Martin Sahlén

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data.

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge, and the emergence of the new field “Philosophy of Cosmology.” One central issue is what defines a “good” model. I discuss how “good” models are conventionally chosen, and how those methods operate in data-sparse situations: enabling the implicit introduction of value judgments, which can determine inference and lead to inferential polarization, e.g., on the question of ultimate explanation. Additional dimensions for comparing models are needed. A three-legged comparison is proposed: evidence, elegance and beneficence. This explicitly considers the categories of criteria that are always at least implicitly used. A tentative path to an implementation of the proposed model comparison framework is presented. This extends the Bayesian statistical framework. Model comparison methodology is fertile ground for dialogue between the sciences and the humanities. The proposed framework might facilitate such a dialogue.