The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories

Abstract

Bayesian model selection in cosmology and particle physics is often performed where posterior odds inherit a strong, often unacknowledged dependence on the prior assigned to competing models. Standard responses -- reference priors, hierarchical priors, or appeals to naturalness -- ignore relevant theoretical knowledge or rely on criteria hard to define operationally. We propose the \emph{Coherence Principle}: a reproducible prescription for assigning model priors according to compatibility with the validated structure of an existing theory. This structure, or \emph{grammar}, includes symmetries, conservation laws, locality, Lorentz invariance, and universality patterns. Unmotivated violations of these rules incur a coherence cost, converted into a prior weight through a maximum-entropy exponential form controlled by one calibratable parameter $α$. The resulting prior is distinct from both the Bayesian Occam factor and naturalness: it penalizes not parameter volume or fine tuning, but departures from validated theoretical grammar. We illustrate the principle with examples from cosmology and fundamental physics: neutrino mass mechanisms, dark energy and modified gravity, inflation, beyond-Standard-Model sectors, and hierarchical astrophysical inference. We test it also on four historical cases -- general relativity, Pauli's neutrino, parity violation, and special relativity -- where evidential and theoretical contexts can be reconstructed. These examples show that it favors the historically successful choice when the proper grammar is defined in the correct domain and time. The Coherence Principle makes explicit a common but usually tacit part of physical reasoning: trust in validated structural rules. It turns this judgment into a transparent, testable, and overrulable component of Bayesian inference, leaving empirical likelihoods free to dominate when data are sufficiently constraining.