quote:

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Originally posted by drag:

quote:

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Originally posted by Tom:
No, I still don't see it. A paradox is an assertion that purports to be
a statement, but cannot be assigned a definite truth value
(as in, "this sentence is false").

0 = infinity can be assigned a definite truth value. More specifically, it is false.

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Exactly. That is why it implies a paradox.

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???

Drag, I had just told you that a paradox is something to which one cannot assign a definite truth value (T or F), and I had further just told you that I can assign a value of F to 0=.

I'm at a loss as to why you think it is a paradox.

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The difference between this statement and others
is that this statement is supposed to be a true discription
of reality.

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How so?

quote:

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Hence, if the true discription of reality
achieved through logic does not follow logic, it is a paradox.

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You've completely lost me here.

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Suppose, for a moment, that there was no way (or at least
it would seem more likely = logical, that there is no way) to
have a physical theory that could combine GR and QM.
In such a case, you would have logical conclusions
which do not follow logic. And, you'd have to abandon logic.
This would be a logical paradox. The same thing
happens with the paradox of existence, only it seems
impenetrable through any reasoning system.

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The GR/QM story is quite different. As Fliption and I have pointed out, a paradox ensues in one of two circumstances:

1. For some statement X, both X and ~X can be derived from the same set of axioms.

2. Some statement X is self-referential.

The part in red is important, because the axioms of GR and QM are not part of one system, but two.

So, yes, GR and QM contradict one another, but this is not a paradox!

I'm skipping the part about God and pink elephants...

quote:

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quote:

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Originally posted by Tom:
They are not self-referential, at least not in the Goedel sense.
It only makes sense to say that statements are self-referential.

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These "statements" discribe reality...
Hence, if they are self-referential then reality is too.
To prove that this is not the case, you'll have to show
that the constituents are not basic and thus the statements
are false, but then you'll just have new constituents.

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No. A statement is self-referential when it refers to its own truth or falsity. The concept has nothing to do with physical entities.

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Anyway, Tom, I do not see your side in this argument.
Your original message above says : "I'm lost."
I find that very difficult to believe, in your case.

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That was pretty much my point ("I'm lost"), but if I were forced to pick a "side" in this argument, it would be the following:

Almost nobody here knows what the heck a paradox is.

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Originally posted by Tom:
Almost nobody here knows what the heck a paradox is.

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Definitely agree with this.

"What is essential here is the presence of the spirit of dialogue, which is in short, the ability to hold many points of view in suspension, along with a primary interest in the creation of common meaning."

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No. A statement is self-referential when it refers to its own truth or falsity. The concept has nothing to do with physical entities.

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Tom, this is true from logician's point of view but leaves out the more common use of the word paradox. Relativity, for example, is considered paradoxical in the common sense of the word because it is self-referential and contradicts everyday observation.

First, you yourself state the logician's definition of a paradox, and I thought that is what you were trying to talk about. The only thing I noticed is that, while you state that definition, you do not correctly identify paradoxical statements.

Second, SR is neither self-referential nor contrary to everyday observation.

Third, even if SR were contrary to everyday observation, that would not make it paradoxical. It would make it wrong.

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Wuli,

First, you yourself state the logician's definition of a paradox, and I thought that is what you were trying to talk about. The only thing I noticed is that, while you state that definition, you do not correctly identify paradoxical statements.

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Yeah, as I have said all along I'm just makin' this stuff up as I go. I think I have this particular kink worked out, but help is greatly appreciated. Essentially, I think it is reasonable to say that because of the paradox of existence, all irrational statements, and perhaps everything in general, are potentially paradoxes in the final analysis and demonstrate the same kinds of synergistic reflective and free association relationships with the human mind if nothing else.

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Second, SR is neither self-referential nor contrary to everyday observation.

Third, even if SR were contrary to everyday observation, that would not make it paradoxical. It would make it wrong.

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According to relativity, a hot iron weighs more than a cold one. This contradicts everyday, ordinary observation. Likewise, mass=energy=space=time, etc. is self-referential.

