How would resolving the Paradox change the story for you?

[iQuestor]

So what about experience? Well, that has shown the universe to be contradictory, not merely provided the possibility.

Malik, I understand your point. I am not saying the universe follows human logic. You seem to give our human point of view a lot of credence. But then again, we dont have another one, so I understand.

It is human experience that has shown the universe to be contradictory -- and we humans are often wrong. We look at the universe from a peephole, and only get bits and pieces of how it looks and works. we try to understand and comprehend. Like the blind men and the elephant, many things dont fit together and some things dont make sense. We make up laws and apply them to what we see and then experiment to see if they hold up. it is baffling to us.

What I am saying is that there is logic to the universe. It has nothing to do with human perception or human logic. It is governed by some set of laws that we do not fully understand. Lets call it god-logic for lack of a better term.

When (if) we understand the universe through the perspective of god-logic, then my position is there will be no paradoxes; it would make perfect sense from that perspective.

[Zarathustra]

It is human experience that has shown the universe to be contradictory -- and we humans are often wrong.

How can we humans be wrong about two atomic clocks having different times? You don't have to be a god to read the time on a clock. Have you heard about this experiment? Two atomic clocks were synchronized. One clock was flown around the earth in a super-sonic jet, and the other was "stationary" (relative to the flying clock). Afterwards, these two synchronized clocks read different times, as predicted by Einstein's theories.

Either the universe is so misleading, so illusory, that everyday objects are mere phantoms (including us), or you're going to have to admit that humans can have SOME bare knowledge of their world. Such as, the discrepancy between two clocks. At the very least, your "peephole" theory must account for why our "merely human" view accuaretly confirms Einsteins theories down to the nanosecond. Using your blind man and elephant analogy, that's like the blind man accurately predicting the precise genetic code of this animal he can't see, and then conducting an experiment and learning he was right. Clearly, with this level of confirmation, you'd have to admit that the blind man was fixing upon some kind of Truth.

I agree that our view of the universe is limited. However, this inherent limitation should keep us from postulating BEYOND what we experience, becuase it is precisely in that area--that which is beyond our experience--where we have the LEAST amount of credibility. However, this is exactly what you're doing when you propose a "God's view" or a "God's logic."

What I am saying is that there is logic to the universe. It has nothing to do with human perception or human logic. It is governed by some set of laws that we do not fully understand. Lets call it god-logic for lack of a better term.

When (if) we understand the universe through the perspective of god-logic, then my position is there will be no paradoxes; it would make perfect sense from that perspective.

Where did you get this idea? What's your evidence? What's your reasoning? I intend no insult when I say, it sounds like religious mysticism to me.

Logic is univesal. Mathematics are universal. If there is a God, he might have a bigger piece of them, but he'd have to use the same logic and math that we do. If there is some level at which 1+1 does not equal 2, then you're talking about something more paradoxical than I am.

[Zarathustra]

Consider another example: Observers A and B are standing on the opposite sides of a road. A car moves past them. A says that the car moves right-to-left. B says the car moves left-to-right. How can this be? Does the universe itself violate logic?!?

That's a very good example. I'm having a hard time finding a significant difference between it and the relativistic example which I gave. However, "left" and "right" have always been terms defined by individual reference frames. Time has not. Yes, that's merely a historical distinction, but are you truly at peace with a universe that has no universal time? Don't you think that two observers measuring different amounts of time between the same two events is a little bit strange?

If so, then perhaps you are more open to paradox than you're letting on. I think the problem here is that some of us (well, some of you) define paradox in such a way that includes: "impossibility." If something is possible, then you think it's not paradoxical. I don't define paradox in a way that includes this restriction, so perhaps we're using the term to refer to different things. I don't think that a paradox necessarily means, "a violation of logic," either. It's not exactly the same thing as a contradiction. In fact, Einstein's relativity IS the "god-view" or "god-logic" which Iquestor is talking about; it is the rational, mathematical explanation which makes sense of the two different time measurements.

However, this isn't the same thing as saying the two different measurements are illusory, or that our view of each is incomplete. In fact, one might define paradox as: "two different perspectives being at the same time true." Relativism, or perspectivism is inherently paradoxical--even in your example. Indeed, Einstein's theory is a rational, mathematic PROOF that time is paradoxical, that paradox exists within our universe. In no way does this resolve the paradox (thus making it "go away"). Each observer's measurements are valid, and not illusory. Explaining a paradox doesn't make it go away. This expectation arises from believing that paradox is impossible to begin with, causing you to misinterpret proofs of paradox as eliminations of paradox.

If you really have no problem with relativistic time, then ask yourself: how old is the universe? Scientists say it's about 15 billion years old. (Who cares how accurate their guess is.) Then ask yourself this: 15 billion years relative to what? Which reference frame are we talking about here? Relative to the "universe as a whole?" If that's what they mean, then why can't we use "the universe as a whole" as a universal reference frame? If we do this, then we can toss Einstein's theories out the window and go back to Newtonian absolute time and space. Yet, if we cling to relativistic time--to "explain away" the paradox of different measurements--then it makes absolutely no sense to talk about how old the universe is. To me, it's 34 years old. But seriously, relativistic time DOES preserve paradoxical results. This is just one example.

