RE: Thinking about infinity
April 27, 2016 at 10:43 am
(This post was last modified: April 27, 2016 at 10:54 am by Ignorant.)
(April 27, 2016 at 7:49 am)Alex K Wrote: What does it actually mean for the set of natural numbers to exist? It's not like all these numbers are somehow represented explicitly by anything in the universe. What we have is the notion of taking another step to the next one, and a notion of that being always possible. Does the existence of these ideas already warrant the statement that "the natural numbers exist in the universe"?
I certainly agree that, for our conceptualization of any such infinite set of numbers, we MUST rely on a notional reality of infinity as any number's potential addition by 1. I said it "seems to exist", for that very reason. It seems logically possible that it exists (in whatever way a number might exist in the abstract). Does such an infinite set, in fact, exist? I don't know. I certainly couldn't "point to" it. But logically, it seems possible.
(April 27, 2016 at 8:04 am)Whateverist the White Wrote: So better to say "the natural numbers exist in potential"?...
I mean you could get to any of them with enough time, just take another step. <=
I think this is the classical definition of "potential infinity" going back to at least Aristotle, but I've been wrong before.
(April 27, 2016 at 8:52 am)robvalue Wrote: ... Something exists if it can be uniquely identified as a subsection of our (assumed) objective reality.
Thoughts?...
That seems ok to me for now for the sake of this discussion.
(April 27, 2016 at 8:52 am)robvalue Wrote: For things like numbers, I would say they only exist abstractly; minds are able to have images that represent the concept. They are a step removed from reality. They can represent arbitrary groups of things in reality, but they do not themselves uniquely identify something in reality. You can of course have abstract concepts that do identify something existent. We could also have abstract concepts that represent qualities of existent things, such as length.
Things can theoretically be dissected into infinitely parts. We can model them mathematically, and slice them up as we wish. Can they in practice? That depends on the nature of reality. Maybe, maybe not. If there is some "smallest measurement" actually possible in reality, then such a thing wouldn't work.
I see no logical problem with an infinite past...
Great. Infinite time: yes. Infinite-divisibility: maybe. Infinity of numbers: only in concept, not as real "things". Sound like I've got it?
(April 27, 2016 at 9:37 am)vorlon13 Wrote: Line are defined as a string of points, and any 2 points are defined as being separable by another point between, so the infinities associated with lines are there because humans decreed it.
So, do you think the infinity associated with a finite line-segment is something other than an infinity existing as a finite thing?
(April 27, 2016 at 9:41 am)SteveII Wrote: My understanding is that infinities are useful fictions in math equations. When used in physics, they are always converted back to finite quantities (unless you are Hawkings and then you don't).
So actual infinities do not exist in reality? Do you think it is even possible for an infinite set of things to exist as a single thing?
