Define Infinity - and is anything infinite?: Philosophy Forums

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Define Infinity - and is anything infinite?

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Define Infinity - and is anything infinite?

Mr. J
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Posted 06/22/09 - 01:42 PM:	#51
I just read through this thread and I think Cantors definition of infinity is a good definition. As to whether infinity is substantiated is an interesting question. My understanding is that Cantor did not believe that infinity existed substantially as in an infinite amount of cubic meters. However; my understanding of the Universe is that if it is flat or negatively curved it is infinite, and to our best measurement it is indeed flat or negatively curved. My understanding is that this would mean that the universe is countably infinite in that it would be infinite in spatial extent. In other words it would contain a countably infinite amount of cubic meters. This is still true even if it is bounded in time. It might not be temporally infinite but it can still spatially infinite So, here we have an example of a physical instance of a countable infinity. If the quantum multiverse hypothesis is true I think the states in this multiverse are in one to one correspondence to the physically infinite universe so it would also be countably infinite in fact it would not add anything to a physically infinite universe. If the inflationary multiverse hypothesis is true I think it actually might be an uncountable infinity. That leaves Cantor’s Absolute Infinity but I have no idea what that is.

oag
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Posted 06/22/09 - 01:59 PM:	#52
I find countable infinity an oxymoron. I also disagree that the universe can be finite temporally and infinite spatially as I find it a time/space continuum. Perhaps if I were a mathematician I could express it with all sorts of wild formulas but I think Einstein probably already did that by demonstrating relativity. The long and short of it is that time loses meaning in the face of infinite space and vice versa because the word infinite doesn't actually contain practical meaning. It means going on forever but we can never point to anything that does that.

Mr. J
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Posted 06/22/09 - 02:43 PM:	#53
Well I did not invent anything, I am only using Cantor’s definition of infinity and the meaning of countably infinite is infinite like the integers (e.g. 1,2,3,4,5….) in order to distinguish it from a different sort of infinity such as what is called the uncountable infinity given by the example of all the real numbers. I am using Einstein space to prove an actual infinity in that if the universe has a flat or negative curvature it is infinite in spatial extent. Even if you consider space-time a continuum you can have some dimensions being bound and others being infinite. For example the positive coordinates of a Cartesian plain are infinite and unbounded in two sides and bounded by the x and y axis on two sides. In a similar way you can have the time dimension bounded and the space dimension unbounded. But actually I just wanted to make a sort of minimal claim about the space dimensions leaving out whether or not the time dimensions are bounded.

oag
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Posted 06/22/09 - 04:06 PM:	#54
I do get that you mean unbounded, without end, having no discernible stopping point. I honestly get that. My point is that it is nonsense in any real and practical sense. You can give me a mathematical abstract that represents this but I don't need that. All I need is the word infinite. I know what that means and I understand the abstract concept that it represents. My only point is that it is not something that can ever be confirmed. You can never say that something is infinite and actually verify that it is. It is never more than a statement of faith. The only reason it concerns me is that when people use the words infinite, objective or perfect they have gone out of the realm of human experience and into the abstract. We can go there for a day trip to stretch our minds but we cannot use those concepts in a real and meaningful way back in the real world. Humans can never have anything infinite, perfect or objective to point to. Those things reside always and forever as wistful ideals in our minds.

Mr. J
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Posted 06/23/09 - 07:49 AM:	#55
I re-read your posts and what I gather you are saying is that humans can never experience infinity. I think that is true but we can still use the concept. Also shouldn’t the universe be infinite or not infinite independent of our ability to measure it? There are probably lots of things that are true that we will never measure. I overstated my own case as well. The measurement of the curvature of the universe does not prove that the universe is infinite, it seems to be a likely possibility but we can not prove it. It is my understanding that the measurement has a 2% margin of error. http://map.gsfc.nasa.gov/universe/uni_shape.html It is true we can’t prove anything in science, every measurement has an error. It’s just at a certain point you say this is our best understanding. I think we can say to the best of our understanding the universe is infinite.

