I will split my answer in a few sections. Do not take my answer as a complete one, but merely as some considerations to have when wondering about "objectivity."
You must ask yourself whether truth exists and how to attain truth. If you believe truth does not exist, you cannot be objective. If you believe truth exists, then you have to find a process which garantees you will not be wrong. More recent philosophy tends to take a historical perspective. Have Utilitarians always been right? Have scientists ever made a mistake? A school of thought called Neopragmatism (ref. Richard Rorty) says that we call true a belief that we have justified; we know how we use it, we don't need to define it. Likewise with "objectivity," or "scientific," which are often a shorthand for "reliable." Is there a fully "reliable" process? Maybe, maybe not. I would argue (my subjective opinion) that we should not so much focus on objectivity or bias, but rather about processes that are more reliable, and which have absorbed more criticism, instead of using older processes that have not adapted to criticism. This approach in turns seems to analogize to an attempt to be "more objective."
We might call people subjective or biased; the statement in itself is rarely insightful; it is merely a shorthand for saying we don't trust them or believe them wrong. It would be more constructive to describe reasonable criticism which they might not have internalized. Only then could they tell you "I was not being completely objective."
Realism is the philosophical position that "truth" exists, traceable to an absolute, a certainty, something which "definitely exists." This is as old as Socrates and especially Plato.
Plato argued that there existed metaphysical universals, which embodied the essence of concepts. To simplify, Plato argued that using reason, rationality, logic, and so on, one could intimate universal concepts. For instance, one could have a conversation on what was virtuous, or what it meant for something to be courageous. A more banal example of an universal is the concept of "redness" as a fundamental concept dissociated from any particular example of red stuff.
The appeal of Plato's universal is well represented in his allegory of the cave. Plato suggested that men tied up in a cave, seeing only the shadows of shapes, would come to understand the world in terms of these shadows - since they had no other visual experience. Yet these shadows would be "false" representations of reality, as only a fraction of the "true" thing.
Plato's universals were recycled by Christians in a movement known as neo-platonism, adding concepts of the immortal soul and the eternal God as a universal. To neo-platonists, reaching truth is analogous to intimating a property of God.
Much later, Descartes followed in this tradition intimating truth by a philosophical experiment of radical doubt. Descartes said famously "I think therefore I am," a maxim, which many consider to be absolutely objective; one cannot doubt one's existence, or yet, one cannot doubt that one doubts. Descartes went to justify other things which are more controversial, like the existence of God. Most people will casually remember him for the former argument.
Naturalism or Natural Realism are positions that point out that a lot of these conceptions of "minds" and "God" seem quite subjective, especially in the face of a scientific method that is increasingly sophisticated and popular. While not all Natural Realists are equal, most will liken empirical evidence - or observations of the laws of nature - as a tool to attain "truth." For instance, a neuroscientist might say that morality "exists" because we have scientific evidence that a human brain can formulate moral instincts, and that this means that morality is "real."
Critics of the latter position, called Moral Naturalism, will say that it begs the question: yes what we call moral instincts might have footing in the brain, but what makes us believe that those instincts are correct? We have plenty of instincts that we commonly accept as incorrect.
The Moral Naturalist might wield Utilitarianism, saying that we have instincts about diminishing harm and maximizing happiness, and all other moral instincts are merely abstractions which seek to achieve this goal. Therefore, Utilitarianism is obviously the ground for morality. Or is it? Plenty of arguments have been levied against Utilitarianism. Kantiant and Neo-Kantiant philosophers think Utilitarianism a poor ground for morality, one too mathematical, mechanical, or even inhumane. Do all of these philosophers have the "wrong instincts"?
While some might have staked out a position by this point, others might find that there are few positions devoid of criticism and turn away from Realism.
Anti-Realism is the position that truth does not exist, or that it cannot be achieved. You can be a Realist on some positions, and an Anti-Realist on others.
For instance, you could believe that the non-contradiction axiom (Something cannot be both true and false) to be purely true, purely objective. You would be realist on (at least some) logic or math.
And even if you are a logical realist, you might be a moral anti-realist, someone who believes there is no right answer to any moral question. A moral anti-realist might respond: "Killing a human is not necessarily immoral. You could do it in self-defense, it would be more moot. If you investigate the circumstances, you might realize that you caused the altercation, and are therefore responsible for the murder. If you zoom out, you might realize that through a butterfly effect, you have prevented the genocide of a billion human beings a thousand years from now by murdering this person. Is it still moral? Is there even a correct answer here?"
Moral anti-realists might use the Repugnant Conclusion to argue that a purely logical, formalized view of morality is rather absurd. Others would rather claim that unrealistic hypotheticals don't really say much about morality.
Okay. Morality might be debatable. Math feels a bit abstract. How about science? Maybe we can achieve truth through the scientific method...?
Philosophy of Science
Philosophy of science has a long history. A lot of philosophers have returned to the problem of induction as a basis for whether Science can achieve truth or not. The problem is, very briefly:
When making a prediction about the future based on an observation in the past, this prediction can only be valid if the laws of the universe concerning this prediction do not change. If the laws of the universe change, then science is useless. But we cannot prove that the laws of the universe will not change! Therefore, nothing is proven through science!!!
A more contemporary response (and mine) would be that, at the very least, the laws of the universe don't appear to have changed in a way that fundamentally breaks our stronger scientific theories yet, so I believe we are justified in believing this is not really a problem.
From this fairly fundamental starting point, we can skim through some history of philosophy of science:
- Positivism: the position that the scientific method, when used correctly, leads to accurate statements about reality (via the process of formulating rational methodology, and/or repeatable experiments which test hypotheses).
- Falsificationism (ref. Karl Popper): Science cannot achieve truth. Instead, what it achieves is a reduction of possible claims about reality, by proving hypotheses wrong. A "scientific" theory is a theory that can be falsified through experiments, and which has not yet been falsified despite opening itself up to such "vulnerabilities."
- (ref. Thomas Kuhn) Scientific theories have protective belts of axioms which can be altered or discarded instead of sacrificing the whole theory. That is, showing a prediction to be wrong is not sufficient to discard the whole theory. This opens itself up to Quine's Problem of Holism, which speculates that scientific theories might be able to sneak around disproving evidence by shaking up their methodology enough to avoid controversy.
- (ref. Imre Lakatos) Scientific Research Programmes, or the idea that a scientific theory is measured by how it is Progressive or Degenerative. If it seeks to sharpen its methodology and in some way or another eliminate paths of inquiry, to increase its empirical foothold, to make more and more predictions, etc., then the theory is Progressive. If a scientific theory is instead falling behind, accumulating contradictions and incorrect predictions, or becoming increasingly bloated with unhelpful complexities, the theory is Degenerative. The idea, then, is that a better theory (more progressive, less degenerative) will supplant a worse theory naturally, simply by its utility and accuracy. Two competing theories might even coexist if they make accurate predictions in different circumstances (e.g. Special Relativity vs Quantum Mechanics).
My purpose is merely to impress the complexity of conversations around science. Those each have strong arguments for and against. For instance, one could say that the advent of Special Relativity has shown that, in some non-negligible way, Newton's Laws of motion were not quite accurate. And what about the fact that we don't even really understand why Gravity exists? That doesn't make the theory of gravity unscientific, though. What is the relationship between Special Relativity and Quantum Mechanics? It sounds like most of science is at least, plausibly, a "little" false. We could argue the more optimistic view that we are at least "approaching" truth. If we are approaching truth, then what does it even mean to be closer to truth? Will we ever know when we achieve correspondence with reality?
Oh, right, objectivity
Objectivity is the notion that, from any perspective, something will remain the same. Regardless your subjective experience, you can be objective if you find a process that is always the same regardless of who you ask, granted that the subject is competent.
It sounds like without a firm grasp on "truth," we're already conceding that objectivity isn't really achievable in an absolute sense. Maybe Descartes was right, that we cannot doubt that we exist... but what of everything else? Maybe objectivity stops at the simplicity of looking at an apple on a table, and confirming by third parties that the apple is in fact there (something called intersubjectivity; the idea that we achieve a relative level of objectivity by combining subjective accounts).
