Space Is Expanding So It Can’t Be Infinite?
1. Assume space is infinite
2. It is expanding
3. Implying it is not infinite (if it was size X, it is now size X+1, meaning X was not infinite)
Also, space started with the big bang 14 billion years ago. It can only have grown to a finite extent.
2. It is expanding
3. Implying it is not infinite (if it was size X, it is now size X+1, meaning X was not infinite)
Also, space started with the big bang 14 billion years ago. It can only have grown to a finite extent.
Comments (170)
You missed the most important premise.
0. Assume your own idiosyncratic definition of 'infinite', with which virtually no-one here seems to agree.
Once we add that, then brilliant... Perfectly valid argument, well done.
So space must be finite.
That's not the standard definition of infinity and you've had as much explained to you a hundred times.
You've presented your argument about what you think infinity means, most ultimately disagreed. Just have the dignity to accept that instead of keep starting threads which basically hang on exactly the same disputed definition.
a number greater than any assignable quantity or countable number
If there exists a number X+1, then X cannot be infinite... so by the standard definition of infinity, my argument holds.
It is accepted by virtually every mathematician that there are an infinite number of negative integers, there are also an infinite number number of positive integers. The number of integers is greater than the number of negative integers (by the number of positive integers), despite all of these being an infinite number.
That is the standard definition of infinity and by it, some infinities are contained within others.
The size of the universe is either infinite or not infinite. If it can grow, it is by definition not infinite. Only finite sized things can grow.
The DICTIONARY mathematical definition of infinity:
a number greater than any assignable quantity or countable number
There clearly only one such possible number - the existence of such a number by definition rules out any other infinite numbers. There is only one infinity.
One way to view it is to say that galaxies are staying still while there is some underlying space expanding, but no entity called "space" has ever been observed expanding or stretching, when we say space expands we're saying nothing more than galaxies move away from each other at a rate proportional to the distance between them, which doesn't require an expanding space to describe.
The universe could have been arbitrarily large at the time of the big bang, and could be arbitrarily large today.
Saying the universe is infinite is just fantasy talk, in the sense that's not something that could be deduced from observation. Also the concept of infinity is not something that can be directly grasped, we can conceive of something going on forever, but we can't conceive of the entirety of that thing, so we can't conceive of that entire thing growing bigger. But mathematicians have no problem imagining something that goes on forever inside something that goes on forever, like there being an infinity of real numbers between two natural numbers and there being an infinity of natural numbers, but it's just mind games really. At the end of the day, saying the universe is infinite is the same as saying in some imaginary world pigs can fly, sure we can imagine it but how is it relevant to anything in our lives besides it being some mind game?
But the metric is expanding. So we can equate the metric to space without having to resort to a believe in spacetime. And if the metric is expanding, the metric, IE space, cannot be infinite.
As I said. The entire mathematical community disagrees with you here. Rather than just make another post about it in a slightly different way, why not try to understand why they've reached that conclusion. Accept that others see things differently, you might learn something.
Its a belief called Finitism:
https://en.wikipedia.org/wiki/Finitism
Used to be more popular than it is nowadays but there are still a few proponents (Max Tegmark, William Craig Lane) for it around.
You should have respect for and consider other peoples viewpoints; not dismiss them blindly.
You should realise it is a fact that not everything you were taught in school is correct... learn to be more skeptical and keep an open mind to new ideas.
...perhaps the confusion would stop...and the definitive statements like "Space Is Expanding So It Can’t Be Infinite?"...would also stop.
Please, folks, stop thinking that humans are the ultimate thinking machines. Stop supposing that OUR concepts of reality...ARE the REALITY.
There is nothing wrong with a totally blind guess that "infinity " or "eternally" do not exist. But all it will ever be IS A BLIND GUESS.
What we humans consider the universe may be expanding...but "what we humans consider the universe" may be but nothing within an INFINITE universe.
Good point. If our universe is expanding and our universe is contained in the larger universe, that means the larger universe must be expanding too hence it can't be infinite either.
Quoting Devans99
If anything...it is a BLIND GUESS called Finitism...which you are disguising by calling it a "belief."
It may be correct...and it may be incorrect.
No way to know right now.
That's the way things go with blind guesses about something as unfathomable as the REALITY.
BUT...the REALITY MAY be that all there is...is infinity.
There may be no expanding...just the illusion of expanding.
Sorta like the illusion of the sun going across the sky.
What then is your explanation for the redshift of distant galaxies?
Well you can imagine a finite part of the universe and visualize the metric expanding in that part, and imagine that the same goes on in every part of an universe that goes on forever.
Like you can imagine a finite part of the natural numbers (say {1; 2}) and visualize adding real numbers in that part (so it becomes say {1; 1.01; 1.001; 1.0001; 1.00001; ...; 2}), and imagine that the same goes on in all other parts of the natural numbers ({2; 3}, {3; 4}, {4; 5}, ...) that go on forever.
You just can't imagine an infinite universe as a whole doing that, like you can't imagine all the natural numbers at once doing that, you can just imagine the process. Then some might say "our mind is not able to grasp it all at once but that's only a limit of our mind", while others might say "something that cannot be conceived as a whole doesn't exist or is impossible".
If it goes on forever, there is no room for any expansion; there is nowhere to expand to.
Quoting leo
I'm of the 2nd believe. That head spinning feeling when we think of infinity is our minds choking on a very illogical concept I think.
Why so? It applies to the metric - that can't be both expanding and infinite at the same times so it applies to space/'the area'?
I can make some guesses about what MAY BE the possible explanation:
It may be part of the illusion.
It may be a part of what we humans do not know about physics.
There is that term again.
YOU BLINDLY GUESS THAT MATTER CANNOT BE INFINITE.
Aside: There is a decent chance that "matter" is infinite. Science at the moment is saying that matter breaks down into smaller and smaller constituent parts...until at the quantum level...it is suggested that there is nothing but energy...not actual particles of what we humans would call matter.