Jehu
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Posted 06/23/09 - 05:49 PM:	#56
I overstated my own case as well. The measurement of the curvature of the universe does not prove that the universe is infinite, it seems to be a likely possibility but we can not prove it. It is my understanding that the measurement has a 2% margin of error. The term “Universe” entails everything that exists, and for this reason, it is necessarily unbounded, for there can be (exist) nothing beyond it. In other words, there is no greater universe of discourse than is that which is called “being” (existence), for there is only “what is”, and naught else. Further, the Universe is necessarily complete, that is to say, it must already contain that which is necessary and sufficient to its being, and so we cannot say that it incomplete (infinite). When we speak of an “infinite set”, for example, we are speaking of an “incomplete set”, in that all such sets are lacking a final element. However, even an infinite set is bounded, for like all sets, it is defined either by its elements, which are, in this case, necessarily incomplete, or by some specified criterion, i.e., having no final element. Consequently, such sets are necessarily bounded, by all those sets which do not conform to that criterion.
It is not that which the eye can see, but that whereby the eye is able to see, that is the true reality.

oag
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Posted 06/23/09 - 10:17 PM:	#57
Mr. J wrote: I re-read your posts and what I gather you are saying is that humans can never experience infinity. I think that is true but we can still use the concept. Then we must agree to disagree. I don't find the concept useful. To me it has the same value as nothing because it is everything. We can never have absolutely nothing in any practical sense because we are still there making the observation. We can never have everything because we cannot possibly observe or confirm that we indeed have it. Also shouldn’t the universe be infinite or not infinite independent of our ability to measure it? Those are the only two options but without the ability to measure it we can never know which one. There are probably lots of things that are true that we will never measure. We never have the means with which to measure absolute truth so your statement could be modified that there are no things or all things... As for whether the universe if infinite or not I suggest we apply Occam's Razor rather than an abstract mathematical formula. Since there is absolutely nothing in human experience or observation that is infinite why does it make sense to declare any one thing to be infinite? It is true we can’t prove anything in science, every measurement has an error. It’s just at a certain point you say this is our best understanding. I think we can say to the best of our understanding the universe is infinite. My contention is not that we can't say that but that saying it has no meaning. We might as well say that to the best of our understanding the universe is perfect.

ssu
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Posted 06/26/09 - 12:25 AM:	#58
oag, I think that everyone agrees that infinity is an abstract concept (if we can agree upon what an abstract concept is). There is no way to confirm or verify it...as something concrete. But as an mathematical object infinity is important. Many times when this subject, infinity, is discussed some people tend to handle it from the view of physics or physical reality...as if there lies the understanding of the abstract concept. This is not a question of whether the universe/multiverse (or whatever) is or isn't infinite. I simply do not understand this logic. Is 3 or 46 then real? Then how real is perhaps a centillion or 53 googolplex? Absurd to say that "wait a minute! This number doesn't fit into the universe!" But some times I see this kind of reasoning (especially with small numbers and Planck length). Why would we base our notions of real numbers, imaginary numbers or hyperreals on some findings on what astronomy and physics? Now another and quite interesting way to look at this is the usefulness of the abstract concepts. Sure we have use for real numbers, even imaginary numbers. But do all mathematical concepts have use in the natural sciences? For instance, the bigger infinities (that Cantor observed), HAVE NOT HAD much use in physics (to my knowledge). That tells something. The only way to look at the problem of existence is to look at the underlying mathematical logic. And really if you think of it: if we have not been able (and perhaps are not able) to answer the continuum hypothesis, we really REALLY don't understand this "Cantorian paradise".

oag
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Posted 06/26/09 - 05:34 AM:	#59
ssu wrote: oag, I think that everyone agrees that infinity is an abstract concept (if we can agree upon what an abstract concept is). There is no way to confirm or verify it...as something concrete. But as an mathematical object infinity is important. While I agree with the sentiment I have to object to the wording. Infinity cannot be an object. The concept of infinity is used in mathematics. I understand this. I even understand how and why it is important. I'm not saying that abstractions are utterly useless conceptions because humans have need of ideals. I'm just saying that they have no real and practical applications and that one cannot use them in any description of the universe. By way of answering the OP or thread title, nothing is infinite.

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