• Using Bayes’ Theorem

Can Probabilistic Thinking be a Unified theory for reason and belief updating? It would need to fully subordinate Bayes’ Theorem and Solomonoff Induction (the latter of which may already be a Unified theory of its own).

Bayes’ Theorem (whether implicitly or explicitly) is what is used to direct “belief energy” towards true beliefs. This is like how a machine needs energy input to continue running.

Using Bayes’ Theorem, if you have two phenomena that have any non-independence, then their influence on each other is symmetric.

1. Bayes’ Theorem: posteriors are determined by a combination of prior probabilities and data / likelihood

Bayes’ Theorem

Using Bayes’ Theorem, if you have two phenomena that have any non-independence, then their influence on each other is symmetric.

With evidence and insight we can update those beliefs, and the mathematically accurate way to update those beliefs is using Bayes’ Theorem.^[ Rationality, From A to Z#^0917ad] Even if we don’t choose to be mathematically precise when we update our beliefs, it is useful to have an internalized version of Bayes’ Theorem so that we can avoid making systematically incorrect updates to our beliefs.

An intuitive way to think about updating according to Bayes’ Theorem is to understand at least the following:

It may even be more than a metaphor, if we take the idea that Entropy is the tendency of a system to progress towards technical simplicity, and Bayes’ Theorem may be a tool for helping us see the flow of Entropy.

• Week 3, Bayes’ Theorem

It is possible that science is an “approximation to some probability-theoretic ideal of rationality”.^[ Rationality, From A to Z#^9281a1] In which case, it is possible that science is a social and approximate version of Bayes’ Theorem and Solomonoff Induction.

I believe Bayes’ Theorem is the tool to use for inductive logic, because A belief is a degree of certainty.

We can create markers of important shifting areas and call them orders of magnitude for probability. One can use Bayes’ Theorem to create these markers.

Create a course that teaches Bayes’ Theorem and Solomonoff Induction. Integrate the course with Spaced Repetition learning.