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Thanks for the link to that interesting essay. It seems to rely on the possibility of inter-subjective truths (i.e. truths that should persuade) that are not objective (i.e. based on empirical results). Basically, I don't believe in inter-subjective truths of that kind because they are capable of proving too much. For example, "God exists" is a plausible candidate for inter-subjective truth, but there are empirical things I would expect in a world where God exists that do not appear to be present. In short, there seems to be no limit to what can be labeled inter-subjective, non-objective truth.
This asserted fragility of society is inconsistent with historical evidence. You can pick just about any moral taboo (E.g. human sacrifice or incest) and find a society that violated it but continued on, and fell for reasons independent of the violation of the moral taboo. For example, Nazi Germany didn't lose WWII because they were immoral jerkwads. Germany lost WWII because it picked a fight with a more powerful opponent (who happened to also be an immoral jerkwad).
I don't think "truths that should persuade" is a good definition of what Szabo (or others) mean by "inter-subjective truths".
Wikipedia is not very helpful, but I understand it more as "things whose truth-value depends of how many people believe in them", i.e. "children are expected to obey their parents", "you should drive on the left side of the road", etc.