Yet it can seem wrong to say objectivity is largely bunk. After all, wouldn't it be a miracle if science was wrong (an argument often used by defenders of scientific realism)? Maybe to focus too much on the imperfections of science (and the rest), we are throwing the baby out with the bath water. Computers work... don't they? Vaccines seem to work when we aggregate the data (if you trust the process, I suppose). Climate change is something that we might want to take seriously, considering the evidence that we have for it and the projected consequences.
In many scientific fields, and even in math, we have developed better and better tools to control observations and formulate convincing conclusions. The field of psychology had a period during which it relied mostly on personal accounts of introspection, a process that allowed psychology researchers to... do their own research. Freud had interesting ideas, too, but has been criticized for wild speculation, overgeneralization as well as making a poor job of controlling for the influences he might have on his patients. Modern psychology still has a lot of soft aspects, but it is undeniably more reliable than it used to be. Cognitive Psychology is one of the most empirical subfields of psychology, with very strict tests measuring cognitive abilities with precise data. A success story in the history of the science of psychology, if there ever was one.
If we compare science and religion, we might also say that Creationism is an older theory, which did not use newer tools to make its arguments. As a result, many now see Creationism as less convincing than Evolution. Is Creationism falsifiable, progressive, degenerative? Should we choose to adopt these new philosophical constructs to judge the validity of Creationism? Maybe! Should we blame people for not adopting these tools? Maybe, maybe not, the human experience is complicated.
At the end of the day, Realism, Objectivity, Reliability, Science, are all political insofar as they demand us to reject certain human cultures and embrace others. It is so political that completely incompatible political positions will often call each other scientific while calling the opposition unscientific.
Pragmatism is a philosophical current which seeks to simplify some of this philosophical conversation by appealing to the utility of these concepts. Some pragmatists are realists, some pragmatists are anti-realist. Some even argue that the distinction between realism and anti-realism should be abandonned; it is surprisingly not rare for a radical anti-realist to agree on every point with a realist. And if that is possible, it seems like the distinction is not entirely useful.
Neopragmatism is a philosophical movement attributed largely to Richard Rorty. It claims that, rather than fighting over the definition of words like truth, objectivity, science, moral, immoral... we should instead focus on how they are used (in a social context).
- "This is true" => "This is a belief that I have justified."
- "This is moral" => This is an something I find desirable."
- "This is scientific/objective" => "This is something I find reliable."
- "This is biased" => "This is untrustworthy, or wrong" (unless you 'bias' as a statistical variance away from the mean. Different contexts can have different attitudes towards the same words.)
I wrote all of this treatise to reflect on the nature of the question: Is it possible to be COMPLETELY objective?
Well, we could simplify this to: "How can I know my reasoning is reliable." When you add the "completely" you transform it into "How can I know my reasoning is so reliable that I can pat myself on the back about how reliable it is." And at the end of the day, it really depends how you fit in the (fraction of the) philosophical conversation I've laid out in this text.
Personally, I find more "reliable" approaches which internalize more criticisms. There is an undeniable subjective element to it, since the way in which a philosophical critique affects human beings is not especially clear, and human beings can easily dismiss what might appear to be a strong criticism to another. I think a good approach is to repeat the criticism, or counter-position back to your ideological opponent until they agree it is their position. At this point, you have achieved a fair approximation of your opposition, and you can probably rest assured that you could not be "more informed" about criticism against your position. Education appears to be a good way to do this.
The kind of "objectivity" we are talking about will tend to correlate with the degree of certainty we ascribe to the field in question (Physics, psychology, politics...). Regardless I think my approach is suitable for each, since each can be studied, and each can have their methodology internalized and criticized. You don't need to educate yourself, since this is not a moral argument; if you feel it tiring (or socially compromising) you don't need to "try to be completely objective." It is a reflection for you to make as an individual and as a member of a social group.
I would argue we all like a bit of reliability, and some processes are more objective than others, it seems; we might want to prefer those processes, all else equal. After all, math feels more objective than, say, philosophy... Oops.