The concept of infinity is paradoxical, that is, it describes self-contradictory and irrational things that cannot be communicated clearly using linear logic. Lao Tzu expressed the conundrum of infinities and paradoxes with classic elegant flare some twenty-five hundred years ago:

The mother of nature.
It has no name,
But I call it "the Way";
It has no limit, but I call it "limitless".

To say something is infinite is to say that it has no limits. However, this presents a paradox because the statement contradicts itself. To say something has no limits is to impose a limit, specifically, the limit that there are no limits. Lao Tzu acknowledged this difficulty and when he wrote, “It has no limit, but I call it limitless”.

Despite this limitation in our ability to express infinities and their resultant paradoxes clearly, people find the terms quite useful for everything from casual everyday use to scientific ones as well. Infinity, for example, is central to the Calculus, which has revolutionized modern science. Thus, paradoxes and infinities are not so easily ignored as meaningless, trivial, or useless.

The paradox of existence in particular presents the distinct possibility that at least one paradox actually does exist in the real world. Since the dawn of civilization people have noted that the origins of existence are shrouded in paradox. Theologians, philosophers, and others have attempted to explain the paradox of existence in countless ways but every one of these explanations leads back to impenetrable paradox.

Whether invoking the concepts of eternity, God(s), oneness, or whatever each new attempt to explain the origin of existence ultimately ends in paradox. For something to be eternal or God or all encompassing implies the self-contradictory and self-referential paradox of infinity. If God or eternity can explain existence, then where did they come from? Rational explanations to this question of origins are patently impossible by the accepted rules of logic if it truly is a paradox.

Therefore a more pragmatic approach to the paradox of existence is to just assume it is utterly impenetrable to reason and then move on to determine how useful the paradox of existence can be. As I said before, infinity and paradox have proven extremely useful in a number of ways. Since the paradox of existence may involve infinity, it is potentially infinitely useful but that possibility presents yet another paradox.

An ancient popular Chinese poem that predates Lao Tzu provides one glimpse of how to possibly comprehend the myriad uses of paradoxes:

Tools

Thirty spokes meet at a nave;
Because of the hole we may use the wheel.
Clay is molded into a vessel;
Because of the hollow we may use the cup.
Walls are built around a hearth;
Because of the doors we may use the house.
Thus tools come from what exists,
But use from what does not.

The Chinese are inordinately fond of paradoxes and often hang them on their walls as a kind of mirror for the mind. For example, I might hang a paradox on my own walls that says, “Infinitely Finite Infinity.” Such a statement has no linear logical definition, no inherent grammar structure or anything else necessary to what we normally think of as the productive use of the English language. Precisely for this reason our minds are free to contemplate whatever meaning to the words we might freely associate.

Just as a bathroom mirror is useful for examining ourselves then, paradoxes as well can be useful for examining ourselves. Likewise, just as mirrors are useful for looking under your car or couch, paradoxes can be used to examine the world around us in a variety of ways. The converse is also true and conventional bathroom mirrors as well can reflect our minds to a certain extent. Our body language can betray our feelings and our actions viewed in the mirror can betray our intentions.

Exactly how large and highly polished the mirror, its composition and how clear the room lighting determines how accurate and detailed the reflection. In addition, how clear our minds and eyesight are, also determine how useful the mirror may be. Similar limitations apply to the use of paradoxes for all applications.

Many of these paradoxical mirrors for the mind might be said to more closely resemble fun house mirrors than the ones in our bathrooms. An example of this fun house mirror effect can be seen in the famous nonsense poem by Louis Carol, “The Jabberwocky” as demonstrated in the first two stanzas:

“Twil brilling, and the slithy toves
Did gyre and gimble in the wabe,
All mimsey were the borogoves,
And the mome raths outgrave.

“Beware the Jabberwock my son!
The Jaws that bite, the claws that catch!
Beware the Jujub bird, and shun
The frumious Bandersnach!”

