The existence of God

Originally posted by twhitehead
I have seen that one before, and the argument does not work. It is based on an uncomfortableness with infinity and is in some ways related to the Achilles and the tortoise paradox.

You say that, but why does it not work?

Originally posted by DeepThought
You say that, but why does it not work?

Here is the key phrase or premise in the argument you had brought up:

But If the universe is infinitely old then to get from a time infinitely far in the past to now requires an infinite amount of time to have elapsed...

This implicitly embeds the notion that there is some specific time in the past that is infinitely remote from the present. And the general view amongst philosophers and logicians is that this is based on a misrepresentation of an infinite past time. The reality is rather different: that if one considers any specific time in the past, there is only a finite stretch of time to be traversed from that specific time to the present. That being the case, the intuitive appeal of the original problem seems to dissolve.

Originally posted by LemonJello
That being the case, the intuitive appeal of the original problem seems to dissolve.

Further, the intuitive appeal of the original problem, is intuitive, but not logical. There is no actual mathematical rule that says infinities cannot exist, or that an infinite of time cannot pass.
Another problem is the argument relies on a view of time that is flowing from past to future with 'existence' being only at 'the present', whereas other models such as a complete spacetime universe are possible.

The argument must explain why time is different from say real numbers and why the same argument does not rule out the existence of the real numberline (given that it consists of numbers from minus infinity.)

Originally posted by LemonJello
Here is the key phrase or premise in the argument you had brought up:

But If the universe is infinitely old then to get from a time infinitely far in the past to now requires an infinite amount of time to have elapsed...

This implicitly embeds the notion that there is some specific time in the past that is infinitely remote from the p ...[text shortened]... e present. That being the case, the intuitive appeal of the original problem seems to dissolve.

It depends how one sets up one's space. What I wanted was to see was what twhitehead thought the connection between this notion and the Tortoise and Hare paradox is. In the case of the real line then yes, what you say is true, but that isn't the only way of setting up a one dimensional space. One can have a space with specific points that are an infinite distance apart, the simplest example is the extended real line which is the normal real line with points at infinity and minus infinity. The distance between the point at minus infinity and the point at zero is infinite. So while what you say is my knee jerk response I'm not convinced the argument is necessarily invalid.

Originally posted by DeepThought
If the universe is infinitely old then it is eternal in nature. Now, what is your reason for thinking that the universe is not infinitely old?

"...that the universe necessarily cannot be infinitely old?"

If the "universe" were infinitely old than it would wind down. If the cause of the universe
were not a part of the universe, than the "time" the universe was around would not matter
to the cause since it isn't the universe.

Originally posted by DeepThought
It depends how one sets up one's space. What I wanted was to see was what twhitehead thought the connection between this notion and the Tortoise and Hare paradox is.

The tortoise and the hare paradox makes the claim that infinities cannot be traversed, and also uses the concept of time flowing in a given direction - and crucially being divisible into a countable sequence. LemonJello is correct that in the case of infinite time, it is not a requirement that infinities be traversed. And as we all know, movement is possible proving Zeno's paradox does not break reality.

One can have a space with specific points that are an infinite distance apart, the simplest example is the extended real line which is the normal real line with points at infinity and minus infinity.
A construct that obviously has issues. But why use that construct? And even if you did, demonstrating a problem would only rule out that construct.

The distance between the point at minus infinity and the point at zero is infinite.
But is there an actual logical argument that says that such an infinity is impossible? If so, why haven't mathematicians thrown out that construct as untenable?

Originally posted by DeepThought
Copy and paste of my answer to the identical question in the other thread:

Stephen Hawking presents an entropy argument. Essentially entropy always increases and it's possible to show that it has a maximum - subject to some assumptions about the system being closed. However, there is a way round this. In models of eternal inflation, where th ...[text shortened]... prior cause, but if that is the case then it is hard to see why it should apply to the universe.

This is what a "what if this happen clause" to make the universe date older than what we
date it without actually have some reason to believe it happen, other than no one wants the
universe to have a cause outside of itself?

Originally posted by DeepThought
It depends how one sets up one's space. What I wanted was to see was what twhitehead thought the connection between this notion and the Tortoise and Hare paradox is. In the case of the real line then yes, what you say is true, but that isn't the only way of setting up a one dimensional space. One can have a space with specific points that are an infin ...[text shortened]... ile what you say is my knee jerk response I'm not convinced the argument is necessarily invalid.

I think I see what you are saying. I guess my reaction to that would be that it can immediately be disputed that the extended real line represents an example with specific points that are an infinite distance apart. Infinity and minus-infinity are elements of the space but not themselves specific real numbers. When you claim for example that there is an infinite distance between the latter and, say, zero, it doesn't follow that there is an infinite distance between zero and any specific prior real number. So I would presume that a perfectly symmetric dialectic objection still holds. In this case, the objector would hold that introducing the element minus-infinity is dialectically symmetric to implicitly embedding some infinitely remote "starting point" to the timeline. But this is precisely what the objector thinks misrepresents the notion of an infinite past time.

