Does the universe allow for paradoxes?

[Mentat]

Please give the reason for your choices.

 

[Mentat]

I suppose I'll set the example, in showing the reason for our choices:

I picked "no", because I have always seen the universe as governed by a set of laws (hence the possibility of a T.O.E.). If it is governed by a set of laws, then the propositions that make up those laws, could not contradict each other (IMO) or else we'd be able to break the so-called "laws". A conclusion that is based on contradictory propositions is a paradox.

 

[Mentat]

Alright, it appears that someone has already broken the rule .

Please, include the reason for voting as you do.

 

[Fliption]

I voted 'no'. Obviously I cannot know this with 100% certainty but so far no one has shown an existing paradox outside of word games. And whenever one is found, it turns out to only be paradoxical because of a lack of information. Once more information is obtained, the paradox disappears.

 

[FZ+]

paradox

A paradox is a statement or concept that contains conflicting ideas. In logic, a paradox is a statement that contradicts itself; for example, the statement "I never tell the truth" is a paradox because if the statement is true (T), it must be false (F) and if it is false (F), it must be true (T). In everyday language, a paradox is a concept that seems absurd or contradictory, yet is true. In a Windows environment, for instance, it is a paradox that when a user wants to shut down their computer, it is necessary to click "start".

from whatis.com.
From the second definition, it is pretty clear that paradoxes do exist. Indeed, this definition is that used by much of science - see eg. the twins paradox.
The first definition is more interesting. We may never know, as this is a question that extends beyond evidence. However, it is likely that our sense of logic, evolved as it has to describe the immediately observable world, may place as paradoxes things that are actually true. Eg. Schrödinger's cat.
If a paradox exists only as long as it cannot be solved, does it still exist is another question Flipton's post raises. Since we will never know everything, there will always be an apparent paradox just over the horizon.
Of course, there may well be other universes with laws that directly contradict ours... does that count?
How about a maybe option?

 

[RuroumiKenshin]

I chose yes. For FZ+'s very reason. Also because there will always be something that is weird, so to speak. I'm thinking of the grandfather paradox. Anyone could make a paradoxical scenario, that could very well be possible by combining multiple histories.

 

[Ishop]

I said no because I asumed you are talking about a physical manifestation of paradox in which real laws of physics are completely parrallel to one another and defy the laws.

However I reconize that paradox's can live in concept (imagination). But again I believe "paradox" is a lame excuse for not knowing or trying to know.

 

[Fliption]

Originally posted by Sensei
an infinite number of nothings, makes up something. that to me reeks slightly of paradox.
[/B]

No an infinite number of nothings does not equal 1. An infinite number of 1/infinity = 1. 1/infinity does NOT = zero.

 

[RuroumiKenshin]

So what does it equal? Is it undefined?

 

[CJames]

1/0 and 1/[oo] are undefined. There is no mathematical definition for them because, well, of the paradoxes you speek of. As you said, infinity is a concept not a number, which is why you can't perform these operations on it. In other words, this sounds like a paradox of the mind. The mind or any rules created by it just may not be capable of completely understanding concepts like infinity.

 

[Loren Booda]

Whenever observers observe themselves or the universe which contains them, or their very observations influence an object, such situations involve subjective paradox.

Paradox often associates with insight, paradoxically.

 

[Fliption]

Originally posted by Sensei
Disagreement is encouraged, but with the hope that it can be supported, and not conclusory.

Sorry, I didn't think it needed any explanation. It's just simple math to me. But you have said something in this latest post that you didn't really say in the first one...

infinity is an infinite number of 0's, then since 1/0 is 0, 1 divided by an infinite number of 0's should not be any different thus resulting again, in a 0.

You're saying here that infinity = an infinite number of zero's. Thats not how I interpret the word "infinity" when used in a mathematical sense. Infinity is the ever increasing number series.
1/1 = 1 and 1/2 = .5 The denominator can continue on to infinity and the answer will continue to decrease getting closer and closer to zero for infinity. It will never reach zero. "Infinity" is a concept and is not really a number so the phrase 1/infinity doesn't really mean anything except to go through the exercise I did above.

And by the way...1 divided by 0 is not 0. It is "undefined" Put it in your calculator and see

 

[CJames]

I've never seen a calculator that said positive infinity when I divided by 0.

1/0=infinity
multiply both sides by 0:
infinity(0)=1
divide both sides by infinity:
0=1/infinity

OK, that's all welll and good, but:

2/0=(1/0)+(1/0)
=infinity+infinity
=infinity
2/0=infinity
infinity(0)=2

infinity(0)=2
infinity(0)=1
1=2

Uh, no. The concept of infinity just can't be used like that.

