 This, in brief, is Wittgenstein’s Tractarian theory of mathematics. In the Introduction to the Tractatus, Russell wrote that Wittgenstein’s “theory of number” “stands in need of greater technical development”, primarily because Wittgenstein had not shown how it could deal with transfinite numbers (Russell 1922[1974]: xx). Similarly, in his review of the Tractatus, Frank Ramsey wrote that Wittgenstein’s ‘account’ does not cover all of mathematics partly because Wittgenstein’s theory of equations cannot explain inequalities (Ramsey 1923: 475). Though it is doubtful that, in 1923, Wittgenstein would have thought these issues problematic, it certainly is true that the Tractarian theory of mathematics is essentially a sketch, especially in comparison with what Wittgenstein begins to develop six years later.