Meaning and Intellectual Beauty

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The vast number of "uh's" (that is, the "schwa" sound) in the unaccented syllables of English leads to certain sensitivities to expression which foreign speakers find very difficult to master. Spoken English words are very "fuzzy;" it is very easy to hear them in several different ways and make associations with a variety of other words and meanings. That is why English speakers are more prone to making puns than most continental Europeans. Foreigners often find English speakers vague and imprecise; part of the reason is that we are constantly moving around in a fog of associations in what we say. English also lacks the grammatical structures of declension and conjugation which make most other Indo-European languages more certain and precise in their expression. This is all very good for poetry, but has disadvantages in everyday, practical communication.

As an example, consider this little story: If most native English speakers hear it read aloud in normal, unaccented English, they immediately know what it is and what it is about, for it is a story which they have often heard. I wager that most foreigners, no matter how good their English is, will be at sea as to what is going on! In a couple of days, I will provide a "translation" which indicates how most English speakers hear the story:

Ladle Rat Rotten Hut

The above site also has the story read aloud.

LADLE RAT ROTTEN HUT

Wants pawn term, dare worsted ladle gull hoe lift wetter murder inner ladle cordage, honor itch offer lodge dock florist. Disk ladle gull orphan worry ladle cluck wetter putty ladle rat hut, an fur disk raisin pimple colder Ladle Rat Rotten Hut.

Wan moaning, Rat Rotten Hut's murder colder inset, "Ladle Rat Rotten Hut, heresy ladle basking winsome burden barter an shirker cockles. Tick disk ladle basking tutor cordage offer groin-murder hoe lifts honor udder site offer florist. Shaker lake! Dun stopper laundry wrote! An yonder nor sorghum-stenches, dun stopper torque wet strainers!"

"Hoe-cake, murder," resplendent Ladle Rat Rotten Hut, an tickle ladle basking an stuttered oft. Honor wrote tutor cordage offer groin-murder, Ladle Rat Rotten Hut mitten anomalous woof. "Wail, wail, wail!" set disk wicket woof, "Evanescent Ladle Rat Rotten Hut! Wares are putty ladle gull goring wizard ladle basking?"

"Armor goring tumor groin-murder's," reprisal ladle gull. "Grammar's seeking bet. Armor ticking arson burden barter an shirker cockles."

"O hoe! Heifer blessing woke," setter wicket woof, butter taught tomb shelf, "Oil tickle shirt court tutor cordage offer groin-murder. Oil ketchup wetter letter, an den - O bore!"

Soda wicket woof tucker shirt court, an whinny retched a cordage offer groin-murder, picked inner widow, an sore debtor pore oil worming worse lion inner bet. Inner flesh, disk abdominal woof lipped honor bet an at a rope. Den knee poled honor groin-murder's nut cup an gnat-gun, any curdled dope inner bet.

Inner ladle wile, Ladle Rat Rotten Hut a raft attar cordage, an ranker dough belle. "Comb ink, sweat hard," setter wicket woof, disgracing is verse. Ladle Rat Rotten Hut entity bet rum an stud buyer groin-murder's bet.

"O Grammar!" crater ladle gull, "Wood bag icer gut! A nervous sausage bag ice!"

"Battered lucky chew whiff, doling," whiskered disk ratchet woof, wetter wicket small.

"O Grammar, water bag noise! A nervous sore suture anomalous prognosis!"

"Battered small your whiff," insert a woof, ants mouse worse waddling.

"O Grammar, water bag mousy gut! A nervous sore suture bag mouse!"

Daze worry on-forger-nut gulls lest warts. Oil offer sodden, throne offer carvers an sprinkling otter bet, disk curl and bloat-thursday woof ceased pore Ladle Rat Rotten Hut an garbled erupt.

Mural: Yonder nor sorghum stenches shut ladle gulls stopper torque wet strainers.
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.LITTLE RED RIDING HOOD

Once upon a time, there was a little girl who lived with her mother in a little cottage on the edge of a large, dark forest. This little girl often wore a little cloak, with a pretty little red hood, and for this reason people called her Little Red Riding Hood.
One morning, Red Riding Hood's mother called her and said: "Little Red Riding Hood, Here is a little basket, with some bread-and-butter and sugar cookies.
Take this little basket to the cottage of your grand-mother who lives on the other side of the forest.
Shake a leg! Don't stop along the road; and under no circumstances, don't stop to talk with strangers."
"Okay, mother," responded Little Red Riding Hood, and took the little basket and started off.
On the road to the cottage of her grand-mother, Little Red Riding Hood met an enormous wolf.
"Well, well, well," said this wicked wolf, "If it isn't Little Red Riding Hood! Where's our pretty little girl going with her little basket?"
"I'm going to my grand-mother's," replied the little girl.
"Grand-ma's sick in bed. I'm taking her some bread-and-butter and sugar cookies."
"Oh, ho! Have a pleasant walk," said the wicked wolf, but he thought to himself, "I'll take a short-cut to the cottage of her grand-mother. I'll catch up with her later, and then ---- Oh, boy!"
So the wicked wolf took a short-cut, and when he reached the cottage of the grand-mother, he peeked in the window and saw that the poor old woman was lying in her bed. In a flash, this abominable wolf leaped on her bed and ate her up.
Then he pulled on the grand-mother's night-cap and night-gown, and he curled up in her bed.
In a little while, Little Red Riding Hood arrived at the cottage and rang the door-bell.
"Come in, sweet-heart," said the wicked wolf, disguising his voice.
Little Red Riding Hood entered the bed room and stood by her grand-mother's bed.
"Oh, Grand-ma!" cried the little girl, "What big eyes you've got! I never saw such big eyes!"
"Better to look at you with, darling," whispered this wretched wolf, with a wicked smile.
"Oh, Grand-ma! What a big nose! I never saw such an enormous proboscis!"
"Better to smell you with," answered the wolf, and his mouth was watering.
"Oh, Grand-ma! What a big mouth you've got! I never saw such a big mouth!"
These were the unfortunate girl's last words. All of a sudden, throwing off the covers and springing out of bed, this cruel and blood-thirsty wolf seized Little Red Riding Hood and gobbled her up.
Moral: Under no circumstances should little girls stop to talk with strangers.

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More is involved here than an amusing word game. There is a deep and subtle philosophical point: Where is the dividing line between normal, permissible variation in speech or writing (or for that matter, in any pattern or form) and a regime in which we must say that cryptological analysis is necessary? I hope that the story of "Ladle Rat Rotten Hut" strongly suggests to the reader that, ultimately, no firm-and-fast dividing line is possible. In fact, for a computer, the cryptological analysis in Edgar Allan Poe's story, "The Gold Bug," would be far easier to accomplish than a correct reading of "Ladle Rat Rotten Hut." A relatively simple, mechanical, mathematical algorithm would suffice for Poe's coded message; but it is very difficult to imagine that a computer, ever, could unriddle the story of "Ladle Rat Rotten Hut." The problem is very far beyond the capabilities of any electronic speech-recognition system which presently exists. Certainly any computer which could solve the enigma of "Rat Rotten Hut" would be inconceivably more complex and sophisticated than any we might imagine today.

Westerners seem to have a fundamental limitation in their thought due to their extremely egoistic way of thinking. All too often they fall into the fallacy of thinking,
"I am the master of my fate:
I am the captain of my soul."
And even if they are not quite that insane, they still tend to feel that every phenomenon is isolated, complete, existent in and of itself. Such an attitude is, of course, absurd; but it is a current which runs throught the warped thinking of most Westerners.
Is "Ladle Rat Rotten Hut" gibberish, or is it an easily understandable variant of the story "Little Red Riding Hood?" That depends on the mind which is reading the story. It should be obvious that a volume of the Encyclopaedia Britannica, here in my library, is quite different from the same volume transported to Tang Dynasty China, or teleported to the hyper-dimensional plasma-beings of planet Qwerty.

In 1901 the German writer, Kurd Laßwitz, wrote a short story entitled, "Die Universalbibliotek." Here is a link to an on-line copy:

Die Universalbibliothek von Kurd Laßwitz - Text im Projekt Gutenberg

His story of a Universal Library was improved upon by Jorge Luis Borges in his short story, "The Library of Babel," on-line version at:

http://jubal.westnet.com/hyperdiscordia/library_of_babel.html

In the Library of Babel, every book is a random jumble of letters, spaces and typographical symbols. Any possible combination of symbols will occur on some line, page or book somewhere in the library. One must travel light-years to discover a single, grammatical sentence of English. Yet not a single sentence in the library is without a clear and distinct meaning. For there are an infinite number of possible languages, and the grammars and manuals of instruction for those languages must all exist in an infinite library, and each sentence in the library will have one or many meanings in certain languages. Even a sentence consisting of "aaaaaaaaaa...." will have a meaning in some cryptological code, and that code will be explained in one or more volumes somewhere in the library.
It is a corollary of the mathematical proofs of Georg Cantor that although the Library consists of an almost infinite number of books distributed in a disorder of infinite extent, this infinity is exceeded by the hyper-infinity of the languages and codes which explicate even a single volume of the Library ---- and this hyper-infinity is "enfolded" in the relatively small infinity of the volumes in the Library!
Into such deep and subtle matters is the story of "Ladle Rat Rotten Hut" a gateway.

Mysterious and yet more mysterious:
The Gateway into the teeming Wonders.
---Dao-De Jing (1)
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It is very difficult to convey the divine beauty of mathematics to a non-mathematician. Thomas Aquinas, attempting to describe what he conceived as angelic consciousness, noted one aspect: that an angel, seeing a simple geometric figure, such as a triangle, would instantaneously and simultaneously perceive, as an act of intuition and not of discursive reason, all propositions of geometry and, indeed, the whole structure of geometry, as a single divine, Platonic Idea in the mind of God. Now whatever you may conceive to be the ontological status of God and angels, it is a fact that, for a good mathematician, his intuition of geometry is not radically different from that of Aquinas's angel.

A more concrete metaphor may help to convey the mysterious grandeur of mathematics. Imagine that a beautiful and subtle novel has come into your hands, and that you have read it through with great aesthetic pleasure. Now imagine that you change each of the letters in the novel according to some simple rule---say, A to B, B to C, C to D, etc. You find to your amazement that you have not produced gibberish, but a completely new novel, of even better quality than the first! And you find that you can go on in this fashion forever, producing ever more beautiful, subtle and mysterious works of art.

This is a dim image of the wonders of mathematics.
This aspect of mathematics was well-known to the greatest thinkers of ancient Greece, and led them to the conception of Platonic Forms ---- objects of Super-Reality whose dim and mutable shadows are all we know of matter and sensation, and whose awful majesty radiates through the ephemeral illusions of time and space. We may see this awareness in the arrangements of the propositions of Euclid.

Proposition 47 of Book I is a proof of the famous Pythagorean Theorem: "The square on the hypotenuse of a right-triangle is equal in area to the areas of the squares produced on the two legs of the triangle."

Euclid's Elements, Book I, Proposition 47

It is a proof, but it is not the easiest proof; it is relatively complex, a fact which has puzzled many people. The reason is that it is meant to be understood in connection with a very similarly constructed proof concerning all possible triangles and the parallelograms that can be constructed on the sides of any triangle. This proof appears in Pappus, and it shows that the Pythagorean Theorem is merely a special case of a more general proof concerning the Platonic nature of all triangles.

Pappus

We see a similar development of thought in Book III, Proposition 31 of Euclid where it is first proved that an inscribed triangle, constructed upon the diameter of a circle and touching the circumference at the third point of the triangle, is a right-triangle; and as you move this third point around the circumference you generate all possible right-triangles.

Euclid's Elements, Book III, Proposition 31

Next is a generalization from this and deals with triangles constructed on all possible chords of a circle---thereby generating all possible triangles. This demonstrates that circles and triangles are identical ---- there is no difference between them in their Platonic essence. They are both aspects of a single nature.
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Blowhard, this thread is meant for people who have minds and can think.

You should go back to your threads about adult toys and gluttony.
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God is, after all, ultimate reality. And you can't argue that ultimate
reality doesn't really exist. You can only ask what it's all about.
---Logan Pearsall Smith

Beauty, Harmony, Truth are my shining lodestars, or ---- to give them all a single name, as Plato did ---- the Good.

The Absolute cannot be precisely defined, as Kurt Gödel proved mathematically. But Beauty is a finger pointing to the Absolute, shining at the Infinite Horizon.

