Spiritual teachers from every age and every tradition have baffled us with seemingly paradoxical statements: To find myself, I must lose myself; to live, I must die; I must yield in order to overcome. We are taught “In order to be full, empty yourself; to become everything, become nothing.” Perhaps my favorite paradoxical teaching is from the Indian sage Nisargadatta Maharaj who said, “Wisdom tells me I am nothing. Love tells me I am everything. And between the two my life flows.” 
The nature of existence itself is paradoxical-- it appears in many forms. A paradox at the core of human nature itself lies in the very deep drive for self-preservation and the equally powerful drive for self- transcendence. As humans we are filled with paradoxical drives: the desire to unite with others and the desire for autonomy; the desire for freedom and the desire for security; the desire to conform and the desire to be different. And, the universe itself seems to be paradoxical. Matter, at its essence, seems to simultaneously be wave and particle; local and nonlocal; existent and nonexistent.
And yet, paradox exists only from the perspective of the human mind-- it does not exist in reality. The human mind can function only within the context of duality. The mind must divide, compare, and classify in order to understand anything--self or other. This is necessary for humanity to function at our present stage of development--but we must remember that our understanding of reality is itself a product of our present stage of evolution. When we attempt to apply our mental processes to ultimate reality we will always encounter paradox because we are trying to divide the indivisible; we are trying to limit the unlimited; we are trying to describe the indescribable.
For example, an electron exists simultaneously as a wave and a particle. But in our observations of the electron we can only see it as a wave or a particle. We are like a blind man trying to understand what an elephant is, but can only touch one part of the elephant at a time. To such a blind man an elephant would appear quite paradoxical: “It’s like a big palm leaf (ear), and yet it’s like a large tree (leg) and yet it’s like a very big snake (trunk).” We see (and understand) reality only from a particular perspective.
Mystics tell us, time and again, that reality can be known, but cannot be described. Words and concepts are always perspectival; reality is aperspectival, holistic, unfathomable to the mind limited by words and thoughts. Spiritual practice usually includes suspending or (at least) quieting the human mind. Some spiritual practices, such as Rinzai Zen, will deliberately frustrate the mind with conundrums called koans, such as “What is the sound of one hand clapping?” There is of course no logical answer, but there can be an enlightened response to that question. The Zen master is quite skilled at ascertaining such a response which is not based upon the words but upon the quality of awareness demonstrated by the responder.
It’s important that we not demand that reality fit into our understanding of it, but rather let us pray that our understanding expands to embrace reality in ever more clear and accurate ways. This is the purpose of spiritual practice.
I will close with another of my favorite quotes from Nisargadatta, who said, “The mind creates the abyss, the heart crosses it.”
 Nisargadatta Maharaj. I Am That: Talks with Sri Nisargadatta Maharaj.