In his 2011 book Universal Darwinism: The Path of Knowledge, Campbell wrote...

The Universal Darwinism meta-theory contains the numerous scientific theories which employ a Darwinian process to explain the creation and evolution of their subject matter as well as an exposition of the general principles these theories have in common. The ‘universal’ aspect of this theory is justified by the broad scope of subject matter included under its umbrella. The literature contains numerous scientific theories in quantum physics, atomic and molecular physics, cosmology, biology and culture.

This book will make the argument that Universal Darwinism provides a further advance in the unification of scientific understanding; that Universal Darwinism is a means of consolidating a wide swath of seemingly disparate scientific subject matter within a single theoretical paradigm. The forces and interactions of the micro-world are viewed by modern particle physics in terms of information. John Archibald Wheeler, one of the past century’s most influential physicists, liked to say that his career had moved through three phases, from “Everything is particles” to “Everything is fields” to “Everything is information” (Ford 2010). The concept of information not only has a central explanatory role within particle physics it is also central to explanations of emergent levels of complex reality such as biology and culture. The increased focus of scientific explanation on information holds promise for a single theory with the ability to unite many branches of science within the same theoretical framework. For the past 60 years a single theory that is able to explain all fundamental interaction in terms of information has been physic’s Holy Grail and is often referred to as the Theory of Everything (TOE). The presumptuous title is due to the hope that given a single theory of the building blocks we would be able to explain all the more complex emergent systems, such as chemistry and life, which arise from them.

Universal Darwinism, pp. 3-5

In his 2016 article, Universal Darwinism As a Process of Bayesian Inference, Campbell wrote...

Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes ~ncluding the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an •experiment" in the external wood environment, and the results of that "experiment" or the "surprise· entailed by predicted and actual outcomes of the "experiment." Minimization of free energy impfies that the implicit measure of •surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generafized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evldenoe-based knowledge. This algorittvn is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The vanational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.

"Universal Darwinism as a process of Bayesian inference." Frontiers in Systems Neuroscience, 10, 49.

Campbell assumed that Darwinian processes are an implementation of Bayesian inference.
He explored the growth of knowledge and the complexity of internal modeling under selection, beginning with the quantum wave function, as described in Wojciech Zurek's theory of Quantum Darwinism, and extended this information-based model to biological organisms, nervous systems, evolutionary psychology, human culture and scientific knowledge.

Campbell's 2019 paper, with British neuroscientist and active inference theorist Karl Friston marked the beginning of a collaboration between Campbell and Friston.

Campbell's 2021 book, The Knowing Universe further builds on the work of Friston and his Free Energy Principle.

A largely unheralded scientific revolution is sweeping through the research community. One aspect of this revolution is a growing body of research centred on Karl Friston's notions of the Bayesian Brain and the Free Energy Principle and based on this work, Friston is rated the most influential neuroscientist of our day. His research reveals that the computation of Bayesian inferences, or the solving of mathematical relationships between hypotheses and evidence, is the brain's main problem-solving mechanism. As documented in the flood of research papers currently published at a rate of over one thousand a year referring to the free energy principle, it appears the brain uses Bayesian inference over and over again to solve the many puzzles confronting it.

The Knowing Universe, book jacket