'Nuff said?
Another blind guess being called a "belief."
It is that you say space is expanding, not defining what space your talking about and using both when it works to your advantage.
When I say it believe I'm saying is have a resoning, but there is always room for doubt.
The reason I believe there isn't an infinite about of matter is because of the propertys of infinite things.
And yes I know about the quantum level.
Yes. I think we've all gathered that. Repeating it doesn't seem to be helping.
Quoting Devans99
Yes we can't imagine it, we can just imagine the process. Honestly I think those who try to apply the concept of infinity to the universe just do it on aesthetic grounds, they see beauty in the idea of something that goes on forever rather than something with borders. But they couldn't make any objective observation that would prove the universe goes on forever.
Area, in this context, is all the room matter can be. Astronomers cannot be saying what I call area is expanding or we would know of the answer to this already.
But even if you got cosmologists to stop talking about an infinite space that expands, that wouldn't change much in the grand scheme of things.
Yes and you could add the fact we only ever observe finite things is strong inductive support for the proposition 'infinity does not exist'.
Quoting leo
I see it as one battle in a war. I believe infinity is impossible in general. There are proofs but people don't buy the proofs. So I've settled for trying to show each instance of infinity leads to a contradiction. Infinite space is one of these instances.
What is there to gain by winning the war though?
It would also be generally useful if we could rule out infinity so we could teach the kids something more useful/truthful than Cantor's infinite set theory.
Plus it would simplify science if we knew for sure that Actual Infinity is impossible. Certainly in cosmology, that would cut down the range of possible models of the universe.
Apparently, even MATTER is not made up of MATTER.
Ultimately, it is made up of energy.
Or of an infinitely regressing halving of a unit of matter...or at least that is what present-day human science is saying.
One of the HUGE problems in these kinds of discussions is the reluctance of participants to acknowledge, "I do not know."
Even when a begrudging acknowledgement is made...it is almost always followed by a "But the preponderance of evidence indicates that it is more likely A than B...
...even though that is bullshit.
Discuss the subject.,..it is a very interesting one...but stop with the "definites."
Neither infinity nor eternity are impossible...and both are every bit as likely as no-eternity and no-infinity.
The people claiming one or the other definitely IS the reality...AND the people claiming one is more likely than the other...are allowing their blind guesses to go ape!
Or everything in it is shrinking...?
If space is expanding, within what is it expanding?
I guess it is expanding within nothingness. So the nothingness has no space or no time associated with it. Maybe time slows down as you get closer to the edge of the universe and stops on the boundary? If the boundary was expanding at the speed of light, that would make some sense.
Infinity can grow can it not?
I hear that there are infinite infinities each larger than the other.
[i]'MATHEMATICS
a number greater than any assignable quantity or countable number (symbol ?)'[/i]
So if infinity grows, it was not infinity to start with (because there was a number greater than infinity).
By the same definition, it is not possible to have more than one infinity, although as you say maths goes on to contradict its own definition of infinity by introducing multiple infinities.
Cantor imagined a hierarchy of different sized infinities terminating with 'Absolute Infinity' at the top. This concept Cantor said was beyond maths and he associated it with God. Cantor believed God communicated these ideas to him directly. Cantor was a looney IMO.
If infinity is a number; it is a number larger than any other number. So if infinity+1 (IE it grows) is a number, then infinity is not infinity.
If infinity is a number; it is a number larger than any other number. There can be only one such 'number larger than any other number'.
OK, so infinity cannot grow, or have anything greater than it, so the universe's size/age/whatever cannot be infinite.
Fine, the universe's size/age/whatever must be some other thing which can grow and have something greater than it but which still is not a finite number. What do you want to call that thing? Pick a name and we'll all happily use it.
I don't think it's the case that we need some 'number' other than infinity to describe the universe. The size of the universe is a number, numbers have fixed values, so the size of the universe is a finite number.
I think whatever hypothesis we develop should not overlook the facts we're working with. The fact is we've noticed the galaxies moving apart in space. However, we can't say anything conclusive about that space. Whether space is expanding along with the galaxies or it is constant while the galaxies expand within it is yet to be determined.
Quoting Devans99
I think space is a very difficult subject/object to define even before the inclusion of another even lesser defined abstract as nothingness. The unknown factors are too great for any conclusions.
For me, the two abstracts seem to obscure any logical connections I might want to make. Nothing is just a placeholder for an idea that expresses a relative, tentative and conditional situation and thus cannot be a 'something'.
Devans...are there any days where you are not pontificating?
"The 'size' of the universe" MAY not be a number at all. It MAY be infinity.
What we humans call "the universe" MAY itself be infinite.
We do not know.
Your pontifications are used gratuitously in order for you to arrive at "the universe is not infinite" which you need for wherever you ultimately want to go.
Can you truly not see that?
Thats a contradictory statement - size is always a number.
Quoting Frank Apisa
If we adopted your approach to philosophy and science which seems to consist of 'I don't know' and 'its unknowable' I think progress would grind to a halt.
Quoting BrianW
Galaxies are flying apart at faster than the speed of light so it is space that is expanding I believe.
"Size" is NOT always a number.
"Large" IS NOT a number. Neither is "narrow." Both are sizes.
The UNIVERSE, Devans, MAY be infinite. Use that as a number...or a size...or whatever. But get off your nonsense that you KNOW it cannot be infinite.
Your need to get to "the universe is not infinite" is astounding...and futile.
That is not so at all...and we touched on this earlier.
Both disciplines can proceed with dispatch...without the nonsense of pontificating...which, by the way, was what held up science and philosophy not many centuries ago.
You are positive that the universe cannot be infinite and eternal...because you are determined that it has to be a creation...and has to have a creator.
That is not science nor philosophy. It is charletanism.
But they are not. Shame.
