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.