You said, "For the purposes of this discussion 'truth' means everything objective." Truth is not an empirical thing. Anything "true" can be wrong when the context changes. "This is blue." "Donald Trump is an idiot." "1 + 1 = 2" "Jupiter is bigger than Earth." Every one of these "truths" can be proved right or wrong within a specific contexts. So when you "search for truth", you need to define the context within which this truth exists. And we are back at the start of our conversation again... there are no empirical truths, so your search for truth must be the search for the truth within a specific context. You can't just say "this is true" and "this is false" because you deem it thus. (Well... I guess you can, but then you would have to be the only person in your universe.)
I suspect we are actually agreeing but using different words. You are talking about sentences whereas I am talking about propositions. Using your language: There are no absolute truths (i.e true sentences) because the proposition that each sentence maps to has to be defined from context. However, I meant: There are absolute truths (i.e true propositions) because the truth value of at least some propositions are unchanging (at least from a certain point on) and not dependant on context. . The context is usually known by the people participating in or watching the conversation so there's no need to worry there.