1. An infinite universe should have no boundaries so cannot expand
2. There is nothing beyond an infinite universe to expand into
3. Expanding means that size(t1) > size(t0). IE we know the universe was once smaller than it is today. There is only one kind of infinity here; size is an Aleph One infinity. So size(t0) must be a finite number.
4. The universe can't have been expanding for ever; if we trace back in time far enough, we will always find a point in time when two distant points are co-located so no further expansion is possible. Hence the universe must have finite size.
According to your idiosyncratic definition of infinite.
Quoting Devans99
According to your idiosyncratic definition of infinite.
Quoting Devans99
According to your idiosyncratic definition of infinite.
Quoting Devans99
According to your idiosyncratic definition of infinite.
?+1=?
In english, this means there exists something that when you change it, it does not change. Absolute nonsense.
Yes, we all know what you think. This is not your personal blog, it's a philosophy discussion forum, so unless you have something to discuss, rather than merely declare to be the case, then I can't much see the point in you posting.
The universe is not one point with the other; it's not a beginning with an end, wherein the end is ever-growing from the beginning. The universe, following the infinity concept, has no end nor a beginning; so interstitial positions between matter and particles are increasing, it's growing further from each particle.
So the universe is infinite.
- There are proofs that infinity does not exist.
- There are no proofs that infinity does exist.
- What exactly can we deduce from that apart from infinity does not exist?
Modern physics seems to be leaning in the direction of spacetime having a start:
https://www.michaelgstrauss.com/2017/01/the-significance-of-bgv-theorem.html
The BGV theorem states, as you'd expect, that an expanding universe must have a start.
You're just doing it again.
But you're not discussing this, you're just repeatedly declaring it to be the case. You haven't addressed the arguments of those mathematicians who advance modern infinity theory, you've just declared them all to be 'wrong'.
It's fine to have axiomatic beliefs, but if you cannot find someone who shares those beliefs, then there is no one with whom you can discuss the implications thereof.
It would be like me declaring an axiomatic belief that Robert DeNiro was God and expecting to hold a discussion about what colour his tie would be.
The circumference of the topographical position of any country, is infinite. To begin, you measure distance of the shore by kilometers, but as you zoom in, more corrugations start to appear. From meters, centimeters, millimeters, to intangible and imperceptible microscopic substances, corrugations constantly appear. That's fractalism; fractalism is argued to consist of a beginning, but not an end.
However, infinity can consist of a beginning. Suppose there was a race track shaped like the infinity symbol, it has no substantial beginning, nor an end — but it's infinite, it's constantly going on. A race-car, which is not infinite, due to it's analytical limitations, might have an end - that's not evidence to say the race track is not.
The point is, infinity is not something comprehensible to empirical sense, infinity is a concept that requires our ability to rationalize. Far greatly: Space, Time, and other abstract concepts rely on rationalization, it is a common intuition that is driven by our humanly perspective; our ability to rationalize.
If you're going to take it from a theistic point of view, the universe does have a beginning.
Christian philosopher Thomas Aquinas, who was also a devoted Aristotelian, argued that; God, who should be known to possess and harness infinite resources, must be able to create the universe with a stagnant beginning, but in a way that it was and will always be, infinite.
Us Humans as contingent beings, may not look upon it as a concept that is logically possible, because of our humanly intuitions. We cannot comprehend the presence of both at the same status temporally, we think they are not mutually exclusive. So I would conclude, that the universe is infinite yet inheres a beginning.
Now the reason why we don't understand that as humans, is because we know infinity (For a Godly concept, not fractalism) cannot inhere a beginning.
Just to remind, , if you would say that infinity does have a beginning, your atheistic viewpoint will collapse, or if not, weaken. If you say otherwise, your 'impossibility of infinity' viewpoint will collapse as an already precarious theory.
Eventually, zooming in, you reach atom level. So the circumference is not infinite.
Quoting Isaac
I have addressed them - sorry for repeating myself- but If infinity were a number it would be a number X such that it is greater than all other numbers. But X+1>X so infinity is not a number. If you can disprove this argument please tell me how - I've been posting it for months and no-one seems to have a valid counter argument.
If you look at set theory, all it does is axiomatically declare that an infinite set exists - it does not prove anything at all and yet its easy to show infinity does not exist - see above - or see any of the numerous contradictions that are thrown up with infinity.
[img]https://media1.tenor.com/images/06655070b3cc8faaff4824eee848adc0/tenor.gif?itemid=5436796[img]
I wasn't asking for a repeat of your assertion, I was asking you to address the counter arguments of mathematicians. What do your opposition have to say about this, what counter arguments have you read, and where are they wrong?
Quoting Devans99
Of course I can't disprove that argument. I don't know the first thing about maths (beyond what I've read in 'popular maths' type books. My interest is in how you are supporting your argument. What do you think is going through the minds of the world's top mathematicians, the absolute geniuses at the top of their game, when they think about infinity and reach a conclusion which even some random internet poster can see is wrong? What exactly do you imagine they are all thinking at that moment? "I hope no one notices that this is all wrong"? "I don't know how I blagged my way to the top of the maths department because the truth is I don't even understand this basic explanation"?
I'm fascinated by how your mind might work through this, how it rejects the possibility that there is a very good argument for the conventional view which you either have not come across or do not understand, in favour of what seems to be the completely untenable position that you are right and every one else is wrong.
But I know of no objections to my argument. Hence my reason for posting this argument is to gather any such objections. Philosophers tend to be more open minded and have less invested in infinity than mathematicians, hence this audience.
I have a 1st in maths so I do understand the maths.
It is the case that there is a huge flaw in the root of set theory called 'the axiom of infinity'. As I mentioned to you before, there was a big debate at the turn of the century as to whether infinity should be included in maths. Cantor won the debate and its been taught in schools ever since.
So I think there is groupthink going on here. There are only a few people around like me who are actually speaking out on the obvious flaws of infinity. I also think mathematicians are working at too high a level of abstraction - the flaws are obvious in that, for example, infinity is completely incompatible with basic arithmetic - but most mathematicians cannot see the wood for the trees - they are too immersed in higher level abstractions to see the basic problems.