Originally posted by DeepThought
This is essentially an entropy based argument, so see the post immediately above this one.

That argument strikes me as a dodge, not a real answer. We can always come up with a
what if statement no matter the topic.

Originally posted by twhitehead
The tortoise and the hare paradox makes the claim that infinities cannot be traversed, and also uses the concept of time flowing in a given direction - and crucially being divisible into a countable sequence. LemonJello is correct that in the case of infinite time, it is not a requirement that infinities be traversed. And as we all know, movement is possi ...[text shortened]... nfinity is impossible? If so, why haven't mathematicians thrown out that construct as untenable?

The critical difference is that in the Tortoise and Hare paradox the interval being divided has finite measure. Here we are looking at a space with infinite measure. There is no overarching reason not to set up a space consisting of a countably infinite number of points pairwise separated by intervals with infinite measure. There's this construction called the Mobius plane which is the normal plane plus a point at infinity and some additional structure. So I don't think one can invoke a no-go theorem based on mathematical arguments. The other problem is that you have two things to rule out, one is the construction of the space and the other is the universe not having a beginning. So if there is a contradiction you don't know whether to rule out the way the space is constructed or the universe being infinitely old. You seem to be confusing mathematically tenable with physically realized.

Originally posted by DeepThought
You seem to be confusing mathematically tenable with physically realized.

And you appear to by trying very hard to make up impossible scenarios. But if they are mathematically tenable, why are they physically untenable? You haven't actually made any actual argument as to why you think even with a point at infinity, it would be physically untenable.

I must say that I am somewhat confused by the concept of a point at infinity. I said space, is there another point just beyond that one, or is that the last one? Wikipedia suggests it results in a closed loop.
https://en.wikipedia.org/wiki/Point_at_infinity

Intuitively one then thinks the loop is finite, but it isn't. So infinite time, but repeating is what you are proposing?

Originally posted by LemonJello
I think I see what you are saying. I guess my reaction to that would be that it can immediately be disputed that the extended real line represents an example with specific points that are an infinite distance apart. Infinity and minus-infinity are elements of the space but not themselves specific real numbers. When you claim for example that there ...[text shortened]... ut this is precisely what the objector thinks misrepresents the notion of an infinite past time.

I don't agree with the first part of that but do the second, if I've understood what you are saying. My problem with the first part is that as elements of the set the points at infinity are specific extended real numbers, with the admittedly odd property of being infinitely far from any specific element of the real subset. I think the argument in the second half works if you are saying what I think you are. The eternalistic claim is that God or the universe or whatever has no cause and as things with a beginning need a cause the causeless thing must be infinitely old. The argument then goes on to claim that getting to now is impossible due to an infinite amount of time having to be traversed to get to now. However, to avoid the problem you raised that the time elapsed since any specific point in time is only a finite amount of time in the past I suggested adding points at infinity. But to add a point at minus infinity is to add a beginning so the procedure defeats the purpose of the argument.

Originally posted by twhitehead
And you appear to by trying very hard to make up impossible scenarios. But if they are mathematically tenable, why are they physically untenable? You haven't actually made any actual argument as to why you think even with a point at infinity, it would be physically untenable.

I must say that I am somewhat confused by the concept of a point at infinity. ...[text shortened]... nks the loop is finite, but it isn't. So infinite time, but repeating is what you are proposing?

I said physically unrealized, not untenable. I've got two points at infinity, one at each end, so it's not a circle. With a single point at infinity there is an isomorphism with a circle - look up stereographic projection if you want to see the difference.

Originally posted by DeepThought
I said physically unrealized, not untenable.

I am not clear what the distinction is.

In addition, if these points are 'extensions' and not real numbers, then their analogs are not real points in time, and there remains no actual problem of infinity being traversed.
It is similar to Zenos paradox in that you are setting up a form of discontinuity. You have an open infinite set then you tag on an extra point to close it then declare that you cannot reach the extra point. But I think the resolution is different. In Zeno's paradox, the flaw is in confusion over infinity and sequences, whereas in your case I think the existence of a point at infinity is highly suspect and an unnecessary invention.

Originally posted by KellyJay
That argument strikes me as a dodge, not a real answer. We can always come up with a
what if statement no matter the topic.

Well, the original claim was along the lines of "God necessarily exists because the universe had a beginning, things which begin must be caused, and without God there is no first cause.", so I'm entitled to "what if's" to knock down the certainty of the premises. On physics grounds alone eternal inflation is no more or less likely than the standard Big Bang theory.