Physical implications of Kalām argument

[Dorfl]

This thread (http://forums.randi.org/showthread.php?t=150286) more or less instantly got derailed into a discussion of the Kalām cosmological argument. The argument—as I understand it—goes basically:

1. No infinite set (http://en.wikipedia.org/wiki/Actual_infinite) can exist in the physical world.

2. Therefore, the universe cannot have existed forever.

3. Therefore, the universe must have begun at some point.

4. (A bunch of additional steps to show why this implies the existence of the arguers favourite creator god. Not very relevant to the science subforum.)

Whether the argument is sound or not is already being discussed in the other thread. What I wonder about is the physical implications that the premise #1 would have, if it were true. For example, it seems to imply that the universe is finite in both space and time—requiring a big crunch—and that space and time are both quantized.

Are there any other implications that #1 would have, and are they correct, as far as we know?

[Mashuna]

This thread (http://forums.randi.org/showthread.php?t=150286) more or less instantly got derailed into a discussion of the Kalām cosmological argument. The argument—as I understand it—goes basically:

1. No infinite set (http://en.wikipedia.org/wiki/Actual_infinite) can exist in the physical world.

2. Therefore, the universe cannot have existed forever.

3. Therefore, the universe must have begun at some point.

4. (A bunch of additional steps to show why this implies the existence of the arguers favourite creator god. Not very relevant to the science subforum.)

Whether the argument is sound or not is already being discussed in the other thread. What I wonder about is the physical implications that the premise #1 would have, if it were true. For example, it seems to imply that the universe is finite in both space and time—requiring a big crunch—and that space and time are both quantized.

Are there any other implications that #1 would have, and are they correct, as far as we know?

Could you elaborate on why the universe being finite in space and time would require a big crunch?

[Dorfl]

Could you elaborate on why the universe being finite in space and time would require a big crunch?

At least, the universe would need to end somehow. Not necessarily through a Big Crunch, I admit, but time would need to be bounded in some way.

[Mashuna]

At least, the universe would need to end somehow. Not necessarily through a Big Crunch, I admit, but time would need to be bounded in some way.

As long as it's bound at the start (by the Big Bang), I don't understand why you'd need to have a defined end point. It's not like you can get to infinity by counting.

[Dorfl]

As long as it's bound at the start (by the Big Bang), I don't understand why you'd need to have a defined end point. It's not like you can get to infinity by counting.
I might be wrong, but it seems to me that even if I will obviously never reach t=∞, spacetime would still contain an infinite number of events, which would contradict #1.

[Mashuna]

I might be wrong, but it seems to me that even if I will obviously never reach t=∞, spacetime would still contain an infinite number of events, which would contradict #1.

I'm not sure either. I'm off to start counting events - I'll let you know how I get on.

<sets off to start his supertasks>

[Guybrush Threepwood]

I might be wrong, but it seems to me that even if I will obviously never reach t=∞, spacetime would still contain an infinite number of events, which would contradict #1.

I would have thought not, since at any point t=reallyreallyreallybig, you just wait for 1s and click your fingers, that's another event, so at t=reallyreallyreallybig there hadn't been an infinite number of events.

[Dorfl]

I'm not sure either. I'm off to start counting events - I'll let you know how I get on.

<sets off to start his supertasks>

Ask Chuck Norris to do it instead. ;)

[Dorfl]

I would have thought not, since at any point t=reallyreallyreallybig, you just wait for 1s and click your fingers, that's another event, so at t=reallyreallyreallybig there hadn't been an infinite number of events.

Well, yes. But in any infinite countable set, any particular member is member #(A finite number). That doesn't mean the set is not infinite.

Note however that I have not formally studied set theory yet, so I may be talking out of my donkey.

[Mashuna]

Ask Chuck Norris to do it instead. ;)

I only got as far as three hundred and forty six, then I got into trouble for doing my supertasks before I'd finished my normal tasks. :(

I reckon I was almost half-way through, so I estimate that there are no more than a thousand events in all of spacetime.





I've always been good at estimating.

[Dancing David]

At least, the universe would need to end somehow. Not necessarily through a Big Crunch, I admit, but time would need to be bounded in some way.


I don't know. The universe is not required to meet our expectations and thought constructs.

[Dancing David]

I would have thought not, since at any point t=reallyreallyreallybig, you just wait for 1s and click your fingers, that's another event, so at t=reallyreallyreallybig there hadn't been an infinite number of events.

Well in discussions of the Big Bang, the people who understand it talk about infinitity being spread in the 'smaller space' of the early universe. My eyes glaze over, but it would appear that the universe could be infinite.

[drkitten]

Whether the argument is sound or not is already being discussed in the other thread. What I wonder about is the physical implications that the premise #1 would have, if it were true. For example, it seems to imply that the universe is finite in both space and time—requiring a big crunch—and that space and time are both quantized.

Are there any other implications that #1 would have, and are they correct, as far as we know?

Well, as far as I know, #1 is a load of horse-pucky from beginning to end.

But in particular, I want to know what he thinks it means for a "set" to "exist in the physical universe." A set is an abstract concept, and we can easily have sets of other abstract concepts such as numbers. If he's suggesting that, for example, the set of all prime numbers isn't exist,.... well, put down that crack pipe, back away slowly, and no one gets hurt.

Having said this, there are a lot of apparently physical things that are also abstract. "The set of all places a penguin could be," for example.

So, no. I don't see #1 as demanding finiteness in either time or space. Our measuring system is not a part of the physical universe any more than our counting system is.

[ddt]

Well, as far as I know, #1 is a load of horse-pucky from beginning to end.

But in particular, I want to know what he thinks it means for a "set" to "exist in the physical universe." A set is an abstract concept, and we can easily have sets of other abstract concepts such as numbers. If he's suggesting that, for example, the set of all prime numbers isn't exist,.... well, put down that crack pipe, back away slowly, and no one gets hurt.

Having said this, there are a lot of apparently physical things that are also abstract. "The set of all places a penguin could be," for example.
Someone called? :)

So then, following your argument, there's a potentially infinite amount of places a penguin can be. But can there be actually an infinite amount of penguins? That is what the discussion of an "actual infinite" amounts to, as far as I understand.