Aesthetic relativism, like moral relativism, can carry you only so far. Moreover, one should make a distinction between Art and craft (or, more likely, the lack of craftsmanship). There are many styles of art and many techniques of craftsmanship, but Art and Beauty transcend all of them. There are many systems of mathematics, an infinity and a hyper-infinity of them, but it is a logical and provable necessity that they cannot, in their dizzyingly infinite totality, exhaust Mathematics Itself ---- which overarches them all in a way which is, in strict logic, inexpressible and transcendent.

Creation is the irruption of a transcendent order of Reality into the limited realm of Being which we inhabit.
---- Yours Truly

But why do we live for anything but Beauty; What is there that gives a meaning to the world but Beauty; ---- these splendors that seem to fall upon us from the empyrean, from climes of bliss beyond the constellations?
---- Logan Pearsall Smith

Das schönste, was wir erleben können, ist das Geheimnisvolle. Er ist das Grundgefühl, das an der Wiege von wahrer Kunst und Wissenschaft steht.
---Albert Einstein, Wie ich die Welt sehe
[The most beautiful thing which we are able to experience is Mystery. It is the fundamental emotion which stands at the cradle of true Art and Science]

I think that there are many things in the universe that we cannot perceive or penetrate and that also we experience some of the most beautiful things in life only in a very primitive form. These mysteries I sense deeply.
---Albert Einstein, The Private Albert Einstein

Mathematics, like the Nile, begins in minuteness, but ends in magnificence.
---James Sylvester

Probably the most concrete introduction to the wonders of mathematics is the Mandelbrot Set. This is an object created by a ridiculously simple recursive function that is, quite literally, an infinite object, and one of breathtaking and supernal beauty. As such, it is an excellent metaphor for mathematics itself.

Here is a Deep Mandelbrot Set Animation. It is equivalent to starting from far beyond the observable universe and zooming down to far below the dimensions of an elementary particle --- but it is just a tiny part of the environment of the Mandelbrot Set, and could go on forever.

Now how is this possible? How can such awesome beauty arise from what is, after all, a mere game, a mindless procedure which a machine like a computer can create by an infinitely tedious series of repetitive steps? This is the mystery which we must set out to understand.

As a hint, it can be pointed out that no contradiction is involved here. Mathematics can be a realm of Divine Beauty and Truth, and it can also be totally mindless, repetitive procedure.

The two apparent opposites are enfolded together seamlessly, in a Unity that (almost) defies understanding. It is like a picture which, when you look at it one way, is a jolly, pretty lady, and when you look at it another way, is an ugly old crone. The picture is what it is; only your viewpoint changes.



The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.
---Niels Bohr
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By the way, this picture:



is an excellent illustration of a four-valued logic common in Far Eastern philosophy --- as opposed to the two-valued logic of Western Aristotelian logic (A or not-A).

1) It is A --- a picture of a pretty lady.

2) It is not-A --- it is not a pretty lady, it is an old crone.

3) It is both A and not-A --- both completely a pretty lady and completely an old crone.

4) It is neither A nor not-A --- it is just what it is, colors and lines on a screen.
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Aufgeblassen said:

To the limit, 1/infinity = 0

Click to expand...

Or, 1/0 = infinity. However, division by 0 is undefined. You can only say that , in the expression 1/n, as n goes to infinity, 1/n approaches 0 (1/n ---> 0), not that 1/n equals 0!

Consider Grandi's Series:

1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + ...

Using parentheses,

(1 − 1) + (1 − 1) + (1 − 1) + ... = 0 + 0 + 0 + ... = 0.

Alternately,

1 + (−1 + 1) + (−1 + 1) + (−1 + 1) + ... = 1 + 0 + 0 + 0 + ... = 1.

Or,

S = 1 − 1 + 1 − 1 + ..., so
1 − S = 1 − (1 − 1 + 1 − 1 + ...) = 1 − 1 + 1 − 1 + ... = S
1 - S = S
1 = 2*S, resulting in S = 1/2 !!

This is an example of a divergent series --- which, appropriately analysed, can sum to an infinite different numbers.

This may be perceived intuitively in the example of a Thomson Lamp.

A Thomson Lamp is free of all the constraints of physics, so that it may be a pure mathematical thought experiment.

