The concept of paradox has many meanings. Essentially it refers to the apparently contradictory but true, contrary to common sense, inexplicable, or self-referential and self-contradictory. Thousands of years ago in ancient Greece formal logic was first developed and, when this occurred, it began a heated conflict that is still going on today. Zeno of Elias was perhaps the first famous western philosopher to point out that whatever explanation you could put forward for existence led to a paradox. Basically he argued as many Asians have that the universe is in reality indivisible, indestructible, eternal, and unchanging. Like his teacher before him, Parmenides, the idea of a constantly changing universe with all its complexity was vulgar and undignified. To prove this he invented several deceptively simple paradoxes demonstrating motion was paradoxical which went largely unchallenged until the invention of calculus millennia later. As difficult to argue with as Zeno’s paradoxes and philosophy were, they were pretty much useless, except for exasperating other philosophers with more rational views of life. For the most part, only young men adopted his ascetic hermetic lifestyle and philosophy. After a while they usually rejoined society and focused on more productive things. Ignoring Zeno’s direct attack on the logical foundations of their philosophies, the champions of reason continued to put forth much more useful ideas. Socrates, for example, was the first to formalize a system of inquiry and logic around the idea that paradox is inherently wrong and, in doing so, originated the division between eastern and western philosophies. Meanwhile the Pythagorean mystics invented much of the foundations of mathematics and physics. Later Plato combined ideas from these two schools of thought into an artistic ethical philosophy arguably still the most popular to come out of the west. However, it was Plato’s student, Aristotle, who combined these philosophies to invented the most useful, if not as attractive or righteous, of all the Greek philosophies. So useful were his ideas that they became the basis for organizing the sciences. In the process of accomplishing this monumental feat, he successfully banned the use of certain paradoxes in academia as inherently wrong and impractical. Caught in the middle of this fight was Democritus, the most famous of the Atomists. He argued that existence is random in a manner similar to what Quantum Mechanics asserts today. First Zeno pounded away at the inherent paradoxes of the Atomists and, later, Plato used his influence with the Romans to have all of Democritus’ books burned as “ugly and demeaning.” Beauty, ethics, and logical inquiry became the catchwords of the day while all else was condemned. Zeno’s ideas subsequently lost their popular youthful following. When the early Christians then burned down the library of Alexandria all but a few of the remaining copies of the seventy books Democritus had written were lost forever. It was another of these same rational philosophers, Augustine, who integrated this bias against paradox, ugliness, and amorality within the Catholic Church and, in so doing, firmly established the pursuit of truth, justice, and aesthetics as the western tradition mandated not only by the realities of life but God himself. For the next thousand years western philosophy and sciences largely ignored paradox and had it not been for Arabic scholars preserving a few of the ancient Greek’s works on the subject, they might have been lost as well. How many more works on paradox have been lost is, of course, anyone’s guess. Eventually though, the arrival of Newtonian Mechanics and his new calculus drew the attention of western academia back to the subject of paradox. Newton succeeded in accomplishing what had widely been considered utterly impossible by all reasonable standards. He successfully incorporated not only paradoxical infinities into his mathematics in defiance of Aristotle, but also an ethereal vision of space and time, as well as an almost magical view of the action-at-a-distance of gravity. Had Henry the Eighth not previously kicked the Catholic Church out of England and his new inventions proved so resoundingly successful, he might have been executed on the spot for such heresy. Another philosopher of Newton’s day, Spinoza, also evaded the death sentence of the Catholic Church and became the first to highlight this once again changing attitude towards the use of paradox and the social upheaval all this was leading up to. Spinoza’s socially acceptably elegant and ethical philosophy was extremely compatible with Newtonian Mechanics, but had an unmistakable paradoxical Asian flavor much like Zeno’s. His Pantheism was so radical and culturally alien that among others Newton’s close compatriot, Leibnitz, publicly lambasted the man ruthlessly. As a result of all these difficulties Pantheism and other paradoxical philosophical concepts perceived as a threat to the western cultural status quo languished until another scientific revolution was ushered in with the introduction of the pantheistic theory of Relativity three hundred years later. Concurrent with the discovery of Relativity, however, another even more powerful theory began taking shape that was yet again more outrageously paradoxical, culturally unacceptable, and entirely irrational. The introduction of Quantum Mechanics threw a large monkey wrench into the development of mechanistic philosophies of any sort including those based on Pantheism. Einstein refused to accept the new theory and, echoing his ancient Greek counterparts, argued that Quantum Mechanics was so irrational, ugly, and meaningless it just couldn’t be true. Without a doubt, the irrational and extremely paradoxical is exactly what the theory is based on. After a hundred years of failure to find a logical explanation for the foundations of Quantum Mechanics, today many western physicists and philosophers are once again resigned to the pervasive use of paradox and the irrational after a hiatus of twenty-five hundred years. However, the philosophical community in general tends to be a great deal more conservative on this issue than the physics community, which had little choice in the matter. Thus far no one has found the philosophical equivalent of the sweeping and powerful physical theory of Quantum Mechanics. However, significant strides in this direction have been made in the last few decades, most notably with the introduction of Neutrosophy and Relational Frame Theory, both of which have already resolved certain problems that have remained intractable using more narrow traditional approaches. Neutrosophy uses trivalent logic that extends Fuzzy Logic and has applications in Quantum Mechanics, AI, psychology, and other fields. Relational Frame Theory has successfully reconciled the quantifiable rigor of Behaviorism with cognitive theories and spawned successful and radically different applications in linguistics and psychology.