A bit of conceptual analysis: the book-keeper and the invisible hand [MR-2b]

I’ve got a footnote to my earlier post on marginalism as a Rank 4 concept. During its explication, Claude made the following observation:

The transition from double-entry bookkeeping to supply-and-demand might itself be seen as a Rank 3 reflective abstraction: going meta on the bookkeeping closure principle to ask what maintains closure at the level of the entire market, not just a firm's ledger.

Let’s take a look at what is going on here. In the case of double-entry bookkeeping it is the book-keeper that is the agent that maintains the closure over the accounts. In the case of supply-and-demand there is no explicit agent governing market closure, that is, the balance between supply and demand. The agent is abstract. Adam Smith famously used the metaphor of the invisible hand to mediate the conceptual gap between an actual book-keeper working on the books and the abstract market in which the actions of individual buyers and sellers are constrained in a way that keeps closure.

Making such abstractive leaps is not trivial. For it is not only the book-keeper that must be rendered abstract. So must the books. They become the market place. And the book-keeper’s actions of making entries into the debit and credit ledges must be abstracted into individual acts of buying and selling, taken as a collectivity.

The change in conceptual ontology is similar to that of abstracting over salt to come up sodium chloride. In this case the act of abstraction applies to the same physical object. In the case of supply and demand the act of abstraction gives us a new concept and about a different entity. Markets existed before the concept of supply and demand, but that concept gives us a new understanding of them. And the abstract concept of sodium chloride gives us a different way of thinking about and dealing with salt.

Thus we are brought to the notion of conceptual ontology, which is beyond the scope of this short note. You might want to consult these working papers: Ontology in Cognition: The Assignment Relation and the Great Chain of Being, Ontology in Knowledge Representation.