Although the words of Mr. Carol’s poem sound meaningful and darkly compelling, but they are nonsense words the author made up. As such they present an example of the irrational or paradoxical, but one that is distorted expressly for the purpose of touching us emotionally in a manner very similar to that of fun house mirrors.

Some have argued that appearances to the contrary, the paradox of existence does not really exist. From this point of view what are called paradoxes might more closely resemble shadows than mirrors. These shadows can be considered more of an indication of what is missing than a reflection of what actually exists. Instead of mirrors for the mind, paradoxes could be presenting deeply shadowed wells for our minds to tumble endlessly into and the reflections we see are merely our minds bouncing off whatever boundaries to reality the paradox might arbitrarily touch upon.

Adopting the perspective of paradoxes as shadows provides yet again additional uses and avenues of exploration. A shady tree can be very useful on a hot summer’s day and the tree’s shadow can be used to get an idea of what is casting the shadow. Similarly, the shadows of paradoxes can be used in countless ways to create anything from works of art like those presented here to examining our selves and the world around us.

Comparing the shadowy and mirror views of the paradox of existence is exactly how progress is often made in understanding phenomena. Sometimes this occurs when opposing views clash competitively and, at other times, they are in harmony. Such is life. In either case, both views continue to not only drive progress individually, but taken together may synergistically provide a third view neither is capable of alone.

Synergistic views of paradox notably include what many artists, philosophers, theologians, mystics, and others have so poetically described through the eons as surrender or acceptance. A child dancing spontaneously, a musician becoming lost in their music, and religious epiphanies all are common examples of surrender. Acceptance or surrender in turn is thought by some to be the source of creativity, understanding, and compassion. Again, the Tao Te Ching has an elegant and revealing expression of this:

Experience

The spirit of the Way never dies,
It is called the mysterious female:
Its entrance, the root of the world,
The Way moves within it:
Draw upon its experience; it will not run dry.

Taoism is recognized as the most feminine of the world’s popular religions and its intense focus on paradoxes is at least one reason why. The Chinese believe each of us has a bit of the feminine and masculine in us, however, true paradoxes are considered especially feminine precisely because they do not assert anything but, instead, are resoundingly receptive. Feminine traits for the Chinese also include acceptance or surrender, nurturing, and other maternal behaviors and, most pointedly, attitudes.

Such an open affect, of course, supports research into paradoxes and provides more alternative avenues for fruitful exploration. Explored from all three viewpoints (mirrors for the mind, shadows, or something altogether indescribable) paradoxes provide a depth and richness to studies unrivaled by vantage points of narrower scope. In recent decades, for example, it has proven especially useful in reconciling cognitive and behavioral perspectives where less broadly defined approaches failed.

No matter what your personal views of paradox might be, I hope I have managed to convey here some of their general characteristics, how they can be used and examined, and given a coherent rough overview of the many ways they are currently being approached in studies. Not merely how they are used in philosophy and science but, instead, within the entire range of human activity. The focus of paradoxes can be intensely personal in nature or seemingly objective and impersonal, but no matter what the case they remain potentially useful to serious scholarly studies as well as for more prosaic undertakings.

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Originally posted by wuliheron:
The Use of Paradox

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Originally posted by wuliheron:
The paradox of existence in particular presents the distinct possibility that at least one paradox actually does exist in the real world. Since the dawn of civilization people have noted that the origins of existence are shrouded in paradox. Theologians, philosophers, and others have attempted to explain the paradox of existence in countless ways but every one of these explanations leads back to impenetrable paradox.

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Originally posted by wuliheron:
Whether invoking the concepts of eternity, God(s), oneness, or whatever each new attempt to explain the origin of existence ultimately ends in paradox. For something to be eternal or God or all encompassing implies the self-contradictory and self-referential paradox of infinity. If God or eternity can explain existence, then where did they come from? Rational explanations to this question of origins are patently impossible by the accepted rules of logic if it truly is a paradox.

