The Illusion of Induction in Scientific Progress

The Premise of Solomonoff Induction

At the heart of many debates regarding artificial intelligence and scientific methodology lies the theory of Solomonoff induction. This framework posits that if one aims to find a theory explaining a phenomenon—theoretically encoded as a binary string—the most accurate approach is to utilize a probability-weighted theory. This method accounts for all possible theories but assigns weight based on complexity. The underlying logic is that simpler explanations are inherently more likely to be true than complex ones. By summing these possibilities, one arrives at a probability distribution function for a given explanation.

The Bayesian Connection

Solomonoff induction shares significant DNA with Bayesianism. Both frameworks operate on the foundational assumption that one can enumerate all the possible theories relevant to a problem. However, this is where the theory encounters a fundamental obstacle: the nature of human creativity. In reality, it is impossible to enumerate all potential theories because the generation of a new explanation is an act of creativity. Science rarely presents us with multiple viable theories simultaneously; the transition from Newtonian theory of gravity to general relativity stands as one of the rare historical exceptions where two competing theories existed. It is almost unknown for three or more to coexist, which underscores the scarcity of competing explanations.

Constrained Spaces vs. New Knowledge

There is a common confusion regarding the efficacy of induction and Bayesianism. While these tools function exceptionally well within finite, constrained spaces that are already known, they fail when applied to the generation of new explanations.

Bayesianism is essentially a mechanism for processing new information. It allows an agent to weight previous probability predictions and adjust their priors based on new data. A classic illustration is the Monty Hall show problem. Many people initially struggle with the intuition that switching doors increases their odds of winning. However, once framed as a scenario with 100 doors—where 98 are opened to reveal nothing—the Bayesian update becomes intuitive. People often conclude that because they can perform this calculation, they are "smart Bayesians."

The Fallacy of Bayesian Discovery

While Bayesianism is an "uncontroversial use" of mathematics and serves as a "very powerful tool" in fields like medicine to determine which treatments might be more effective, it is a mistake to equate this with the acquisition of new knowledge. Bayesianism does not, and cannot, help one discover new explanations.

Ultimately, the generation of new explanations relies entirely on creativity. When it comes to judging one explanation against another, we do not rely on probabilistic weighting. Instead, we utilize experimental refutation or the straightforward criticism of identifying an explanation as inherently "bad." By conflating the management of known probabilities with the creation of new knowledge, we risk misunderstanding the very nature of scientific advancement.