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Notes -
None of these are meaningful in the way you mean. I am not that good at math, but I am good at mathematical model building and interpretation.
These are not meaningful because we can easily write different examples with different results, so the key question for, say, society is whether society satisfies another given property that is not the ones you mentioned.
Economics has models where agents who are part of the model and know or learn the model. Yet, self-fulfilling prophecies are not guaranteed or fully ruled out.
Economics would also have models that imply tradeoffs. Yet, in general not every improvement leads to a tradeoff because there are always dumb actions. Stop being dumb and you get an improvement without losing anything.
We can also come up with processes that generate large numbers from small and make that process loop or collapse or anything we want. The question is not whether such processes exist, but whether we can identify which kind better represents society, if any of them do.
I do think that some math is useful to recognize whether a kind of argument is plausible or ruled out. But most math is not even useful for that.
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