Abstract:
A general mechanical procedure for reasoning about the probability calculus is presented. This procedure is then used to solve various problems in Bayesian Philosophy of Science (in particular, in Bayesian confirmation theory). Our procedure provides a vindication of the dreams of Boole (and Leibniz) to have a usable "Probability Machine" with which to investigate the cogency of (arbitrary) arguments involving the probability calculus. All necessary technical and philosophical background will be provided during the talk.