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These observable descriptions of possible worlds are general enough and different enough that it's hard to say something about them, except that they make sense in a mathematical way. Still, given any property $X$ we could try to see what is the chance that it's true in the set of observable descriptions.  If our universe is not designed, then any possible universe could have existed (and maybe all possible universes actually exist). Focusing only on universes which have a space-time and in which intelligent beings can exist, if we would want to pick a random one, for a reasonable definition of random, each universe would have a zero probability of being chosen. If we further restrict these universes to ones which allow a predictive set of axioms for the entire universe, then each set of axioms is as likely to be randomly picked as any other, so each has a zero probability. I argue that, even more, the observable descriptions, i.e. the  sets of axioms that describethe  universes as perceived by the intelligent beings in them, have each a zero probability. In other words, any reasonable probability distribution over these axiom sets is continuous. As a parenthesis, above I required that there is a predictive axiom set for the entire universe. That was done for simplicity, but a similar parallel construction could be made for the case when only a part of the universe can have a predictive set of axioms. 
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We can then say that for virtually all descriptions, only properties with non-zero probability are true. This means that, if the probability of our world being designed is non-zero, the only rational choices are that either our world is designed or only non-zero probability properties are true.  Now, let us return to the issue of observable descriptions being finite or infinite. With an a  finite alphabet, the set of finite observable descriptions is countable. Then the \ghilimele{is finite} property is a zero-probability one, so either our universe is designed, or at any point in time there will be an important part of our universe that we can observe but can't model no matter how hard we try. \section{Approximations}