I don't see any reason to believe in some mystical force residing in biological circuitry and not in silicon.

True. But this doesn't mean that the brain is a turing machine. Nor does it mean that a "mystical force" must be responsible for the difference. I'm sure it's a natural force (rooted in quantum effects). The problem lies in your model: an ideal Turing maching as a model for what the brain does.

Roger Penrose wrote a fascinating book which argues aggressively against functionalism (which is what you're proposing). SHADOWS OF THE MIND. Check it out. His basic argument is that we, as conscious creatures, can do things which no computer--no matter how complex--can EVER do. Turing machines ONLY process algorithms. By definition. Yet, conscious beings like us can intuit things beyond algorithms, even construct proofs which PROVE the limitations of algorithms (such as Godel's Incompleteness Theorem en.wikipedia.org/wiki/G%C3%B6del's_inco ... ss_theorem ). Coming up with--and understanding--such a theorem is absolutely impossible for a computer to do because such an intuition steps outside of the algorithmic process, which transcends the definition of a Turing machine.

[iQuestor]

Malik23 wrote:

How can we humans be wrong about two atomic clocks having different times? You don't have to be a god to read the time on a clock. Have you heard about this experiment?

This is a perfect example of what I am trying to say. The different readings on the clocks is not a paradox, unless you do not understand frame dragging or time dilation. We weren't wrong about the readings on the clocks, we were wrong in assuming they would agree -- why did they read different? That doesn't make sense! We would expect the same reading because we thought space and time were completely separate, but they are not. We were wrong in our understanding of the Laws of the Universe, in this case, General Relativity. Against Human Logic, Time slows with greater speed, and is relative to space and matter. Hence Einstein's GTR.

Frame dragging, black holes, and bumblebees having the ability to fly despite fat bodies and stubby wings. These are all paradoxes or mysteries that we have (possibly) unravelled through our experiments. At one time, we dismissed these ideas, and said they were wrong or couldn't exist or didnt make sense. The real issue here is that Human logic was wrong. Once we understood a little more about the universe, then we could resolve these seeming paradoxes.

Logic is universal. Mathematics are universal. If there is a God, he might have a bigger piece of them, but he'd have to use the same logic and math that we do. If there is some level at which 1+1 does not equal 2, then you're talking about something more paradoxical than I am.

You have misunderstood me here I think. I fully agree that logic and math are universal in that they are the Laws that the Universe is governed by; I merely relate that human logic and human math are not perfected yet and not completely in tune with reality, and that when we attempt to describe the universe with our faulty logic and math, the things that don't fit in our understanding are called paradoxes. When I say Human math, I mean what we understand of it. Yes we have 2+2 down pat, but no one is debating that. But we don't have Quantum physics all the way down, or string theory, or many others. You seem to assume Human logic and the human grasp of mathematics is perfect and complete on a universal basis. they are not. If they were, we'd understand the universe, and complete understanding means no paradoxes!!

why do you think it is the Theory of General Relativity, and not the Law of General Relativity? it is because we don't know for sure that it will hold up in all cases, only in what we have observed so far. We can't prove it.

i said:

What I am saying is that there is logic to the universe. It has nothing to do with human perception or human logic. It is governed by some set of laws that we do not fully understand. Lets call it god-logic for lack of a better term.

When (if) we understand the universe through the perspective of god-logic, then my position is there will be no paradoxes; it would make perfect sense from that perspective.

Where did you get this idea? What's your evidence? What's your reasoning? I intend no insult when I say, it sounds like religious mysticism to me.

I am not a religous person at all. I am an atheist, or at best an agnostic. that is why I said god-logic versus God-logic. No mysticism here. I meant that we do not know everything about math nor logic. we dotn yet have a universal theory of everything. and BTW: If there is a God, and his math says 2 + 2 = 1, then we are obviously wrong in our understanding of Math.

At any rate this is my own idea. I obviously have no evidence. it is based on my assumption that the universe follows some law, be it natural or created. (I think when you say Logic and Math are universal, you also mean this.)

I postulate this because the universe does seems to follow some Law from all we can tell, although we do not understand some of these laws. Our lack of full grasp of these laws causes us to misunderstand nature. This is what we call a paradox.

[I'm Murrin]

why do you think it is the Theory of General Relativity, and not the Law of General Relativity? it is because we don't know for sure that it will hold up in all cases, only in what we have observed so far. We can't prove it.

Sorry, but I just can't let you get away with that. If we have to object to creationists misusing the word, we can't let ourselves make the same mistake.

the·o·ry
–noun, plural -ries.
1. a coherent group of general propositions used as principles of explanation for a class of phenomena: Einstein's theory of relativity.

Definition number 2, the one you have referred to, has a different context.

[Zarathustra]

I agree, Murrin.

Actually, if you're going to be nit-picky, there are no Laws of science, either, because we can never observer every case to make sure our law holds.

Iquestor, I haven't read your post yet. I'll get back with you.