Again, the dictionary definition says a more common usage of the word paradox is something that may be true, but contradicts everyday observation and is self-referential. Note that both the logician's definition and this more common use of the word can both fit into my use here.

Again, I appreciate your feedback and consider you among the very best for constructive feedback.

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Originally posted by Tom:

quote:

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Exactly. That is why it implies a paradox.

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???

Drag, I had just told you that a paradox is something to which one cannot assign a definite truth value (T or F), and I had further just told you that I can assign a value of F to 0=.

I'm at a loss as to why you think it is a paradox.

quote:

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The difference between this statement and others
is that this statement is supposed to be a true discription
of reality.

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How so?

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For example, we see everything fall to the ground.
Hence, we see a pattern at work here and can assert
that there is some principle - a law, "behind" this
phenomenon. Further more, all our previous observations
of the Universe seem to confirm that if things followed
a certain pattern in an isolated physical system then
that pattern is likely to persist (part of the reasoning
system called logic). Following from that, we can formulate
a physical law that would be Universal for everyone.
However, if you, I or Newton had to "really" discribe
why they think this law shall apply to the next rock we
throw in the air it would look something like this :
Since I was born I believe(that is find it likely that I
saw, because I can never fully prove it's true) saw
everything follow this pattern. Further more, I
received input from other individuals and human-made
info sources that there is a formulated pattern-law
for this phenomenon(for us not Newton... ), that
all mankind seems to agree that it actually applies
in the Universe.
As a result,I find it most probable(according to the logical reasoning
system I adopt) that the rock I'll throw is going to follow
this law, but I can never be 100% certain that it will.

This is the "full" discription of the reasoning one should
have (if one adopts the logical reasoning system) as
to why the next rock should fall to the ground.

What does this give us ?
This is a demonstration of how we think (or at least,
should think) about the Universe.

For example, if a person born on a spaceship orbiting the
Earth and with no windows finds the formula and
basic explanation for the above law then he should not
(in other words, it would not be reasonable for him according
to the logical reasoning system I assume here he adopts, as
opposed to a reasoning system which says : you will find the
Universal laws written in your spaceship - a system which
could form as a result of such experience repeating itself)
accept this law as true. He should test it first. But, if that person
also sees this law written on a computer system that will tell
him it was formulated and accepted by all of mankind
living on the planet Earth and tells him more stuff about
himself and the spaceship and other laws he can
verify, then it would be reasonable for that person to
think this law is true, even without verifying it first.
Much the same way I think that GR formulas are correct
even though I've never tested them or really
saw them "at work" with my basic senses, which are
one's most reliable sources of input in many cases.

Now, the above lenghty demonstration was designed to
show one basic principle : We think about the Universe by
applying some sort of reasoning system. We then apply
this reasoning system and get certain results (like laws).
As a direct consequence, if the application of the resoning
system to the Universe creates a paradox then either we
abandon that reasoning system or we accept the paradox
as real.

The tiny little problem with the paradox of existence
(like I said and demonstrated in this and other threads) is
that it not only creates a logical paradox but it also
creates a paradox using any other reasoning system.
This both suggests that discarding logic will do no good
in this case and that this is a "real" Universal paradox.

Now, I'm not playing with "logic" or other reasoning systems
here. I am not intrested at this point in verbal definitions/
violations/excersises with logic or any other reasoning system.
I am talking about its application to the "real" world - Universe.

AS A RESULT, as far as I can see, there are 2 parts you can argue
with me over here :
1. That one should/does not apply a reasoning system of any kind
to the Universe.
I wonder though, how would one build an argument of this sort
if one does not make use of some resoning system...
2. About the application of a reasoning system (of any kind)
to the Universe by me in this particuilar case.
For this second objection I can see two paths you can
follow :
1. You can show that my use of the logical reasoning
system was incorrect.
And, show the same for the basic principles of a
reasoning system in general or the part about their
violation by the paradox of existence I talked about.
2. You can demonstrate that my argument is subjective.
That is, that it includes a conclusion that does not
reasonably follow from the argument.
That should prove somewhat difficult as every part
of my argument is also a part of a logical chain that
is in the Universe (time/space/electrons), except for the
final conclusion about a paradox.

