2 + 2 = 1 (modulo 3). There are just a finite number of rational numbers if you are considering a finite field. Two parallel lines: 1) never meet; 2) always meet; 3) don't exist depending on what geometry you are considering. At one time, each of these mathematical statements was considered to be absolutely untrue and even to be absurd until a more advanced (more general) mathematical structure was discovered (or invented, depending on your beliefs). So, even if there was total agreement that some statement were absolutely true, might that just be a temporary consensus awaiting discovery of a larger but more tenuous truth?
Would the statement "There are no absolute statements, except for this one." solve the conundrum of the self-contradictory statements discussed in previous posts? Or, is this issue just a distraction from the intent of the OP?
Some logicians attempt to bypass the problems of the self-referential statement but still create the innately contradictory situation through use of set theory: Define "S" to be the set of all sets that do not contain themselves as an element. Does S contain itself as an element? I actually don't see the difference or that anything has been achieved in this way.