Simplicity and Measurability in Science

Luigi Scorzato (Roskilde) gives a talk at the MCMP Colloquium (16 January, 2013) titled "Simplicity and Measurability in Science". Abstract: Simple assumptions represent a decisive reason to prefer one theory to another in everyday scientific praxis. But this praxis has little philosophical justification, since there exist many notions of simplicity, and those that can be defined precisely strongly depend on the language in which the theory is formulated. Moreover, according to a common general argument, the simplicity of a theory is always trivial in a suitably chosen language. However, this "trivialization argument" is always either applied to toy-models of scientific theories or applied with little regard for the empirical content of the theory. In this paper I show that the trivialization argument fails, when one considers realistic theories and requires their empirical content to be preserved. In fact, the concepts that enable a very simple formulation, are not necessarily measurable, in general. Moreover, the inspection of a theory describing a chaotic billiard shows that precisely those concepts that naturally make the theory extremely simple are provably not measurable. This suggests that, whenever a theory possesses sufficiently complex consequences, the constraint of measurability prevents too simple formulations in any language. In this paper I propose a way to introduce the constraint of measurability in the formulation of a scientific theory in such a way that the notion of simplicity acquires a general and sufficiently precise meaning. I argue that this explains why the scientists often regard their assessments of simplicity as largely unambiguous.