If by “uncountable”, you mean of cardinality greater than aleph-nought, then I think that you are using the wrong mathematical machinery. It is measure theory that we are concerned with here, not cardinality.
The two are related. Most relevantly, if my set is countable then I must have some singletons with non-zero measure. Moreover, the subset of points who have zero measure itself has zero measure, so they don’t matter at all. It is only in higher cardinality sets that you can have a collection of points each with zero measure that still have positive measure.
Ok, I can see that this tends to rule out my use of the unit-square analogy to justify my suggestion that the probability of the God Hypothesis is infinitesimal. I’m going to have to look more closely at the math, and in particular at my references for non-standard analysis to see whether any of my intuitions can be saved.
The two are related. Most relevantly, if my set is countable then I must have some singletons with non-zero measure. Moreover, the subset of points who have zero measure itself has zero measure, so they don’t matter at all. It is only in higher cardinality sets that you can have a collection of points each with zero measure that still have positive measure.
Ok, I can see that this tends to rule out my use of the unit-square analogy to justify my suggestion that the probability of the God Hypothesis is infinitesimal. I’m going to have to look more closely at the math, and in particular at my references for non-standard analysis to see whether any of my intuitions can be saved.