One turns a Thomson Lamp on-and-off over a period of one minute.

Specifically, one turns it on for a period of 30 seconds, and then turns it off for 15 seconds, turns it on for 7-and-a-half seconds, turns it off for 3-and-three-quarters seconds, and so on --- reducing the time by one-half each time.

The question is: at precisely the one minute mark, when the lamp has been turned on-and-off an infinite number of times,

is the lamp on, or is it off?

The relationship with Grandi's Series should be obvious.
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I always suspected that you were a solipsist. ---
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Ah! The wonderous nature of the prime numbers!!
The very mention of them is enough to send me into rhapsodies of praise -- at least, into such rhapsodies of which my nature is capable! · ·

God created the primes -- all the rest is a series of footnotes to the primes
[My apologies to both Leopold Kronecker and to Alfred North Whitehead] · ·

From the Riemann Zeta-Function, to quantum mechanics, chaotic spectra, entropy and into the utmost reaches of mathematics -- having penetrated into the innermost chambers of the Holy of Holies -- one finds the primes on their divine throne, wreathed with supernal beauty, intricacy and subtlety, far, far beyond the works of Man and Nature, literally infinite in glory, sending shafts of purest radiance out to every region of existence, penetrating the inner core of all things!!

I particularly like exploring the sum of the reciprocals of the prime numbers*.

* Merrifield, C.W., "The Sums of the Series of the Reciprocals of the Prime Numbers," Proceedings of the Royal Society, vol. 33, Nov. 17, 1881, pp. 4-10

The sum of the reciprocals of the natural numbers approaches, as a limit, ln(n) plus the Euler-Mascheroni Constant.

The sum of the reciprocals of the primes approaches, as a limit, ln(ln(p)) plus a constant. This very interesting constant, which is sometimes called Mertens Constant, can be derived from the Euler-Mascheroni Constant minus an infinite series whose terms consist of the sums of the reciprocals of the natural numbers raised to integer powers in a fairly complex, but regular, way. This constant, which as far as I know has no generally recognized name, is approximately 0.3157184520.... It was, as far as I know, first calculated by Merrifield and Glaisher in the 19th century, but due to the calculational limitations of their time, they did not truly recognize its significance. That was done later by Hadamard de la Vallée Poussin and others.

Anyway, the sum of the reciprocals of the prime numbers possesses internal relationships which are truly astonishing, breathtaking and supremely beautiful.
The divine economy is more truly revealed in mathematics than in any other region of human experience.
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All my life I have heard so much blither about Plato! If only people would actually read Plato, rather than parroting the clichés they have heard about him!

For instance, people seem to be determined to misunderstand the Republic! Plato had his political ideas, but the Republic should be viewed primarily as an extended metaphor, as a disquisition upon the proper ordering of the individual human soul. For cryin' out loud, Plato himself says this as clearly as anyone could:

"[Glaucon and the rest] wanted to arrive at the truth, first, about the nature of justice and injustice, and secondly, about their relative advantages. I told them what I really thought: that the enquiry would be of a serious nature, and would require very good eyes. Seeing then, I said, that we are no great wits, I think that we had better adopt a method which I may illustrate thus: suppose that a short-sighted person had been asked by some one to read small letters from a distance; and it occurred to some one else that they might be found in another place, which was larger, and in which the letters were larger --if they were the same text, and he could read the larger letters first, and then proceed to the smaller -- this would have been a rare piece of good fortune!

Very true, said Adeimantus; but how does the illustration apply to our enquiry?

I will tell you, I replied; justice, which is the subject of our enquiry, is, as you know, sometimes spoken of as the virtue of an individual, and sometimes as the virtue of a State.

True, he replied.

And is not a State larger than an individual?

It is.

Then, in the larger, the quantity of justice is likely to be larger and more easily discernible. I propose therefore that we enquire into the nature of justice and injustice, first as they appear in the State, and secondly in the individual, proceeding from the greater to the smaller and comparing them."
--- Book II, 368D

Click to expand...