[iQuestor]

Murrin said:

Sorry, but I just can't let you get away with that. If we have to object to creationists misusing the word, we can't let ourselves make the same mistake.

Ummm, what does that mean?? I am not a creationist, I am just saying that we know the Theory of Relativity is not perfect and doesn't account for everything we observe in the universe; I think it is kinda close to truth, but it doesn't explain everything -- which is why science isn't done messing with it. It needs to be tweaked to include that which doesnt yet fit into it. Exactly what am I getting away with here? I am really confused. It is a theory. we can't prove it holds for all cases.

I guess I am not making myself clear. My only point is that we do not know everything in the universe. we know a lot about math, but not enough to explain the behavior of the very small and the very large. We know a lot about logic, but find we can't explain why black holes act the way they do. We hopefully someday will be able to do that with science.

If we knew all of the absolute truths about math and logic in the universe, and nothing was left that we didn't know, then there would be no paradoxes, because we would understand the truth and there would be no mystery. thats all I am saying, to Maliks position that paradoxes could still hold true even if we did know everything. which I dont agree with.

[I'm Murrin]

I apologise for my phrasing before. I simply meant that you had defined 'theory' incorrectly--in fact, made the same mistake as creationists who say the theory of evolution is 'only a theory'. A theory is not called such because it is uncertain--'theory' is a word for a group of principles of explanation. A theory can be completely correct and accurate, and the word 'theory' would still apply.

I agree with what you meant, but I disagreed with you saying that the use of the word 'theory' demonstrated your point.

Semantics, nothing more.

[iQuestor]

Murrin, thanks for clearing that up..

[The Dark Overlord]

I believe Murrin is mistaken, a theory MAY be (completely) correct but whether or not that is so has not been proven, THAT is why it is called a theory. There are aspects or Einstiens Relativity which are still ''theortical''- in other words, they haven't been proven- that's why it is still called a theory. Theories that have been PROVEN are referred to as facts, priciples, or LAWS and are NO LONGER theories but PROVEN FACTS- thus the LAWS of physics as opposed to theories(the first and second LAWS or principles of thermodynamics come to mind). That is why creationists and intelligent designists will forever plague evolutionists; evolutionary science, unlike biology, chemisty and physics is not an observable science. It is more like forensic science(which interpets discovered evidence) but much less exact and with A LOT more GUESSWORK. Much of forensic science IS observable(fingerprints, DNA, etc.) but some of it IS inconclusive and much of evolutionary science is like crimminal forensics in the mid 1800's before exact sciences were discovered and applied to it. There is a lot of evidence but what does it mean? When rocks formed from volcanoes in Hawaii and other Pacific islands in the 1800's(and that information is correct) are dated by several ''reliable'' methods to be over two and half billion years old it puts a damper on my ability to believe the evolutionists and geologists when the say they have the thing ''locked in''. However much they whine, evolutionists cannot perform experiments like chemists(in test tubes and such) or physicists to prove their theories(some physicists also deal with unprovable theories-like the big bang- which ultimately are only SPECULATION). There are many other examples like the volcano rocks and I have found the evolutionists have just as many holes in their theory as creationists. BOTH come to the evidence with their preconceived notions and DO NOT evaluate it objectively but rather INTERPET it according to their dogma. A perfect example of science doing this is in an article a few years back by U. S. News in which mounting evidence that primtive (pre Viking) Europeans were in North America as early and EARLIER than Native Americans was ignored and discounted. Professors and archeologists who insisted on evaluating( and not ignoring) the initial evidence were CASTIGATED, THREATENED, INSULTED, DECLARED INCOMPETENT, SHUNNED, AND FIRED, DEMOTED, DENIED PROMOTIONS, AND LOST THEIR POSITIONS/EMPLOYMENT. The group doing this was dubbed ''The Clovis Mafia''(Clovis being the oldest and deepest layers in which Native Americans could be found) In fact the Clovis group( the dominant majority) STOPPED digging whenever they hit the Clovis layer. When other archeologists/professors dug and found artifacts and bones under the Clovis layer(and in many instances under Native American artifacts and bones) but completely different from these Clovis ones- the evidences were scorned as anomolies and thrown in a ''closet'' (the author's term). It was only when the bones (especially skulls ) became too numerous that the Clovis group finally conceded. Thus we see the ''objectivity'' of science. The initial troublemaker for the evolutionists was Michael Denton with his book''Evolution, a Theory in Crisis'' I Have yet to see any of the issues raised in this book addressed. Jay Gould just seems unintelligible and Richard Dawkins just uses bluster and bombast and seems more like a fundamentalist than they do. I've seen points raised on either side. Humans share 94%-or is it 97%?- identical DNA with chimpanzees. Seems fairly conclusive, but then someone says a mouse and a whale share 92% identical DNA, well what does THAT mean? Anything you want! And humans share 47% identical DNA with DAFFODILS-you know, the FLOWER? You can interpet all this ANYWAY you want. The evolutionists says common ancestry! Too much similar function on cellular (and other) levels! The creationists say God just used the same ways to solve the problems of cellular aspiration and metabolism in all creatures. So if God just used the same design( ha ha) for cellular respiration and functions and larger functions like mobilty etc, OF COURSE there are going to be similarities in DNA and physical structure. So who's right? The only other non-creationist(and thus possibly objective) book on intelligent to have any merit(that I've seen so far) is Michael Behe's ''Darwin Black Box''. While reiterating much of what Denton says, he does bring up other points and finds other examples especially the flagellum and cilia(some of which SPIN- rotary motors don't blindly evovle). One last point- someone just on TV just said that Ford motors makes different cars, some might have antilock brakes or no and all look different but Ford solved the basic issues( of motion[wheels, axles] and fuel processesing[carborators or fuel injection])in common ways for ALL cars so they LOOK completely different but have have the same functional DESIGN(ha ha) underneath. So they function similarly and are structured similarly because of a common designer, designing them for a common environment.

