The particular examples of infeasible numbers put forward by Yessenin-Volpin and others use exponential or iterated exponential notations such as n₁^n₂ or n₁^(n₂^n₃).

If we regard such expressions as tokens rather than types, then it makes sense to consider the task of concretely ‘counting up to’ a number by constructing its unary representation in the sense described by Yessenin-Volpin. g. the unary numerals are generated by applying the formation rule \(\sigma \mapsto \sigma'\) to the initial symbol \(0\). e. [49] In attempting to accommodate (S1)–(S3) simultaneously, we must confront a tension which has led many authors to follow Dummett (1975) in conclu