The universe is infinite, the amount of matter is not.
That is, the universe extends infinitely far in every direction (theoretically obviously) but matter simply occupies an ever-increasing “sphere” of existence within the universe. Matter (and time) was created, for all intents and purposes, in the big bang, and has been expanding - from a singularity - ever since.
Therefore, the logical problems you present with regards to infinity, assuming I have it right, need no longer apply.
kjeevah:
my philosophy of language is that as long as you are understood, there’s no need to get all nitpicky about shit like that. I think many philosophers spend far too much time analyzing language.
everyone else:
I’m hardly an expert in the field, but the subject of infinity does pique my intrest. anyway, if the universe IS in fact infinite (all signs point to ‘no’) than there would be literally an infinite amount of EVERYTHING. that means there would be an infinite amount of me’s that typed this exact response, but didn’t caplitalize the ‘everything.’
HVD is right, JP is not. Let me explain why JP is wrong:
what i like to call ‘GCS’ or the ‘grand cosmic situation’ (it’s called by many other names in physics texts; superspace, hyperspace, multiverse, ect…) is basically reality as we know it. Quantum mechaics reigns supreme in this arena, and nothing strictly forbidden not only can happen, it HAS TO happen. anyway, our universe is just one universe amoung many other universes. I bet a lot of you have heard of this concept before, it’s called ‘The Anthropic Principle’ for those who havn’t. Anyway, time and space are unlimited in this ‘GCS,’ in any number of dimensions. our universe just happens to be in 3 dimensions of space, and one dimension of time.
(this is all theoretical information of course, but in the realm of modern physics, it’s the best guess of the leading people)
Correct. There may be an infinite number of universes, but, with our current understanding of astrophysics there is absolutely no way to demonstrate this.
At the moment, any theories that propose the exitence of “other universes” or of a universe that extends well beyond what we currently know and understand about our little pocket of it, are highly speculative, and corrborating evidence is difficult to find. Therefore, given that the only universe we know is the one in which we currently reside (given that the existence of any other universes is highly speculative and somewhat dubious) my point was simply that our universe, as we understand it, contains only a finite amount of matter which makes the infinity principles you propose entirely undemonstrable.
The anthropic principle simply suggests that the only reason we are here, and able to view the universe, is because its natural laws (gravity, thermodynamics, matter exceeding antimatter etc.) just happened to be perfect attuned to the conditions necessary for the existence of beingssuch as ourselves. We shouldn’t take this as any major miracle though (as many short-sighted Christians do), for if the universe had turned out even slightly differently, we wouldn’t be here to view it and there would be some other sentient being - suited to its GCS - saying exactly the same thing.
Keep in mind though, that the anthropic principle makes no predictions about the existence of other universes. Just because the universe could have turned out differently, it doesn’t mean that every possible universe must necessarily exist, as you, in some way, seem to be suggesting.
Even if it could be proven that there is such a thing as a “greater universe” - i.e. a universe that extends beyond our small pocket of it - that is still no guarantee that this greater universe must necessarily be infinite in size, time or both. There may well be a very large number of universes, but even if we assume that there are 1000^1000^1000 universes it is still a long way from reaching the concept of infinity and the paradoxes you presented above.
I’m not saying you’re wrong, just that you’re making some fairly grandiose assumptions that will either need to be justified or toned down.
I am not going to give a long winded re definition of what everybody above has said because they have all said it far better than i could. however what you are all assuming is that the concept of a hyper sphere and the laws of thermodynamics are correct. only by these things can you make the premises that the universe os infinite or not. im not an expert in physics (so much so i dont know if i have spelt it correctly…) but i am going to make a little statement i thought of the other night whilst trying to sleep. what if the universe is not an infinite hyper sphere as we have imagined or one part of and ever shifting mulitiverse created by energy shifts on the many dimensions blah blah blah… but that the universe contains a fold somewhere within it, hence created the illusion off the infinite. if you cant break free of the loop and are continually retracing yourself it would give the impression off the hyper sphere and of ever increading mass if the loop was growing larger. actually im lost now and tired, il rethink that and come back to it. feel free to criticize as muc as you like
JP:
Yes, all of that stuff is extremely theoretical, but it’s still very good guesses from the leading minds in physics…mind boggling stuff to ponder.