[Zarathustra]

This is a perfect example of what I am trying to say. The different readings on the clocks is not a paradox, unless you do not understand frame dragging or time dilation. We weren't wrong about the readings on the clocks, we were wrong in assuming they would agree -- why did they read different? That doesn't make sense! We would expect the same reading because we thought space and time were completely separate, but they are not. We were wrong in our understanding of the Laws of the Universe, in this case, General Relativity. Against Human Logic, Time slows with greater speed, and is relative to space and matter. Hence Einstein's GTR.

Nooo . . . this is a perfect example of what I'm trying to say. As I said above, I think we may have different definitions of the word, "paradox," and it is precisely due to this difference that the disagreement in our beliefs about paradox arises.

You seem to think paradox means something "impossible, inexplicable, and contradictory," like a square circle. A square circle isn't a paradox--it's nonsense. Literally, it doesn't make any sense. The concept itself represents a juxtoposition of ideas which can never exist together (not even in the imagination). The same thing goes for Zeno's paradoxes. They aren't really paradoxes, because the "impossible, inexplicable, and contradictory" nature of motion --which his "paradoxes" supposedly illustrates--is brought on by framing the problem of motion in a nonsensical manner.

Therefore, if you're going to define paradox in such a way, of course you are going to believe there is no such thing as paradox, because you are begging the question. In other words, of course you are going to dismiss all my examples, claiming they aren't really paradoxes, because you've already got a built-in bias against paradox existing in the first place. Because you think paradox means "impossible, inexplicable, and contradictory," when I give examples that exist, are explainable, and don't contradict logic, you dismiss them and claim they're not really paradox. As soon as an explanation is presented (such as Einstein's GTR), you think that the paradox disappears because it has been explained.

Obviously, I think your definition is wrong. Paradox, I believe, is better characterized as, "two conflicting perspectives which are--despite their opposition--both true, real, and valid." I believe this definition fits the subject matter at hand, too: Covenant's paradox. The paradox of the white gold (and indeed the First Chronicles) is illustrated by the marrowmeld sculpture that looks like both Bannor and Covenant. It is both rigid control and extravagant power--two conflicting principles which are nevertheless inextricably tied.

In the GI, Donaldson said:

"Mhoram learned to find his own version of "the eye of the paradox": the point where both passion and control can be affirmed . . . Blake wrote, "Reason is the circumference of energy." Gichin Funakoshi wrote, "If your hand goes forth, withhold your anger. If your anger goes forth, withhold your hand." Someone (I've forgotten who) wrote, "Beauty is controlled passion." Mhoram learned to understand this. The fatal flaw of the Haruchai (and of Atiaran, and of Trell, and of Troy, and of the Unhomed, and of Kevin--and of Covenant early on) is that they did not."
(11/24/2004)

Again:

"I like to credit William Blake, who wrote, "Reason is the circumference of energy." This struck me when I first read it, and still strikes me today, as an ideal expression of the paradox which makes art, beauty, and even humanity possible. If energy (chaos) is not controlled by reason (order), it remains formless and destructive. If reason is not constantly challenged and stretched by energy, it remains rigid and destructive.
(06/01/2005)

Are you saying that Donaldson is wrong, that his insights aren't really paradoxical? [Note, I'm not using the argument by authority fallacy, I'm just trying to push this back on topic. I'm curious about your take on the control/passion paradox--or the chaos/order paradox, for that mattrer.]

Frame dragging, black holes, and bumblebees having the ability to fly despite fat bodies and stubby wings. These are all paradoxes or mysteries that we have (possibly) unravelled through our experiments. At one time, we dismissed these ideas, and said they were wrong or couldn't exist or didnt make sense. The real issue here is that Human logic was wrong. Once we understood a little more about the universe, then we could resolve these seeming paradoxes.

"Seeming paradox." Bingo. A bumblebee flying is not really a paradox. Therefore, disproving the apparently paradoxical nature of bumblebee flight DOES NOT disprove the existence of paradox. It merely illustrates (again) how you think paradox means, "something inexplicable." Paradox was never intended to mean "something we can't explain."

While this next subject doesn't really deal with paradox, let me take it bit-by-bit, because it is exceedingly complex.

