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Symmetry, Invariance and Ontology in Physics and Statistics
Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo 05508-090, Brazil
Received: 23 February 2011; in revised form: 25 August 2011 / Accepted: 26 August 2011 / Published: 1 September 2011
Abstract: This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance 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 Finetti-type 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 realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion.
Keywords: cognitive constructivism; de Finetti’s and Noether’s theorems; information geometry; MaxEnt formalism; objective ontologies; reference priors; subjectivism
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MDPI and ACS Style
Stern, J.M. Symmetry, Invariance and Ontology in Physics and Statistics. Symmetry 2011, 3, 611-635.
Stern JM. Symmetry, Invariance and Ontology in Physics and Statistics. Symmetry. 2011; 3(3):611-635.
Stern, Julio Michael. 2011. "Symmetry, Invariance and Ontology in Physics and Statistics." Symmetry 3, no. 3: 611-635.