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Religious notions have long played a role in epistemology. Theological thought experiments, in particular, have been effective in a wide range of situations in the sciences. Some of these are merely picturesque, others have been heuristically important, and still others, as I will argue, have played a role that could be called essential. I will illustrate the difference between heuristic and essential with two examples. One of these stems from the Newton−Leibniz debate over the nature of space and time; the other is a thought experiment of my own constructed with the aim of making a case for a more liberal view of evidence in mathematics.