 As regards #3, Black, Savitt, and Frascolla have argued that, since we ascertain the truth of tautologies and mathematical equations without any appeal to “states of affairs” or “facts”, true mathematical equations and tautologies are so analogous that we can “aptly” describe “the philosophy of arithmetic of the Tractatus… as a kind of logicism” (Frascolla 1994: 37). The rejoinder to this is that the similarity that Frascolla, Black and Savitt recognize does not make Wittgenstein’s theory a “kind of logicism” in Frege’s or Russell’s sense, because Wittgenstein does not define numbers “logically” in either Frege’s way or Russell’s way, and the similarity (or analogy) between tautologies and true mathematical equations is neither an identity nor a relation of reducibility.