Unqualified objective truth can not exist. Heavily qualified objective truth probably does.
a proposition is generally considered objectively true (to have objective truth) when its truth conditions are met without biases caused by feelings, ideas, opinions of a sentient subject. A second, broader meaning of the term refers to the ability in any context to judge fairly, without partiality or external influence.
If you consider just this universe that we inhabit, the nearest you can get to objective truth seems to be the very low level basic laws of physics.
The “law” of gravity suggests that whoever drops a marble from shoulder height to the floor, at sea level on planet Earth, can expect that marble to be attracted to the centre of the earth by gravity. And thus drop to the floor.
And yet, despite Einstein, we do not yet really know what gravity is. And what is a “graviton”? Scientists are still looking.
Whatever it is, it seems reasonably certain to most of us that gravity exists, whatever it is. But the qualification (and a heavy one) is: “in this universe”.
Many scientists posit that we are in fact living in an infinitely large multiverse and that there will be universes where the physical laws are completely different from those which attain here.
“Objective truth” is supposedly something on which we all (or the great majority of us) agree. The basic sciences contain many such apparently objective truths: the constancy of the speed of light, the number of atoms in a molecule of hydrogen and so on.
And yet even in many of these basic laws we seems to come across exceptions or revisions of interpretation. Leaving aside the complication of alternate universes where such laws do not apply at all.
But then consider the “emergent” sciences: biology, psychology, systems theory for instance. This is where objectivity really begin to disappear down its own throat.
Aristotle said that “the whole is greater than the sum of its parts” meaning the “whole” has properties its “parts” do not have. A human being is made of a few basic elements from the periodic table: largely hydrogen, oxygen and carbon.
It is difficult to understand a human being by reference only to these three elements. The “whole” (human) is unimaginably more complex than its constituent “parts” (carbon, oxygen and hydrogen).
Once these three elements (and a few others) get combined and grow into a human, there are a few “truths” about that human which may be called “objective”. But again, objective in a qualified sense. At present for instance most humans are born with a fairly standard set of organs and none of us can exist without breathing air and drinking water.
But who knows what life may evolve into. The “objective truth” that humans mostly have two legs must be qualified by “at present”.
But now take human behaviour and physiology. And in particular think about drug trials for instance or PTSD.
Does x drug cure y condition? Does Prozac cure depression? Does cisplatin cure cancer of the bladder?
Suddenly you are into statistics and probability. Far from objective truth.
Or take a complex adaptive system such as the weather or the stock market. Are they deterministic or random? Predictable or not?
Now pan out again to the multiverse: will we ever know much that is “objectively true” about the multiverse? Except perhaps that it is big.
Nothing is certain except uncertainty. Perhaps that is what stops us getting bored.