In fact, I think that the main problem is here. That is,
most people find it difficult to make this last step and
recognize this "faceless" and perhaps for some - frightning
conclusion. God, for example, can be recognized with
much greater ease by people because it saves the
strict investigation of the entire issue and presents
a much more "friendly" solution. But, God is basicly
just the same thing as the paradox of existence, stuffed
with unreasonable and baseless qualities.

BTW, Tom, you did not adress my "open" system remark.

quote:

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You've completely lost me here.

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quote:

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The GR/QM story is quite different. As Fliption and I have pointed out, a paradox ensues in one of two circumstances:

1. For some statement X, both X and ~X can be derived from the same set of axioms.

2. Some statement X is self-referential.

The part in red is important, because the axioms of GR and QM are not part of one system, but two.

So, yes, GR and QM contradict one another, but this is not a paradox!

I'm skipping the part about God and pink elephants...

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It seems to me as though you keep adressing just logic
not APPLIED logic.

All dogs are red.
All cats are green.
Hence, no dogs are cats.

This is logic, but it is not applied logic.
There are no absolute truths in applied logic
about things INSIDE the Universe. There are
no absolute terms in applied logic for things
INSIDE the Universe. A dog is just a bunch of
atoms which are a bunch of particles which are
a bunch of other stuff and if this chain is halted
then there's something wrong either with our
applied logic or because we find a real paradox.

What is the logic of an apple ?

In "just logic" this is an ill-formulated question.
In applied logic the logic of the apple is that it is the
effect of an apple tree. (It also consists of atoms.
It is also subject to Universal laws of some sort.)
Now ask the same about the Universe as a whole.

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That was pretty much my point ("I'm lost"), but if I were forced to pick a "side" in this argument, it would be the following:

Almost nobody here knows what the heck a paradox is.

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Live long and prosper.

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Originally posted by wuliheron:
The logicians they all cried,
"It's a nightmare come to life!"
But everbody else,
Simply accepted paradox itself,
And left logic behind.
[/i][/center] [/size=4]

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Live long and prosper.

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Originally posted by Fliption:

quote:

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Originally posted by Tom:
Almost nobody here knows what the heck a paradox is.

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Definitely agree with this.

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Live long and prosper.

Tao is no more a privileged means of access to knowledge and understanding than any other, and I am sure it is easy to take potshots at paradox and find it falls miserably short of answering what is being asked of it.

Tom's clear head in this debate, in which paradox is being used as a defence of confusion and obscurity, is admirable. Anyone of us can speak nonsense and dress up that nonsense in a system or school of thought. Much nonsense is being spoken here in the name of Tao.

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It is odd, and perhaps a little amusing, that every specialist views their speciality as the answer to all the important questions. Those who dabble and traffic in Tao seem to think that Paradox is the great and grand answer to all manner of questions.

Tao is no more a privileged means of access to knowledge and understanding than any other, and I am sure it is easy to take potshots at paradox and find it falls miserably short of answering what is being asked of it.

Tom's clear head in this debate, in which paradox is being used as a defence of confusion and obscurity, is admirable. Anyone of us can speak nonsense and dress up that nonsense in a system or school of thought. Much nonsense is being spoken here in the name of Tao.

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Nice hint of British reserve.... I can lmost hear the royal we in your voice....

Unfortunately for you, we are discussing paradox here. My Taoist references are nothing more than that, simple references. If you believe paradoxes to be useless, by all means prove your case. Otherwise I shall just consider this another biased intrusion. As I already indicated, I too value Tom's opinion in these matters, its just sometimes hard to get his answer.

