Singularity and unanimity

Examples are adduced which lead one to ask if the following rule of unanimity makes sense: Given, a classical dynamical problem. Given, that all solutions of the equations of motion (a) run into a singularity or (b) are free of singularity], except a set of measure zero. Then (rule of unanimity), all solutions of the corresponding quantum mechanical problem are (a) singular or (b) free of singularity]. If valid, this rule would imply that quantization of Einstein's standard general relativity model for a closed universe gives no escape from the singularity of gravitational collapse.Dedicated to Achille Papapetrou on the occasion of his retirement.