Could anything be clearer than that?! The entire Republic is primarily an investigation of the individual psyche, and is only secondarily about "politics" as we understand them! Yet vast masses of brainwashed "intellectuals" continue to drone out the same tired clichés that Plato was some sort of proto-fascist---as though you could meaningfully compare the politics of someone living in the 4th century BC with those of an inhabitant of the 21st century AD!
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Analytic philosophers have done yeoman work clearing much dead wood away from our thinking, but they are not the last word in philosophy. They have tried hard to demonstrate that we must eschew vague, general ideas as meaningless. But, as has often been pointed out, their own views are general ideas, and they have notoriously had great difficulty in proving that their views are free from vagueness. It is a joke, but one with a sting in its tail, that the assertion that all metaphysical views are meaningless is itself a metaphysical view, and therefore meaningless.

Philosophers write endlessly trying to find truth, but if words are all we have, then it is merely a meaningless game with words; all views must be defined with words, words must be defined with other words, and we finish with words chasing their own tails endlessly through the dictionary.

If we are to get anywhere, we must go beyond the dictionary, into a wider realm; meaning in a closed system must arise from a meta-system.

"Creation is the irruption of a transcendent order of Reality into the limited realm of Being which we inhabit."

Analytic philosophers would say that we must find meaning for our theories in what we observe in the real world revealed to us by our senses. That is a major part of science.

Alas! What a slippery thing it is to understand that little word, "real". And recognition of the unreliability of the senses goes back beyond the fable of the Five Blind Men and the Elephant.

What is clear, to me, is that the creation of meaning comes from outside a system, not from inside. Whatever meaning can be deduced from my dictionary is one thing to me, another to an inhabitant of Tang dynasty China, and yet another for the multi-dimensional plasma-beings of planet Qwerty.

The meaning of a system arises from a meta-system; yet, inevitably, the meaning of the meta-system arises from a meta-meta-system, and so on, without end.

A major question of philosophy for me is whether this process goes on without end into infinity, or whether the process somehow curves in on itself, like a snake eating its tail---boundless, but finite.

Since I think there is a fair amount of evidence that nature abhors infinities, I suspect that the second view is more tenable; but, as a sceptic, I am open to opposing evidence.

Consider the Library of Babel, which I mentioned at the beginning of this thread. There can be no random string of letters which is without a meaning or translation in the Library, either in some language, natural or artificial, or in some cryptological code. The grammars of all these languages occur in the library, as do the explanations of all the cryptological codes. Following the work of Georg Cantor and Kurt Gödel, the infinity of cryptological codes is higher and greater than the infinity of messages to be deciphered.

The hyper-infinity of cryptological codes represents a meta-system of the infinite system of messages to be de-coded.

The work of Kurt Gödel has been extended in a very interesting fashion by Gregory Chaitin:

OMEGA and why maths has no TOEs (Theories of Everything)

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One of the clever things that Borges does in his "Library of Babel," and which I imagine few readers notice, is that he slips in oblique references to a world outside the Library, though the assumption of the story is that there is nothing other than the Library. Thus, he indicates that no matter how hard we try, it is impossible to postulate a totally enclosed system, devoid of any sort of opposing frame of reference.
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When old age shall this generation waste,
Thou shalt remain, in midst of other woe
Than ours, a friend to man, to whom thou say'st,
"Beauty is truth, truth beauty,"---that is all
Ye know on earth, and all ye need to know.
---John Keats, "Ode on a Grecian Urn"

Clear definition is important, but it is not the be-all and end-all of philosophy. Often, it is not necessary, desirable---or even possible!---to define.

As examples of defined words, we might take "circle," "the square root of minus one," "entropy," etc. Within a particular frame of reference, they have very clear and well-defined meanings.

Indicative words are words like "good," "art," "beauty," "God," "mind," and I would suggest words like "being" and even "matter." These words are notoriously difficult to define, and I suggest their usefulness comes precisely from their lack of clarity, their vagueness, and perhaps even from their logical incoherence.

What I call "indicative" words are like arrows pointing out a direction to travel along. Their very lack of meaning may make them suitable to be "pointers" in a large variety of frames of reference.

In ancient China, Gong-sun Long-zi understood this and came very close to the essence of Kurt Gödel's recent arguments. His influence on later Chinese thought was both profound and far-reaching. In his essay, "Discussing the Designation of Things," he showed that the meaning of a thing is not the thing itself: the terms of a system are dependent on the terms of a meta-system.

