I'm not claiming that the are a finite moments in time, and I don't personally think this is true - you asked me to assume this as true as part of the point of this thread.
I was trying to work within your request.
I don't think it's possible for me to continue in the thread until there's some clarification of what you're trying to achieve here.
I'm sorry, but we seem to be failing very badly to communicate. You never claimed that there is a finite number of moments in time. I never said that you did. But some of your post seem to imply that it is—in principle—possible to have a finite number of moments in a spacetime which is not discrete and bounded, and that is what confused me.
What I'm trying to achieve is basically this:
I have heard the Kalām argument a couple of times. It always consists of starting from premise #1 and trying to demonstrate that therefore, time cannot stretch infinitely far
back, because that is generally the only thing the person using the argument is interested in—showing that there had to be a moment of creation.
I've never heard anyone ask what other effects #1 would have if it were true. For example, it seems equally reasonable to say that it implies that time cannot stretch infinitely forward, which actually does make a sort of prediction about the universe (it will not expand forever, for example). What I want to achieve with this thread is to see which actual predictions can be made about the universe, assuming #1 is true. There is no real reason for doing this, beyond curiosity.
I'm not the only one. The previous poster reflects my thoughts: finite contents does not make a finite container.
Again: I think you'll have to clarify what assumptions we're supposed to make, because I was under the impression that the question was about consequences of assuming that the universe is finite, not ask if it may or may not be finite.
It seems more like you're asking us to back off of that, and are you asking if the universe is finite or not? Are you also maybe asking if spacetime may be discreetly segmented or granular instead of continuous?
This sounds like you actually are interested in evaluating the merits of Premise #1. To address that last question: the universe could be discreet but still infinite.
I'm asking if the universe being finite and discrete necessarily follows from #1. In post #31 I tried to explain that I think both of them necessarily follow because, as you said, an infinite discrete space is still infinite, albeit countably.
I suppose you could see this as a way of evaluating #1, but what I'm doing is just trying to make predictions based on #1 and—if possible, which I admit does not seem to be very often—checking them off against reality.
Hm... We seem to be meaning slightly different things when saying that space is "infinite". I'd consider any space with finite volume to be finite—I'm not saying that it has to have any borders or anything.
This is actually
is related to Kalam's argument in that he misunderstood (or had never heard of) cardinality. (a philosopher making math arguments when he probably hasn't taken a math course since grade 9)
Consider these two exercises:
- The impact of finite sets on the dimension.
Consider the set of integers between 0 and 2 ({1}) - this is a finite set. Why would anybody believe that this implies or proves that the numbering system must end somewhere before it reaches infinity? I think a more rigid proof is required to endorse this claim.
- The impact of cardinality on the dimension.
The set of digits is not continuous on the number line. It is completely discretized. Why would this imply that they are finite, or that the numbering system cannot extend infinitely?
This was Kalam's argument, basically: "I don't understand infinity, so it can't be a real thing."
(or rephrased: "I have assumed the concept of infinity is false, and thus proven that the universe is not infinitely large." - a circular argument)
Who knows? This is a philosophical exercise in metaphysics, not an investigation about physics.
Yes. A discussion of whether #1 is actually a reasonable premise is philosophical, which is why I've tried to avoid it.
The confusing part about this, though, is that the universe is regarded as pretty much bounded in spacetime anyway, so the 'consequences' of this being true are: 'see all current scientific theories.'
True. But #1 would, for example, (once again, assuming I'm correct that #1 in turn implies that space is closed) imply that the universe does not have a hyperbolic geometry. This is not much of a prediction, since we were pretty sure of that already, I admit.
ps.
Kalām isn't a person.