What was all that stuff you wrote at the bottom of your last post. It's completely contradictory. Where are you getting that 1/0 is 0?

 

[GlamGein]

its all so "eery", its nonsensical. Maybe that Microsoft calculator you used was built so that whenever you divided anything by 0, it came out to 0 in order to screw the other, less powerful calculator manufacturers in the country.

 

[steppenwolf]

the last time i read anything about this topic the theory was that 1/infinity was equal to an infinitesimal, the 'opposite' of infinity.

as fliption rightly pointed out infinity is a concept not a number therefore you cannot really hope to get a number when manipulating it, the infinitesimal is just another concept so fits right in.

that is some crazy math sensei, but i like the idea that infinity might be the key to understanding paradox

 

[wuliheron]

Does the universe allow for paradoxes?

This question is its own answer and, thus, a paradox in its own rite. If the universe did not allow for paradoxes you could not ask the question. It is a bit along the lines of asking, "Can I ask a question?" Without supplying a context it is logically meaningless.

There is an old riddle in physics:

"What happens when an irresistable force meets an immovable object?"

The answer is supposidly that an irresistable force can never meet an immovable object because the two cannot exist in the same universe without creating a paradox. Our's is observably a universe of unceasing change and irresistable forces like black holes rather than a static unchanging universe with immovable objects. However, Relativity implies that our universe is static and unchanging.

A naked singularity is both the irresistable force and the immovable object. A magical thing that is no-thing. It may well be that a naked singularity is also just another way to describe the paradox of existence.

 

[Fliption]

Originally posted by Sensei
Peace be with you. [/B]

My XP machine calculator says "undefined". My NT calculator say "Cannot divide by zero". All of this math that you are presenting is based on some loose assumption that "undefined" means infinity. The words of a microsoft calculator are insufficient to prove this point. Undefined does not mean 0 or infinity. It means that it is a meaningless exercise.

Also, infinity does not equal an infinity of zeros. Not if we're going to talk math.

And lastly, there are all sorts of theories that can be supported by a mathematical model( which we don't even have here). That doesn't make them true. Paradoxes exists due to lack of knowledge and understanding. Paradoxes exists in the mind.

 

[Fliption]

Originally posted by wuliheron
Does the universe allow for paradoxes?

This question is its own answer and, thus, a paradox in its own rite. If the universe did not allow for paradoxes you could not ask the question. It is a bit along the lines of asking, "Can I ask a question?" Without supplying a context it is logically meaningless.

Hmmm I don't see the paradox in either of these questions.

"What happens when an irresistable force meets an immovable object?"

In this one I do. But does it really exists? Thats the question of the thread and I have speculated it does not. Point to an instance of it and I'll point you to something that you most likely lack information on.

 

[GlamGein]

[/QUOTE]
And lastly, there are all sorts of theories that can be supported by a mathematical model( which we don't even have here). That doesn't make them true. Paradoxes exists due to lack of knowledge and understanding. Paradoxes exists in the mind. [/B][/QUOTE]

I concurr.

 

[chosenone]

The universe may have it in it to think of all types of possible paradoxes that could acure under the right circumstances,but have you ever seen one can you prove they can happen,does logic say they must not exist to be don't or anyone could destroy the universe if they so chosed.would'nt the universe in it design be created perfect as we see it,never to allow such a thing to happen ,unless the universe what create by design to be destroy by its own creations if they so chosed.I think not,but paradoxes are fun to think about,thats all they ever will be,unless you would like to prove one could happen by youself,like proving relativity.but if you don't do it because what would happen and not one else trys because there not stupid either,no one will ever know if they can happen ever,so you will never prove they can,I think that ends this cvonversation!

 

[wuliheron]

And lastly, there are all sorts of theories that can be supported by a mathematical model( which we don't even have here). That doesn't make them true. Paradoxes exists due to lack of knowledge and understanding. Paradoxes exists in the mind.

If paradox only exists within the mind then we cannot trust our minds and this presents another paradox with no logical resolution. If we cannot trust our mind then we cannot trust the assumption that paradox does not exist ad infinitum. A rather negative and self-contradicting, if humorous, view of existence and ourselves.

In this one I do. But does it really exists? Thats the question of the thread and I have speculated it does not. Point to an instance of it and I'll point you to something that you most likely lack information on.

Sorry, but that is not the question of the thread. The original question was "Does the universe allow for paradoxes?" Nowhere does it ask anything about "reality". Personally though, I don't believe in naked singularities or paradoxes either, but then, I don't disbelieve in them either for that matter. I don't know how many times I have to say this before people understand, but it just doesn't matter either way. You might as well argue how many angels can fit on the head of a pin.

