On the role of simplicity 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. The language dependence is a natural feature - to some extent - but it is also believed to be a fatal problem, because, according to a common general argument, the simplicity of a theory is always trivial in a suitably chosen language. But, this trivialization argument is typically either applied to toy-models of scientific theories or applied with little regard for the empirical content of the theory. This paper shows 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. This explains why the scientists often regard their assessments of simplicity as largely unambiguous. In order to reveal a cultural bias in the scientists' assessment, one should explicitly identify different characterizations of simplicity of the assumptions that lead to different theory selections. General arguments are not sufficient.