Against Bayesian Epistemology

Summarising some points from David Deutsch's appearances onthe Jolly Swagman Podcast where he talks about Bayesian epistemology.

Probability for Justified True Belief

Bayesian Thinking

Bayes theorem is a tool for calculating conditional probabilities. Bayesian thinking is about applying this tool to avoid the trap of thinking in unconditional probabilities.

Bayesian Epistemology

Bayesian epistemology uses Bayesian thinking as a theory of knowledge, i.e., figuring what can be justified as true. This is done by assigning probability to competing theories by accumulating instances that support the theory and instances that go against the theory. The theory which has the best balance of support vs. non-supporting instances is the most probable theory, and therefore can be justified true belief.

Why is this wrong?

Deutsch explains that this form of reasoning is wrong because it's a species of inductivism. With this framework, the aim is to justify theories by seeking confirming instances. If more confirming instances are found, the theory is more justified. This kind of reasoning is flawed. Confirming instances may match a theory but they cannot prove the theory in an absolute sense. Deutsch's view (Popperian epistemology) is that theories cannot be proven in an absolute sense at all (justified), theories can only be less wrong until falsified.

Problem of induction

Inductive reasoning is a kind of naive reasoning by pattern matching. Deutsch uses the example of by observing that the sun has risen every morning in the past, it's possible to infer the sun will rise tomorrow. This seems logical on the surface, but when thought about seriously, (like Popper, as he puts it) this logic breaks down. The sun's inextricable link to our biology and human life makes this example a bit obtuse, but taking this example to limit reveals how inductive reasoning falls apart, i.e., at some point in the the distant cosmologicaly future of the solar system, our sun will expand swallow the earth and end the cycle of sun rises. Observing the history of sun rises on earth will not have predicted this end.

Nassem Tablem, popularised more examples of this kind of reasoning in his book Black Swan. The titular example being that you cannot infer the non-existence of black swans with observations of only white swans (in an unbounded context, at least). Nassem, an expert in Bird Law Philosophy, also provides the example of the Thanks Giving turkey. A turkey is fed every day by a farmer, and the turkey infers that the farmer is a friend. This inference is based on the pattern of behaviour of the farmer. However, the turkey is slaughtered on Thanksgiving, and the turkey's inference is proven wrong.

Popperian Epistemology

Does this mean it cannot be predicted that the sun will rise or the turkey will be slaughtered? No. Deutsch would argue that explanatory theories are better ways to make predictions. For example, we can predict the sun will rise based on the explanatory theory of the physics of our solar system. We can predict the turkey will be slaughtered based on a theory of the social and economic constructs of Thanks Giving.

The future of civilisation unpredictable in principle

The future of civilisation is entirely dependent on future knowledge creation, or lack thereof. Knowledge, by definition, cannot be predicted. Therefore, projecting forward is prophecising rather than predicting. Deutsch uses the example of trying to project the future of the world's energy production in 1900. In 1900, the knowledge of nuclear power was not known. Being able to accurately predict energy production and arrival of nuclear power would be the equivalent of discovering the knowledge of nuclear power itself – impossible. Predicting what knowledge will be uncovered in how that will shape the future is unknowable. Deutsch also points out the problematic view that there is less knowledge to uncovered in the future i.e., no more low hangin fruit. Deutsch believes knowledge is infinite, and therefore there is still an infinite amount of knowledge to be uncovered in the future.

Predicting Technologically-caused Catastrophe

Deutsch discusses why he thinks Bostrom's Vulnerable World Hypothesis is flawed. Bostrom's hypothesis is that as technology is developed, the probability of discovering technology that can cause a catastrophic event increases, therefore the probability of a major human-ending catastrophe increases as technology is developed. This can used as a argument to slow down technological advancement (topic de jour is AI alignment/safety). Deutsch points out there is a flaw in this thinking because new kinds of knowledge will mitigate catastrophe-causing nature of other new technology. Deutsch also considers the purposeful technological deceleration as a path to totalitarianism.

Technological Advancement is Catastrophe-Avoiding

It's Deutsch's view is that history shows that catastrophe is actually the default outcome and technological advancement is the only path to avoid it. Deutsch explains that the downfall of every civilisation in history can be explained by a lack of knowledge and no civilisation has ever been destroyed by too much technological progress.