Suppose there existed a natural probability (or density, or weakening of such) on the “set” of all models of the Zermelo-Fraenkel set-theory axioms. Suppose some “natural” mathematical statement had the property of having positive probability, different from 1, of holding in a random model. How should we interpret such a situation? Say, if the Continuum Hypothesis has probability *6/π ^{2}*, of being false?

And if some natural statement *P* was shown to be a consequence of two other statements, having probability *p* and *q*, respectively, of holding in a random model, with *p+q>1*… so that the existence of a model where *P* holds would follow in highly non-constructive fashion… What would you think, philosophically or intuitively, of the “truth” of that statement?