Please give the reason for your choices.
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.
Alright, it appears that someone has already broken the rule .
Please, include the reason for voting as you do.
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.
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. Schrodinger'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?
I chose yes. For FZ+'s very reason. Also because there will always be something that is wierd, 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.
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.
No an infinite number of nothings does not equal 1. An infinite number of 1/infinity = 1. 1/infinity does NOT = zero.
So what does it equal? Is it undefined?
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.
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.
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....
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
I've never seen a calculator that said positive infinity when I divided by 0.
multiply both sides by 0:
divide both sides by infinity:
OK, that's all welll and good, but:
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?
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.
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
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.
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.
Hmmm I don't see the paradox in either of these questions.
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.
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]
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 dont 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 dont 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!
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.
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.
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.
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 existance 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.
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.
I was going to vote yes, but then I read this:
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......
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?
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