 It seems not altogether unreasonable to extend the meaning of the term “solution” this way, for, just like a concrete solution, an impossibility proof also provides what might be called “epistemic closure”: like a concrete solution, it provides a completely convincing reason to stop working on a certain problem. (This kind of “higher-order” solution is also familiar from Hilbert’s Program, e.g., Hilbert 1900: 51.) Note that this justification of Ex Falso makes no attempt to describe a counterfactual mathematical construction process; thus, Kolmogorov’s justification in 1932 is not really incompatible with the ground for his rejection of Ex Falso in 1925, namely, that one cannot constructively assert consequences of something impossible. Rather, the solution from 1932 introduces a stipulation to achieve completion of the logical theory for its own sake.