Originally posted by wuliheron
Does the universe allow for paradoxes?

This question is its own answer and, thus, a paradox in its own rite. If the universe did not allow for paradoxes you could not ask the question. It is a bit along the lines of asking, "Can I ask a question?" Without supplying a context it is logically meaningless.

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

Hmmm I don't see the paradox in either of these questions.

The "question" of "Can I ask a question?" answers itself because it IS a question. Thus it is self-referential and self-contradictory like the liar's paradox, "Everything I say is a lie."

Likewise, the same holds true for "Does the universe allow for paradoxes?"

Ya'll just don't get it do you? Paradox is slippery, the ultimate logical sandpit. Try to deny it and you create it. Try to ignore it and you find yourself creating it again. All you can do is accept it and move on.

 

[chosenone]

well if we put paradoxes in different type,other than putting them all into one concept maybe it would help.no win situations where you trapped,ever option you tried failed and you can get out of it,happens all the time.math problems that blow up with infinite answers,your logic you used to deduce the factors you used may be in error more that the answer you get can really happen but you would'nt question the results.time travel,where you went back and killed you father before you were ever born,such that you could'nt have went back to kill your father if your father was'nt alive for you to go back in the first place,are usually the type of paradoxes I'd refer to as the ones to look at,to know if they can happen or not,because the universe and our existence depends on them not being allowed by the laws of physics.anything else really does matter,other than there fun to create and think about.

 

[wuliheron]

The big drawback to this idea is that infinity is a patently paradoxical concept dude. Check out my thread on the Paradox of existence for more details.

I don't know how many people I've seen here promoting infinity and "nothing" (of all things!) as the answer to life, the universe, and everything. If I were to believe them all I'd be worshipping countless Gods and studying countless contradictory philosophies. Infinity is just a cheap cop out that allows people to believe whatever they want to believe, but it doesn't make arguments against such ideas futile.

 

[russ_watters]

I was going to vote yes, but then I read this:

It seems the limited mind in attempting to define the unlimited, sees paradoxes. In a mind state where one could see all, it may be that no paradoxes would exist because each paradox would be a compartment of truth for a larger truth.

Clearly the diffraction of light APPEARS to be a paradox: How can something discrete be in two places at once? But maybe we only THINK its a paradox because we don't yet know enough about quantum mechanics.

So my vote is: uuuuuuuuuuhhhhhhhhhhhhh...

 

[Mentat]

First off, thanks for all of the responses, I enjoy hearing everyone's opinion.

Now, I should clear up that I was talking about physical paradoxes. Yes, conceptual paradoxes abound. But, do physical ones really exist?

 

[wuliheron]

Sorry about that, I just get sick of the usual irrational stuff some people constantly push on this forum and then deny it is irrational against all logical and scientific arguments to the contrary. I have enough trouble communicating ideas about paradoxical concepts without that kind of nonsense.

I think its great to play with infinity and paradox, it stretches the mind to say the least. It's just the unjustified and unsupportable claims that remind me of the old patent medicine men claiming their booze could cure everything from cancer to all the world's problems. A few drinks now and then loosen things up, but too much and people tend to get violent and ill. :0)

 

[Fliption]

Originally posted by wuliheron ]If paradox only exists within the mind then we cannot trust our minds and this presents another paradox with no logical resolution. If we cannot trust our mind then we cannot trust the assumption that paradox does not exist ad infinitum. A rather negative and self-contradicting, if humorous, view of existence and ourselves.

This is stretching it a bit I believe. Paradoxes exists in the mind when there is a lack of knowledge of reality. Once more information is obtained paradoxes disappear. Again...they aren't REALLY paradoxes. So they cannot play a part in some "self contradictory paradox of ourselves" So boiling all this down, all you're saying is that a lack of knowledge(mind paradoxes) keeps us from saying that paradoxes don't really exists. While this is true, it can also be said for god and magical elves on Mars. It's pretty meaningless.

Sorry, but that is not the question of the thread. The original question was "Does the universe allow for paradoxes?" Nowhere does it ask anything about "reality".

These 2 are exactly the same thing to me. The question of whether the universe allows for paradoxes can be restated as "does the universe allow for paradoxes to exist in reality?" If I've misunderstood the original posters intentions I apologize.

The "question" of "Can I ask a question?" answers itself because it IS a question. Thus it is self-referential and self-contradictory like the liar's paradox, "Everything I say is a lie."

Likewise, the same holds true for "Does the universe allow for paradoxes?"