Quoting Devans99
For a start, these two statements contradict one another. You clearly do know of objections to your argument. Presumably Cantor, and those who follow him, haven't just written "some infinities are bigger than others" on the back of an envelope and that's what's guided mathematics for the last hundred years. I presume there is an argument, and quite a long one I'll bet, as to why Cantor thought some infinities could/should be larger than others. So why don't you lay out his argument, step by step and show where he went wrong.
Quoting Devans99
I have a first in psychology, but that doesn't alone give me authority to dismiss any arguments in that field without analysis.
Lay out the arguments Cantor, and others, have made, and show exactly where they went wrong. That way people here (probably not me) can actually get involved in the debate.
That is what they have done. The axiom of infinity could fit on the back of an envelope and just baldly states that infinity exists. They have no logical justification for including Actual Infinity in maths.
Quoting Isaac
For example the bijection procedure gives spurious results (like naturals and rationals being the same size). Or all the paradoxes listed here:
https://en.wikipedia.org/wiki/List_of_paradoxes#Infinity_and_infinitesimals
A paradox is usually the sign that you are working with something contradictory. The common thread through all these paradoxes is infinity - it is the contradictory thing that leads to those paradoxes.
But none of the paradoxes you've referenced here remain problematic. In fact most of them seem to be resolved by ZF or ZFC theory which, I understand, is the basis of most mathematics. Probably why it's so popular.
Open a thread disputing the resolution of these paradoxes by ZFC and I'm sure you'll get more interest from the many keen mathematiciand here than you'll get by just declaring it to be wrong.
[i]'Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. In his final scientific work, Two New Sciences, Galileo Galilei made apparently contradictory statements about the positive integers. First, some numbers are squares, while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares. And yet, for every square there is exactly one positive number that is its square root, and for every number there is exactly one square; hence, there cannot be more of one than of the other. This is an early use, though not the first, of the idea of one-to-one correspondence in the context of infinite sets.
Galileo concluded that the ideas of less, equal, and greater apply to (what we would now call) finite sets, but not to infinite sets. In the nineteenth century Cantor found a framework in which this restriction is not necessary; it is possible to define comparisons amongst infinite sets in a meaningful way (by which definition the two sets, integers and squares, have "the same size"), and that by this definition some infinite sets are strictly larger than others.'[/i]
https://en.wikipedia.org/wiki/Galileo%27s_paradox
It remains the case that bijection claims that the number of non-squares is the same as the number of squares. But in every finite interval (of reasonable size) we examine, the number of non-squares is greater than the number of squares. The paradox still stands. The resolution to the paradox is not Cantor's bijection procedure but Galileo's earlier observation that infinite sets cannot be compared. An infinite set is not fully defined (that is what the ... indicates), meaning it is not defined period and it is not permissible to perform operations on it (like comparing sizes).
It says in Wikipedia that...
"Galileo concluded that the ideas of less, equal, and greater apply to (what we would now call) finite sets, but not to infinite sets. In the nineteenth century Cantor found a framework in which this restriction is not necessary; it is possible to define comparisons amongst infinite sets in a meaningful way (by which definition the two sets, integers and squares, have "the same size"), and that by this definition some infinite sets are strictly larger than others."
If all you're going to say is" The resolution to the paradox is not Cantor's bijection procedure ", which is exactly what everyone else seems to think the resolution is, then we're back to square one again with you just making bare assertions.
{ 1, 4, 9, 16, ... }
{ 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, ... }
When the 2nd is clearly larger than the first. So how exactly is that a sound resolution to the paradox?
Well, it seems pretty obvious to me that the second set is not obviously larger. They both have little ellipses, indicating that they go on forever.
We certainly can't conclude that they are equal (as set theory does) as they are not fully defined as indicated by the ellipses.
But we evidently don't. We come full circle to the root cause of the problem, you presume that the world must be exactly how it seems to you to be. You inductively understand the second set is 'larger', other people do not because they think differently to you. You cannot simply presume that what is inductively evident to you is deductively necessary.
Something infinite has no fixed size so it cannot be compared to anything else. An infinite set has no size (cardinality) is the only valid conclusion and thus they cannot be compared.
What Cantor did (in his madness) was to invent numbers to represent the sizes of infinite sets... they are pure inventions... derived from nothing... there is no math behind them... its all a pure figment of Cantor's imagination.
As I said, we're back to a series of bare assertions without any support.
Quoting Devans99
An assertion.
Quoting Devans99
An assertion.
This is a waste of my time if we're just going to go back to assertion.
If you cannot count something, how can it have a size?
I wouldn't claim anything on the subject. I would defer to my epistemic betters. The point I'm making here is a psychological one. That which is evident to you is not so to others, that which you do not understand may seem incoherent but your incredulity alone is not evidence of it being so.
What do you think of this:
1. Assume N+ is infinite.
2. If defined recursivly (with Start n_1=1 and n_x=n_(x-1) + 1), N is expanding.
3. Implying N is not infinite (if N was size X, it is now X+1, meaning X was not infinite.
Doesn't this show the flaw of trying to understand infinite as specific value instead of using infinite as concept that is not a specific value.
Afterall in math infinite is not understood as value thats why inf +1 = inf.
Aren't you making it yourself a bit to easy by ignoring this view completley and simply stating inf is a specific value like any value in N. Basically equivicating properties of the category with the properties of it's elements?
I don't believe infinity is a logical concept and reality is logical so again the size of the universe is not infinite.
Quoting CaZaNOx
Maths claims that infinity is a number (at least set theory does).
Devans...exactly what would happen if everyone here deferred to you in this...and agreed that there is no way the universe can be infinite?
What would result? What would be the logical inferences?
Would that, as you suggest, imply that it was created?
