the tl;dr key points
THE BAYESIAN CALCULATOR: WHY YOU SHOULD CARE ABOUT IT
Tomorrow, I'll be giving my last lecture on Bayesianism for the course "Phil 60: Introduction to Philosophy of Science" at Stanford University.
There, I'll be talking about a Bayesian solution to the problem of underdetermination, associated with Pierre Duhem and Willard van Orman Quine.
The problem essentially concerns the limited ability of evidence to support or rule out isolated hypotheses. For example, if you run an experiment to test whether a putative piece of iron melts at 1538 degrees Celsius, and the piece doesn't melt at that temperature, then you have at least two possible responses: you could rule out the hypothesis that iron melts at 1538 degrees Celsius, or you could instead rule out the hypothesis that the piece of metal was actually iron as opposed to another substance. As Duhem put it, the experiment itself does not tell you which specific hypothesis is false: