Scientists routinely solve the problem of supplementing one’s store of variables with new theoretical posits that can explain the previously inexplicable. The banality of success at this task obscures a remarkable fact. Generating hypotheses that contain novel variables and accurately project over a limited amount of additional data is so difficult—the space of possibilities so vast—that succeeding through guesswork is overwhelmingly unlikely despite a very large number of attempts. And yet scientists do generate hypotheses of this sort in very few tries. I argue that this poses a dilemma: either the long history of scientific success is a miracle, or there exists at least one method or algorithm for generating novel hypotheses with at least limited projectibility on the basis of what’s available to the scientist at a time, namely a set of observations, the history of past conjectures, and some prior theoretical commitments. In other words, either ordinary scientific success is miraculous or there exists a logic of discovery at the heart of actual scientific method.