Anyway, you are correct about the anthropic principle, but when people have explained it to me, they’ve taken it one step further with “wormhole genesis,” which basically means that since this universe seems to have all the right conditions to sustain life. But if you look at the universe as a whole, it seems as if the main purpose is to produce black holes, because theres so many of them, and they are being created constantly. One would assume looking at our universe that it’s purpose is to make these things called black holes. Well, when a black hole forms, it also creates a ‘wormhole,’ which is a break in the fabric of space and time,and this wormhole branchs off and forms another universe. (again, this is all pure theory) so universes with the right conditions to make black holes can kind of ‘reproduce’ throught these wormholes, and make more universes that have similar conditions.
The point of this, is that taken to it’s extreme, the anthropic principle suggests that life is just a side effect for the creation of new universes. i’m not sure if i explaned this very well, if i didn’t, let me know and i’ll try to explain better.
Yep, I understand where you’re coming from Luke - and you have some interesting ideas - but I’m still not sure I agree with you.
The anthropic principle - by definition - is simply a way to account for the actuality of the GCS given our human mode of perception. It cannot have any application beyond humanity. It is simply used to describe why the GCS is how it is, and why it seems to conform so neatly with what we humans need in order to exist. It cannot be used as a predictive tool, nor can it be applied to anything other than humans without grossly changing its fundamental elements.
If you wish to advocate the notion that the universe seems to exist purely to facilitate the creation of further universes, then firstly you’re going to have to demonstrate that the universe has any purpose at all (which goes against the passive-nihilistic philosophy of recent times) and incorporate a different principle to demonsrate this. The universe is not bound to the laws of the anthropic principle, the anthropic principle is bound to the laws of the universe. So, as such, the anthropic principle cannot dictate what the universe should and shouldn’t “be”, rather it is dictated by what the universe “is”. If the universe was any different, either the anthropic principle wouldn’t exist (as we wouldn’t be here) or, at the very least, it would have to be different to accomodate the universe’s different actuality.
Er, so I hope you understand where I’m coming from. I also hope I understand where you’re coming from otherwise this post isn’t going to make much sense. 
Here’s my theory:
First of all, i would like to point out that i am 14, and not an educated physicist or anything (yet). I have, however, done a large amount of research on physics, and i own quite a few books by steven hawking.
I don’t like the theory that the universe has a finite size, because that seems too simple. I also don’t like the big bang theory, because i think the universe is infinite in time and space.
No, thats not true. Our universe contains a finite number of galaxies, each containing a finite number of star systems, each containing a finite number of planets and satellites.
prove it
Surely everything tangible is finite. It is just easier for us to say it is infinite because there is such a large number of objects (e.g. grains of sand), or the number of objects is increasing at a large or unpredictable rate, or we are unable (or just can’t be bothered) to locate and count them.
I’m not against infinity at all. It is a very important concept in mathematics, but I feel it is very much overused with topics such as space where, lets face it, we don’t know much for certain, and so “infinity” is perhaps a quick and easy get out clause.
I am fully expecting someone to find a counter-example for the above!
Oh… and you have counted them?.
Give me a ballpark figure.
No of course I haven’t.
It’s people like you asking people like me how many of something exists that causes words like “infinite” to be thrown about.
I stand a much better chance of giving you a ballpark figure than you do bringing me an infinite number of anything.
Sorry, not to you. To the doctor from India. She totally dismissed his view, so I want her to prove it.