I don't see it this way at all. The statement "Everything I say is a lie" is self contradictory because it is both true and false. If it's true then it must also be false and vice versa. This is not the case with the question "Can I ask a question?" This question simply answers itself and the answer is "yes". It does not contradict itself. To me, a paradoxical question would not only answer itself but it would give 2 opposing answers (no, yes).

Ya'll just don't get it do you? Paradox is slippery, the ultimate logical sandpit. Try to deny it and you create it. Try to ignore it and you find yourself creating it again. All you can do is accept it and move on. [/B]

I don't get it I admit. It should not be any more slippery than anything else if it is properly defined and understood. The question above that you think is a paradox and that I do not is a clear example of a lack of common understanding.

So after all the words that you have typed on this topic I still don't quite understand exactly what your point is. You start your topics off with words that claim paradox is everywhere and unavoidable then, once someone explains to you that you have mis-used concepts, you say it doesn't matter . Honestly, sometimes I wonder if you aren't intentionally typing self contradictory statements in order to prove your point in some strange way. If you are doing this please let me know.

 

[wuliheron]

This is stretching it a bit I believe. Paradoxes exists in the mind when there is a lack of knowledge of reality. Once more information is obtained paradoxes disappear. Again...they aren't REALLY paradoxes. So they cannot play a part in some "self contradictory paradox of ourselves" So boiling all this down, all you're saying is that a lack of knowledge(mind paradoxes) keeps us from saying that paradoxes don't really exists. While this is true, it can also be said for god and magical elves on Mars. It's pretty meaningless.

This is, again, a self-referential logic. Although western science has largely progressed through the eons by disproving paradoxes and the irrational, it has also made huge strides by developing and accepting them. If we all still took Aristotle's position that paradoxes are not real and should not be used calculus would never have been invented.

Newtonian Mechanics was eventually replaced by irrational Quantum Mechanics. To say every paradox has a resolution and we should assume they are all false flies in the face of emperical evidence. It also biases science which is supposed to be objective.

As for magical events, Stephen Hawking once wrote that a black hole could theoretically emit a color tv or the complete works of Proust in leather bound volumes. I will take his word over yours that magical theories like Quantum Mechanics are useful.

I don't see it this way at all. The statement "Everything I say is a lie" is self contradictory because it is both true and false. If it's true then it must also be false and vice versa. This is not the case with the question "Can I ask a question?" This question simply answers itself and the answer is "yes". It does not contradict itself. To me, a paradoxical question would not only answer itself but it would give 2 opposing answers (no, yes).

"Can I ask a question?" is self-contradictory in that it obviously is a question. If you could not ask a question, then you could not ask this question.

I don't get it I admit. It should not be any more slippery than anything else if it is properly defined and understood. The question above that you think is a paradox and that I do not is a clear example of a lack of common understanding.

That you cannot understand such a simple paradox is perhaps due to your bias against them.

So after all the words that you have typed on this topic I still don't quite understand exactly what your point is. You start your topics off with words that claim paradox is everywhere and unavoidable then, once someone explains to you that you have mis-used concepts, you say it doesn't matter . Honestly, sometimes I wonder if you aren't intentionally typing self contradictory statements in order to prove your point in some strange way. If you are doing this please let me know.

Judge for yourself. People who deny paradox are often blind to them, including Asians. They are as slippery as it gets conceptually and there is no easy way around this problem. I can no more make someone acknowledge paradox than I can explain color to a blind man. The difference here is that blind men don't usually try to argue that colors don't exist.

 

[Fliption]

Originally posted by wuliheron
This is, again, a self-referential logic. Although western science has largely progressed through the eons by disproving paradoxes and the irrational, it has also made huge strides by developing and accepting them. If we all still took Aristotle's position that paradoxes are not real and should not be used calculus would never have been invented.

I haven't said anything about whether paradoxes were useful. All I'm saying is that IMO a paradox is a concept of the mind. It does not exists outside of that. There are no contradictions outside of the mind. However, many things of the mind are useful. Including calculus.

Newtonian Mechanics was eventually replaced by irrational Quantum Mechanics. To say every paradox has a resolution and we should assume they are all false flies in the face of emperical evidence. It also biases science which is supposed to be objective.

LOL. Quantum mechanists is irrational only because we lack information. It does not behave the way that we would have expected so therefore it is irrational. I'm sure lightning was mysterious to ancient man but there's no paradox.

And I don't think anyone is assuming that paradoxes don't exist. It's just that so far, no one has proved that they do. All so called "paradoxes" in the sciences are always found in the highest level, most obscure areas of science. Once the strange is understood, the paradoxes have always gone away. The question of the thread was asking for opinions. So based on the above my opinion is "no". I'm not proclaiming any truths.

