 As noted above, Proofs and Refutations takes the form of an imaginary dialogue between a teacher and a group of students. It reconstructs the history of attempts to prove the Descartes-Euler conjecture about polyhedra, namely, that for all polyhedra, the number of vertices minus the number of edges plus the number of faces is two (V – E + F = 2). The teacher presents an informal proof of this conjecture, due to Cauchy. This is a “thought experiment which suggest a decomposition of the original conjecture into subconjectures or lemmas” from which the original conjecture is supposed to follow. We now have, as well as the original conjecture or conclusion, the subconjectures or premises, and the meta-conjecture that the latter entail the former. Clearly, this kind of “informal proof” is quite different from the “formalist” idea that an informal proof is a formal proof with gaps (PP2: 63). Equally clearly, any of these conjectures might be refuted by counterexamples.