Inductive Skepticism and the Probability Calculus I: Popper and Earman on the Probability of Laws

Attempts to utilize the probability calculus to prove or disprove various inductive or inductive skeptical theses are, I believe, highly problematic. Inductivism and inductive skepticism are substantive (logically consistent) philosophical positions that do not allow of merely formal proofs or disproofs. Often the problems with particular alleged formal proofs of inductive or inductive sceptical theses turn on subtle technical considerations. In the following I highlight such considerations in pointing out the flaws of two proofs, one an alleged proof of an inductive sceptical conclusion due to Karl Popper, the other an alleged proof of an inductivist thesis originally due to Harold Jeffreys and later advocated by John Earman. Surprisingly, in examining Popper's argument it is shown that certain apparently weak premises, often embraced by both inductivists and deductivists, lend themselves to inductive conclusions. However, it is argued, those premises are still philosophically substantive and not amenable to a purely formal demonstration. The lesson to be learnt here is twofold. First, we need to be very careful in determining which formal theses entail, and which are entailed by, inductive skepticism and inductivism. Second, we need to take great care in laying out and examining the assumptions presumed in formal arguments directed for and against such formal theses.Article