 Ex Falso was excluded from this fragment: Kolmogorov said that, just like PEM, Ex Falso “has no intuitive foundation” (van Heijenoort 1967: 419). In particular, he says that Ex Falso is unacceptable for the reason that it asserts something about the consequences of something impossible (van Heijenoort 1967: 421). Note that that is a very strong rejection: it not only rules out Ex Falso in its full generality, but also specific instances such as “If 3.15 is an initial segment of \(\pi\), then 3.1 is an initial segment of \(\pi\)”. It also indicates an incoherence in Kolmogorov’s position: one cannot at the same time accept \(A \rightarrow (B \rightarrow A)\) as an axiom and deny that anything can be asserted about the consequences of an impossible \(B\).