Stick to the subject...... please Sir whoever you are. If you are a gentleman, then please do not obfuscate what is on the table.

quote:

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Originally posted by N_Quire:
Tom's clear head in this debate, in which paradox is being used as a defence of confusion and obscurity, is admirable. Anyone of us can speak nonsense and dress up that nonsense in a system or school of thought. Much nonsense is being spoken here in the name of Tao.

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And where's Tom anyway ?

Peace and long life.

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The discussion here is not about Tao, it is about a fundumental
quality of the Universe which, in my opinion, should
be evident through any in-depth reasoning about
this subject.

And where's Tom anyway ?

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Of course, you know I disagree that any fundamental quality of existence is evident in any in-depth reasoning, unless of course you consider paradox a quality. Nature herself, of course, displays countless qualities which all are apparently organized holistically.

Tom's a busy guy, but sometimes I also think I scare him or at least challange him.

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Originally posted by drag:
How many messagees did you read before you
posted this ?
What is Tao anyway ? I hate my own ignorance but
I have no idea about what it is, except for apparently
being a type of eastern philosophy.
The discussion here is not about Tao, it is about a fundumental
quality of the Universe which, in my opinion, should
be evident through any in-depth reasoning about
this subject.

And where's Tom anyway ?

Peace and long life.

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I read all of a thread before commenting. If I don't have anything to say, I keep quiet. As Wuli pointed out, he's winging it, making up the argument as he goes along. That's good. Creative thought should not be shackled, nor should we be worried about asking daft questions. And we should be prepared for people to tell us we are asking daft questions.

In many of the philosophy threads, Tao is mentioned in the same breath as paradox so it seems valid to comment on this and question whether the paradox that some people perceive to be a feature of the world in itself isn't often a feature of the way the word is used in conversation. The term is also thrown about very loosely and takes on many meanings.

I would think that all the thoughts of Tao are translatable into western language use and thought; it's a question of conversation and negotiation. I doubt whether it has any special or privileged insights that are not available to all thinking, reading, conversing people.

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As Wuli pointed out, he's winging it, making up the argument as he goes along. That's good. Creative thought should not be shackled, nor should we be worried about asking daft questions. And we should be prepared for people to tell us we are asking daft questions.

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The Daffier the better I say, "Out of the mouths of babes...."

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In many of the philosophy threads, Tao is mentioned in the same breath as paradox so it seems valid to comment on this and question whether the paradox that some people perceive to be a feature of the world in itself isn't often a feature of the way the word is used in conversation. The term is also thrown about very loosely and takes on many meanings.

I would think that all the thoughts of Tao are translatable into western language use and thought; it's a question of conversation and negotiation. I doubt whether it has any special or privileged insights that are not available to all thinking, reading, conversing people.

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Chinese is a wholistic language. "Dao" has eighty distinct meanings depending upon how you pronounce it, yet all eighty are considered somehow related. There are relationships in Chinese that westerners simply do not recognize as relatioships. Its a bit like attempting to express anger or joy using nothing but mathematical symbols that were never intended for the job.

You are right in my opinion to bring this up. For our purposes here Dao translates roughly as "The way things are". Thus, the Tao that can be spoken of is not the eternal Tao, and the paradox that can be proven is not the eternal paradox. If you note, we could dispense with the use of taoist references altogether and everything I have written still makes sense on its own.

Mysticisms such as Taoism are personal practices. This discussion is about the uses of paradox, of which mysticism is only one possible use and one I would avoid here for the sake of clarity and harmony in discussing the issue.

quote:

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Originally posted by wuliheron:

quote:

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Originally posted by Tom:
Second, SR is neither self-referential nor contrary to everyday observation.

Third, even if SR were contrary to everyday observation, that would not make it paradoxical. It would make it wrong.

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According to relativity, a hot iron weighs more than a cold one. This contradicts everyday, ordinary observation.

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This viewpoint of yours is highly subjective. It's like trying to call something 'illogical' because it contradicts 'common sense'. Who's common sense, exactly? Who's everyday experience, exactly?

