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RE: Actual Infinity in Reality?
February 14, 2018 at 9:32 pm
Hilbert's Hotel is not showing a contradiction. It *is* a paradox, in the sense that it shows how infinite sets differ from finite ones. But there is no specific contradiction you can point out.
And it is even OK to talk about infinite cardinal numbers. They just don't obey the same rules of arithmetic that finite numbers do (although they do obey some of them).
Saying that the infinity of all positive numbers is different than the infinity of even numbers is problematic. It's like saying the three for the set {1,2,3} is different than the three for the set {3,4,5}. Yes, sure, but so what? The sizes are the same in the Cantorian sense. In other senses, the sizes are different. And that is one thing that needs to be addressed when discussing infinite sets: there are many different notions of 'size' and they may disagree here. Proper subsets may be the 'same size' as the 'larger' set. In fact, that is one *definition* of what it means to be an infinite set!
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RE: Actual Infinity in Reality?
February 14, 2018 at 9:44 pm
(This post was last modified: February 14, 2018 at 9:57 pm by GrandizerII.)
(February 14, 2018 at 9:32 pm)polymath257 Wrote: Saying that the infinity of all positive numbers is different than the infinity of even numbers is problematic. It's like saying the three for the set {1,2,3} is different than the three for the set {3,4,5}. Yes, sure, but so what? The sizes are the same in the Cantorian sense.
The sizes are the same, but the elements are different. It may be a "so what?" for finite numbers, but it's very relevant to point out when trying to pinpoint what Christian apologists are missing with their Hilbert's Hotel argument.
Remember his inf - inf = 3 equation? Do we get this with 3 - 3? Or 4 - 4? Or any number - the same number?
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RE: Actual Infinity in Reality?
February 14, 2018 at 10:00 pm
I will say i find the poll poorly worded
Seek strength, not to be greater than my brother, but to fight my greatest enemy -- myself.
Inuit Proverb
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RE: Actual Infinity in Reality?
February 14, 2018 at 10:01 pm
(February 14, 2018 at 10:00 pm)Tizheruk Wrote: I will say i find the poll poorly worded
Yeah, no "fuck polls" option as well. Or "fuck Christian apologetics" 
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RE: Actual Infinity in Reality?
February 14, 2018 at 10:55 pm
The term actual infinity is contradictory.
Quote:The mathematical meaning of the term "actual" in actual infinity is synonymous with definite, completed, extended or existential, but not to be mistaken for physically existing. [ wiki ]
Infinite of course refers to limitless or endless. It cannot be ended, or completed. It cannot be contained or actualized in it's entirety or limited. Therefore when you put the two together, it is a contradiction.
Quote:Infinity turns out to be the opposite of what people say it is. It is not 'that which has nothing beyond itself' that is infinite, but 'that which always has something beyond itself'. (Aristotle)
Infinity means that there is no limit, that there is always something more. You cannot bind it and say "here is infinity" at any given point. You will have a potential infinity, which may be increased.
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. - Alexander Vilenkin
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther
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RE: Actual Infinity in Reality?
February 14, 2018 at 11:08 pm
(February 14, 2018 at 10:55 pm)RoadRunner79 Wrote: The term actual infinity is contradictory.
Quote:The mathematical meaning of the term "actual" in actual infinity is synonymous with definite, completed, extended or existential, but not to be mistaken for physically existing. [ wiki ]
Infinite of course refers to limitless or endless. It cannot be ended, or completed. It cannot be contained or actualized in it's entirety or limited. Therefore when you put the two together, it is a contradiction.
Quote:Infinity turns out to be the opposite of what people say it is. It is not 'that which has nothing beyond itself' that is infinite, but 'that which always has something beyond itself'. (Aristotle)
Infinity means that there is no limit, that there is always something more. You cannot bind it and say "here is infinity" at any given point. You will have a potential infinity, which may be increased.
Wiki articles tend to be a confusing mess, and it's not always clear who is saying what, and in response to what, and in what context.
