Can two things opposed to each other both be true?
Consider this theater demonstration. A ball is painted white on one side and black on the other. A magician on stage holds the ball, standing between two volunteers who are dozens of feet apart, aloft carefully, with the line of demarcation directly centered. The audience titters, already seeing the trick. “What color is this sphere?” he asks. The woman on stage left sees only the black side of the ball, and states clearly, “the ball is black!” But a man on stage right sees only the white side of the ball, and says “no, it is white!” Both see the truth. But only from their perspective.
Truth does not exist. It can only be perceived by an observer, who by his or her nature of viewing only part of the universe’s data can only misjudge the truth. This is important because when we interact with others, we must also consider truth from their perspective.
To dig deeper, consider that much of what we believe isn’t real at all. Religion, nation-states, money, advertising impressions, the value of gold, your relation to family, the company you work for — all don’t really exist. The historian/philosopher Yuval Noah Harari suggests even something as believable as “good” or “human rights” are only figments of our imagination. If one human harms another, we feel this is wrong. But to test this “good vs. bad” thesis, if we saw an ant chase another ant into a roadway where the first was crushed by a car, we wouldn’t feel horror for the insect. It’s just a dead bug in the road. When we have chicken for dinner, we don’t feel bad that it was killed at 6 weeks after arriving at prime chicken-weight when the poor bird should have lived to age 10. Because as humans we can’t wield enough empathy for smaller creatures. But the dead insects and animals, in their last gasp, might decry car tires or human forks for abuse. Our belief in the truth of “rights” is all warped perspective.
The politics of modern America bear this out. President Donald Trump has fewer than half of all U.S. adults supporting him, but those who do believe he tells the truth. Put a liberal Democrat and a MAGA Republican in the same room, and both will swear h/she is right and the other is wrong, because the facts on Fox News/MSNBC support them. This sounds absurd. But both see truth.
In the complexity of our everyday world, an Einstein of ethics might surmise we all bend the vectors of truth toward our own selves, simply to filter out the swarm of too much information, just as planets and stars warp space around them. Our very existence as points in morality makes us biased toward ourselves.
Now, certainly, there are some truths that should outweigh others. If life itself is a noble cause, because the rising complexity of our various organic beings fights the negative entropy that can only lead to the heat death of the universe, then anything that enhances life should be “good” and all killers of life are “bad.” Jesus, good. Hitler, bad. But even this is a perspective wrought by living beings who prefer wiggly atoms to those particles that don’t hook up. If the universe devolves eventually to burned out chards of hydrogen, will those little bits complain? Of, if they retain a last, tiny grasp of consciousness, will they simply sing in unison, “at last, we’ve achieved the peace of stasis!”
My point is we humans should consider the gradations and mutations of “truth” in our interpersonal interactions. Every day, I am certain I am following the truth, and any friction with others means they are wrong. But what if those others are right? Or more clearly, what if we both are right? The sight lines of perspective make more than one truth possible.
It sounds crazy, but perhaps we should believe in opposites. Truth is not a singular direction. It is a rubber sheet stretched across the universe, upon which we, as leaden balls, stretch morality into the stories we tell ourselves.
velmotus 
Ultimately, all we have is our perceptions. One could push the argument to the extreme and say that _nothing_ exists unless it is perceived by a conscious mind and then it only exists as qualia in that mind. If one takes that viewpoint, then everything is subjective and “opposites” can be simultaneously true, but only in separate minds. While such a viewpoint is interesting to ponder, it is rather impoverished in terms of utility.
While all truths are, ultimately, subjective (in the sense described above), some are less subjective than others. Science is a process–an algorithm–for identifying (or even, creating) minimally subjective truths.
Many years (decades!) ago, my wife and I began using the term “UFR” (pronounced YOU-fer) to mean the “underlying, fixed reality.” That’s a reality that exists independently of any observer. Technically, it is impossible to prove there actually is a UFR, but it is useful (and parsimonious; think Occam’s razor) to accept the existence of a UFR as an axiom.
I prefer to identify a “Truth” as a claim that is consistent with the UFR (and not merely consistent with any given individual’s perception of the UFR). Thus, when people make conflicting claims, the most useful approach is not to simply accept all claims as equally true, but rather to hypothesize that each person is perceiving the UFR differently and to try to identify a cause for that difference.
When FOX says A and MSNBC says not-A, they are not (likely) equally true. One is more consistent with the UFR. And we have an algorithm for evaluating which is which.
An interesting thought experiment is to select a claim and then eliminate all record of that claim from human civilization — no memories, no artifacts, no writings, recordings, etc. Completely wiped away. Then ask yourself how likely is it that the very same claim would eventually resurface and become a consensus belief? For example, consider these two claims: a) light refracts when crossing a boundary between two different mediums; and b) the ruling planet of a person born between February 19 and March 20 is Neptune. I’d suggest the former would be very, very likely to be (re)discovered as a truth. The latter, not so much.