If you are a scientist with the intstruments that are sensitive enough to detect the small deviations in measurements due to relativistic effects, then for you, relativity is right in line with "everyday observation".

In any case, this notion of conflict with everyday observation has nothing to do with what a paradox is.

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Likewise, mass=energy=space=time, etc. is self-referential.

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According to what definition of "self-referential"? The definition used by logicians is that a self-referential statement is a statement that refers to its own truth or falsity. No statement of relativity satisfies this definition.

quote:

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Again, the dictionary definition says a more common usage of the word paradox is something that may be true, but contradicts everyday observation and is self-referential. Note that both the logician's definition and this more common use of the word can both fit into my use here.

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I saw where you quoted the dictionary definition (on page 7) and I also saw where you stated the logician's definition (on page 8), so I know that the two are interchangable in your mind. However, they are not so in mine.

The dictionary definition introduces all manner of subjectivity when it says that a paradox is contrary to "opinion" or "common sense". By that definition, there is no way for two people to agree on whether or not something is truly "paradoxical".

The logician's definition, on the other hand, is a mechanical decision procedure that anyone can follow.

1. When is a logical system contradictory? When, for some statement X, both X and ~X can be proven within that system.

2. When is a statement self-referential? When that statement refers to its own truth or falsity.

3. When have you encountered a paradox? When you run into either a self-contradiction or self-reference.

Now it is possible for any two people to agree when a paradox is encountered, according to the logician's definition of "paradox".

quote:

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Again, I appreciate your feedback and consider you among the very best for constructive feedback.

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Thanks for listening.

quote:

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This viewpoint of yours is highly subjective. It's like trying to call something 'illogical' because it contradicts 'common sense'. Who's common sense, exactly? Who's everyday experience, exactly?

If you are a scientist with the intstruments that are sensitive enough to detect the small deviations in measurements due to relativistic effects, then for you, relativity is right in line with "everyday observation".

In any case, this notion of conflict with everyday observation has nothing to do with what a paradox is.

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Paradox is irrational. Whether or not anything actually is irrational in the final analysis is debatable because objectively, there is no way to prove definitively that anything is irrational. All you can do is disprove it is rational. The genuinely irrational simply does not fit into Karl Popper's criteria for a scientific theory because it cannot be disproved. Thus, paradox and the irrational are axiomatically ruled out by many modern scientists and logicians. Hear no evil, see no evil, speak no evil.

Reguardless of this difficulty, the irrational and paradoxical have proven inordinately useful when approached holistically. This is why I am sort of mushing the definitions a little here looking for something better. Again, I'm just making this up as I go.

The paradox of existence and, indeed, Quantum Mechanics as well, imply that everything may ultimately be irrational and the rational could well be a human bias. A statistical fluke if you will, and a self-fulling prophecy. If so, then a new scientific approach is obviously required because the old one is biased against the irrational and holistic.

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Likewise, mass=energy=space=time, etc. is self-referential.

--------------------------------------------------------------------------------

According to what definition of "self-referential"? The definition used by logicians is that a self-referential statement is a statement that refers to its own truth or falsity. No statement of relativity satisfies this definition.

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What is space? What is time? For that matter, just what are Quanta?

What is Existence?

The more extreme, broad, and yet simplified these definitions become....the more these modern theories begin mixing what for eons were considered disparate parts of nature........... the more confused the exact identities of these "things" becomes. Relativity, for example, is a metric theory which can describe existence as consisting of nothing but space.

Einstein himself thought of existence as a kind of beautiful hyper-symmetrical N-dimensional jewel fundamentally no different from Plato's original vision. Today theories attempt to describe existence in terms of pure consciousness, logic, time, etc. Why? Because they are self-referential holistic theories which inevitably still cannot answer the paradox of existence.

That means "space" is Relativity's metric "yardstick" so to speak and is self-referential as well as defying everyday observation. Although scientists do possess the ability to measure things, their yardsticks and approaches to nature are ultimately biased against the irrational and increasingly self-referential. The implication of this situation is that what we describe as orderly and disorderly may ultimately only be a question of how we choose to define such things and the scale at which we choose to observe phenomena.