You have misunderstood me here I think. I fully agree that logic and math are universal in that they are the Laws that the Universe is governed by;

No, no, and again no. The universe is NOT governed by math and logic. The universe exhibits properties that can be quantified in mathematical models. However, these mathematical models do not govern or dictate the universe. There is no logical principle which forces the universe to conform to ANY mathematical order. Indeed, the bare fact that the universe DOES seem to conform to a mathematical order is a complete mystery. We don't know if it appears this way to us because we impose the filter of consciousness upon all our dealings with the universe, or if it is one of the most unlikely accidents imaginable. One version of the anthropic principle theorizes that there are numerous universes, and it just so happens that the freaky universe that is so delicately balanced to conform to mathematical models is precisely the kind of universe in which conscious, intelligent beings have a chance to come into being to ponder this mysterious correspondence.

So, what I mean about math and logic being universal is that they are not subjective. They are not dependent upon individual insights, nor are they like opinions which can be "true" for one person but not for another person. My math is the same as your math. My "number 3" is the same exact "number 3" which you understand. Math is universal, but it doesn't govern the universe. [David Hume's and Edmond Husserl's writings are invaluable resources for these subjects, if you want to delve deeper.]

. . . I merely relate that human logic and human math are not perfected yet and not completely in tune with reality, and that when we attempt to describe the universe with our faulty logic and math, the things that don't fit in our understanding are called paradoxes.

I really have no idea what you're describing in this context with the qualifier, "human." Math is math. The amount we have formulated or discovered isn't significantly different from what we will formulate or discover later. Our math and logic isn't "faulty." Maybe "incomplete" is a better word. However, paradox isn't a description of the universe using incomplete math, nor is it a phenomenon which resists our understanding--as I've said above. You're arguing with a "faulty" definition.

When I say Human math, I mean what we understand of it. Yes we have 2+2 down pat, but no one is debating that. But we don't have Quantum physics all the way down, or string theory, or many others. You seem to assume Human logic and the human grasp of mathematics is perfect and complete on a universal basis. they are not. If they were, we'd understand the universe, and complete understanding means no paradoxes!!

Quantum physics, string theory, etc. are not examples of math or logic. This is why I'm confused about your definition of "human math." These are examples of theories to explain the world. True, they are incomplete. But showing their incompleteness doesn't prove anything at all about math/logic, because they are not examples of math/logic. This seems to be a common technique you use in your argument: equivocation.

why do you think it is the Theory of General Relativity, and not the Law of General Relativity? it is because we don't know for sure that it will hold up in all cases, only in what we have observed so far. We can't prove it.

This is true for every theory. At no point is a theory ever elevated to the status of Law. This is due to the problem of induction (more Hume). Every single scientific theory relies upon inductive reasoning, i.e. using isolated examples as empirical evidence to "back up" a general principle. But no amount of individual examples can ever completely prove a general principle. There are no Laws of Physics. Only theories. And, due to the problem induction, there never will be any Laws of Physics. This is not merely a limit of "human logic," it is the nature of subjective selves living in a universe. It's not a "fault." It's simply the way our existence is, and will always be.

So this leaves us with an interesting conclusion (if anyone is still reading). If, as you say, "apparent paradox" really is a temporarily inexplicable phenomenon . . . then what's the status of "paradox" once you realize that the universe is fundamentally, permanently beyond explanation? If, as you say, theories aren't laws, and we can never be sure that our theories are absolutely true, then how can you possibly say that any paradox is ever explained? Even by your own definition, paradox is an essential feature of our existence in this universe, because our existence is fundamentally limited in such a way that we will never fully explain it. There are no Laws, only theories.

What I am saying is that there is logic to the universe. It has nothing to do with human perception or human logic. It is governed by some set of laws that we do not fully understand. Lets call it god-logic for lack of a better term.

We can't possibly know if there is "logic to the universe." All we can ever know is that this is how it looks to us. Logic and math are systems we use to model the universe. The apparent correspondance between logic and the universe is a contingent curiousity. Your theory that the universe is governed by some underlying logic can never be proven; there may be some pocket of the universe that violates logic and math completely. How do you know?

Logic and math are ideal, abstract systems of thought. What's the connection between an ideal, abstract "object" and a physical entity? How can abstract, ideal "objects" connect with physical entities at all? I smell a paradox . . .

When (if) we understand the universe through the perspective of god-logic, then my position is there will be no paradoxes; it would make perfect sense from that perspective.

Again, this sounds like religious mysticism--and not because you use the word "god." It's because you hold beliefs about math which can't possibly be proven (we call that "faith"). You are arguing with the false assumption that because something is demonstrably incomlete, that on some level it exists in a complete form. That's like saying that even though numbers are infinite, there's a "god-view" from which you can see them all. That's a nonsensical belief; it does not make sense. In fact, due to Godel's proof, math and logic are intrinsically incomplete, and they always will be, even if our intelligence were infinite. All there is is "human logic."

we dotn yet have a universal theory of everything.

How would we know when we had it? Even if we had one, it would still be "just a theory."

If there is a God, and his math says 2 + 2 = 1, then we are obviously wrong in our understanding of Math.

I wouldn't say that we were wrong, just that God was testing us.

