 It is not clear why one should expect the various non-deductive methods used in mathematics to share any substantive features other than their non-deductiveness. Philosophers looking at the role of non-deductive reasoning in the context of discovery have often talked as if there is some unity to be found (for example, the subtitle to Lakatos’s Proofs and Refutations is “the Logic of Mathematical Discovery.” More likely is that the array of non-deductive methods is diverse and heterogeneous. (Compare Stanislaw Ulam’s remark that “the study of non-linear physics is like the study of non-elephant biology.”)