#### PeterDonis

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Yes.If I were to make a direct comparison between the H - P singularity theorems and Inflationary theory, Ekpyrotic theory and Steady State theory, that would be incorrect, wouldn't it? The first isn't an empirical theory, while the others are. That would be like comparing oranges and apples, right?

Yes. As Bertrand Russell famously said, "Mathematics is the subject in which we do not know what we are talking about, nor whether what we are saying is true."if I were to claim that the first must be true, because it is proven, then I'd be making an error. A mathematical proof (even though it relates to the origin of the universe) cannot be taken as legitimately describing the universe in the same way that an empirical does. Is that so?