At any rate this is my own idea. I obviously have no evidence. it is based on my assumption that the universe follows some law, be it natural or created. (I think when you say Logic and Math are universal, you also mean this.)

Yes, you have no evidence. Yes, it is based on an unprovable assumption. And, no, that's not what I mean by "Logic and Math are universal."

Whew!

[wayfriend]

You seem to think paradox means something "impossible, inexplicable, and contradictory," like a square circle. ... Paradox, I believe, is better characterized as, "two conflicting perspectives which are--despite their opposition--both true, real, and valid."

Just to butt in ... a paradox is, indeed, "something impossible, explicable, and contradictory" - but which exists nonetheless. A square circle would indeed be a paradox, if you had found one. The sentence, "This sentence is not true", is a paradox. It is impossible, inexplicable, and contradictory, but nonetheless it exists right there before you.

Two perspectives are just that ... two perspectives. They seem different, but arise from the same thing.

I'm not sure what you mean by "conflicting perspectives". In your subsequent text, you imply it means perspectives which are "in opposition". Opponents, and opposing forces, can exist without there being a paradox. Passion and Control are not paradoxical, just in opposition.

Then there are "seeming paradoxes", which are things which appear to be paradoxes but which, when you dig deeper, are found to be not paradoxical. However, until you discover the resolution, they remain a paradox in truth. Someday, someone will explain how the sentence "This sentence is not true" works, at which point, it won't be a paradox any more.

Of course, there are degrees of "seeming". Some "seeming paradoxes" apear to be more easily resolved than others. There is a scale from obvious to world-class stumper in the paradox world. Mhoram was able to work through the paradox of passion and control... but we have not yet worked through the paradox of the Land being real or not real.

[Zarathustra]

Just to butt in ... a paradox is, indeed, "something impossible, explicable, and contradictory" - but which exists nonetheless.

If it is impossible, then how can it exist (nonetheless)? Impossible things don't exist.

A square circle would indeed be a paradox, if you had found one.

You can never find one because they are impossible. You can't even form a concept of one because the idea is nonsensical. This isn't a paradox, it's a fantasy.

The sentence, "This sentence is not true", is a paradox. It is impossible, inexplicable, and contradictory, but nonetheless it exists right there before you.

Before me? The sentence exists in space? Your figurative language betrays you. It is a semantic (or syntactic?) paradox. However, sentences don't really exist. Sure, squiggly lines exist--but the meaning we infer from these symbols are abstract "objects", or ideal objects. They don't exist as actual objects exist. Meaning doesn't exist anymore than the number 3 exists. It is possible to have contradictory ideas, propositions, or meanings. It is impossible to have contradictory objects. Objects don't contradict each other. Not even their properties condradict each other. Thus, while one can construct sentences or arguments which contradict themselves, such sentences never represent states of affairs in the world.

However, concepts representing real properties like chaos and order can be used to construct sentences which represent real states of affairs in the world, and yet these concepts are in opposition. They are not contradictory. They are counterparts. Contradiction has a strict logical definition. "A and not A," is an example of contradiction. However, chaos and order, or energy (passion) and control, are properties which occupy a spectrum, rather than binary values (like "true or false"). That's roughly the difference between "in opposition" and "contradictory." Properties of actual objects can be in opposition (creating actual paradox when joined), whereas properties of ideal objects can be in contradiction, which is really nothing more than nonsense.

Passion and Control are not paradoxical, just in opposition.

While this isn't a semantic paradox (contradiction), it is an actual paradox. It seems your personal definition for paradox is "semantic contradiction," which, too, begs the question of whether or not paradox exists in the world as a real feature of reality (since semantic meanings don't exist in the world). You "define it away" by restricting it to logical knots.

Someday, someone will explain how the sentence "This sentence is not true" works, at which point, it won't be a paradox any more.

I'm not sure what you mean by the sentence "working." Obviously, it can never be shown to refer to anything in the world. It refers to itself. Nor can it be relieved of its contradiction--no more than "A and not A" can be relieved of contradiction. Regardless, I don't agree with your assumption that things which are explained are not paradoxical. It can be explained how both chaos and order are necessary for growth or creativity--though it remains paradoxical. It can be explained how we can both measure two different times for the same event, yet it remains paradoxical. What other word would you use to describe such a state of affairs?

[wayfriend]

Just to butt in ... a paradox is, indeed, "something impossible, explicable, and contradictory" - but which exists nonetheless.

If it is impossible, then how can it exist (nonetheless)? Impossible things don't exist.

Ah, but they do. That's why they are called paradoxes, silly.

[The Dark Overlord]

One thing I would like to know: to state with absolute certainty that the universe is NOT governed by math and logic seems a bit presumptuous- or absolute scientific laws(with exceptions for circumstsances like black holes that would STILL be consistant- it would be how those SAME laws operate in those different and extreme circunstances) for that matter. How do we KNOW Hume and Husserl and Godel and the ''anthropic priciple'' are even right? Suppose their reasoning is filled with faulty logic or outright sophistry?

