the possibility of inter-subjective truths (i.e. truths that should persuade)

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.