And if it was created...what would you be suggesting about that CREATION?
So the universe being finite does not imply creation but does allow creation.
[b]Devans...exactly what would happen if everyone here deferred to you in this...and agreed that there is no way the universe can be infinite?
What would result? What would be the logical inferences?[/b]
It would add weight to the general arguments against infinity if we could establish the universe has a finite size.
The fact that its impossible to create something infinite (you would never finish) is in itself suggestive the universe is finite (the universe is a creation - there is a start of time).
In other words you are saying that if you are correct in this argument of yours (and you may well be correct)...then it is possible the universe was created!
Why not just say that?
Of course it is possible the universe was "created."
It is also possible the universe was not "created."
Hell...everyone would be agreeing with you.
Are you sure that is where it will lead?
And if so...are you satisfied with that?
Like I would maybe say that calling the matrix multiplication "multiplication" seems a bit dubious.
It is obviously clear why see similarity between common multiplication, scalar multiplication, matrix multiplication ect. it is also obvious that those concepts are useful.
I think this illustrates that despite similarity in concept and name cardinal numbers and common numbers are different things that one should not confuse. Cardinal numbers get used to quantify infinite sets however if you question infinity it seems problematic that you try to use a concept that is predicated on the existence of multiple infinities to refer to infinity as a number. This somehow negates your own stance, since cardinal numbers don't negate infinity. It's precisely the opposite they acknowledge infinities and try to form a new concept to work with them.
Further my point was that the argument for the existence of infinity could be located precisely in the continuous growing of the value of integer numbers as done in math. I therefore don't see how the very same continuous growing would undermine asserting the concept of infinity to reality.
Quoting Devans99
I reformulate this as
1) Reality is not logical
2) Conclusion: The size of the universe is not infinite
(feel free to object to my paraphrasing your position if you think I misunderstood you)
I don't understand how you can argue(implication of logic) against or for infinity and assert and value to the conclusion if you take 1) as given.
Even if we dispense this criticism for a while I don't see how you get from 1) to 2) (due to the lack of further steps) without resorting to it being a statement of believe and you being free to believe whatever you want. (I am not opposing this statement and only trying to point out that if you resort to it being a matter of believe there is no point arguing for it.) With this in mind I assume you have a reasonable argument that leads from 1) to 2) that simply isn't spelled out here. So I would appreciate it if you could maybe provide this reasoning in more detail for me to comprehend how you arrive at 2).
And then some. Numbers have fixed values be they natural, real, matrix etc... Infinity has no fixed value so it cannot be a number.
Quoting CaZaNOx
That would be a Potential Infinity which I do not object to. It is Actual Infinity that I believe does not exist.
Quoting CaZaNOx
What I meant was:
1) Reality is logical
2) Infinity is not logical
2) Conclusion: The size of the universe is part of reality so not infinite
There is a danger of confusing very large with infinite. That is maybe what has happened to the universe; it is very large so it is convenient to approximate it with infinity and over time this has become a belief that it could actually be infinite in size.
But you have already responded to my question...
...and it appears all you are aiming at is that it is possible that the universe is finite.
I am sure everyone will agree that it is POSSIBLE that the universe is finite...just as it is POSSIBLE that the universe is infinite.
So...all this haggling seems to be unnecessary.
Why not just agree that it is possible the universe is finite...and that it is possible that the universe is infinite?
There doesn't seem to be anywhere to go with resolving the unresolvable.
The point of this thread is to discuss whether the universe is infinite or not and maybe even reach a conclusion.
By just being what IS, Tim.
IF the universe is infinite...however that is...IS.
If you are saying it is IMPOSSIBLE for the universe to be infinite (and eternal)...you are defying logic. Of course it is POSSIBLE. And, if the probability or likelihood were a gazillion to 1 against...it remains POSSIBLE.
And if that happens to be infinite...it just IS.
Are you arguing that it is IMPOSSIBLE that the universe is infinite? If so, the burden of proof would fall on you...not me.
Cop out...but I understand.
- Size is a number
- Infinity is not a number
- So the universe is not infinite in size
I understand Newtonian physics very well but when you get into the most modern physics there are critical details i'm not aware of so i don't want to make it out like this is a complete answer.
That being said if there is an infinite amount of area for matter and energy to expand into my logic circuits tell me there is an infinite amount of space. Without a doubt i am missing something.
Nothingness itself cannot be said to be infinite (because it is nothing, it has no dimensions).
"Nothingness itself cannot be said to be infinite (because it is nothing, it has no dimensions)."
i have no evidence to say your wrong. This is one of those things that i would have to study for 2 months.
Nitpicking, I'd say ...
1. we employ logic to understand reality
has served us well; for that matter, meaning presupposes identity
2. if ? derives a contradiction, then ? is illogical
and this is not the case in general; we have some examples of veridical paradoxes, which goes to show that ? can have counter-intuitive implications, and that's not the same as illogical; that said, there are some cases where we take a derived ? to indicate a problem; dealing with ? requires special care
3. who knows what exactly is real or not; reality does not have to abide by our thinking
Quoting Devans99
? ? R (not among the reals, requires different treatment)
? requires special care, different treatment than our usual numbers, sort of like a quantity that's not a number.
My opinion is that the very conception of infinity is illogical. ?+1=? implies the existence of something that when it is changed, it does not change. That is deeply illogical.
Quoting jorndoe
My argument is that if infinity was a number X, then X would be greater than all other numbers. But X+1>X. So infinity is not a number.
If you are saying it is impossible that the universe is infinite...you are simply sharing a blind guess about the reality.
To assign it logic is an absurdity.
But...even if the point were conceded...where do we go from there.
Size is not always a number.
We talked about that.
But take the word size out if you must.
Are you saying it is impossible for the universe to be infinite?
You've been on both sides of that question...I'm just wonder if you want to stick with one side or the other.
... is illogical.
As mentioned, ? is not just one of your ordinary numbers, that you can stuff into ordinary arithmetic.