So, no. I don't see #1 as demanding finiteness in either time or space. Our measuring system is not a part of the physical universe any more than our counting system is.

The wiki page on the Kalam cosmological argument (http://en.wikipedia.org/wiki/Kalam_cosmological_argument) mentions also that the following premise is needed:
A beginningless series of events is an actual infinite.
And from that, at least, I infer that time then should be quantized. The series of events:
the earth moves at t = 1 + 1/n
is an actually infinite series which is beginningless.

[blutoski]

It seems like circular reasoning. Premise #1 is a claim, rather than a fact.

ie: "I don't believe the universe is infinite, because I don't believe real things can be infinite."

It's internally consistent, but it's not based on any externally verifiable facts. It's just the same claim reworded twice.

[drkitten]

So then, following your argument, there's a potentially infinite amount of places a penguin can be. But can there be actually an infinite amount of penguins? That is what the discussion of an "actual infinite" amounts to, as far as I understand.

Exactly. We might be able to agree that in principle there could only be a finite number of physical penguins, but an infinite number of potential or imaginary penguins, because our imagination is not physical.



The wiki page on the Kalam cosmological argument (http://en.wikipedia.org/wiki/Kalam_cosmological_argument) mentions also that the following premise is needed:

And from that, at least, I infer that time then should be quantized. The series of events:
the earth moves at t = 1 + 1/n
is an actually infinite series which is beginningless.

That's just Zeno's paradox, and any of the standard resolutions apply.

[Dorfl]

I don't know. The universe is not required to meet our expectations and thought constructs.

Definitely not. My point is that #1 requires time to be bounded, implying an end to time. Not that anything #1 requires is actually the case.

[Dorfl]

It seems like circular reasoning. Premise #1 is a claim, rather than a fact.

ie: "I don't believe the universe is infinite, because I don't believe real things can be infinite."

It's internally consistent, but it's not based on any externally verifiable facts. It's just the same claim reworded twice.

Last I checked, this thread (http://forums.randi.org/showthread.php?t=150286) was at 18 pages and still discussing whether #1 is well-founded or not. What I was curious about is just the physical implications it would have, if it were true.

[Yoink]

Wow. If that Wikipedia page on the Kalam cosmological argument represents the argument accurately it's so trivial as not to be worthy of serious discussion.

Essentially it amounts to "it makes my brain hurt to think about infinitude, therefore the universe must have a beginning and I'm going to call that God." Like every other philosophical "proof" of God, an averagely intelligent eight year old could demonstrate its shortcomings.

Philosophical arguments for the existence of God prove only one thing: the horrible effect religious belief has on people's ability to reason. Otherwise intelligent, even brilliant, people will suddenly become obstinately fixated on the most puerile and pathetic arguments simply because they support their religious prejudices. Sad.

[Dorfl]

I only got as far as three hundred and forty six, then I got into trouble for doing my supertasks before I'd finished my normal tasks. :(

I reckon I was almost half-way through, so I estimate that there are no more than a thousand events in all of spacetime.

I've always been good at estimating.

I was going to build a robot to count the first hundred events, after itself building another robot which could count the next hundred twice as fast, after building a robot in half the time that counted four times as fast...

But I'll accept your estimate. It sounds reasonable.

[Dave Rogers]

Now here's a thought. Suppose that there is no end as such to the Universe, but that the quantum of time is able to increase in size without limit. Is it even logically possible to conceive of a situation in which an infinite time span could nonetheless contain only a finite number of time quanta? If there is such a thing as a supertask, in which an infinite series of operations is completed in a finite length of time, could there be such a thing as a subtask, in which a finite series of operations could not be completed in an infinite length of time?

I think there may be one or two rather insurmountable problems with that, but it's the only way I can see of having a finite universe with unbounded time unless time is cyclical.

Dave

[stup_id]

Regarding the first axiom?, it is something I've had in my mind for quite sometime, I mean, existing a range of I think 10^80 atoms in the Universe that is more or less the upper limit of things that can exist of at least one atom, from there if you want to add subparticles... well maybe the number already includes it.. not sure.. the point being, there's a finite (but mind-boggling giant) number of things (at least of matter ) in the universe, maybe if you take probabilities into account.. that sort of thing can be infinite... but dunno.. sounds like cheating to me... can someone give an examplo of something physical and infinite in the Universe?

[Dancing David]

Definitely not. My point is that #1 requires time to be bounded, implying an end to time. Not that anything #1 requires is actually the case.

Fair 'nuff

[Dancing David]

Regarding the first axiom?, it is something I've had in my mind for quite sometime, I mean, existing a range of I think 10^80 atoms in the Universe that is more or less the upper limit of things that can exist of at least one atom, from there if you want to add subparticles... well maybe the number already includes it.. not sure.. the point being, there's a finite (but mind-boggling giant) number of things (at least of matter ) in the universe, maybe if you take probabilities into account.. that sort of thing can be infinite... but dunno.. sounds like cheating to me... can someone give an examplo of something physical and infinite in the Universe?


That is not likely to be the number of partciles in the universe, just the observable universe?

[Dorfl]

Now here's a thought. Suppose that there is no end as such to the Universe, but that the quantum of time is able to increase in size without limit. Is it even logically possible to conceive of a situation in which an infinite time span could nonetheless contain only a finite number of time quanta? If there is such a thing as a supertask, in which an infinite series of operations is completed in a finite length of time, could there be such a thing as a subtask, in which a finite series of operations could not be completed in an infinite length of time?

I think there may be one or two rather insurmountable problems with that, but it's the only way I can see of having a finite universe with unbounded time unless time is cyclical.

It's a cool idea, but I'm not really sure what it would mean for a quantum of time to "increase in size". Aren't quanta of time what time is measured in, in the first place? Seems like the effect would be indistinguishable from time just stopping at one moment, Thief of Time-style.

[blutoski]

Last I checked, this thread (http://forums.randi.org/showthread.php?t=150286) was at 18 pages and still discussing whether #1 is well-founded or not. What I was curious about is just the physical implications it would have, if it were true.

Regardless, the argument as stated in the original post is still question-begging from what I can see: its conclusion is one of its premises re-worded.