In my ordinary everday life, atoms and subatomic particles do not appear to me to be extremely chaotic, but Quantum Mechanics suggests otherwise. Is it that Quantum Mechanics really is chaotic, or is it merely that the way we view quanta currently is just biased by our altogether human viewpoints, including the human viewpoints of scientists? Scale is not only critical to physics, it is becoming increasingly paramount in every way.

In the specific case of Relativity, for example, its scale is based on four dimensional mathematics, which was a new mathematical invention of Einstein's day. In the nineteen sixties mathematicians invented Fractal Geometry which pointedly brings into question just exactly what the heck a dimension really is and mathematicians are still debating. It also brought with it new issues concerning the importance of scale.

The increasing ambiguity of our definitions of spacetime, mass, energy, dimension, scale, rational and the irrational demand at one and the same time that we develop and impliment both linear logical and holistic definitions of these terms. In my opinion, this is exactly what people are doing currently and the attention to detail that this requires is in part to blame for the fact that most significant theoretical physics papers today require over a hundred contributers.

Anyway, what I present here is the diametrically opposed holistic view of paradox and a way to approach the subject within the current traditional scientific context. Instead of demanding falsifiability as karl Popper does, it demands more skepticism of what we consider falsifiable. Instead of being largely quantitatively oriented, it is largely qualitatively oriented, instead of focused on content it is focused on context, and so forth.

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The dictionary definition introduces all manner of subjectivity when it says that a paradox is contrary to "opinion" or "common sense". By that definition, there is no way for two people to agree on whether or not something is truly "paradoxical".

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It does not matter whether they agree or not in some respects. This is the central issue I am attempting to adress here. What matters is that these two observers have their own perspectives and can compare their maps. The map is not the territory. By using distinctly different kinds of maps we can understand the territory better.

Although qualitative and possibly purely symbolic maps have their drawbacks they also have their uses. The central question from a scientific viewpoint is how to best capitalize upon their uses. By searching for and accepting the irrational and being skeptical of the rational, valuable alternative maps that make important qualitative differences can be created.

Wuliheron, as always I partly agree and partly disagree
with you. I remmember what happened the last time
I actually tried to confront you in a different thread
so I'll pass this time. (BTW, 4D geometry predates SR by
almost half a century... )
Anyway, what has science done to you ? You adress
it with such great pessimism and ambivalence and talk
about it as though many scientists agree with your
pessimistic views. I assure you, that is not the case.
Be optimistic dude !

Tom... Hi ! My username is Drag and I believe we were
in the middle of a discussion here. If you totally disagree with
me or something or simply aren't intrested in discussing
this subject with me I'd really appriaciate it if you just
say so, out of pure courtesy, you know...

Peace and long life.

quote:

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(BTW, 4D geometry predates SR by
almost half a century... )

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Yes, of course, that was Einstein's day. About twenty years before his birth, but a relatively new invention considering 3d Euclidean geometry had ruled unchallanged for over two thousand years.

quote:

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Anyway, what has science done to you ? You adress
it with such great pessimism and ambivalence and talk
about it as though many scientists agree with your
pessimistic views. I assure you, that is not the case.
Be optimistic dude !

---

The word is skepticism, not pessimism. Science has brought many wonders, but also many terrors like the atom bomb and now cloning. Without turning that same skepticism and objectivity on science itself it becomes nothing more than another dogma.

quote:

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Tom... Hi ! My username is Drag and I believe we were
in the middle of a discussion here. If you totally disagree with
me or something or simply aren't intrested in discussing
this subject with me I'd really appriaciate it if you just
say so, out of pure courtesy, you know...

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I'd appreciate a response as well, but I am not appealing to courtesy. Just the scientific method. When rational views based on varifiable evidence are ignored or merely poo pooed by the scientific establishment it is cause for investigation.