That would be the illogical part, not ?.
That is the standard definition of infinity and by it, some infinities are contained within others.''[/i]
Could it be argued that since the universe is all we know and nothing exists outside of it by definition, it can't be enclosed by anything larger than it. So in a sense it would be the ultimate infinity and not part of a subset. Since the universe is expanding, using OP's argument that "if it was size X, it is now size X+1, meaning X was not infinite", then the universe by definition is finite.
A line that extends to infinity, contained within a circle of fixed area.
Now, suppose the circle was expanding, and taking the Kotch Snowflake with it....
And hence this shows your odd notion of "exists". As if, despite our being able to talk about them, you were to say that there is no such thing as a Koch Snowflake.
My suggestion is that what has led you to rejecting the mathematics of infinity is just such a confusion.
What he said was:
Quoting Devans99
Which is just false. Infinity plus one is still infinity.
What you propose here is quite different.
Infinity is not realisable - its not possible to construct anything infinite in size (you would never finish)
Infinity is not logical - see above comments in previous posts.
Quoting Banno
But expansion says there exists a number X+1 (the new size) that is greater than X (the old size). So how exactly can X be infinite?
Anyway:
- ?+1=? explicitly says infinity can't expand.
- Infinity is unmeasurable so it has no size so it can't expand.
- Infinity does not exist.
Whether or not matter is discrete is still in contention...and probably will be for a very long time.
Atoms were once thought to be the ultimate smallest thing.
Using "matter is discrete" as part of the argument for "the universe is finite" is essentially using a guess...which allows for the possibility that the universe IS infinite. (But of course, we all already realize that.)
Are you suggesting a never-ending faberge egg style arrangement with an unending sequence of smaller and smaller sub-atomic particles?
Or are you suggesting we will discover a sub-atomic particle that is continuous (IE infinity divisible)?
Both seem rather far fetched so I lean heavily towards matter being discrete.
I am not suggesting anything, Devans.
I am stating as an absolute fact that the question of whether matter is discrete or continuous...has not been answered absolutely. And then I am speculating that it will be a LONG TIME before it is...if ever.
You are correct, what I worded was different to what OP actually said. I did that out of sheer laziness, will edit it.
if i add 1 + 1 + 1 + 1 that is 4. If i do the same thing again that is 8. If i die tommorow and never do this process again and at the same time have never heard of the term 12 i might conclude that `12 doesn't exist. The problem is our ability to testify what we believe is true is limited by our time on this earth. Infinte is not necessarily a fake construct its just we personally only have a limited time to testify to the things we hold to be true. If the universe keeps expanding i believe it is certainly possible that it could expand to twice as big, three times as big, 4 times as big and so on.
https://en.m.wikipedia.org/wiki/Actual_infinity
Its possible to keep counting indefinitely but even if you do you will never reach infinity (because it's impossible to count to infinity). So Potential Infinity is OK, but Actual Infinity never happens IMO.
It's impossible to construct something infinite as you'd never finish doing it.
I get what you're trying to get at, but I think this is a very weak analogy.
Thats fair.
i'm just ok at mathematics but i do get better with age so maybe in 10 years i'll have a better analogy or maybe i won't.
"
https://en.m.wikipedia.org/wiki/Actual_infinity
Its possible to keep counting indefinitely but even if you do you will never reach infinity (because it's impossible to count to infinity). So Potential Infinity is OK, but Actual Infinity never happens IMO.
It's impossible to construct something infinite as you'd never finish doing it. "
My understanding of physics is that what you said is true. There is a law in thermodynamics that things go from high order to low order so if made a computer program that used robotics to farm the land that robot would eventually fall apart or degrade itself unless i did things to actively make repairs to the system. Yeah i think you are right on this if i understand what you are saying. Perhaps if there were other universes (not sure why scientists say there are other universes) where the laws of physics are different then i think the above might not be the case.
The laws of math should be invariant across all such universes.
I am of the opinion if there are other universes, they will be like this one. They are all made of the same stuff, go through the same processes and end up at the same temperature/density so all universes should end up similar.
"The laws of math should be invariant across all such universes.
I am of the opinion if there are other universes, they will be like this one. They are all made of the same stuff, go through the same processes and end up at the same temperature/density so all universes should end up similar. "
Yeah i definitely agree with that the laws of math would be the same across all universes. As to whether other universes would have the same laws of physics, i've wondered that myself. I certainly can't say your wrong about that.
As I see it...what we "believe" is nothing more than what we blindly guess about the unknown.
Anyone can make a guess at any time...nothing wrong with guessing. I do it all the time...and I imagine most people do it often also.
I always refer to my guesses...as guesses.
Some people call their guesses "beliefs."
Why is it that you stray off the path of this thread so often...and discuss matters that are off topic with others...
...and yet tell me I cannot...and refuse to answer my questions that are closer to being on issue than this stuff you are discussing right now?
"As I see it...what we "believe" is nothing more than what we blindly guess about the unknown.
Anyone can make a guess at any time...nothing wrong with guessing. I do it all the time...and I imagine most people do it often also.
I always refer to my guesses...as guesses.
Some people call their guesses "beliefs."
Under that logic why don't we just sit around on this forum and discuss our favorite type of icecream or what we think is the best color. I believe the belief that objective truth exists is paramount to having a stable society. I do not believe it is arragant to say that objective truth exists but i will say it is very hard to come by.
I think you should place more weight in inductive reasoning; it is this, rather than deductive reasoning, that guides us though our daily lives.
If CERN published an article claiming detection of a new particle at five nines certainty, what is your attitude? Do you adopt a working assumption that the particle exists? Or do you continue to assume it is unknown whether the particle exists?
I agree with that statement. I lost the quote but you said something to the effect that modern cosmologists are very often athiests.