I'm not sure why a philosophy question would be in the science section, instead of the philosophy section.

There is an entire segment of philosophy inquiring whether mathematical concepts are reified.

See Wikipedia: [Philosophy of mathematics (http://en.wikipedia.org/wiki/Philosophy_of_mathematics)]

Also: [Reification (fallacy) (http://en.wikipedia.org/wiki/Reification_(fallacy))]


It's hard to evaluate the quality of an argument that has imaginary premises. eg: "If my grandmother was a car, would she be a Datsun or a Chevy?"

[blutoski]

2. Therefore, the universe cannot have existed forever.

I think the weakness with this one is that they are treating time as a set of things, instead of what it is: a dimension. aka a direction. Like up, down, left, right, forward, backward, future, past.

Does 'right' end? Or could it go on forever? I can't see why not.

Even in a universe with finite objects, distance and time could extend without bound in all directions from any origin. Many coordinates in fourspace would have no events or objects.

[arthwollipot]

Regarding the first axiom?, it is something I've had in my mind for quite sometime, I mean, existing a range of I think 10^80 atoms in the Universe that is more or less the upper limit of things that can exist of at least one atom, from there if you want to add subparticles... well maybe the number already includes it.. not sure.. the point being, there's a finite (but mind-boggling giant) number of things (at least of matter ) in the universe, maybe if you take probabilities into account.. that sort of thing can be infinite... but dunno.. sounds like cheating to me... can someone give an examplo of something physical and infinite in the Universe?Prime numbers?

[Roboramma]

It's hard to evaluate the quality of an argument that has imaginary premises. eg: "If my grandmother was a car, would she be a Datsun or a Chevy?"

But the point of this thread isn't to evaluate the argument, its to look at the implications of one of its premises and see if they match the real world.

[Dorfl]

Regardless, the argument as stated in the original post is still question-begging from what I can see: its conclusion is one of its premises re-worded.

I'm not sure why a philosophy question would be in the science section, instead of the philosophy section.

There is an entire segment of philosophy inquiring whether mathematical concepts are reified.

See Wikipedia: [Philosophy of mathematics (http://en.wikipedia.org/wiki/Philosophy_of_mathematics)]

Also: [Reification (fallacy) (http://en.wikipedia.org/wiki/Reification_(fallacy))]

It's hard to evaluate the quality of an argument that has imaginary premises. eg: "If my grandmother was a car, would she be a Datsun or a Chevy?"
But I'm not asking a philosophical question. The entire point of the thread is what physical effects it would have if #1 were true. I don't give a rotten öre—I think this is called a "wooden nickel" in English—about the quality of the argument itself.

[Dorfl]

I think the weakness with this one is that they are treating time as a set of things, instead of what it is: a dimension. aka a direction. Like up, down, left, right, forward, backward, future, past.

Does 'right' end? Or could it go on forever? I can't see why not.

Even in a universe with finite objects, distance and time could extend without bound in all directions from any origin. Many coordinates in fourspace would have no events or objects.

I could be wrong but I was thinking of spacetime as a set of points. If it is, it would have to be quantized not to be uncountably infinite, and also bounded or closed in each direction, to avoid being infinite. That could be a naïve view of spacetime, though.

[sol invictus]

I could be wrong but I was thinking of spacetime as a set of points. If it is, it would have to be quantized not to be uncountably infinite, and also bounded or closed in each direction, to avoid being infinite. That could be a naïve view of spacetime, though.

That might be true, although neither current theory nor any experimental evidence support it. And even in a universe like that, one can still construct infinite sets: the set of all ordered sets of points, for example.

In physics it's a fact that sufficiently fine-grained discretization is impossible to distinguish from a continuum... although things like black holes create surprising opportunities.

[blutoski]

But I'm not asking a philosophical question. The entire point of the thread is what physical effects it would have if #1 were true. I don't give a rotten öre—I think this is called a "wooden nickel" in English—about the quality of the argument itself.

#1 "No infinite set can exist in the physical world." is true without question. There are no infinite sets in the physical world. It is also true that there are no finite sets in the physical world. This is because sets are a mathematical concept, rather than a physical thing. There are no 'odd numbers' in watermelons, and no LaGrange Multipliers in the colour red, no numerators in moon rocks, no prime numbers in my pants.

So having accepted that #1 is true, I move to #2: "Therefore, the universe cannot have existed forever." The truth of this premise can be evaluated, but it is not related to the truth or falsehood of #1 in any way.

Alternatively, if you're planning to connect #1 to #2, you are engaged in a philosophical argument about the reification of mathematical concepts. Ergo, the two links I provided on the history of this debate.



Now, it's possible that I misunderstood premise #1, and perhaps it could be rephrased such that it is not using mathematical vocabulary. Perhaps it's merely saying that the universe cannot be infinite. If so: this is the same claim as #2 and redundant, and we're still examining #2 on its own merit.

[blutoski]

I could be wrong but I was thinking of spacetime as a set of points.

It could be represented as such. But that doesn't mean it is a set of points.


If it is, it would have to be quantized not to be uncountably infinite, and also bounded or closed in each direction, to avoid being infinite.

Yes, it could be bounded to avoid being infinite. It could be unbounded to be infinite. I don't know how this answers a question about whether it is or is not actually infinite?

[blutoski]

But the point of this thread isn't to evaluate the argument, its to look at the implications of one of its premises and see if they match the real world.

Ah. So just one premise? Which premise are we evaluating? There's four there.

[Dorfl]

#1 "No infinite set can exist in the physical world." is true without question. There are no infinite sets in the physical world. It is also true that there are no finite sets in the physical world. This is because sets are a mathematical concept, rather than a physical thing. There are no 'odd numbers' in watermelons, and no LaGrange Multipliers in the colour red, no numerators in moon rocks, no prime numbers in my pants.

So having accepted that #1 is true, I move to #2: "Therefore, the universe cannot have existed forever." The truth of this premise can be evaluated, but it is not related to the truth or falsehood of #1 in any way.

Alternatively, if you're planning to connect #1 to #2, you are engaged in a philosophical argument about the reification of mathematical concepts. Ergo, the two links I provided on the history of this debate.


