Can there ever be objectivity in any human matter?
Each word, each phrase, each definition: all carry with them hidden subjective meanings and biases. Objectivity is the realm of the God, not humans.
If you detaches from the body/mind then you can have a "pure experience." I would call that experience objective, I suppose, because it does not pass through the often opaque filter of the mind. How do I know that what I experience is objective and not some alternate "video game reality?" I suppose I don't. But it is very curious that anyone who meditates regularly for a while (the amount of time varies from individual to individual) will get in touch with "pure experience" and, to take it one step further, if these individuals continue practicing meditation they will become non-dual. Experiencing non-dual, or unity, consciousness … that would be transcending all opposites and becoming one with the foundation of the universe.
Neurologically speaking, there is supposed to be a part of the brain (the pineal gland) that connects with the universe on a more fundamental wavelength-frequency than the mechanism of the "self-conscious." Call it whatever you will: collective-unconscious, spiritual, God, etc.
The dissolving of the "I" happens when the mind tunes into that central-universe nugget in the brain around which all word and idea and motion gravitate. We are antennae for this fundamental wavelength-frequency. And if there is no "I," that means there is no longer a separation between objectivity and subjectivity. Also it is interesting that certain drugs can dissolve the "I" so to speak.
The truth is …
The primary truth is trans-rational. We can use the mind to help us get there, but the truth will only be experienced in its totality beyond the limits of the mind. We use words and thoughts to deconstruct reality in an attempt to understand what is going on (which is extremely helpful), but, alas, the whole is greater than the sum of its parts and so words can never really do reality justice.