Suppose someone proves the polynomial-time hierarchy collapses. Then it didn't collapse because it was always collapsed and in fact was never a true hierarchy. The only reason we call it a hierarchy today is because we don't know that it isn't.
In mathematical reasoning we can't know whether a statement is true unless we have a proof of that statement. However once we have a proof of a theorem like P≠NP then not only do we have P≠NP now but in fact P≠NP was always true even before we had the proof. Despite this we can't help thinking that theorems become true as we see a proof. A year ago undirected connectivity wasn't in log space and now it is. However the theorems that were proven before I started graduate school were all true since the dawn of time.
not sure if you're asking for help, or whether this is helpful anyway, but you might want to look at "causality" by judea pearl
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