Now, it's possible that I misunderstood premise #1, and perhaps it could be rephrased such that it is not using mathematical vocabulary. Perhaps it's merely saying that the universe cannot be infinite. If so: this is the same claim as #2 and redundant, and we're still examining #2 on its own merit.

I may have stated #1 badly. Is it clearer if we restate it as "The universe cannot contain an infinite number of anything, whether elementary particles, points in spacetime or other objects", or does that make it too fuzzy?

[Dorfl]

That might be true, although neither current theory nor any experimental evidence support it. And even in a universe like that, one can still construct infinite sets: the set of all ordered sets of points, for example.
Now I'm beginning to wish I had studied set theory properly yet. Is there any short version of how that is done, or some link that explains it in more detail?


In physics it's a fact that sufficiently fine-grained discretization is impossible to distinguish from a continuum... although things like black holes create surprising opportunities.
That's annoyingly inconvenient... Is there no way that singularities could—even just in principle—be used to test if space is quantized on any level?

[Yoink]

Ah. So just one premise? Which premise are we evaluating? There's four there.

The first.

[blutoski]

The first.

I thought Dorfl asked us to assume that #1 was true. I thought that was the one we weren't supposed to evaluate.

I'm getting mixed instructions: are we to evaluate the argument in terms of premise #1 being accepted as true, or are we allowed to evaluate the merits of #1 as a premise (given Dorfl's rewording in the most recent post).

[Yoink]

I thought Dorfl asked us to assume that #1 was true. I thought that was the one we weren't supposed to evaluate.

I'm getting mixed instructions: are we to evaluate the argument in terms of premise #1 being accepted as true, or are we allowed to evaluate the merits of #1 as a premise (given Dorfl's rewording in the most recent post).

Just read the OP. Or, here, I'll cut and paste it for you:

What I wonder about is the physical implications that the premise #1 would have, if it were true. For example, it seems to imply that the universe is finite in both space and time—requiring a big crunch—and that space and time are both quantized.

Are there any other implications that #1 would have, and are they correct, as far as we know?

Pretty straightforward, don't you think?

[ddt]

That might be true, although neither current theory nor any experimental evidence support it. And even in a universe like that, one can still construct infinite sets: the set of all ordered sets of points, for example.


Now I'm beginning to wish I had studied set theory properly yet. Is there any short version of how that is done, or some link that explains it in more detail?
I studied set theory, and I'm puzzled too by sol's comment. We are arguing about a universe with a finite number of points (call it N), aren't we?

Then the number of possible orderings on all points is also finite. Let's see:

Take two points x and y. They can be either ordered as x < y, or x > y, or not - that's 3 possibilities. There are N * (N-1) / 2 possible unordered pairs of x and y, so the number of orderings is bounded by 3 ^ (N(N-1)/2). I say bounded, because not all combinations are valid; an ordering must adhere to the law of transitivity:

if x < y and y < z, then x < z

So there's a finite number of possible orderings of N points. If you include the orderings of subsets of those points, for each size n of such a subset, there's a finite number of ways to get a subset of size n, and per subset you get the same upper bound for the number of orderings as above (with n instead of N), so - all in all - you still get a finite number of orderings.

Did I miss something?

[stup_id]

That is not likely to be the number of partciles in the universe, just the observable universe?

Thanks, there's a huge difference in that, I'm not familiar however as how they've reached this number, I hope is not one of those "fun facts" such as "we only use 10% of our brain" :P

Prime numbers?

Yep yep, I know that, but that's why I made the dinstinction of "physical" things, you know... made of matter :) can there exist and infinite amount of things of such?

[sol invictus]

Now I'm beginning to wish I had studied set theory properly yet. Is there any short version of how that is done, or some link that explains it in more detail?

Nothing fancy - see below.


That's annoyingly inconvenient... Is there no way that singularities could—even just in principle—be used to test if space is quantized on any level?

It's very hard to make completely general statements. Certainly in any given theory in which space and time are discretized, there are certain potentially observable consequences. Usually those consequences get milder and milder as the discreteness scale goes to zero, but there are some surprising exceptions - black hole horizons (and singularities, if you could access them) are often among them.

I studied set theory, and I'm puzzled too by sol's comment. We are arguing about a universe with a finite number of points (call it N), aren't we?
<snip>


You're assuming that each point can only appear once. I probably should have said "list" or "sequence".

But anyway, it's a rather nonsensical discussion, because (as has been pointed out) it's very unclear what it means to place the mathematical restriction of finiteness on things the universe contains. Does the universe contain numbers? If so, does it contain infinite sequences of numbers? If not, why not? Does it contain spacetime points? What about sequences of spacetime points, as I had in mind?

[blutoski]

I may have stated #1 badly. Is it clearer if we restate it as "The universe cannot contain an infinite number of anything, whether elementary particles, points in spacetime or other objects", or does that make it too fuzzy?

OK, but now #1 appears to be three orthogonal premises glommed together (it is possible for some or all parts to be true or false independently):

#1a: the universe does not contain an infinite amount of matter
#1b: the universe does not contain an infinite number of coordinates (points in space)
#1c: the universe does not contain an infinite number of moments (points in time)



premise #1c seems the most relevant to premise #2, and there are two orthogonal re-wordings that further clarify meaning:

#1c/i: the universe does not contain a moment that is infinitely large or small
#1c/ii: the universe consists of a limited number of moments


Now: premise #1c/i is the interpretation I was using when I said it was a duplicate of premise #2. I still think this interpretation is a duplicate.

However, if the actual meaning is clarified by premise #1c/ii, then its truth does not imply that the universe must have a beginning and end. Consider the scenario where the universe has a meagre three points (moments) in time: a point infinitely far in the past, a point right now, and a point infinitely far in the future. So, we have a finite number of points in time, but in a universe that nevertheless is infinite in duration.

[blutoski]

Just read the OP. Or, here, I'll cut and paste it for you:



Pretty straightforward, don't you think?

I think so...

... so why did you say ([in this post (http://forums.randi.org/showthread.php?p=5005565#post5005565)]) that we were evaluating the first premise when it's clear from the quote you just excerpted that Dorfl has asked us not to? (if we're assuming it is true, this means we don't have to evaluate it)

[Yoink]

I think so...

