I personally believe in truth. But definitions of it, as you say, are pretty much impossible to agree on. So we have alternatives: a radical Postmodernism that sees everything as subjective and consensus, let alone truth, as impossible; a world in which speculation and paranoia drive “knowledge” and verification is a bad word; and the means we have long used to determine authority. To say “Authority is constructed” does not in any way imply that there is no method to the construction. In fact, the very essence of scholarship is the set of careful methodologies we have developed to help us determine what we should believe. We can find agreement on many things. Our information environment is not one of ever questioning and never finding resolution. Scholarship is a quest with a goal. Method drives that goal or we really are doomed.
I could hope that everyone would define truth in the same way (so that it could actually be truth), but I don’t see that happening. What I hope for, instead, is that we will use our conversations, our methodologies, our authority construction work to find a path to agreement about many things, while continuing to do battle over others. The enemy at the gates today is conjecture and speculation masquerading as authority.