Yes, mathematical infinity doesn't automatically translate to physical infinity but, short of evidence to the contrary, it does mean that it is at least possible in the actual world. If there are logical constraints in the physical world that would prevent an actual infinity from being a thing, what are they then? Point them out if you have any.
Why can't a physical infinity have ALL the elements present already? Maybe your problem is that you're focusing on the "ends" too much and thinking about how you are able to get there? How about thinking the elements are all there, but as for whether or not I can go through them one by one is another story?
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RE: Actual Infinity in Reality?
February 14, 2018 at 11:14 pm
(February 14, 2018 at 8:36 pm)pocaracas Wrote: Is there Universe beyond the observable Universe? Cosmologists typically say that there doesn't seem to be.
Which cosmologists are those?
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RE: Actual Infinity in Reality?
February 14, 2018 at 11:14 pm
(February 14, 2018 at 11:08 pm)Grandizer Wrote: (February 14, 2018 at 10:55 pm)RoadRunner79 Wrote: The term actual infinity is contradictory.
Infinite of course refers to limitless or endless. It cannot be ended, or completed. It cannot be contained or actualized in it's entirety or limited. Therefore when you put the two together, it is a contradiction.
Infinity means that there is no limit, that there is always something more. You cannot bind it and say "here is infinity" at any given point. You will have a potential infinity, which may be increased.
Wiki articles tend to be a confusing mess, and it's not always clear who is saying what, and in response to what, and in what context.
Yes, mathematical infinity doesn't automatically translate to physical infinity but, short of evidence to the contrary, it does mean that it is at least possible in the actual world. If there are logical constraints in the physical world that would prevent an actual infinity from being a thing, what are they then? Point them out if you have any.
Why can't a physical infinity have ALL the elements present already? Maybe your problem is that you're focusing on the "ends" too much and thinking about how you are able to get there? How about thinking the elements are all there, but as for whether or not I can go through them one by one is another story?
You don’t see a problem in having all the elements present, and it being infinite. If the are all there, then they are limited and thus finite. You still have a contradiction.
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. - Alexander Vilenkin
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther
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RE: Actual Infinity in Reality?
February 14, 2018 at 11:15 pm
(February 14, 2018 at 9:18 pm)polymath257 Wrote: Yes, of course, it is *logically* possible. There is no internal contradiction to the concept of an actual infinity.
Now, I don't know if you consider time to be abstract or concrete, but there is certainly no internal contradiction to the concept of an infinite time.
There is also no contradiction in the possibility of an infinite number of stars in our universe if the universe is infinite in spatial extent.
My naive intuitions balk more at the idea of a first moment than at the idea that there will always be another moment before any moment you choose. To insist that there was once a brand spanking new, first ever moment before which there was no before .. certainly requires a lot of support.
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RE: Actual Infinity in Reality?
February 14, 2018 at 11:16 pm
(This post was last modified: February 14, 2018 at 11:17 pm by GrandizerII.)
(February 14, 2018 at 11:14 pm)RoadRunner79 Wrote: (February 14, 2018 at 11:08 pm)Grandizer Wrote: Wiki articles tend to be a confusing mess, and it's not always clear who is saying what, and in response to what, and in what context.
Yes, mathematical infinity doesn't automatically translate to physical infinity but, short of evidence to the contrary, it does mean that it is at least possible in the actual world. If there are logical constraints in the physical world that would prevent an actual infinity from being a thing, what are they then? Point them out if you have any.
Why can't a physical infinity have ALL the elements present already? Maybe your problem is that you're focusing on the "ends" too much and thinking about how you are able to get there? How about thinking the elements are all there, but as for whether or not I can go through them one by one is another story?
You don’t see a problem in having all the elements present, and it being infinite. If the are all there, then they are limited and thus finite. You still have a contradiction.
They are all there, but there is an infinite number of them. That's what makes it an infinity.
I'm not arguing that it's intuitive, btw. Just saying that there is no logical problem with it.
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