Actual Infinities

[Mudhammam]

A popular claim made in conjunction with the Kalam argument for God's existence is something like the following: past time cannot terminate in an infinite regress because it would take an infinite amount of time to arrive at the present moment, and one cannot reach the end - which would be the present - of an actual infinity. It's often stated that only potential infinities can exist - that is, a future continuance of time which never ceases - but not actual infinities. Is there any validity to this latter assertion? If so, how can an omniscient being, with actual infinite knowledge of the potentially infinite future, avoid the very same predicament imposed by actual infinities?

[Alex K]

A popular claim made in conjunction with the Kalam argument for God's existence is something like the following: past time cannot terminate in an infinite regress because it would take an infinite amount of time to arrive at the present moment, and one cannot reach the end - which would be the present - of an actual infinity. It's often stated that only potential infinities can exist - that is, a future continuance of time which never ceases - but not actual infinities. Is there any validity to this latter assertion? If so, how can an omniscient being, with actual infinite knowledge of the potentially infinite future, avoid the very same predicament imposed by actual infinities?

This sounds intriguing, but I am not yet entirely sure I understand the argument. Can we start from the basics - why exactly is past infinity a problem?

[Mudhammam]

A popular claim made in conjunction with the Kalam argument for God's existence is something like the following: past time cannot terminate in an infinite regress because it would take an infinite amount of time to arrive at the present moment, and one cannot reach the end - which would be the present - of an actual infinity. It's often stated that only potential infinities can exist - that is, a future continuance of time which never ceases - but not actual infinities. Is there any validity to this latter assertion? If so, how can an omniscient being, with actual infinite knowledge of the potentially infinite future, avoid the very same predicament imposed by actual infinities?

This sounds intriguing, but I am not yet entirely sure I understand the argument. Can we start from the basics - why exactly is past infinity a problem?

As I see it, it's incoherent to suggest that infinity can exist as a complete set - think of infinity as a number. You can always seemingly add to whatever that infinite number "is" - hence, it could not actually be infinite. So, if past time were infinite, the present could not arrive, for it would require an infinite amount of time for every prior successive moment to reach completion, which doesn't appear to mean anything. But if we grant infinite past time, there is no need for God. I'm more interested in granting the logical impossibility of actual infinities for the sake of argument, and then asking how it is that God is also not made logically impossible?

[Jenny A]

This sounds intriguing,  but I am not yet entirely sure I understand the argument.  Can we start from the basics -  why exactly is past infinity a problem?

As I see it, it's incoherent to suggest that infinity can exist as a complete set - think of infinity as a number. You can always seemingly add to whatever that infinite number "is" - hence, it could not actually be infinite. So, if past time were infinite, the present could not arrive, for it would require an infinite amount of time for every prior successive moment to reach completion, which doesn't appear to mean anything. But if we grant infinite past time, there is no need for God. I'm more interested in granting the logical impossibility of actual infinities for the sake of argument, and then asking how it is that God is also not made logically impossible?

How is the problem of an infinite regress never reaching the present different than the problem of an arrow never reaching it's mark because there are an infinite number of points between where it was shot and its mark? The arrow does reach its mark whether we can describe how it gets through an infinity of points or not.

[Foxaèr]

Except doesn't an arrow thrown always reach its mark?

[Jenny A]

Except doesn't an arrow thrown always reach its mark?

That would be the point.

[houseofcantor]

And you're going to use this argument against people who are essentially in slippers because shoelaces are too complicated?

The Zeno bit with the arrow is solved because quantum, i.e., spacetime is quantized, discrete. Also with Planck length is Planck time, so I'm failing to see how the one cannot be extrapolated to the other. Further, it seems likely that this universe is 13.82 billion years old, making the whole excercize rather moot. To include infinite speculations to rationalize a point that should be clear with fractal geometry and evolution seems to be unnecessary construction. If your intended audience refuses to hear the ABCs and 123s why do you think it's going to listen to the Alephs?

Color me confused. 

[robvalue]

I think it's an argument from incredulity. They can't imagine an infinite past, so there isn't one.

The thing is, time and linear causality are just models we've come up with to try and make sense of whatever the smeg is actually going on. Some people mistake this for prescribing what is going on. This is the problem with trying to use an argument in place of evidence.

[GrandizerII]

And you're going to use this argument against people who are essentially in slippers because shoelaces are too complicated?

The Zeno bit with the arrow is solved because quantum, i.e., spacetime is quantized, discrete. Also with Planck length is Planck time, so I'm failing to see how the one cannot be extrapolated to the other. Further, it seems likely that this universe is 13.82 billion years old, making the whole excercize rather moot. To include infinite speculations to rationalize a point that should be clear with fractal geometry and evolution seems to be unnecessary construction. If your intended audience refuses to hear the ABCs and 123s why do you think it's going to listen to the Alephs?

Color me confused. 

That was so deep ... ... ...

[robvalue]

It's funny how people who can't imagine this infinite past find it incredibly easy to imagine a god with exactly the same properties.

Of course, they try and make him special by using such nonsense terms as "timeless".

We experience reality, so our ideas about it get constantly challenged. I agree that imagining an infinite past is difficult, because it kind of clashes with our intuition about how things seem to work. Since no one actually experiences God outside of their own head, it never falls under the same scrutiny. People can merrily use whatever words they want to describe it and it can break all the rules that apparently cause these paradoxes in the first place, because it never actually shows up to challenge those claims.

If it did show up, our natural curiosity would be asking all the same questions we ask of the universe.