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Originally posted by wuliheron:
Therefore a more pragmatic approach to the paradox of existence is to just assume it is utterly impenetrable to reason and then move on to determine how useful the paradox of existence can be. As I said before, infinity and paradox have proven extremely useful in a number of ways. Since the paradox of existence may involve infinity, it is potentially infinitely useful but that possibility presents yet another paradox.

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More responses for this thread will be most welcome !
I love philosophical arguments !
They test the edge of one's intellectual capacity,
and no math is required...

Live long and prosper.

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The other idea, that there can be a final theory that will
also have room for the paradox is false in my opinion,
because I think that scientific theories can always be
expanded. I do not have a logical proof for this claim
and I'm not certain there is one, though. I'll think about
it and try to determine one, nevertheless.

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If a TOE or something like it is discovered in the near future it seems likely to be a wholistic theory just as Quantum Mechanics and Relativity are. Paradoxes are the philosophical version of a black hole in many respects and can accomodate both linear logical views and wholistic ones. However, this same open and receptive nature of paradoxes that is their strength is also there weakness for applications.

Because of the complexity of wholistic theories they are much more difficult to develop and the paradox of existence could be considered possibly the most complex of wholistic theories. As such what one might expect from such a theory may be very different from what you imagine.

Wholistic languages can often be interpreted in a huge variety of ways. My name for example, Wu Li, has no less than eighty distinct meanings in chinese. Japanese haiki poetry consists of short poems that can be read in twenty distinct ways, each of which makes perfect sense in its own rite but none of which may seem related to us in any way shape or form. For example, read one way a poem might say something like "I sit by the fire" and read another it might say "the grass is green".

This kind of wholistic complexity will likely get both better and worse. Two steps forward, one step back.

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Originally posted by wuliheron:
If a TOE or something like it is discovered in the near future it seems likely to be a wholistic theory just as Quantum Mechanics and Relativity are. Paradoxes are the philosophical version of a black hole in many respects and can accomodate both linear logical views and wholistic ones. However, this same open and receptive nature of paradoxes that is their strength is also there weakness for applications.

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Originally posted by wuliheron:
Because of the complexity of wholistic theories they are much more difficult to develop and the paradox of existence could be considered possibly the most complex of wholistic theories. As such what one might expect from such a theory may be very different from what you imagine.

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Originally posted by wuliheron:
Wholistic languages can often be interpreted in a huge variety of ways. My name for example, Wu Li, has no less than eighty distinct meanings in chinese. Japanese haiki poetry consists of short poems that can be read in twenty distinct ways, each of which makes perfect sense in its own rite but none of which may seem related to us in any way shape or form. For example, read one way a poem might say something like "I sit by the fire" and read another it might say "the grass is green".

This kind of wholistic complexity will likely get both better and worse. Two steps forward, one step back.

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Live long and prosper.

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If I am not mistaken you seem to suggest that the paradox
of existence could be solved by a theory - I strongly disagree
with that, like I said in my above message !

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You seem to have assumed this from the beginning of your post. I am not suggesting anything can solve the paradox of existence.

What I am suggesting is that precisely because it may really be a paradox the most compatable theories that can describe the most observable things will also have to be wholistic. By the way, string theory combines relativity and quantum mechanics quite nicely into a wholistic theory and is the leading theory today.

(Note: the nature of existence is logical, because existence (the universe, if you wish) defines "logic")

There are many ways to "solve" the "paradox of existence", one becoming clear when examining the concept of "begin" and "end", which implies a linear process.

In order for something to come into existence, it has to have a beginning, but to change or end, it needs something else. This introduces the concept of "time", or the changing of one configuration of that which exists into another configuration, using a set of rules ("laws of physics").

To come into existence implies change, thus requiring "time", thus the first time that something (the universe) comes into existence is the first time that it changes, the first of a possibly endless number of changes. This is the beginning of existence.

We don't know what time is, nor do we understand "change", but once we do, we'll find that there many ways to solve the "paradox of existence".

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Any paradox is only an illusion, because the nature of existence is logical, and a paradox defies logic, thus any paradox does not really exist.

