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> The proposition that infinity is "real" As far as I can tell, numbers aren't real either. "Twelve" isn't a thing that exists in itself in the physical univer

> The proposition that infinity is "real" As far as I can tell, numbers aren't real either. "Twelve" isn't a thing that exists in itself in the physical universe, it's an abstraction over some features of reality. "Infinity" is another abstraction, but it's not the same kind of abstraction as "Twelve". It's a further step. All mathematics is abstractions, layered on each other. See also "God created the integers, all else is the work of man"

marcus_holmes 5mo ago
Agreed, but I can say "there are 102 keys on this keyboard" or "there is 105ml of coffee in this cup" and that meaningfully describes reality to some extent. "there are infinite stars" does not meaningfully describe reality. For a number of reasons, not least of which would be how we would verify that - we cannot count the stars if they are infinite because we would need an infinite amount of time to do it. We can't shortcut this process, either, any method of counting stars that allowed us to count more stars more quickly would still run into the problem that it would take infinite time to count them. We can never know if something "real" is actually infinite, or if it's just very large. But disallowing infinities from our concept of the universe does do cool things; we no longer get the endless "in an infinite universe, everything possible must happen an infinite number of times, so therefore <this ridiculous thing> must be happening" arguments. The universe is not infinite, or if it is infinite we cannot measure that or confirm it, so <ridiculous thing> isn't happening unless probability says it will happen in a merely very large universe.
- SideburnsOfDoom 5mo ago
  > but I can say "there are 102 keys on this keyboard" You can, but are there? Is the space bar grouped with them? You can decide either way, and either choice is defensible, so the count is dependant on our human categories. Each key is unique, with the printed letter and with the precise arrangement of atoms differing. None of them are interchangeable. So you could decide that each key is in their own category. Or you could throw them in a bag with some dice and pebbles too and count the objects. Numbers are regarded as interchangeable, one "102" is the same as any other "102". Physical objects are not. That's what I mean by saying that counting is an abstraction, and a number isn't a thing that exists in itself in the physical universe - it only occurs not "in itself", but once we can subjectively group things. There are "twelve keys" if you decide to group them as the same thing though they're actually not really. There's no physically existent "twelve". I fully agree that "infinity" is a different kind of concept, less physically relatable even than "102". It's a further abstraction.

marcus_holmes 5mo ago

Agreed, but I can say "there are 102 keys on this keyboard" or "there is 105ml of coffee in this cup" and that meaningfully describes reality to some extent. "there are infinite stars" does not meaningfully describe reality. For a number of reasons, not least of which would be how we would verify that - we cannot count the stars if they are infinite because we would need an infinite amount of time to do it. We can't shortcut this process, either, any method of counting stars that allowed us to count more stars more quickly would still run into the problem that it would take infinite time to count them. We can never know if something "real" is actually infinite, or if it's just very large. But disallowing infinities from our concept of the universe does do cool things; we no longer get the endless "in an infinite universe, everything possible must happen an infinite number of times, so therefore <this ridiculous thing> must be happening" arguments. The universe is not infinite, or if it is infinite we cannot measure that or confirm it, so <ridiculous thing> isn't happening unless probability says it will happen in a merely very large universe.

SideburnsOfDoom 5mo ago
> but I can say "there are 102 keys on this keyboard" You can, but are there? Is the space bar grouped with them? You can decide either way, and either choice is defensible, so the count is dependant on our human categories. Each key is unique, with the printed letter and with the precise arrangement of atoms differing. None of them are interchangeable. So you could decide that each key is in their own category. Or you could throw them in a bag with some dice and pebbles too and count the objects. Numbers are regarded as interchangeable, one "102" is the same as any other "102". Physical objects are not. That's what I mean by saying that counting is an abstraction, and a number isn't a thing that exists in itself in the physical universe - it only occurs not "in itself", but once we can subjectively group things. There are "twelve keys" if you decide to group them as the same thing though they're actually not really. There's no physically existent "twelve". I fully agree that "infinity" is a different kind of concept, less physically relatable even than "102". It's a further abstraction.