I'm not going to say what religion Isaac Newton was but he did have a religion and what alot of people don't realize is that much of modern technology can be built using nothing more than physics principles that were discovered in the 19th (1800s) century or even just using Newtonian physics. The point i'm trying to make is people over estimate the ability of alot of modern scientists to solve all the world's problems. I believe science is great and the healthy person of belief will embrace science but that being said we shouldn't just bend over backwards to listen to modern scientists.
If you want to discuss those things...fine with me. I'll offer my favorites.
But the necessity to do that does not derive from my position...and I have no idea of why you think that.
Interesting opinion. Could be right...could be dead wrong.
We can discuss your opinions...and the opinions of others instead of ice cream.
I do not "believe" it either...but then again, I do not do "believing."
If you are saying however, that you believe it is not arrogant to say that objective truth exists...I disagree.
The wording structure "I do not believe..." has to be used carefully in a discussion in a philosophy forum.
You are free to do that.
The very last thing I am, however, is a "defeatest."
I will argue a point that I consider significant until my fingers are bloody from typing...and then some.
You are certainly free to think that...although that is a bit out-of-line.
If scientists come up with information that looks valid...I accept it the way a scientist would. Valid until shown to be wrong.
What is "five nines?"
I would just like to point out that Einstein, Sagan, Feynman and many other scientists identified as agnostics rather than atheists...and those three actually got angry when people called them atheists.
" Under that logic why don't we just sit around on this forum and discuss our favorite type of icecream or what we think is the best color. — christian2017
If you want to discuss those things...fine with me. I'll offer my favorites.
But the necessity to do that does not derive from my position...and I have no idea of why you think that.
I believe the belief that objective truth exists is paramount to having a stable society. — Christian
Interesting opinion. Could be right...could be dead wrong.
We can discuss your opinions...and the opinions of others instead of ice cream.
I do not believe it is arragant to say that objective truth exists but i will say it is very hard to come by. — Christian
I do not "believe" it either...but then again, I do not do "believing."
If you are saying however, that you believe it is not arrogant to say that objective truth exists...I disagree.
The wording structure "I do not believe..." has to be used carefully in a discussion in a philosophy forum. "
Yeah i've been wrong before but as the last thing you said in that post you should not be offended by the word "believe". Belief implies some form of opinion based on very little or sometimes alot of evidence. Its just a word. If i believe the color brown is best its probably based on the way my brain works or the way i am built. On the other hand i could accuse you that you won't be swayed on anything but you could also accuse me of not being able to be swayed on some things. I believe a cd or compact disc is a close representation of a recorded song however if you increased the sampling rate by some great order of magnitude, somebody somewhere would probably notice an improvement in sound quality.
My point was at what threshold do you admit inductive evidence into the set of assumptions you hold about the real world?
"I would just like to point out that Einstein, Sagan, Feynman and many other scientists identified as agnostics rather than atheists...and those three actually got angry when people called them atheists. "
I do agree with that in that there is an enormous difference between an atheist and an agnostic.
What are you talking about?
And why are you doing it in a thread that asserts "space cannot be infinite" when you are so dismissive of me asking questions that are tangential to the thread topic?
Thank you, Christian.
I'm not dismissive of your questions... sorry if I missed any.
You were dismissive of my question which I will paraphrase here:
Let's assume that you are correct...that the universe is not infinite...and in fact is a creation.
Where do we go from there? What are the implications of that? What is the point of you insisting that the universe cannot be infinite?
- It is a step in the road towards a better overall understanding of the universe. Cosmologists have models that are infinite in space or time. If we can eliminate these models, then the cosmologists can concentrate on the models that are possible.
- It is a step towards understanding the nature of infinity (it does not exist).
Then guess the universe is infinite...or guess that it is finite.
How does that give any movement toward understanding?
Finer minds than are available here are working on problems that may one day get us closer...although I doubt we will be appreciable closer than we are right now.
Stop that nonsense. It doesn't look good on you at all.
The important part is to see that all @Devans99's issues are dissolved if one accepts the logic of infinity he rejects.
That is, the problems are there because he talks about infinity in the wrong way.
The knots in the large scale structure appear to be forming an endless cloud of something like quarks - sound familiar. I believe it to be doing the same on ever larger scales Less defined As you pull back.
If this happened then DArk matter is all the stuff that did not fall into the singularities that make up the particles of matter. Dark energy is the result of gravity since it cause space to compress and therefor must expand somewhere else.
A black hole sees time go by fast but the stuff outside sees it take forever. When the knots in the large scale structure form particles and cool as the matter around us did - If you were made out of that and looked back at the creation of the particles that made you - it would look like it happened in a bang yet looking up from here it looks like it will take billions if not trillions of years
You can still add to infinity. Yes the answer will still be infinity but growing, as you describe it, is the possibility for addition, an operation you can apply to infinity.
Expansion means it is bigger now that it once was. So it can't have been infinite.
s0 at time 0
s1 at time 1
s2 at time 2
We have by the definition of expansion:
s0 < s1 < s2
So s0 can't be infinite.
There are not different sorts of infinity, but if you insist on this bullshit:
- We know that s0, s1, s2 are the same kind of infinity: aleph-one.
- The continuum hypothesis states that there are no intermediate cardinal numbers between aleph-null and aleph-one.
-We know aleph-one is s2, so means at best s1 us aleph-null and s0 IS ALWAYS FINITE.
Think I mentioned that.
I don't see a connection between the premise and conclusion.
Ok.
What directs to such a conclusion?
As you have pointed out, Quoting Devans99
This could even imply that if space were infinite, then it is just as possible for galaxies to keep moving apart without the need for space to expand. Anyway, this is just more conjecture on an unknown. I think there's no need to calculate probabilities of unknown factors.
Imo, if by space is meant the limits within the universe, then it is probable that it is expanding since by universe we define some sort of limits. If, on the other hand, by space is meant limits pertaining to reality's capacity to contain 'things', then perhaps infinite is a better tag given reality isn't really limited even by our standards.
