Mapping Ebola Event Risk by Postulating a Financial Markets Ontology.
1. As we said last time, correlation is not causation. This is an important distinction in science. If we wish to do science in law and finance, then using a Category Theory approach, we should translate our statements made of legal and financial terms into SCIENTIFIC PROPOSITIONS that adhere to at least a FIRST ORDER LOGIC. Translated into this first order logic, we can check our premises and inspect our deductions and inferences for their weaknesses and soundness. If you would like to know what scientific language would look like, you can turn to Spivak's A Category Theory for Scientists (Old Version) 2013-14 which is freely available on the Web. In brief, theories and models within theories are written in propositional form using "arrow-language", thus, f:A-->B, where f designates the name of the arrow between A and B. If you trace Spivak's work who is at MIT, you'll note that he wrote a paper together with Robert E. Kent on "Ologs", which are basically "ontological statements" of real processes. Robert E. Kent (who's affiliation to any academic institution appears non-existent) has written on the INSTITUTIONAL APPROACH which is a version of Category Theory that is translated for use among people who work and play in the area of INSTITUTIONAL THEORY. As far as I can tell with my almost total ignorance of the field, the first successful transplantation of a fundamental device from Category Theory into Institutional Theory was by Dimaggio & Powell in their extremely well-cited paper (over 27,000 citations so far) on "The Iron Cage Revisited: Institutional Isomorphism and Collective Rationality in Organizational Fields" (1983) see Jistor. They used the concept of isomorphism which in Category Theory means f:A->B and g:B->A, so that the morphisms f and g which represent "processes" link the two objects A and B in a manner such that the objects are isomorphic, that is, that A and B are unique up to isomorphism. Even if you don't quite understand what this "definition" means, you should understand that isomorphism is the way Category Theorists think about "equivalence." It is all process driven.
2. Now Robert E. Kent's work on the Institutional Approach is part of a blossoming field called ONTOLOGIES. An ontology is simply a model of real processes involving people and machines, especially computational devices that can be linked. The link between Category Theory and Ontology goes back to a prescient genius named Goguen who was at the University of California San Diego. His paper on "A Categorical Manifesto" 1991 is a must read. And the paper co-authored with Burstal on: INSTITUTIONS: ABSTRACT MODEL THEORY FOR SPECIFICATION AND PROGRAMMING (1992). This paper lays out a fantastic theory of institutions that is rigged according to category theory formalities. Now how do these theories relate to the Ebola versus Financial Charts above?
3. Well, the point is that it is genuinely difficult to understand what the above charts MEAN unless we have some kind of FINANCIAL MARKET ONTOLOGY buzzing away in the back of our minds. That ontology would need to be made explicit in order for us to have an explicit understanding of the EVENT RISK that Ebola (as an event) poses onto the minds of financial traders.
4. To do that which is required in 3 may seem very complicated indeed! But I don't think so. We will examine that space--the space of financial market ontology--in further blogs.