 Sentential operators are conceived as mapping not signs, nor inscriptions, to other signs and ascriptions but rather propositions, (in Wittgenstein’s rather course-grained sense of the term) to propositions. On Wittgenstein’s account of proposition, repeated application of an operation such as negation \(\ldots p, {\sim}p, {\sim}{\sim}p\ldots\) may take one back to an earlier point. Nonetheless Wittgenstein attempts to explicate arithmetic in terms of sentential operators applied to non-mathematical language. (One can see intimations here of Church’s later rigorous working out of a similar idea in his treatment of numbers in the lambda calculus as functions which repeatedly apply input functions.) In slogan form, numbers are exponents of operations (ibid., ¶6.021). Thus where \(\Omega\) is schematic for an operator and \(\Omega p\) (or \(\Omega(p))\) for its application to a proposition, then we can view the series