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Gorgias
Guest
Nothing. In fact, even the ‘boundary’ is not a ‘thing’, but a concept.Gorgias:
What is outside the boundary?
That would lead merely to an assertion of ‘uncountability’, not ‘infinity’, wouldn’t it?
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AlNg
Guest
An uncountable number of objects is automatically infinite.
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Gorgias
Guest
Hmm… good point. I guess I was thinking about bounded, countably infinite sets. Sort of in a “Zeno’s paradox” kind of way. Although there are an infinite number of points between, say, two posts one mile apart, and Zeno’s paradox asserts that, if you go half way in each time period, you’ll never reach your destination, nevertheless you reach a point where you can’t physically go “half the distance” – the distances are too small.
So, although there are an infinite number of points, you’re bounded – you converge to the end of the line.
In the case of an “infinite regress”, though, it needs to be unbounded in order to work. And, worse, there’s no convergence going on – you just keep going back another iteration, and another, and another. Therefore, this cannot lead to the kind of answer it purports to find.
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AlNg
Guest
That is not a problem because there is a way of mapping a bounded interval onto the whole unbounded real line in a 1-1 bijective manner.
Let f(x) = ln(x/(1-x)). Let 0 < x <1, be the unit interval with x between 0 and 1 but not including the two endpoints. Then f maps this unit interval onto the whole real line.
For example.
f(0.5) = 0
f(1/n) → - infinity as 1/n → 0
f(n/(n+1)) → + infinity as n/(n+1) → 1.
So f(<0, 1>) = R the whole real line from – infinity to + infinity.
You can also go the reverse way and map the whole unbounded real line onto the bounded unit interval <0,1> by using the inverse transformation g(x) = 1/ (1 + exp(-x)).
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Wesrock
Guest
It’s also possible that our universe is a surface and not a volume. Anyone with a background in topology should know what I mean. Look at a basketball. The interior is a three dimensional volume. The “boundary” is a two dimensional surface curved in 3D space. You can also consider the Earth. It has a 3D volume but the part we live on can be mapped as a two dimensional surface. The Earth is round, it has no edge (for us surface dwellers. the mole people might map the earth differently).
Likewise, the universe could be a surface, specifically a 3D surface curving through four dimensional space on itself. Like a sailor on Earth’s ocean, if you traveled forever in one direction (assuming traveling faster than the expansion is possible) you might never reach an edge, but simply discover that the universe is “round.”
Probably not a 3-sphere, but some other manifold. Our universe might not have a boundary. It might be a boundary.
Likewise, the universe could be a surface, specifically a 3D surface curving through four dimensional space on itself. Like a sailor on Earth’s ocean, if you traveled forever in one direction (assuming traveling faster than the expansion is possible) you might never reach an edge, but simply discover that the universe is “round.”
Probably not a 3-sphere, but some other manifold. Our universe might not have a boundary. It might be a boundary.
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AlNg
Guest
OK, but if the universe U is the (3D) boundary of (4D) M, then what is M ? For example, the surface of the earth is a boundary, but it is the boundary of a solid planet.
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Wesrock
Guest
We don’t know. Maybe it’s nothing (not even space). Maybe it’s a real part of creation and the universe and we just haven’t learned to tunnel into a fourth dimension yet.Wesrock:
OK, but if the universe U is the (3D) boundary of (4D) M, then what is M ? For example, the surface of the earth is a boundary, but it is the boundary of a solid planet.
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STT
Guest
No, boundary is necessary and it is real when you deal with finite volume.
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Theophilusopher
Guest
Infinite regress is impossible because it requires that something exists that is not ground in God.
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STT
Guest
This is of course not an argument.
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STT
Guest
Unsupported claim.
True.
Doesn’t follow.
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Theophilusopher
Guest
I thought I didn’t need to support it but okay.
“I believe in one God,
the Father almighty,
maker of heaven and earth,
of all things visible and invisible.”
-Nicene Creed
It follows because if God created everything, He is in every chain of causes and effects. If He cannot be in a chain that regresses infinitely, and He is in all chains then no chain regresses infinitely.
“I believe in one God,
the Father almighty,
maker of heaven and earth,
of all things visible and invisible.”
-Nicene Creed
It follows because if God created everything, He is in every chain of causes and effects. If He cannot be in a chain that regresses infinitely, and He is in all chains then no chain regresses infinitely.
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STT
Guest
Here we are arguing why infinite regress is unacceptable. That is one of the thing one has to prove in order to reach to the conclusion that God exists.
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STT
Guest
Yes, some of them are based on the fact that infinite regress is impossible.
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Gorgias
Guest
From a scientific point of view, this is a reasonable point of view: after all, we can’t see further back than the beginning of the Big Bang. So… can it be proven empirically? Of course not; but it can’t be disproven, either.
However, from the theological point of view, it can be demonstrated. So… “unsupported”? Not quite.
… and that means that the proof holds.
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PickyPicky
Guest
Can you count forwards from zero and get to infinity?
That is the same thing as claiming infinite regression is impossible.
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STT
Guest
Well, some of the proof for existence of God works based on the fact that infinite regress is unacceptable. You cannot use those proof to prove that infinite regress is unacceptable.From a scientific point of view, this is a reasonable point of view: after all, we can’t see further back than the beginning of the Big Bang. So… can it be proven empirically? Of course not; but it can’t be disproven, either.
However, from the theological point of view, it can be demonstrated. So… “unsupported”? Not quite.
… and that means that the proof holds.
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