... so why did you say ([in this post (http://forums.randi.org/showthread.php?p=5005565#post5005565)]) that we were evaluating the first premise when it's clear from the quote you just excerpted that Dorfl has asked us not to? (if we're assuming it is true, this means we don't have to evaluate it)

I was responding to your question "Which one are we evaluating. There's four there." "Evaluating" is a pretty vague term. I assumed you meant it in the sense of "which one are we trying to understand the implications of" or "which one is under discussion here." If you meant it to mean "which one are we meant to testing to see if it is true" then I don't know why you asked the question at all: the answer would obviously be "none of them."

[blutoski]

I was responding to your question "Which one are we evaluating. There's four there." "Evaluating" is a pretty vague term. I assumed you meant it in the sense of "which one are we trying to understand the implications of" or "which one is under discussion here." If you meant it to mean "which one are we meant to testing to see if it is true" then I don't know why you asked the question at all: the answer would obviously be "none of them."

Maybe we'll need Dorfl to help us understand what, exactly, he's asking us to do. I'm pretty sure he's not asking us to discuss the implications of a demonstrated true existence of God, per premise #4. That's a big topic, and probably also not really appropriate for the 'science' area in the forum (that would be best suited in the 'religion' area).

I thought he was asking for us to review the merit and naturalistic implications of the argument, with the assumption that premise #1 was true.

[Yoink]

Maybe we'll need Dorfl to help us understand what, exactly, he's asking us to do. I'm pretty sure he's not asking us to discuss the implications of a demonstrated true existence of God, per premise #4. That's a big topic, and probably also not really appropriate for the 'science' area in the forum (that would be best suited in the 'religion' area).

I thought he was asking for us to review the merit and naturalistic implications of the argument, with the assumption that premise #1 was true.

I think what he's asking is "what would be the implications if the premise in #1 were true." I think he wants us to ignore the rest of the argument entirely.

[blutoski]

I thought he was asking for us to review the merit and naturalistic implications of the argument, with the assumption that premise #1 was true.

With that in mind, I still think the primary weakness of the version in the original post (or alternative rephrasings in later posts) is the non sequitur between math concepts that represent limited modelling abstractions from reality vs our understanding of reality itself.

I had a read through the Wikipedia summary of the original argument: [Kalam cosmological argument (http://en.wikipedia.org/wiki/Kalam_cosmological_argument)] and the objections do seem familiar to my thoughts on the subject.

In particular, that there is no compelling reason to accept the first premise as a mathematical truth, and even if it were true, there is no reason to believe that a mathematical truth projects into reality.

The other obvious objection that I overlooked relates to what Dorfl put in the position of a fourth premise (Kalam cosmological argument actually only has two premises) which ties the principle of a beginning of the universe to a creator. The weakness being that if we want to say that the creator did not have a creator, we must accept that premise 1 ("Everything that begins to exist has a cause.") is both true and false, which means the argument appears self-contradictory. This was Bertrand Russel's reason for rejecting it.

It appears to be a fancy version of "argument from contingency" with superfluous reference to 'sets'.

[blutoski]

I think what he's asking is "what would be the implications if the premise in #1 were true." I think he wants us to ignore the rest of the argument entirely.

Well, assuming that, and based on the clarifying re-wording provided that stripped away the debatable stuff about mathematical set theories and just focussed on the claim that: there is a limited amount of matter in the universe, that there is a limited amount of height, width, depth, and time...

I don't think this would have much of an implication for anything else, and for what it's worth, when stated this way, it's probably true. I'm pretty sure the amount of matter in the universe is finite. On the other hand, I'm pretty sure spatial distance is infinite in all directions, although we may find that the local spacetime properties have a perimiter. (Could this be defined as a boundary to our universe?)



But the re-wording Dorfl provided in a more recent post is not the Kalam cosmological argument. The Kalam cosmological argument does say very specifically that mathematical models do map or project to the real universe (eg: that infinite sets can't exist in mathematics, therefore, no concept in the universe can have infinite values). That's a very important supporting premise and distinguishes the Kalam Cosmological argument from other Cosmological arguments that just claim that the universe must be physically and chronolocically bounded a priori.

This really is philosophy.

[Dorfl]

Oops.

Sorry about disappearing with this discussion going on. What I'm asking for is specifically what physical, observable effects it would have on the universe if #1 were true. If #2 and #3 would somehow observably affect our universe (even in just a negative way, such as forcing it to not have an open geometry), then we can ask if they actually follow, assuming #1s truth—as well as what other things about the universe which also would have to be true.

It might have been better if I had left out steps #2 and onwards from the OP, and just asked what the effects of #1 would be, but I wanted to give some background for why I was asking the question anyway.

[Dorfl]

OK, but now #1 appears to be three orthogonal premises glommed together (it is possible for some or all parts to be true or false independently):

#1a: the universe does not contain an infinite amount of matter
#1b: the universe does not contain an infinite number of coordinates (points in space)
#1c: the universe does not contain an infinite number of moments (points in time)


My attempt to restate the Kalām argument was pretty bad, I admit. I'll try to see if I can find any better way of putting it.


premise #1c seems the most relevant to premise #2, and there are two orthogonal re-wordings that further clarify meaning:

#1c/i: the universe does not contain a moment that is infinitely large or small
#1c/ii: the universe consists of a limited number of moments


Now: premise #1c/i is the interpretation I was using when I said it was a duplicate of premise #2. I still think this interpretation is a duplicate.

However, if the actual meaning is clarified by premise #1c/ii, then its truth does not imply that the universe must have a beginning and end. Consider the scenario where the universe has a meagre three points (moments) in time: a point infinitely far in the past, a point right now, and a point infinitely far in the future. So, we have a finite number of points in time, but in a universe that nevertheless is infinite in duration.
I'm not really sure what it means to talk about the "size" of a moment, or the distance between them. Doesn't that require there to be a second, non-discrete time for the discrete time to be measured in?

It seems to me that if a universe contained three moments in time, then that universe's length in time would be three moments, period. Talking about the length between them seems like discussing the "size" of each square on a tic-tac-toe grid.