On the face of it, nothing can move relatively faster than the speed of light, so if galaxies are expanding faster than the speed of light; that suggests space itsself is expanding.
'The expansion of the universe is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. Technically, neither space nor objects in space move. Instead it is the metric governing the size and geometry of spacetime itself that changes in scale. Although light and objects within spacetime cannot travel faster than the speed of light, this limitation does not restrict the metric itself. To an observer it appears that space is expanding and all but the nearest galaxies are receding into the distance'
https://en.wikipedia.org/wiki/Expansion_of_the_universe
So it is the metric that is expanding.
They have specified their limits as those of a universe. This means that it automatically has the potential capacity for intrinsic expansion as with most limits (or objects).
Quoting Devans99
Hypothetically, yes.
But, the space-time reference is another hypothetical. So they're claiming that a hypothetical factor (space-time) with a hypothetical value (the metric), is undergoing a hypothetical change (an unproven expansion). I think that is the scientific version of faith.
The big bang is a theory but not a certainty. There are other theories, all with different probabilities. Right now, the big bang may be the best fit according to our current scientific endeavours.
Quoting Devans99
The measurements are only within the near (reachable, by our facilities) perimeter of our cosmic environment. So, therefore, it is natural for there to be greater familiarity and proximity of a causal relation.
Quoting Devans99
Just a big bang. They have discovered a lot of those and there's no guarantee that the one they reference as 'the big bang' is the first and only one of its kind. It is possible that with the hypothetical of a multiverse, there is potential for multiple big bangs for each universe.
That sort of leads to a pet theory of mine: if big bangs were naturally occurring and time was infinite then there would be (with infinite time) infinite big bangs at each point in space leading to infinite matter density. So either the Big Bang was an unnatural singleton or time has a start.
I must admit I do not get these multiverse theories - at least in the most popular one (Eternal Inflation) you have a thing that generates universes - it must be connected (in space) to each of the generated universes. Therefore it follows that all universes are connected to all universes. In what sense is that a multiverse if they are all connected?
Not necessarily. Even if there was infinite matter density, each part of the universe would only interact in relation to its environment. It does not mean that the potential for the whole universe would act in its absoluteness at every point. Also, there already have been multiple super and mega novas in this supposed universe since that hypothetical big-bang and matter still seems to be relatively well-organised.
Quoting Devans99
A while back and the same could be said of galaxies. Initially it was difficult to tell whether the stars observed all belonged to our galaxy or not. In time, with better facilities even cosmic space will be better perceived. However, personally, the theory that has fewer limitations tends to most approximate what reality has in store. So, for me, if there's one universe, there's bound to be others. And why not?
I'm not sure I follow, can you expand? I do not see how you can avoid infinite matter density with infinite time.
Quoting BrianW
I think we'd have evidence. With infinite time, there should have been born, at each point in the universe, an infinite number of universes. They should all be overlapping each other. That is far from the uniform expansion that astronomy reports. The Big Bang looks like a singleton.
What I'm trying to say is, the working of the universe as we have observed so far seems to be intelligently designed such that there are forces which maintain equilibrium. For example, after the super and mega novas (and even the big bang) there follows a considerable period of 'calming' sorta like regaining equilibrium. Therefore, it may be that even with infinite time and a continued occurrence of big bangs, the equilibrium may still be maintained. Perhaps that's what gravity is for, to ensure recovery to the state of stability for the system (universe) and all its components.
Periods of equilibrium or no, I don't see how the infinite density problem can be avoided.
Since time is infinite in this supposition, it means we have an infinite amount of time prior to this moment. So, how come we have not succumbed to the infinite density problem, and how many more infinities does it take for that to occur?
Also, by principle, whatever has a beginning, must have an end. So, I don't think there's anything like infinite density, else, density would be infinite like time (in this supposition).
so we're back to the initial argument where possibilities abound and there's nothing, as far as we know, that prevents the possibility of a multiverse or other big bangs.
If there is a multiverse then the start of time would be co-incidental with the start of the multiverse. The multiverse should also be finite.
Read this: One, two, many
That is your opinion. Imo, finite or Infinite is a description of time-relations with subjects/objects. Time itself is neither finite nor infinite, just a relation of transciency of the subjects/objects in question.
Quoting Devans99
We have evidence of numerous super/mega novas but we suspect the one which supposedly took place about 13 billion years ago was biggest and the birth of our cosmic neighbourhood which we, so far, choose to designate as our universe. We have not yet dismissed the probability or possibility of other big bangs like it.
space is flat No rotation as far as we can tell and therefore it is infinite. The universe is not expanding as its already infinite. So what's happening - its expanding locally there is another place way far away from here - unimaginably far where space is compressing. There is an infinite number of areas where as far as you can see is expanding and just as many where space is compressing. If the large scale structure goes on forever and there is a similar less defined larger structure and so on and so on out to infinity then the universe is not expanding - it is locally yet for all we can see it is an insignificant spec.
The knots in the large scale structure appear to be forming an endless cloud of something like quarks - sound familiar. I believe it to be doing the same on ever larger scales Less defined As you pull back.
If this happened then DArk matter is all the stuff that did not fall into the singularities that make up the particles of matter. Dark energy is the result of gravity since it cause space to compress and therefor must expand somewhere else.
A black hole sees time go by fast but the stuff outside sees it take forever. When the knots in the large scale structure form particles and cool as the matter around us did - If you were made out of that and looked back at the creation of the particles that made you - it would look like it happened in a bang yet looking up from here it looks like it will take billions if not trillions of years
I know for a fact I and many others here have walked him through this a dozen times before. It's never any different, and shocker, this thread follows that trend. Devan, define what current mathematicians mean by Infinity, lay out their argument for why they ended up accepting that definition, and then argue against that. If you cannot meet that basic task, a task I know I've done to you more than half a dozen times, you're not an honest participant in these constant infinity threads you make. You're an ideologue.