Historically, physicists like Ed Jaynes and his predecessors championed probability theory as an essential tool in scientific inquiry. Garrett argues that scientists are often better positioned than statisticians to innovate in statistical methods because these methods are meant to be practical tools rather than theoretical endpoints.

Contrasting the Bayesian and frequentist approaches, Garrett advocates for Bayesian methods, explaining that they allow scientists to incorporate prior knowledge, which is crucial for practical applications, like estimating probabilities in drug trials or climate science. Unfortunately, frequentist methods dominate, partly due to historical momentum but often fall short in high-stakes or complex fields where a nuanced understanding of uncertainty is needed. Kaplan and Garrett touch on real-world examples, like the insurance industry’s implicit Bayesian methods and the successful use of Bayesian techniques in finding submarines.

Touching on the broader implications of “postmodern” science, Garrett identifies meta-analysis and underpowered datasets as culprits for non-replicability, especially in biomedical sciences. He contrasts this with the relative rigor of physics, which benefits from fewer variables and more mathematical control.

In this bonus episode James Franklin interviews Anton Garrett about his connections to major figures in probability theory, particularly E.T. Jaynes and David Stove. Garrett used Jaynes's work on probability to solve problems in statistical mechanics during his doctorate at Cambridge and Jaynes led him to the work of R.T. Cox. Cox showed that the rules of probability are essential for true-or-false propositions, providing a foundation for objective probability theory.

Garrett knew Jaynes as a shy but brilliant physicist who applied the "maximum entropy method" to astrophysics, leading to significant advancements in deblurring images. He also recalls Jaynes’s love for music and his quiet demeanor, contrasting with his confident academic writing.

The two also discuss David Stove, whom Garrett met at the University of Sydney. Stove criticized Karl Popper’s philosophy of science, arguing that Popper's rejection of inductive logic was flawed. Stove believed that induction, when done correctly, aligns with probability theory and is essential to scientific reasoning.

Garrett also reflects on Stove's concerns about political correctness (or "woke culture") in academia, which he believes is damaging free thought.

In Episode 7, Emily sits down with James Franklin, an Australian philosopher and mathematician. James was a student of David Stove in the 1970s, and later, a close friend. Emily and James dig into Stove’s work on logical probability and philosophy of science, particularly his critique of David Hume's skepticism regarding induction.

During the left-wing activism of the 1970s David Stove's politically conservative views led him to be an outsider, with it taking years for his ideas to gain recognition. His polemical book, Popper and After (https://www.amazon.com/Popper-After-F..., criticized influential philosophers like Karl Popper and Thomas Kuhn, calling them "irrationalists." Popper’s idea that scientific theories could only be falsified, not confirmed, was particularly targeted by Stove, arguing that this undermined the rationality of science, reducing scientific progress to sociological factors rather than evidence. Franklin elaborates on how Stove believed this probabilistic reasoning was essential in fields like science and law.

In addition to discussing Stove, Franklin talks about his own academic work, particularly in logical probability, philosophy of science, mathematics, and ethics. He has written extensively on the objective basis of these fields, arguing for the existence of absolute truths in areas ranging from scientific reasoning to moral philosophy. Franklin’s latest book on ethics, The Worth of Persons: The Foundations of Ethics (https://www.amazon.com/Worth-Persons-..., asserts that ethical truths are grounded in the inherent value of human beings, rejecting relativism in favor of objective moral necessity.