The subtitle of this post is "What is a proof and of what is a proof a proof?". Recently Thomas Forster wrote that he had been revising his SEP entry on NF. (There is apparently some excitement about a surprising theorem that it recently proved, something to do with failure of well-ordered choice). See Quine’s New Foundations by Thomas Forster. In the 11 page 1937 American Mathematical Monthly paper where he introduced the theory, Quine opens with: In Whitehead and Russell's Principia Mathematica we have good evidence that all mathematics is translatable into logic. But this calls for the elucidation of three terms: translation, mathematics, and logic. The units of translation are statements; also statement forms, i.e., expressions abstracted from statements by supplanting constants by variables. Thus it is not held that every symbol or combination of symbols of mathematics, say "Δ" or "d/dx," can be equated directly to an expression of logic. Bu...