As for magical events, Stephen Hawking once wrote that a black hole could theoretically emit a color tv or the complete works of Proust in leather bound volumes. I will take his word over yours that magical theories like Quantum Mechanics are useful.

Hawking is merely trying to reflect on a leading edge idea in such a way as to sell a lot of books. I would be willing to bet that he does not believe there is anything "magical" going on.

And once again, I've said nothing about the word "useful".
Here's your logic.

1) You imply that I have said that paradoxes are not useful
2) You equate paradoxes to Quantum Mechanics
3) Therefore I don't think Quantum mechanics is useful

And then you proceed to stack me up against Hawking in regards to number 3. LOL

I'm sure Siv could find one of those fancy logical fallacies that would apply here.

Anyway, number 1 is not true so the rest is irrelevant.

"Can I ask a question?" is self-contradictory in that it obviously is a question. If you could not ask a question, then you could not ask this question.

I do understand the point here. But I don't see this as a paradox. There is no contradiction here. The answer to the questions is "yes". If the answer was "no", then it would be a paradox.

Anyway, even if you could convince me this sentence was a paradox, I don't see how it carries over to the question in the title of this thread.

That you cannot understand such a simple paradox is perhaps due to your bias against them.

Well it is simple. It a simple amusing question. Not a paradox.

And there's only 1 person participating in this thread that knows whether I'm biased or not. And that's me. Let me remind you that it is me that you in a discussion with so saying I'm biased, when I know I'm not, is not going to convince me of anything. Or could it be that you aren't saying what you're saying for me? Who are we trying to convince?

Judge for yourself. People who deny paradox are often blind to them, including Asians. They are as slippery as it gets conceptually and there is no easy way around this problem. I can no more make someone acknowledge paradox than I can explain color to a blind man. The difference here is that blind men don't usually try to argue that colors don't exist. [/B]

The difference is that "color" is an experience. Paradox is a logical concept. One must have eyes to experience color. But one only needs a brain to understand paradox. There is nothing magical about this.

 

[wuliheron]

Hawking is merely trying to reflect on a leading edge idea in such a way as to sell a lot of books. I would be willing to bet that he does not believe there is anything "magical" going on.

I don't believe Hawking thinks of Quantum Mechanics as magical and neither do I. It is, however, as my quote of him points out, indistinguishable from magic in some respects because of its random nature.

And once again, I've said nothing about the word "useful".
Here's your logic.

1) You imply that I have said that paradoxes are not useful
2) You equate paradoxes to Quantum Mechanics
3) Therefore I don't think Quantum mechanics is useful

The Uncertainty Principle was developed not by someone with your biased attitude that paradoxes only exist in the mind, but by Heisenberg who happened to have a very paradoxical philosophy to begin with.

Einstein rejected the reality of the paradox as well and later admitted he should have deduced uncertainty himself as Heisenberg did from his own discovery of the photo electric effect. Thus an open mind is even more powerful than the issue of whether or not paradoxes really exist. That is what I am implying.

Here is what you wrote:

This is stretching it a bit I believe. Paradoxes exists in the mind when there is a lack of knowledge of reality. Once more information is obtained paradoxes disappear. Again...they aren't REALLY paradoxes. So they cannot play a part in some "self contradictory paradox of ourselves" So boiling all this down, all you're saying is that a lack of knowledge(mind paradoxes) keeps us from saying that paradoxes don't really exists. While this is true, it can also be said for god and magical elves on Mars. It's pretty meaningless.

This is about as biased as it gets, and as I wrote it contradicts the fact that paradoxes do not always "disappear" once more knowledge is obtained. The discovery of Quantum Mechanics was not due to a loss of knowledge, but an increase.

"Can I ask a question?" is self-contradictory in that it obviously is a question. If you could not ask a question, then you could not ask this question.

--------------------------------------------------------------------------------
I do understand the point here. But I don't see this as a paradox. There is no contradiction here. The answer to the questions is "yes". If the answer was "no", then it would be a paradox.

Anyway, even if you could convince me this sentence was a paradox, I don't see how it carries over to the question in the title of this thread.

It was in answer to another post you made:

I don't get it I admit. It should not be any more slippery than anything else if it is properly defined and understood. The question above that you think is a paradox and that I do not is a clear example of a lack of common understanding.

If you cannot follow what you are saying, much less what I am saying and do not understand what paradox is, then that explains why you are having so much trouble. This topic is about paradox, so I brought one up. Sue me.

"Can I ask a question?" is not as strong a paradoxical statement as the liars paradox by the standards of logicians, but is one nonetheless. Its contradiction is implicite rather than explicit as in the case of the liars paradox.