In general usage, objectivity is the capacity to see things as they are.
The striving towards objectivity is a central precept of esoteric work, as seen by the Fourth Way teaching and by the FOTCM. We will look at the question of objectivity from various angles. Few people will directly claim that objectivity or truth are undesirable as such but many will muddle the picture in various ways.
First, before we can speak of objectivity or lack thereof we must recognize that there exists an outside world and a meaningful separation between this world and the observer. Descartes' cogito ergo sum [I think therefore I am] for example states that the only knowable reality is thought and the outside world is unknowable, thus may even exist in the thinker's thought alone. This is called solipsism and is a logically possible proposition but forms a sort of philosophical dead end. The concept of objectivity has no or little place in such a system.
Others, such as many promoters of the New Age, recognize that there is a reality but claim that all in this reality are in fact one and that this reality is a shared illusion brought about by the participant's belief in this same reality. There is no objectivity, aside from shared beliefs producing a semblance of a consistent world about which it is possible to say things.
This argument is a sort of confusion of levels. We may agree that the universe is at some fundamental level a result of consciousness, at least many traditions and modern day channeled sources claim so. From this does not follow that the human level of experience would respond to human thought in any significant or obvious sense. Experience of 'conscious creation' by human thought in the sense of wish fulfillment is scarce and flaky. If man were God, thoughts might create but man isn't God, nor does he become such by suggesting to himself he already were God.
Quantum physics consistently demonstrate observer effects. The state of a system cannot be known without measurement and measurement affects the system. It is unclear whether measurement can be defined completely without involving consciousness at some stage of the process. In this sense, 'objective knowledge' of the specific pre-measurement state of a system is not possible but formulating testable statistical models of a system's behavior is possible. These are "objective" in the measure they correspond to observation, thus a criterion of objective knowledge may be applied. Nature is not arbitrary even if it is non-deterministic from the human perspective.
In philosophy, hermeneutic and phenomenological thinking have arisen as a response to naturalism. These critique the strict observer/observed dichotomy inherent in earlier thought. For example, behavioristic psychology may be criticized of "objectivating" the experimental subject, in fact, a priori denying it being a conscious entity. However, recognizing that in many situations the observational setting is not to be separated from the observation does in no way invalidate the precept of objectivity as we understand it, on the contrary it enriches it by pointing out facts about the world.
Objectivity should not be confused with reductionism. Reductionism or determinism states that given complete information of a system's state, it is possible to make arbitrarily far reaching projections of the system's state into the past and future. There are many obstacles to strict determinism, starting from quantum uncertainty, probable non-local effects, no system being absolutely closed, possible effects of consciousness and observership and so forth. Partly relating to this, Godel has demonstrated that a system cannot be its own meta-system, i.e. contain complete knowledge of itself. This suggests that attaining objective knowledge of any universe from within it is an open-ended quest.
Objectivity, in the sense understood here implies "epistemological realism", which is simply the proposition that reality is knowable by many observers in a compatible and contradiction free manner. This does not imply that absolute identity of experience or experiment were possible but does propose that an apprehension of the world shared between multiple observers can be approached, even while the observers cannot be entirely or demonstrably free of all bias or "reading error".
In a social setting, the word objectivity is sometimes used with the meaning of "neutrality", an absence of emotion or in the sense of listening to all parties of a situation. An "objective assessment" in such a sense could be the average of all claims made about a question. The term is not used in this sense in the present work. Firstly, we note that if objectivity is to aim at knowledge of all which is, it cannot start with the premise of a priori declaring that some part of the observed situation simply does not exist or is irrelevant. Secondly, we can note that the average of a lie and a truth would be a half-truth, thus drawing an average of views is not a reliable or indeed objective means of knowledge.
Specially as regards issues of human interactions, complete objectivity may be elusive but we can give criteria of method even if we cannot formally prove statements.
From the viewpoint of esoteric work, truth or objectivity should be one's principal goal, in other words "knowing God". The study of the universe cannot be entirely separated from this. However, for esoteric purposes we cannot use criteria of knowledge directly copied from natural science. The internal nature of the work requires a certain openness and good faith or at least suspension of disbelief. After this, internal verification of esoteric precepts may be possible. Because of the personal and experiential nature of many observations, making an effort at objectivity is even more important than in natural sciences where this objectivity is more readily verifiable.
Also, we cannot exclude study and work on emotions from esoteric work. Psychology seeks to attain reliable knowledge of emotions by experiments, questionnaires and statistical methods. This works to a degree on 'exterior man' but is not a directly viable approach in esoteric work. The numbers are not large and the issues relevant in each cases may be quite dissimilar, hence a mechanical "cookie cutter" approach is problematical.
George Gurdjieff stresses the attaining of objective reason and objective conscience throughout Beelzebub's Tales to His Grandson. We could say that objective emotion is possible, then in the sense of the emotional center conveying accurate information on the emotional state of the environment. Objective conscience is the simultaneous seeing of one's own emotional state and its response to the broader self's state and actions. In Gurdjieff's words, some impulses are proper to man having 'attained objective reason and conscience.' These are of a generally ethical character such as good will and consideration towards others, striving for self-perfection, striving for knowledge, striving to pay for one's arising and so forth.
The FOTCM links the quest for objectivity to the duality between service to others and service to self. Pronounced subjectivity or wishful thinking are seen as hallmarks of STS. If thoughts or a general internal disposition of observers affects reality, then the FOTCM proposes that this happen as follows: Observation which corresponds to reality creates order in the observer/observed system. Observation which disagrees with reality reduces the amount of order and adds to the entropy of the observer/observed system. Order and entropy are opposites. Entropy corresponds to loss of information and of consciousness, order corresponds to creation. By attempting to force their own conception of reality on the universe, magicians and wishful thinkers in fact add to chaos and dissolution. Any creation compatible with the service to others polarity must start with recognition of what is and needs to take action based on this, not based on a partial reading. The type of action may be freely chosen, depending on which polarity the actor decides to be aligned with.
Objectivity ties in with the concept of free will in the sense that free will without knowledge of possibilities is ineffectual. Also, will which is misinformed cannot be said to be free because it is limited by factors which are outside itself. A near objective knowledge of self, then including knowledge of one's typical subjective bias, is a prerequisite for free will. See Free Will for discussion on the ontological possibility of such in the first place.