But since you went there, I wouldn’t have asked to count it, if I didn’t know that there are two meanings to the word infinite. Infinite meaning boundless/endless and also greater than any pre assigned finite value however large. Have we ever counted the stars?. Nooooo why?, because someone kinda stopped when it reached 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999…
just a thought.
You can do so yourself. Learn a little astronomy and physics and you can estimate the number of galaxies and star systems in our universe.
Counting them directly is not necessary (and not possible either). Very often what we think we’re seeing is not necessarily true. Just think of a magic show and you’ll understand what I’m talking about. 
Objective evidence is the key. Thats what science uses. You measure the effects of a phenomena and verify it.
How do you think scientists discovered the BB ? And about black holes ? By directly observing them ? You must be joking … 
I don’t believe in the big bang. for one, it defies conservation of energy, but you could just argue that the laws of physics were different back then.
But still, if the universe isn’t infinite in time both ways, what was here before the big bang?
the one theory is that the universe has existed infinitely in time, but every thousand trillion years or so, all the matter in the universe contracts to a single point, then explodes, thus causing another “big bang” and the rebeginning of the universe. the theory states that this has been going on forever and will be going on forever. this is the most plausible, in my opinion, theory of the origion of the universe.
Well dear,the LITTLE I do know about science is that it is not so objective as you claim it to be.
You are using other people’s views to create your own and even now, knowing that you know a more about astronomy and physics have not given a figure to how many stars are in the sky. How do you know that the sources that you use are accurate in estimating the number of galaxies and star systems? (a ‘hypallage’ or something…using the term loosely)
you even said it yourself…(Very often what we think we’re seeing is not necessarily true. )
Certain things have to be directly observed in order to obtain a near accurate estimation. I’m sure there is not a pattern to how many stars are in one place… and discovery of black holes is a totally different argument… and since u mentioned that , just a correction. you cannot discover something that you are already directly observing.
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It is not a question of belief, it is a question of evidence [:)]
And important as your beliefs may be to you, they are no indication of the validity of a theory.
No space or time. The BB resulted due to random fluctuations of zero mass-energy into positive and negative mass-energy. So the total mass-energy in the universe is zero.
That you cannot imagine it doesn’t really matter. Our brains evolved to survive and reproduce in the African plains and rainforests. It is not surprising that they are ill-equipped to deal with things like the origin of the universe. So we cannot rely on imagination and instinct for this one … we have to rely only on evidence 
Because I know that it is based on objective evidence. And has been independently verified before and can be again. You and I could, with a little scientific knowledge verify/disprove these theories. It doesn’t require any faith or belief
Nope, direct observation is not always necessary and not always possible either. Science works like this …
You have a hypothesis H. If H were true, using logic, scientists deduce that they should be able to observe a,b and c. Then they go out and observe. If they observe a, b and c (many times, independently) then the hypothesis is valid. But if they dont observe even one of those, it is invalid. Tomorrow if some other scientist comes along and fails to observe c under a certain circumstance or finda nother phenomenon d that should be observed if H were true, but isn’t, then again H is disproved.
no sivakami, science still isn’t very objective. Scientist use paradigms to achieve answers…this is in no way an objective pursuit of knowledge so therefore it doesn’t aim to falsify but confirm theories etc…
For example, u just said :“You have a hypothesis H. If H were true, using logic, scientists deduce that they should be able to observe a,b and c. …” you see, there is a standard procedure for retrieving information in your view; it guides how that evidence it collected and how it should be analyzed and explained.
Can it then be seen as objective??..
Natty 
Every scientific theory has an explicit falsifiable clause. Else it isn’t a valid theory at all . Its religion that states unfalsifiable theories - convenient for belief without evidence
What standard procedure ? The only procedures science follows is logic, objective evidence and skeptical scrutiny. Its only in science that scientists actively try and disprove their own theories and invite other scientists to disprove theirs. Only after theories have been subjected to intense peer review are they accepted. Even then anyone who reveals evidence to the contrary can disprove it anytime.