[Zarathustra]

One thing I would like to know: to state with absolute certainty that the universe is NOT governed by math and logic seems a bit presumptuous- or absolute scientific laws(with exceptions for circumstsances like black holes that would STILL be consistant- it would be how those SAME laws operate in those different and extreme circunstances) for that matter. How do we KNOW Hume and Husserl and Godel and the ''anthropic priciple'' are even right? Suppose their reasoning is filled with faulty logic or outright sophistry?

I'm not stating "with absolute certainty that the universe is NOT governed by math and logic." That would be presumptuous. What I'm doing is pointing out the presumptuous nature of the opposite conclusion, i.e., claiming with absolute certainty that the universe IS governed by math and logic. Perhaps I was too forceful in how I stated it. All I meant was that you shouldn't mistake the map for the territory. Math and logic are used to build models of the universe. When there is a correspondance between observed phenomena and predictions based on mathematical models, we receive a thrill of discovery and think we've inched closer to truth. And perhaps we have. But we must remember that this seemingly "magical" correspondance between events and mathematical models can not be explained, much less given a causal or governing role.

It is presumptuous to think that this completely mysterious relation between math and the world somehow explains the true nature of the world--rather than revealing a much deeper mystery. If you can explain how inanimate, abstract, formal systems like math and logic can control the motions of physical objects, I'm all ears. In the modern scientific age, we usually take this relationship for granted, not even questioning it. And when we actually try to analyze it, it sounds like pure magic. How do numbers make objects move around? The question sounds like mythology or superstition, not science. And that's probably why scientists don't even ask it. They happily proceed with their experiments, satisfied that the relationship between numbers and the world keeps working. But if you ask them, they can't explain why it keeps working.

How do we know Hume and Husserl and Godel were right? Well, unless you've read them and understand them, you can't say, can you? However, some of their points are not merely opinions, they are facts. For instance, it is a simple matter to see Hume's problem of induction. It is a FACT that no amount of individual examples can ever prove the validity of a general rule. A general rule must always be stated with an amount of uncertainty, because there's always the possibility that an exeption to the rule exists which you haven't encountered yet. We only see a small fraction of the physical universe. How can we say that the Laws of Physics works everywhere when we can't possibly look everywhere? THAT would be presumptuous. In addition, there's never any guarantee that the "laws" of the universe will keep working tomorrow. To think otherwise is to ASSUME that the future will be like the past. While this seems reasonable, there's no logical reason to make this assumption. To use the past to justify assumptions about the future is not much better than superstition.

Godel's proof is much more complex, but I've become convinced that his proof is airtight. You'll have to research it and come to your own conclusions.

[iQuestor]

If you can explain how inanimate, abstract, formal systems like math and logic can control the motions of physical objects, I'm all ears. In the modern scientific age, we usually take this relationship for granted, not even questioning it. And when we actually try to analyze it, it sounds like pure magic. How do numbers make objects move around?

I think you are taking that example way out of context; when we say that the laws of Math or Logic 'govern' the universe, it doesn't mean mere numbers move things around; it means that the object's behavior can be described by the Math we are talking about. Keplers Laws don't make the planets move as they do; they describe the motion of the planets about the Sun. The actual behavior is the result of forces, such as gravity, inertia, and/or whatever else happened ot the object.

My point has been that the universe can be described by Math, but not by our current understanding. We dont know enough; maybe the universe will change tomorrow, but armed with the proper understanding, that change could be anticipated and described.

As far as my definition of a paradox, I do think it is a seeming contradiction, but with proper understanding of the system, there would be no real contradiction.

The statement "This sentence is untrue" doesn't count in my book -- we are talking about the physical universe, not about Human's creating a statement that is made to be a paradox.

My position is that the universe is governed by some laws of nature that could be described by a complete understanding of Math, Logic and Science (and whatever), but that our current knowledge doesn't suffice to do so.

And further, that a complete understanding of the universe would preclude paradoxes. There is a difference in what seems right and what is right. It doesn't make sense two clocks would read differently if one is stationary and one travels at a high speed, but they do. This is not a paradox, it is a lack if understanding of the system.

[Zarathustra]

Iquestor, it looks like neither one of us is going to budge. However, it's definitely been an interesting discussion.

On numbers "governing" objects: I don't think I was taking this out of context at all. Think about it. You're now admitting that numbers don't make objects move, but rather the movement of objects can be described numerically. If it's just a description, and not a causal mechanism, then how is this different from a description of the shapes of clouds in terms of familiar objects? To say that it looks like gravity weakens in inverse proportion to the square of the distance is no different from saying that this particular cloud looks like a face. In both instances, the description has nothing to do with why it looks this way; indeed, descriptions never explain--they merely describe. Surely you mean something more than just "description" when you say that math and logic governs the universe. Can you explain how your concept is different from the cloud example, and yet still distinct from numbers causing the motion of objects? Seriously, I'd like to know how your concept fits between these two possibilities.

You say that numbers don't move objects, that forces do. But what is a force? Since Einstein, we've understood the force of gravity as nothing more than the curvature of space. The sun doesn't pull the earth into an elliptical orbit--the earth is merely following the curved space which exists around the sun. The curvature of nothing. Pure geometrical bending. The geometry of space causing the motion of the earth. In this instance, our concept of "force" as an invisible pulling/tugging process is the "face in the cloud"; it doesn't exist, it's just a fanciful description. Apparently, pure geometry is responsible. Numbers moving objects (which, I think, is one of the most paradoxical things imaginable).