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If you'll buy that I have some land in florida I'm looking to sell. What solipsist drug induced twaddle.

Existence as I have been endevoring to point out is both logical and illogical by the standards of logic. Refute me if you can twit or face the reality.

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Originally posted by wuliheron:

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Any paradox is only an illusion, because the nature of existence is logical, and a paradox defies logic, thus any paradox does not really exist.

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If you'll buy that I have some land in florida I'm looking to sell. What solipsist drug induced twaddle.

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Would you be so kind as to restate the above nonsense in a more sensible manner?

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Existence as I have been endevoring to point out is both logical and illogical by the standards of logic. Refute me if you can twit or face the reality.

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But don't worry, few people actually understand existence and thus logic, and I doubt that you're one of those people.

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If you'll buy that I have some land in florida I'm looking to sell. What solipsist drug induced twaddle.

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You've no idea what miracles come forth from a correct usage of grammar.

Would you be so kind as to restate the above nonsense in a more sensible manner?

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Oh, I have some idea believe me. This is an American idiom that basically says you'll buy any story people tell you.

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Existence as I have been endevoring to point out is both logical and illogical by the standards of logic. Refute me if you can twit or face the reality.
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"standards of logic"? What are you talking about? There's logic, and only logic. Logic is defined by existence, by everything which exists. The sole fact that existence defines logic should make it clear to you that existence can't be illogical.

But don't worry, few people actually understand existence and thus logic, and I doubt that you're one of those people.

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If there is logic and only logic, what is the logical definition of the irrationa? That is does not exist? Very funny, I like your sense of humor.

Wuliheron, I think Elledan actually made a good point. The universe works a certain way, and that way is logical, because it would define logic.

BTW, you mentioned the definition of the irrational. Well, I hope you're not refering to mathematical irrationality, because that would be rather hypocritical of you (who refuted others, for doing the same thing, on a different thread).

Besides, didn't you mention infinities as being illogical (paradoxical)? That can't be right, because something that is infinite in one direction, makes perfect sense. Infinite does not mean "all-encompassing", it means "going on forever".

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Wuliheron, I think Elledan actually made a good point. The universe works a certain way, and that way is logical, because it would define logic.

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Nature or the universe works in scientifically varifiable ways which I will be the last to deny are apparently logical, but existence does not and its modus operandi is equally open to scientific scrutiney. For all I know the incredibly logical organization of nature is merely there to balance out existence's irrationality.As for logic, logic dictates that some things are irrational and existence is the most obvious example I know.

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BTW, you mentioned the definition of the irrational. Well, I hope you're not refering to mathematical irrationality, because that would be rather hypocritical of you (who refuted others, for doing the same thing, on a different thread)

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Back to esoteric BS as a way of side stepping addressing the issue head-on. I's just a poor ignorant suburban fool raised on Gilligan's Island and Green Acres. I have presented my case in Mickey Mouse terms, either refute my logic dead on or admit you can not.

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Besides, didn't you mention infinities as being illogical (paradoxical)? That can't be right, because something that is infinite in one direction, makes perfect sense. Infinite does not mean "all-encompassing", it means "going on forever".

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Makes perfect sense to you maybe, but unless you can describe it here rationally and in plain english nobody but the already converted will listen. As far as I can tell you are doing nothing but protecting your fragile ego with every last straw you can muster.

Who the hell cares whether existence is irrational or rational. Think about it, either way you have to live with the reality. I say it is obviously irrational not so much because I care, but because that is what people have been saying sense prehistoric times, that's what it appears to be to me, and that's what you are beginning to look like as well.

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Originally posted by wuliheron:

Back to esoteric BS as a way of side stepping addressing the issue head-on. I's just a poor ignorant suburban fool raised on Gilligan's Island and Green Acres. I have presented my case in Mickey Mouse terms, either refute my logic dead on or admit you can not.

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Who the hell cares whether existence is irrational or rational?

