Functionspaces, simplicity and curve fitting

Abstract

AbstractThe number of adjustable parameters in a model or hypothesis is often taken as the formal expression of its simplicity. I take issue with this `definition´ and argue that comparative simplicity has a quasi-empirical measure, reflecting experts’ judgements who track past use of a model-type in or across domains. Since models are represented by restricted sets of functions in a suitable space, formally speaking, a general `measure of simplicity´ may be defined implicitly for the elements of a function space. This paper sketches such a framework starting from intuitive constraints. It is shown how experts’ judgements feed into this framework and how the usual definition can be recovered. A theorem by H. Akaike in the theory of model-choice has recently been used to shine new light on the relationship between the demand for simplicity and empirical success, or even `truth´. The approach favored here permits an alternative answer based on a reliabilist account of justification: if judgements of simplicity track past successful use of a model-type comparative simplicity is evidential and inductive.