'Among things, there are none which are not designated, but "designation" is not designated.'

'"Designation" is what is not in the world. "Things" are what are in the world. It is not permissible to take what is in the world for what is not in the world.'

'If one is speaking about what is indeterminate [one is not speaking about a 'thing"], for all "things" are determinate.'

'Everything in the world can be pointed to and designated. But "designation" is not a determinate entity which can be pointed to.'

The pointing finger cannot point to itself.

The peculiar power of "designation" resides in the fact that it is not a "thing," in the fact that it is indeterminate. Its being unlimited by a determination is what permits it to be "that which applies to everything in the world."

If "designation" were determinate, it would be limited and circumscribed like all other "things." The clear proof that "designation" belongs to a metasystem lies in the fact that it is impossible to pair "designation" per se with any "thing" in the world. Each "thing" already has its own name. "Designation" is one name which cannot be paired with a thing.

Assuming that it could, a contradiction would arise. For one could then conceive of a "designation" which would point to all things in the world including the supposed "designation"!!
[This is basically Plato's "Third Man Argument," and has an obvious relation with the reductio ad absurdum which Gödel uses to establish the incompleteness of mathematical systems].

"Consciousness will always be one degree above comprehensibility." ----G. Ehrensvard

Since I am fond of ambiguity, my version of this is:

The mind is very adept at showing what it can't do to itself.

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I wish to describe a half-way house for those without training in philosophy on a journey to the understanding of the thought of Plato. It is false to Plato in one supremely important aspect, yet can still be useful.

Let us make a distinction between things that "exist" and things that are "real."

Let us define "existents" as just those "facts" that are in the external world of common experience---the subject matter of science. So we will say that tables and rainbows, sights, sounds, patterns of behaviour and everything else that can be physically measured---"exist."

Let us have another class of objects which are called "real." Things like scientific laws (E=mc^2, h=energy / frequency, etc.) and the theorems of mathematics are "real" things, or "forms."

Both "existing" things and "real" things are part of the world as we know it. We cannot touch or see a circle, or anything else that is "real," yet "real" things can be causally effective (for example, the laws of optics can be used to trigger a bomb). Furthermore, "reality" and "existence" are mutually exclusive classes---things which "exist" are not "real," and things which are "real" do not "exist."

Yet "reality" and "existence" are also mutually dependent; each appears in the world supported by the other. Only insofar as a wheel approaches circularity is it said to "exist" as a wheel. On the other hand, "circularity" is dependent on sensible objects in order to be manifested.

Circularity does not "exist," , but it is manifested by things that do exist. Yet again, things which "exist" do so only through an immense concatenation of "forms." In physics, for example, when we try to understand a material object, we find that it dissolves into a warp of electric and magnetic fields on a woof of curved space-time. These, in turn, when subjected to analysis, reveal new "existences" and new "forms": elementary particles, units of "action" and quantum fields. Each time we try to tease out what is before our eyes, we find that it disappears to reveal a new content functioning through new "forms."

Temporally, "forms" are eternal and unchanging; there is no difference between a circle today and a circle a billion years ago---while things which "exist" are subject to any number of interactions which may alter or destroy them. They are never exactly the same from moment to moment. A "form," however, does not undergo interactions; it is interaction! --- or to put it better, it is a function or law of interaction. When conditions permit it to operate, a "form" or "function" springs forth fully-blown from the brow of Zeus---and then vanishes away without residue when conditions end its functioning. (This is not strictly true---first, it may leave a causal residue which affects the future history of various phenomena; second, no function or force ever ceases completely; we say that it ceases when it becomes too weak to be distinguishable from random fluctuations or is obscured by stronger forces)

For the philosophically naive, the world of experience seems unquestionably solid and enduring. Such people are liable to be suspicious of what I am calling "forms" or "reals." They seem to have a spurious quality, to be the "ghosts of departed quantities," or like the grin on the face of the Cheshire Cat. However, what is "real" is vastly more enduring and immutable than what "exists"---and this is precisely because it does not "exist"!

E=mc^2 does not "exist," it is "real;" it is an invariance in the relationship of matter and energy.