[Dorfl]

It's very hard to make completely general statements. Certainly in any given theory in which space and time are discretized, there are certain potentially observable consequences. Usually those consequences get milder and milder as the discreteness scale goes to zero, but there are some surprising exceptions - black hole horizons (and singularities, if you could access them) are often among them.

That's cool. So now I just need to find a naked singularity...


You're assuming that each point can only appear once. I probably should have said "list" or "sequence".

But anyway, it's a rather nonsensical discussion, because (as has been pointed out) it's very unclear what it means to place the mathematical restriction of finiteness on things the universe contains. Does the universe contain numbers? If so, does it contain infinite sequences of numbers? If not, why not? Does it contain spacetime points? What about sequences of spacetime points, as I had in mind?

True. #1 turned out to be a lot more ambiguous than I thought at first glance. And I'd rather not derail this into a philosophical discussion of which things "exist" and which do not. There was a reason I posted this in Science and not Philosophy.

[Roboramma]

Ah. So just one premise? Which premise are we evaluating? There's four there.

From the OP:


1. No infinite set (http://en.wikipedia.org/wiki/Actual_infinite) can exist in the physical world.
And:

Whether the argument is sound or not is already being discussed in the other thread. What I wonder about is the physical implications that the premise #1 would have, if it were true. For example, it seems to imply that the universe is finite in both space and time—requiring a big crunch—and that space and time are both quantized.

Are there any other implications that #1 would have, and are they correct, as far as we know?

Bolding is mine.

[Monketey Ghost]

*smiling*

Best, most informative section of the forums.

[blutoski]

From the OP:


And:



Bolding is mine.

I appreciate that, and that's how I based my assumption that I was to assume #1 was true.

But in a later post Yoink said that we were to evaluate #1 for truth, rather than assume it was true. I was trying to clarify with Dorfl before proceeding, as I didn't want to try to answer a question he wasn't asking in the first place. It appears that Yoink just misunderstood what I meant by 'evaluate'.

I was using the meaning that is typical in critically evaluating an argument, because the original post had structured the question in the form of an argument.

I think this confusion was resolved a few posts ago.

[blutoski]

My attempt to restate the Kalām argument was pretty bad, I admit. I'll try to see if I can find any better way of putting it.

I'm not sure that's necessary... based on your further clarifications, it looks like we're not dealing with the Kalam argument anyway. The Kalam argument is metaphysics/philosophy.




I'm not really sure what it means to talk about the "size" of a moment, or the distance between them. Doesn't that require there to be a second, non-discrete time for the discrete time to be measured in?

I'm not sure if this has meaning either. But you're asking us to assume it's true, right? So, tell us what to believe so we can answer your question.




It seems to me that if a universe contained three moments in time, then that universe's length in time would be three moments, period. Talking about the length between them seems like discussing the "size" of each square on a tic-tac-toe grid.

Why do you not think this is a philosophical discussion?

[Dorfl]

I'm not sure that's necessary... based on your further clarifications, it looks like we're not dealing with the Kalam argument anyway. The Kalam argument is metaphysics/philosophy.
Ok.

I'm not sure if this has meaning either. But you're asking us to assume it's true, right? So, tell us what to believe so we can answer your question.
I'm asking you to assume that time is quantized—if you agree that necessarily follows from there being a finite number of points in spacetime. I have no idea if that makes it meaningful to claim that a moment has a certain "size" though, beyond "one moment". If you think that it does, I would be interested in hearing why.

Why do you not think this is a philosophical discussion?
Well, I'll agree that the thread is sort of flipping back and forth between science, maths and philosophy, but I'm trying to avoid the latter as much as possible. My argument there was partly that a person inside a universe with quantified time would need to access some external non-discrete time to measure the "size" of a moment. So I didn't see how a statement about the size of a moment could be meaningful.

[blutoski]

I'm asking you to assume that time is quantized—if you agree that necessarily follows from there being a finite number of points in spacetime.

No, that doesn't follow.



I have no idea if that makes it meaningful to claim that a moment has a certain "size" though, beyond "one moment". If you think that it does, I would be interested in hearing why.

I don't think it makes sense to say that a moment has size. It's just a reference.



Well, I'll agree that the thread is sort of flipping back and forth between science, maths and philosophy, but I'm trying to avoid the latter as much as possible. My argument there was partly that a person inside a universe with quantified time would need to access some external non-discrete time to measure the "size" of a moment. So I didn't see how a statement about the size of a moment could be meaningful.

I was treating a moment as the temporal equivalent of a more familiar spacial coordinate: it has no size. It is a reference point along a line.

My point is that whether the moments are themselves finite, the line upon which they lay could be infinitely long. Two of the moments could be plus and minus infinitely far away from this moment now.




I'll move away from the moments thing, because my actual point is being obscured.

Instead, consider a case where there are four (a finite number of) atoms in the universe. The atoms are located infinitely far away from each other. The universe can still be infinitely large while containing finite number of real objects. What I'm saying is that a finite number of objects does not imply a bounded universe.

In the time dimension, the equivalent of matter is 'events.' So consider the case where there are three events in the universe: one infinitely far in the past, one infinitely far into the future, and the current event right now. Finite events, but infinite time.

[Dorfl]

No, that doesn't follow.

I don't think it makes sense to say that a moment has size. It's just a reference.

I was treating a moment as the temporal equivalent of a more familiar spacial coordinate: it has no size. It is a reference point along a line.

My point is that whether the moments are themselves finite, the line upon which they lay could be infinitely long. Two of the moments could be plus and minus infinitely far away from this moment now.

I'll move away from the moments thing, because my actual point is being obscured.
Then you can ignore this bit, if you feel it is going off-topic. But my point is that moments do not lie on a timeline. The timeline is made of moments. So for it to be infinitely long, there would have to be an infinite number of moments.


Instead, consider a case where there are four (a finite number of) atoms in the universe. The atoms are located infinitely far away from each other. The universe can still be infinitely large while containing finite number of real objects. What I'm saying is that a finite number of objects does not imply a bounded universe.

