Parsimony ? The Fourth Substance

Occasionalism is a variation upon Cartesian metaphysics. The latter is the most notorious case of dualism (mind and body, for instance). The mind is a ?mental substance?. The body ? a ?material substance?. What permits the complex interactions which happen between these two disparate ?substances?? The ?unextended mind? and the ?extended body? surely cannot interact without a mediating agency, God. The appearance is that of direct interaction but this is an illusion maintained by Him. He moves the body when the mind is willing and places ideas in the mind when the body comes across other bodies. Descartes postulated that the mind is an active, unextended, thought while the body is a passive, unthinking extension. The First Substance and the Second Substance combine to form the Third Substance, Man. God ? the Fourth, uncreated Substance ? facilitates the direct interaction among the two within the third. Foucher raised the question: how can God ? a mental substance ? interact with a material substance, the body. The answer offered was that God created the body (probably so that He will be able to interact with it). Leibnitz carried this further: his Monads, the units of reality, do not really react and interact. They just seem to be doing so because God created them with a pre-established harmony. The constant divine mediation was, thus, reduced to a one-time act of creation. This was considered to be both a logical result of occasionalism and its refutation by a reductio ad absurdum argument.

But, was the fourth substance necessary at all? Could not an explanation to all the known facts be provided without it? The ratio between the number of known facts (the outcomes of observations) and the number of theory elements and entities employed in order to explain them ? is the parsimony ratio. Every newly discovered fact either reinforces the existing worldview ? or forces the introduction of a new one, through a ?crisis? or a ?revolution? (a ?paradigm shift? in Kuhn?s abandoned phrase). The new worldview need not necessarily be more parsimonious. It could be that a single new fact precipitates the introduction of a dozen new theoretical entities, axioms and functions (curves between data points). The very delineation of the field of study serves to limit the number of facts, which could exercise such an influence upon the existing worldview and still be considered pertinent. Parsimony is achieved, therefore, also by affixing the boundaries of the intellectual arena and / or by declaring quantitative or qualitative limits of relevance and negligibility. The world is thus simplified through idealization. Yet, if this is carried too far, the whole edifice collapses. It is a fine balance that should be maintained between the relevant and the irrelevant, what matters and what could be neglected, the comprehensiveness of the explanation and the partiality of the pre-defined limitations on the field of research.

This does not address the more basic issue of why do we prefer simplicity to complexity. This preference runs through history: Aristotle, William of Ockham, Newton, Pascal ? all praised parsimony and embraced it as a guiding principle of work scientific. Biologically and spiritually, we are inclined to prefer things needed to things not needed. Moreover, we prefer things needed to admixtures of things needed and not needed. This is so, because things needed are needed, encourage survival and enhance its chances. Survival is also assisted by the construction of economic theories. We all engage in theory building as a mundane routine. A tiger beheld means danger ? is one such theory. Theories which incorporated less assumptions were quicker to process and enhanced the chances of survival. In the aforementioned feline example, the virtue of the theory and its efficacy lie in its simplicity (one observation, one prediction). Had the theory been less parsimonious, it would have entailed a longer time to process and this would have rendered the prediction wholly unnecessary. The tiger would have prevailed. Thus, humans are Parsimony Machines (an Ockham Machine): they select the shortest (and, thereby, most efficient) path to the production of true theorems, given a set of facts (observations) and a set of theories. Another way to describe the activity of Ockham Machines: they produce the maximal number of true theorems in any given period of time, given a set of facts and a set of theories. Poincare, the French mathematician and philosopher, thought that Nature