Several writers have argued for the implausibility of there being naturalistic explanations of mystical experience. These writers recognize that the evidential significance of mystical experiences for theism depends upon whether explanations that exclude supernatural agency can be discounted; but they seem unaware of some of the best scientific work done in this area. Part I of the present paper introduces the theory of I. M. Lewis, an anthropologist, and tests it against the case of St Teresa. I use Teresa because (...) of her prominence, and because we have considerable biographical data for her. I conclude that Lewis's approach, suitably supplemented, is strikingly successful in explaining this case. (shrink)