Engeström's contradictions, Searle's Status Functions and Kauffman's Knots

In an analysis of a childrens' hospital, Engeström discusses the contradictions between different aspects of the institution:

(from "Activity Theory as a Framework for analyzing and redesigning work", 2000)

The contradictions are shown by the 'lightning arrows' between the different aspects of the activity theory diagram. For example, between objects and instruments (at the top), there is a contradiction in assuming that patients have simple conditions, for which a 'critical pathway' of care can be provided. Many patients however present multiple conditions: how does the critical pathway cope with this? Similarly, if a patient has multiple problems, and each of those problems is attended to by a different provider, then contradictions arise in the ways that those providers coordinate with each other. Engeström points out that "traditional rules of the hospital organization emphasize that each physician is alone responsible for the care of his or her patients". Similarly, multiple diagnosis patients cause problems between the different professionals attending to them within the organisation (the division of labour). 

I'm interested in the idea of contradiction in activity theory because it paints a picture of complex constraint-relations in organisational culture. Engeström seeks to find ways of working through contradictions in what he calls 'boundary-crossing', 'knotworking' and 'expansive learning'. These are fundamentally communicative engagements which seek to articulate, bring together and transform different perspectives on organisational problems. This works, I suspect, because the sources of the organisational conflict are communicative in the first place. 

In Searle's social ontology, "rules", "divisions of labour", "critical pathways", "hospitals", "doctors" and "patients" all result from what he calls "status functions". From Engeström's perspective that perhaps doesn't add very much to his notion of the nature of organisations as activity systems. However, I think Searle's status functions are more usefully examined as "scarcity functions": to declare x as a rule for conduct y in the hospital, is to say that conduct y is not legitimate within the hospital; to declare a person to be a doctor means that nurses cannot do what the doctor does. "Doctoring" and "acting legitimately" all become scarce through the declarations of those with the deontic power within the hospital (managers). Engeström appears to want to change the status functions (or the scarcity functions) which are declared in the hospital so that the contradictions are addressed. However, for people positioned at different points in the Activity Theory diagram, there will always be issues of scarcity, role and position, rights, obligations, duties and responsibilities. In all organisations, behaviour occurs within constraints which are declared through status (or scarcity) functions. The danger is to blindly reconfigure the constraints of behaviour without fully understanding the deeper dynamics of constraint. The problem is that constraint goes far beyond contradictions between divisions of labour and rules of engagement (say). They operate historically, organisationally, socially, personally, materially, ontogenetically and intersubjectively. Moreover, social behaviour frequently serves to uncover constraints. Engeström's focus on overcoming contradiction may be misplaced: it may be more important to act methodically so as to identify the constraints within which one works in a more comprehensive way. Effective communication may depend more on the mutual understanding of constraints between practitioners than it does on the codification of new practices within the organisation.

More recently I've been reading a brilliant paper by cybernetician Lou Kauffman on Category Theory and knots. Kauffman has a simple idea. Category theory is all about 'mappings' from x to y (the posh word is a 'morphism'). Status functions also are a kind of mapping. So to say "this paper counts as money in social context c" is a mapping from the paper to money within a category (context). Kauffman argues that there can be a meta-mapping z which maps onto a mapping from x to y. In other words, it looks like this:

It seems to me that we could say that the mapping from x->y constrains z. In less formal terms, talk of markets is a mapping onto the mapping about money, or the talk of markets is constrained by the concept of money. It becomes more obvious when Kauffman does this kind of thing:

These, Kauffman explains, are  reflexive examples, because each mapping constrains the other: "every morphism in this category is a morphism of morphisms" (Kauffman, L "Categorical Pairs and the indicative shift", Applied Mathematics and Computation, 2012, vol 218)

My question on reflecting on all this, is whether Engestrom's communicative methods can be enhanced by a deeper characterisation of constraints represented as the 'mappings' of 'status functions'. Indeed, the relationship between the status function and the scarcity function is the difference between the mapping x->y (the status function) and the mapping z to x->y (constraint or scarcity). This is to dimension the inter-relations between different aspects of the activity theory contradictions at different levels of recursion (or meta-level). The recursive layering gives extra dimension to the rather monovalent contradictions described by Engestrom.