But maybe space isn't "nothing." Maybe its curvature isn't "pure geometry." I don't know. Let's back up and pretend we don't know about Einstein's curved space. Forces move objects. So far so good. But what makes forces have a numerical "shape" or structure, instead of being competely erratic? Is this structure accidental? Coincidental? Surely there's a reason. Let's pretend it's possible for us to have this "god math" you mentioned. Would this god-math reveal why forces can be described with numbers? The possibility of such an explanation relies upon the assumption of a mechanism which connects inanimate, abstract numbers with physical objects; i.e., a mechanism that connects forces with their own structure, which causes them to be structured in the first place.

There's no way around it: at some point, you're going to have to admit that numbers connect with physical objects, OR admit that the reason for the mathematical structure of the universe is completely unexplainable. Either way, you're left with paradox:

A. If pure numbers connect with objects (via forces) in such a way as to control their motion, then you have the abstract/inanimate controlling the concrete/physical. (If you don't think that's a paradox, then we're done here. There's nothing I could point out that's more paradoxical than this.)

B. Or, if this relationship between math and the universe is completely unexplainable, well, isn't that what you're calling a paradox? An impossible, unexplainable, mystery?

The only other possiblity is that mathematical descriptions of the universe are nothing more than "faces in the clouds," purely human descriptions which have nothing to do with the underlying truth. Take your pick of these choices and then tell me why it's not paradox.

[iQuestor]

On numbers "governing" objects: I don't think I was taking this out of context at all. Think about it. You're now admitting that numbers don't make objects move, but rather the movement of objects can be described numerically. If it's just a description, and not a causal mechanism, then how is this different from a description of the shapes of clouds in terms of familiar objects? To say that it looks like gravity weakens in inverse proportion to the square of the distance is no different from saying that this particular cloud looks like a face. In both instances, the description has nothing to do with why it looks this way; indeed, descriptions never explain--they merely describe. Surely you mean something more than just "description" when you say that math and logic governs the universe. Can you explain how your concept is different from the cloud example, and yet still distinct from numbers causing the motion of objects? Seriously, I'd like to know how your concept fits between these two possibilities.

Malik, its a pleasure always, no matter how dizzying your intellect is to me

1. A Number is a symbol we humans make up to quantify things we otherwise couldn't express. I disagree wholeheartedly that a number can do anything but be a symbol. Extrapolate that to include the mathematical formulae and theories we use to explain, describe and quantify what we know of the universe.

2. A force is a force. it's not a number. forces exists in the universe, are a part of it. we can describe them down to the nth level, but we have to make up symbols to describe them or no one will be able to talk about them in any more than a very general way.

we can say they are numbers, but that doesn't make them numbers. numbers are symbols, an invention of mankind used to quantify forces and other things. saying forces are numbers is like saying water is a number. its not, its water. but we can describe how much water (2 gallons, 45 cc's, etc) but those numbers mean something only to other human beings. to a dolphin, they either hsave enough to swim in, or not.

3The difference between your cloud example and the inverse proportion rule is that one is an opinion biased toward humankind and the other is a universal rule that could be discerned by any suitably advanced intelligence.

Lats assume the inverse square law is a unervisal truth, meaning anywhere in the universe it holds true. Then, take the point of view of an alien who did not resemble humankind, but was advanced enough to know about planets and gravity from their own labors. I will argue that the alien could and would agree with the inverse square hypothesis -- it can be observed in the alien's own math (although they have different numbers and other symbols) that theory is a universal truth, or close enough for our example. In my opinion, any alien who met such qualifications anywhere in the universe could deduce the inverse square law on their own. (Assuming it works everywhere -- lets assume it is true)

Humans are programmed by evolution to see faces everywhere. However the alien probably would not see or comprehend a human face in the clouds, because that is not a universal truth that the alien could see or discern on their own with out direct contact with humankind, or at least races with similar faces. They may not be wired to see things at all.

Math is universal, humans are not. Our alien might not have eyes, their planet might not have clouds. they migh see body parts for which we have no word or description for in what passes for clouds, because they don't appear on earth life forms. shoot, ask a dolphin -- they may or may not know about clouds, and if so, might not be capable of seeing whales or humans in them.

I would like to add that the paradoxes I am speaking of are ones that would appear to arise from the universe, and not from a some clever thought experiment or trick of human or intelligent beings. I refer to a paradox which would arise from the universe where laws seem to contradict. again my point is that a complete understanding of the universe would resolve all such paradoxes.

[wayfriend]

If it's just a description, and not a causal mechanism, then how is this different from a description of the shapes of clouds in terms of familiar objects?

Ooh ooh! I know! I know!

Because it's a model - a description that predicts what things will do, with accuracy.

It's not a causal relationship. It's a relationship of isomorphism. These objects behave exactly like those equations. Always. Therefore I can use those equations to predict what these objects will do.