
Symmetry 2011
Symmetry, Invariance and Ontology in Physics and StatisticsDOI: 10.3390/sym3030611 Keywords: cognitive constructivism, de Finetti’s and Noether’s theorems, information geometry, MaxEnt formalism, objective ontologies, reference priors, subjectivism Abstract: This paper has three main objectives: (a) Discuss the formal analogy between some important symmetryinvariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finettitype theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective interpretations that are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realismsubjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion.
