Although it would be uncharitable to think that Yessenin-Volpin was unaware of these observations, the first person to directly reply to the charge that (S1)-(S3) are inconsistent appears to have been Parikh (1971).[50] His response can be understood as consisting of two parts, both of which bear on the analysis of the informal notion of feasibility considered in Sections   1.1 and   2.2.   On the one hand, Parikh considers what he refers to as the almost consistent theory \(\mathsf{PA}^F\). This theory is formulated over the language \(\mathcal{L}_a \cup \{F(x)\}\) supplemented with terms for all closed primitive recursive functions and contains the statement \(\neg F(\tau)\) where \(\tau\) is some fixed primitive recursive term intended to denote an ‘infeasible’ number such as \(10^{12}\). Finally, \(\mathsf{PA}^F\) contains the axioms of \(\mathsf{PA}\) with the induction schema restricted to formulas not containing \(F(x)\).