure of the Pekker paper! Real psychological stages are a lot more complicated (and interesting) than the examples of distributive laws in arithmetic. MLC:?The examples have lots of empirical content to illustrate the orders.?But the orders can be done without any reference to the content.?They would not resonate with what we see as stages.?Remember, these are just short hand illustrations.? My question to Michael: can you produce arguments for the details of the 14 ‘Orders of Hierarchical Complexity?? MLC? One using the axioms to generate the sequences.?So far we have over 50 sequences.?Look at the empirical studies that were attached to see how well the orders of hierarchical complexity predicted difficulty. I look back through all your papers at www.dareassociation.org, but seem only to define assertions of these 14 orders, not arguments for them. You assert, for example, that there are 2 stages within each of Piaget’s stages. Where do you argue this? Why 2 and not, say, 3? MLC:?This is proved in the case of primary and concrete in the papers.?But almost all neo-Piagetians have argued this starting with Pascual-Leone.?What the MHC does is show the mathematical reasons that concrete order tasks organize primary order tasks and not pre-operational ones Are you able to point to an online paper or discussion where you introduce those component stages? The scoring manual was an early write up of them.?The chapters if Beyond Formal Operations has a table listing many of the human ones including the postformal ones.?Within positive adult developmental stage theory, there is a consensus on them except for 13, and 14 I see a lot of discussion on the postformal stages, but really I am more interested in the earlier stages up to formal. The Commons et al (1998) paper appears promising, but still (in its Table 1) just asserts all the 14 stages without discussion.