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The Scientific History of Paradox

  1. Mar 21, 2003 #1
    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.
    Last edited: Mar 21, 2003
  2. jcsd
  3. Mar 21, 2003 #2
    This is very good!
  4. Mar 21, 2003 #3
    The Marriage

    Acually what we're getting down to here is the neccessity to incorporate the rational mind with the irrational mind, because both are only relative and cannot exist seperately, unless of course you're schizophrenic.

    Perhaps it's time we went back to ancient Greece, and rediscovered the very thing which allowed it to prosper and flourish? The relationship between the Apollonian order (the rational mind) and the beloved antics of Dionsyus? (the irrational mind). Wow! Is it just a coincidence that this has something to do with the title of my book? I for one don't believe in them. Although I would put it more politely and use the word "synchronicity."

    And yes, we're speaking about the "Marriage of Science and Religion."
  5. Mar 21, 2003 #4
    As Taoists often say, "Many paths, one mountain."

    The west has chosen its path and is firmly rooted to it, but is in the process of transition to a less severely rational one in my opinion. Equally, Asia chose it's highly paradoxical path, but is now in the process of learning the value of rejecting paradox in favor of logic. Sometime in the next several hundred years their paths may start to come close to each other.

    They are what physicists sometimes call "self-organizing" systems. A garden is a good example. You can plant neat rows and weed all you like, but those darn things will still grow to a significant extent the way they want. Some plants will prosper and others will die, bugs will invade, etc. Instead of attempting to force the garden to grow exactly the way you want, you adapt to it to a certain extent.

    In the case of modern science, a useful core philosophy and science of paradox is something westerners can appreciate and will use that will help bring a bit more acceptance on the issue. If ancient philosophies and mysticisms such as Taoism could have done the trick, they would have already.

    Denial runs deep and without such a thing it is just another philosophy, theology, or mysticism.
  6. Mar 22, 2003 #5
    I'm not so sure that fuzzy logics and neutrosophy are not in the very same line of aristotelic logic. They just extend it to more truth values and so reject certain rules of inference but the whole concept is the old one. They are useful but to a very limited extent.

    As for your synopsis of western philosophy, where is Hegel? His logic was very original, but at the same time profoundly routed in Heraclitean philosophy. And where is Heraclitus?

    As for Zeno attacking the foundation of other philosophies, yes, he did it, but using for the first time the reductio ad absurdum to show that, as the thesis of his master brings to contradiction, the same is true of his opponents thesis.

    And still we have not a good logic for a TOE...
  7. Mar 22, 2003 #6
    You are correct I believe, Neutrosophy and Fuzzy logics are decended from Aristotlean logic and an extention of Hegel's logic. The central distinction here is that it does not axiomatically deny the validity, practicality, and worth of paradox, uncertainty, indetermancy, etc. but, instead, attempts to work with and around such things.

    This is essentially what Newton did with the paradoxical concept of infinity in calculus. Instead of listening to Aristotle's opinion that such things are impractical, useless, and/or meaningless he put them to extremely productive work. Rather than assuming all infinities are false, calculus provides a broader and more flexible definition that allows us to mathematically approach infinity without actually having to directly address the inherent paradox. What is at issue is not whether infinities are real or not, but how we can work with the concept.

    As for where Heraclitus might fit into all this, I have no clue. I've been making this philosophy up as a go and that's why I post it here, so I can get feedback. Thanks for the tip.

    I'm really just a philosophical Taoist, a hippy living on a secular commune. People at this website kept asking for me to describe my philosophy, so I made up the paradox of existence as a way to communicate some idea of Taoism to extremely skeptical scientifically oriented people. It worked out so nicely I've just kept developing the philosophy. Like calculus and Neutrosophy, it lacks the depth of mystical philosophical Taoism, but instead, provides an approximation.
  8. Mar 22, 2003 #7
    I missed this point, this is exactly what Neutrosophy and works like it are attempting to address. You appear to be one of the few people who visit this website who has much idea of the history and implications of such work. I would be very grateful for any input you might have. Welcome to the forum!
  9. Mar 22, 2003 #8
    Another point about this occured to me while responding to another post. Neutrosophic logic extends aristotlean logic, but not just by adding more truth values.

    Instead it focuses on neutralities, uncertainties, and the indeterminate. There is no way to prove something is indeterminate, inexplicable, or ineffable for that matter. Nor are these things rationally related to the truth or falsehood of anything except to say they are not related. Thus they provide an entirely new catagory with which to expand logistics much as infinity did for mathematics.
  10. Mar 22, 2003 #9
    Yes, True, False and Indeterminate are the values of Neutrosophic logic. I was reading some of the papers available on line, but I didn't go on...it doesn't sound like the revolutionary logic I'm looking for, rather an interesting all-including one. Some of the papers on neutrosophy have good hints here and there, though.
  11. Mar 22, 2003 #10
    I personally think the philosophical depth is what's missing. Holistic theories can be as personal, deep, and world changing as anything. If nothing else, that is what the twentieth century had to teach us, life always has more dimensions than we can imagine.
  12. Mar 23, 2003 #11
    Paradox of Science

    From an earlier post:

  13. Mar 23, 2003 #12
    Exactly, existence may be utterly ineffable, unspeakable, indescribable. Most Philosophical Taoists like myself are therefore Agnostic, but we don't claim any special knowledge or proof about the nature of existence. As Zeno demonstrated so well, sometimes ignorance is the strongest logical argument.
  14. Mar 23, 2003 #13
    From an earlier post:

    There's no reason why you can't point somebody in the right direction though is there?
  15. Mar 23, 2003 #14
    There is no such thing as converting someone to Taoism and historically they have had no missionaries. As the Tao Te Ching admonishes, "Those who talk about it don't know, and the those who know don't talk about it."

    Likewise the same is true of paradox. You cannot make somebody accept the existence of the inexplicable. But like Zeno and Socrates you can talk about the subject and ask questions. We can study the world from paradoxical viewpoints and demonstrate how useful they are. How we live our lives is often the best demonstration.
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