In the time dimension, the equivalent of matter is 'events.' So consider the case where there are three events in the universe: one infinitely far in the past, one infinitely far into the future, and the current event right now. Finite events, but infinite time.
Isn't "event" just the term for a point in spacetime? According to wiki (http://en.wikipedia.org/w/index.php?title=Spacetime&oldid=307436249):

In spacetime, a coordinate grid that spans the 3+1 dimensions locates "events" (rather than just points in space), so time is added as another dimension to the grid, and another axis.

That's why I claim that a universe which is not finite in both time and space will contain an infinite number of events.

[blutoski]

Then you can ignore this bit, if you feel it is going off-topic. But my point is that moments do not lie on a timeline. The timeline is made of moments. So for it to be infinitely long, there would have to be an infinite number of moments.

Could be; who knows? Depends on how you want to define moment, I guess.

I'm not sure what, exactly, you're asking us to do here. What's your question?






Isn't "event" just the term for a point in spacetime? According to wiki (http://en.wikipedia.org/w/index.php?title=Spacetime&oldid=307436249):

Sure, but I was trying to just get a point across: I'm concerned that you seem more concerned about micromanaging the analogy than with what I'm trying to convey. I've exhausted two analogies and you're not addressing the point I was trying to make with them.

(sigh) What term do you want me to use to refer to positions strictly in time, and I'll use that.






That's why I claim that a universe which is not finite in both time and space will contain an infinite number of events.

I guess, but I thought your 'question' was that we assume a finite universe.

I thought you were asking about the implications of a finite universe, and possibly you were specifically asking about the implications of a universe with a first moment?

I'm really struggling with what you're trying to do here.

[Aepervius]

1. No infinite set (http://en.wikipedia.org/wiki/Actual_infinite) can exist in the physical world.


As far as I can tell we do not know. Spacially we have found the LOWER bound of the universe (what minimum size it has, if sized) if one is to believe some of the peer reviewed article it is somewhere around at least 40 something billion light year. So if the universe is finite (IF) then it is at least that size.

But there is no argument/falsification against the universe being spacially infinite, with only matter being at a certain radius, with us being somwhere inside, and outside that radius emptyness up the wazoo to the inifinity.

[Dorfl]

Could be; who knows? Depends on how you want to define moment, I guess.

(sigh) What term do you want me to use to refer to positions strictly in time, and I'll use that.

I'd define a moment as a coordinate in time, just like you do in post #59. That's why I'm confused by your claim that there can be a finite number of moments in a universe with non-discrete time. If time is continuous, there will be a t=1, t=1.1, t=1.11, etc—an uncountably infinite number of moments.

I'm not sure what, exactly, you're asking us to do here. What's your question?

If I'm correct that requiring a finite number of moments necessarily requires time to have a starting-point, an end-point and also to be discrete.


Sure, but I was trying to just get a point across: I'm concerned that you seem more concerned about micromanaging the analogy than with what I'm trying to convey. I've exhausted two analogies and you're not addressing the point I was trying to make with them.

I still cannot see what your point is, I'm sorry.


I guess, but I thought your 'question' was that we assume a finite universe.

I thought you were asking about the implications of a finite universe, and possibly you were specifically asking about the implications of a universe with a first moment?

I'm really struggling with what you're trying to do here.

I'm asking if the universe is necessarily finite, assuming a finite number of points in spacetime. I think it would have to be, but you seem to disagree. Maybe because we don't seem to agree on what a point in spacetime is.

ETA: Just had a thought about post #59. Could you actually have atoms at an infinite distance from each other? Just because there is no upper bound to how far away they can be, that doesn't mean that they can actually be "infinitely" far away, does it?

[blutoski]

I'd define a moment as a coordinate in time, just like you do in post #59. That's why I'm confused by your claim that there can be a finite number of moments in a universe with non-discrete time. If time is continuous, there will be a t=1, t=1.1, t=1.11, etc—an uncountably infinite number of moments.

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 asking if the universe is necessarily finite, assuming a finite number of points in spacetime. I think it would have to be, but you seem to disagree. Maybe because we don't seem to agree on what a point in spacetime is.

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.

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)





ETA: Just had a thought about post #59. Could you actually have atoms at an infinite distance from each other? Just because there is no upper bound to how far away they can be, that doesn't mean that they can actually be "infinitely" far away, does it?

Who knows? This is a philosophical exercise in metaphysics, not an investigation about physics.

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.'

[Dorfl]

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 (http://en.wikipedia.org/w/index.php?title=Kalam&oldid=306497607) isn't a person.

[Dorfl]

As far as I can tell we do not know. Spacially we have found the LOWER bound of the universe (what minimum size it has, if sized) if one is to believe some of the peer reviewed article it is somewhere around at least 40 something billion light year. So if the universe is finite (IF) then it is at least that size.

But there is no argument/falsification against the universe being spacially infinite, with only matter being at a certain radius, with us being somwhere inside, and outside that radius emptyness up the wazoo to the inifinity.

But if it was discovered that space had—on very large scales—spherical geometry. Wouldn't that make it most reasonable to assume that it was in fact closed, with a finite radius?

ETA: And if it turned out to be hyperbolic, it would most likely be infinite. But as long as it keeps turning out to be flat, on any scale we can see, it will be possible for people to claim that it's either spherical or hyperbolic on a larger scale.

[Perpetual Student]

If the premise #1 in the OP implies that the time is finite (in both directions) then, as has already been stated, the universe must end. So the question is, end how? Big crunch? Dissipate into a thin gas/dust? If it ends in a big crunch, then wouldn't there still be a singularity? Big black hole? How would that go away? Would that singularity exist forever; no -- that is ruled out by #1? There is no physical law (correct me here if I'm wrong) allowing all that mass to disappear. So, #1 is contradicted.
Now if instead we have a big dissipation, again that mass is still there (unimaginably thinned out). Again it cannot simply disappear. So it is there forever -- again that is ruled out by #1. So, unless mass can somehow disappear, it seems that following premise #1 leads to a contradiction, what other implications can it have?

[sol invictus]

If the premise #1 in the OP implies that the time is finite (in both directions) then, as has already been stated, the universe must end. So the question is, end how? Big crunch? Dissipate into a thin gas/dust? If it ends in a big crunch, then wouldn't there still be a singularity? Big black hole? How would that go away? Would that singularity exist forever; no -- that is ruled out by #1? There is no physical law (correct me here if I'm wrong) allowing all that mass to disappear. So, #1 is contradicted.
Now if instead we have a big dissipation, again that mass is still there (unimaginably thinned out). Again it cannot simply disappear. So it is there forever -- again that is ruled out by #1. So, unless mass can somehow disappear, it seems that following premise #1 leads to a contradiction, what other implications can it have?