Each "form" is itself compound, but it is a compound of other forms---just as the definition of each word in the dictionary is meaningless without the definitions of all the other words. "Forms" are defined by other "forms." The "real" defines what "exists," not vice versa. What "exists" manifests what is real, but does not define it. The two are mutually dependent and ontologically equal, but what "exists" is epistemologically subordinate to what is "real."

That which is sensibly perceptible is a flux of many forms. The paradigm of the modern experimental method is to restrict the operation of forms by allowing only one variable to change in a particular experiment---while holding all other variables constant. If successful, this effort will reveal some aspect of the experimental situation to be a function of a particular variable. The theoretician then takes these results and attempts to enunciate a law that will generalize this function to a variety of experimental situations. Thus, step by step, science inches closer to what is "real"---to the revelation of a Platonic Form.
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PUN:

The difference between ANTANACLASIS and PARONOMASIA
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Aufgeblassen said:

Big Government and Big Business ... try the social and cultural unity to impose adults and children. To do this they will use all the techniques of mind-manipulation available and will not hesitate to strengthen these methods of non-rational persuasion through economic constraint and threats of physical violence. If you want to avoid this kind of tyranny, we must immediately begin and educate our children for freedom and self-government. This education for freedom must ... be the first in facts and values ​​- the facts of individual diversity and genetic uniqueness and the values ​​of freedom, tolerance and mutual love are the ethical accompaniments of these facts.

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No hope of that as long as Hollywood, television, advertising, the Deep State and the Military-Industrial Conspiracy exist.
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The ordinary person thinks that he perceives an external world. This world is varied in qualities and inexhaustibly rich in detail. His mind, on the other hand, appears to him (when he thinks about it at all) to be a "little black box," a vacuity behind his eyes, out of which mysteriously pop thoughts, feelings and desires.

For the biologist, however, the world of sensation is a state of the nervous system. Damage or destroy the nervous system, and this all too solid world disintegrates and vanishes, leaving not a wrack behind.

The only things of which we are directly aware are states of sensation, states of mind.

Precisely contrary to the ideas of vulgar common people, this incredibly rich world of ours is "in here," not "out there." It is rather the external world which is, in fact, the "black box"! We can never be certain what is actually "out there," because we only know things as they appear to our minds, not as they are in themselves. Is there anything out there in the black box? Does anything exist other than our sensations?

Science is one way to find out.

Science reveals to us many interconnected series of concomitances---laws and relations---which subsist over and above our immediate sensations. What science reveals to us seems to be the substance of the external world.

But this "substance," these laws and relationships, are nothing but what I have been calling "reals" or "forms"! If there is anything behind our sensations, it must be "forms." They are "real," but they do not "exist"!

Rather a different view from that of the common man! He regards these "forms" as mere ideas, mental constructs, useful fictions. He cannot touch them; therefore they do not exist. The wise person agrees that these forms do not "exist;" they are "real"! And they are "objective" precisely because they are not prisoners of the flux of "existence."

"Reality" is objective, and "existence" is subjective. To a wise person, all ordinary people are autistic. They lie curled up in a ball, totally unaware of the external world. They nibble their fingers, stare at their navels, constantly consumed by a morbid fascination with their own sensations---existing in a state of endless mental masturbation. Aware only of their own sensations, they cannot lift their eyes to look through those sensations out at the "Real" world, the non-subjective world that is the same for all observers who approach it in the spirit of science.

Most people on this site probably regard the work of William Blake as a mass of twaddle, but he was saying, in his poetic way, exactly the same when he wrote:

For the cherub with his flaming sword is hereby commanded to leave his guard at the Tree of Life, and when he does, the whole creation will be consumed and appear infinite and holy, whereas it now appears finite and corrupt.

This will come to pass by an improvement of sensual enjoyment.

But first the notion that man has a body distinct from his soul is to be expunged; this I shall do, by printing in the infernal method, by corrosives, which in Hell are salutary and medicinal, melting apparent surfaces away, and displaying the infinite which was hid.

If the doors of perception were cleansed, every thing would appear to man as it is, infinite.

For man has closed himself up, till he sees all things through narrow chinks of his cavern.
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Aufgeblassen said:

Congratulations! (on your humbleness)

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Curses! You have discovered it !!

And I try so hard not to let people see it ! --- :angel:
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