Of German Tanks and Scientific Theories

During the Second World War, the Allies faced a question colloquially known as the “German Tank Problem”: how many tanks will the Axis ever produce? The answer resulted from an elegant probabilistic argument which was used by Allied mathematicians to make successful upper-bound estimates for the total Axis tank production. This paper shows that if two empirical postulates are true of the history of science, a parallel argument can be used to come up with lower-bound estimates for the number of alternative scientific theories that remain undiscovered. The lower bound in question increases proportionally with the number of theories that have already been discovered. So, the problem of underconsideration is a serious problem and it will get worse, not better, as we discover new theories.