Probability Theory

This is the great insight of probability theory: that we should look at the possible outcomes from a given situation, not what has gone before.

Mathematics is not just a “numbers game,” it is a way of thinking. We will see that probability is a qualitative subject.

More than that. All decision-making under uncertainty is Bayesian – or to put it more accurately, Bayes’ theorem represents ideal decision-making, and the extent to which an agent is obeying Bayes is the extent to which it’s making good decisions. Logic itself, all that stuff you may remember about ‘All men are mortal; Socrates is a man; ergo Socra