Symmetry, Invariance and Ontology in Physics and Statistics

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.

Optimization Models for Reaction Networks: Information Divergence, Quadratic Programming and Kirchhoff’s Laws

“…This article tries to give a very simple and direct derivation of some formalisms for reaction networks that are based primarily on entropy optimization. Our conclusions about these formalisms and how they relate to each other are important for a rigorous discussion of the arguments given in articles [5][6][7], and is also required for future research.…”

“…In articles [5][6][7] we address this issue, showing the importance of sharp hypotheses in the definition of scientific ontologies. This article tries to give a very simple and direct derivation of some formalisms for reaction networks that are based primarily on entropy optimization.…”

Jacob’s Ladder: Logics of Magic, Metaphor and Metaphysics

“…In this view, the legitimacy of a scientific theory should be judged by its predictive power, by the coherence and consistency between well-formulated scientific hypotheses and empirical observations, but also by the elegance and simplicity of its formalism, by the understanding it provides about pertinent phenomena in its field of interest, by the insights and intuitions it brings for current and future research, etc. At Borges and Stern (2007), Stern (2007aStern ( , b, 2008Stern ( , 2011aStern ( , b, 2014Stern ( , 2015 and Stern and Pereira (2014), these ideas are developed much further.…”

“…After all, according to the traditional positivist credo used in statistical science: The role of science should never be to give (causal) explanations for natural phenomena, but only to formulate reliable predictions of future observations! From the previous paragraphs in this introduction, we conclude that the FBST + cognitive constructivism epistemological framework has the potential to completely reverse the traditionally low status attributed to non-observable entities in statistical models, see Stern (2007bStern ( , 2011aStern ( , 2015a. In this new epistemological framework, parametric quantities, latent (hidden) variables, and causal relations can be legitimized and be brought (back) to the center stage of scientific activity and discourse.…”

“…Our and other research groups are also conducting a systematic exploration of the intrinsic properties of the FBST framework, and studying the implications and consequences of its use, including pragmatical use and performance aspects, see for example Diniz et al (2011Diniz et al ( , 2012, Johnson et al (2009), and Lauretto et al (2003; theoretical statistics properties, see for example Madruga et al (2001), Pereira et al (2008), and Stern (2011a, b); and logical properties, see for example Izbicki and Esteves (2015), Stern (2004), Borges and Stern (2007), and Stern and Pereira (2014). Finally, a specific version of Cognitive constructivism has been developed as an epistemological framework amenable to all the aforementioned properties of the FBST, see for example Stern (2007aStern ( , b, 2008Stern ( , 2011a.…”