### Hypothesis and Confirmation

Week 5 of Introduction to Mathematical Philosophy is about what it means for an evidence (E) to confirm a hypothesis (H) relative to background knowledge (K). The issue is addressed using Bayesian Confirmation Theory, which is derived from Bayes' Theorem.

Bayes Theorem describes the relationship between the new (or posterior) probability of a hypothesis (H), after having learned a piece of evidence (E). Using the theorem we can derive a formula known as Bayes' rule.

P(H) is the prior probability of hypothesis
P(E/H) is the likelihood of evidence given the hypothesis
P(E) is the expectedness of the evidence
P(H/E) is the posterior probability of the hypothesis, the new probability given the Evidence

Evidence confirms the hypothesis if the posterior probability is greater than the prior probability of the hypothesis. Evidence disconfirms the hypothesis if the posterior probability is less than the prior probability of the hypothesis, and the evidence is irrelevant if the posterior probability is equal to the prior probability.

The lecturer elaborates Bayesian Confirmation Theory using the example of the famous Monty Hall problem.