Critical Rationalism and Bayesianism

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Critical Rationalism and Bayesianism

Kent Olson Ph.D.
Received: 05 March 2023; Accepted: 22 March 2023; Published: 30 April 2023

Abstract: Most accounts of the scientific method, e.g.s the Deductive-Nomological (D-N), Inductive Statistical (I-S), and so on, attempt to avoid Hume’s problem. Popper’s philosophy of critical rationalism and subjectivist Bayesianism come into conflict here on a number of points. The most noteworthy is on the problem of induction. That is, if science rests on induction (as Sir Francis Bacon would have it), and induction cannot be justified according to the strict demands of classical deductive validity without invoking a circularity, how can we say that science is rational? And how should scientists proceed? Bayesians utilizes a consistent multivalued logic that adheres to the Kolmogorov axioms. And on the other side, Sir Karl Popper maintains that the real logic of science is deductive. It is a myth that induction is even used. I will evaluate both claims through a third-party lens. That is, Micheal Ruse’ s epigenetic account of inferential reasoning. This is a modified version of Hume’s propensity theory. Ultimately, deductivism cannot explain how proto-humans behaved in the wild. How they grew smarter, became tool-using beings, and became the dominant species on the planet.

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Keywords: Induction, Bayes, Bayes’ theorem, critical rationalism, Karl Popper, deductivism, problem of induction, epigenetic

I. Introduction

A debate between Francis Bacon and David Hume sets the stage for our topic. In the A Treatise of Human Nature (1739-40), and his shorter work, the Enquiries Concerning Human Understanding (1748), Hume pointed our attention to the old sceptical idea that thinking subjects cannot know. If we see a billiard ball hit another, we expect the second billiard ball to move. He alleged this connection between cause and effect was only a psychological necessity informed by custom or habit. We are aware of no principle in nature informing us that this must be the case. Since Bacon’s Novum Organum (1620), allegedly the logic of science rested on this type of reasoning. It was steeped in observation and did not resemble the logic of Aristotle which was popular with the scholastic philosophers hitherto in medieval Europe Hume held that reasonings such as all A’s are B’s is the same type of reasoning based on the relation of cause and effect. There may be an A that is not a B no matter how many times in nature I have seen the two being concomitant. It is fallible logic. Aristotle’s syllogistic logic that was prevalent before Bacon, did not have this problem.

To begin, I offer three broad accounts of how to overcome the problem of induction, (i) Bayesian reasoning offers a probabilistic answer. Our answer to the question of whether or not the next raven I see will be black will not be in a binaristic form, but somewhere in between the values of 0 and 1. Our answer will not be deductively valid, nor does it have to be. (ii) Popper’s answer, in contrast, is that scientific reasoning is deductive. We offer hypotheses and then subject them to crucial experiments. The logic follows modus tollens: p →q, ~q ⸫~p. This is entirely deductive. Like Bayesians and Popperians, Michael Ruse’s (iii) epigenetic account of induction dovetails well with Humean scepticism. He relies upon the propensity theory of inductive inference. This is the sceptical conclusion that the necessary connection between cause and effect is a psychological propensity which “speads itself on nature”. It is in agreement with the third position that I will evaluate they first two.

“Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure.”

—Sir Karl Popper
Conjectures and Refutations, p.53
Routledge Classics, 1963