ABSTRACT
After proving Bayes’s theorem, I describe two simple examples in which the theorem can be used to figure out what the probability of a hypothesis is, given an observation. I then explain why using Bayes’s theorem is sometimes controversial in science. Finally, I discuss the relevance of the theorem to Hume’s discussion of the problem of induction.
Thomas Bayes was an eighteenth-century clergyman and a contemporary of Hume’s, though the two never met. After Bayes died, an essay of his was presented before the Royal Society of London. It provides a proof of what is now called “Bayes’s theorem.” Bayes’s derivation was more complicated than the one I’ll describe here. After explaining the theorem, I’ll explain why the theory of nondeductive inference now called “Bayesianism” is controversial in science. I’ll then describe the theorem’s bearing on Hume’s problem of induction (Chapter 17).
