Karl Popper argued that science proceeds not by induction but by offering explanatory theories that scientists then attempt to falsify. What cannot be falsified falls outside the realm of science. In applying his ideas to the writing of history, Popper was particularly scathing about Marxist predictions of future historical development. But he did believe history could be written by looking at the situations in which historical figures found themselves and the problems they attempted to solve. Pentecostal historiography has been divided into four main types: the providential, the historical roots, the multicultural, and the functional. When each of these types is analyzed and judged against Popper’s strictures against induction, we find, among other things, that the unfashionable providential account need not be ruled out.