As we've discussed at length, there is no law of physics (that I'm aware of at least) that forbids time from "ending" or "beginning".

Conservation of energy tells you energy doesn't change with time. It does not tell you time exists on an infinite interval. Does conservation of momentum prove that space must be infinite? No - and the analogy to energy and time is exact.

Causality doesn't tell you that either, nor does the existence of a bounded interval imply either a first or last cause, or that there was an event with no cause.

So while the argument as it was presented in the OP is obviously invalid, it's not because of that.

[Dorfl]

If the premise #1 in the OP implies that the time is finite (in both directions) then, as has already been stated, the universe must end. So the question is, end how? Big crunch? Dissipate into a thin gas/dust? If it ends in a big crunch, then wouldn't there still be a singularity? Big black hole? How would that go away? Would that singularity exist forever; no -- that is ruled out by #1? There is no physical law (correct me here if I'm wrong) allowing all that mass to disappear. So, #1 is contradicted.
Now if instead we have a big dissipation, again that mass is still there (unimaginably thinned out). Again it cannot simply disappear. So it is there forever -- again that is ruled out by #1. So, unless mass can somehow disappear, it seems that following premise #1 leads to a contradiction, what other implications can it have?
I don't know. Most theories involving a Big Crunch I've seen have seemed to imply that time would somehow end there. I read A Brief History of Time recently and the model Hawking described there (which, AFAIK, is no longer used) showed time starting at the Big Bang and ending at the Big Crunch. But now that you mention it, I realise I've never wondered why time would end just because you re-squeeze matter into infinite density.

[Perpetual Student]

As we've discussed at length, there is no law of physics (that I'm aware of at least) that forbids time from "ending" or "beginning".

Conservation of energy tells you energy doesn't change with time. It does not tell you time exists on an infinite interval. Does conservation of momentum prove that space must be infinite? No - and the analogy to energy and time is exact.

Causality doesn't tell you that either, nor does the existence of a bounded interval imply either a first or last cause, or that there was an event with no cause.

So while the argument as it was presented in the OP is obviously invalid, it's not because of that.

But you did not say anything about the point that all the matter in the universe cannot simply vanish. If matter still exists, how can time simply stop?

[sol invictus]

But you did not say anything about the point that all the matter in the universe cannot simply vanish. If matter still exists, how can time simply stop?

Read your question agains, carefully.

"Vanish" means something was there at one time, and at a later time it wasn't. But what if there was no later time? Something vanishing is completely different from time ending - they're two totally separate concepts.

"If matter still exists, how can time simply stop?" - that's like asking "if this pen is yellow, how can it be red"?

And time doesn't have to end for it to be finite - it could be periodic, for example. Maybe your big crunch is also the big bang.

[Perpetual Student]

Read your question agains, carefully.

"Vanish" means something was there at one time, and at a later time it wasn't. But what if there was no later time? Something vanishing is completely different from time ending - they're two totally separate concepts.

"If matter still exists, how can time simply stop?" - that's like asking "if this pen is yellow, how can it be red"?

And time doesn't have to end for it to be finite - it could be periodic, for example. Maybe your big crunch is also the big bang.

OK, we have have a universe full of matter/energy. To my knowledge all models of the universe have that matter/energy doing something like contracting, expanding, oscillating, etc. The matter/energy in the universe is conserved. Since it must always exist, what does it mean to exist if not exist in time? Can it exist in "non-time"? What does that mean?

[sol invictus]

. The matter/energy in the universe is conserved.

All that means is that the total is the same at all times. It says nothing about what those times are. Moreover that total is exactly zero in a closed universe.

Since it must always exist, what does it mean to exist if not exist in time? Can it exist in "non-time"?

You're creating semantic "paradoxes" for yourself again. You declare "it must always exist". That might be true, depending on what "always" means.

What does that mean?

You tell us...

[Perpetual Student]

Moreover that (matter/energy) total is exactly zero in a closed universe.

Why?

[blutoski]

Theoretical******** (Scott Clifton): [I "Kalam" Like I See 'Em... (http://www.youtube.com/watch?v=aD9MtIma5YU)] (YouTube)

[Soapy Sam]

I've always held the naive notion that infinity is an interesting , but wholly imaginary concept.
By definition, the existence of a single infinite quantity of anything leaves no room, material, or time for anything else.
And since inspection reveals at least three or four different things on this keyboard (one of which appears to be alive) there would seem to be no infinite quantity of anything.

As for the more abstract idea of infinite numbers (or any other wholly imaginary things), I will personally believe they exist when I see one actually counted. Until then , I put them in the same box as flying saucers, ghosts and other imaginary things.

Having said that, I'm still unable to see how we get from Point 1 in the OP to point 2.

[arthwollipot]

Having said that, I'm still unable to see how we get from Point 1 in the OP to point 2.Via an infinite series of intermediate points.

[Tormac]

[QUOTE=Dorfl;5000321]This thread (http://forums.randi.org/showthread.php?t=150286) more or less instantly got derailed into a discussion of the Kalām cosmological argument. The argument—as I understand it—goes basically:

1. No infinite set (http://en.wikipedia.org/wiki/Actual_infinite) can exist in the physical world.

. . . QUOTE]

Somebody with more mathematics than me feel free to correct me if I’m wrong, but I thought that fractal geometry has already show how things can be bounded, but infinite, thus kicking #1 in the groin from the get go.

[W.D.Clinger]

Somebody with more mathematics than me feel free to correct me if I’m wrong, but I thought that fractal geometry has already show how things can be bounded, but infinite, thus kicking #1 in the groin from the get go.
Mathematicians have been dealing with bounded but infinite topological spaces for quite a while (before fractal geometry). Mathematicians also deal with finite spaces that have no boundary. Hence the argument is bogus for both of these reasons (among others):

infinite does not imply unbounded
finite does not imply bounded