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If you didn't care, why did you start all of these debates? If you aren't serious about your claim, you've been decieving (lying to) us this entire time.

... stop complaining and 'deal with it'

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YOU were the one who was always picky about people using mathematical infinities! I found your behavior to be rather hypocritical.

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My one and only pickiness about mathematical infinities or any other kind of infinities is the way people throw them around as explanations of anything from Martha Stuwart's hair style to the meaning of life, the universe, and everything. Sure, a lot of people here are adept at math, but their logic skills and, therfore, understanding of the foundations of mathematics are sorely lacking.

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If you didn't care, why did you start all of these debates? If you aren't serious about your claim, you've been decieving (lying to) us this entire time.

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You never heard of objectivity? If I did say I cared would you use it as evidence against me?

I've been serious about this claim all along, but as I have said it really doesn't matter whether existence is paradoxical or not. We have to live with the fact either way. What matters maybe is that people asccept a skunk for what it is, accept BS for what it is, and accept existence for what it is. Namely, irrational.

I'm a natural teacher, I just can't help myself. When people start throwing words like infinity around only the slightest concept of what they mean and what the implications are, and without the slightest awareness of the paradox of existence which stares them in the face every waking moment..... well, as I said, I can't help myself.

I know, its evil to pop people's bubbles and show them their irrational side, its evil to insist that mathematics is based on logic. But I just can't help myself.

Good topic.

For me, your idea of using paradox to try and understand underlying reality makes sense, although it is a little pessimistic.

Quantum mechanics has shown that what our senses tell us is a convenient and useful illusion. The reality that we observe is like the ripple on the pond. It is one minute thread of coherence through an enormous universe.

While it is possible to understand what quantum mechanics is telling us about the universe, this understanding is counter-intuitive to the point of paradox. In fact, most people are not willing to make the leap in order to understand.

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For me, your idea of using paradox to try and understand underlying reality makes sense, although it is a little pessimistic.

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Oh really, what's pessimistic about it for you?

Paradox for me is a lot of things, but pessimistic is not one of them. Just as a chair or pillow can be said to be, in Asia the paradox of existence is often discribed as possessing suchness and isness. The range of positive psychological and philosophical around the subject is huge. The fact that the paradox of existence is imminent, that paradoxes can possess a distinct sense of humor, etc. all add up to a very nurturing and feminine view of existence.

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Quantum mechanics has shown that what our senses tell us is a convenient and useful illusion. The reality that we observe is like the ripple on the pond. It is one minute thread of coherence through an enormous universe.

While it is possible to understand what quantum mechanics is telling us about the universe, this understanding is counter-intuitive to the point of paradox. In fact, most people are not willing to make the leap in order to understand.

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That's why the big boys get paid more. Instead of running away in denial like any sane person they grab the bull by the horns.

I am not without sympathy for westerners who are often brought up their whole lives to hate, fear, and despise certain things.... especially the irrational. But such feelings and their resultant behavior are in their own rite irrational. There ain't nobody home but us chickens and the irrational or paradoxical define us as much as existence. To hate or fear them is to hate or fear yourself.

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either refute my logic dead on or admit you can not.

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"Infinite" as used in philosophy and the sciences doesn't mean "limitless" or "without any properties". If eastern philosophy uses the word for something else, that's not my problem.

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I believe that it is possible to understand, or at least to think about, what quantum mechanics is really telling us witout deferring to the idea that some things simply can not be known because they are too big or too weird. Stated another way, I believe that it is pessimistic to say that one must use paradox in order to think about reality.

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Paradox is more holistic than other approaches to the paradox of existence. That is, it is inclusive and includes all optomistic viewpoints. Why do you believe it is pessimistic?

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"Infinite" as used in philosophy and the sciences doesn't mean "limitless" or "without any properties". If eastern philosophy uses the word for something else, that's not my problem.

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Please, enlighten us as to the mathematical and scientific definitions of infinity that is so different from what I have presented. I'm all ears.

So far, it just sounds more complicated, but the basics remain the same.