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Why is infinity impossible?

000ike
Posts: 11,196
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3/3/2013 2:43:18 PM
Posted: 3 years ago
On an intuitively logical level, I can't see any reason for infinity to be impossible. If numbers are infinite, then surely all things which may be quantified have a capacity for infinity. If there can be an infinite future, then there can be an infinite past. But of course, this is only layman reasoning. It seems that in many debates, people point to either an infinite regress or infinity in general and use that alone as a refutation. For the most part I've just accepted that infinity is impossible, since it seems to be the accepted view. However, just for the sake of understanding it, It'd be nice if someone could explain why this is true.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
SarcasticIndeed
Posts: 2,215
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3/3/2013 2:55:07 PM
Posted: 3 years ago
At 3/3/2013 2:43:18 PM, 000ike wrote:
On an intuitively logical level, I can't see any reason for infinity to be impossible. If numbers are infinite, then surely all things which may be quantified have a capacity for infinity. If there can be an infinite future, then there can be an infinite past. But of course, this is only layman reasoning. It seems that in many debates, people point to either an infinite regress or infinity in general and use that alone as a refutation. For the most part I've just accepted that infinity is impossible, since it seems to be the accepted view. However, just for the sake of understanding it, It'd be nice if someone could explain why this is true.

Well, infinite past cannot exist because time would never reach this point, having infinite moments before this moment to reach. I believe that is how it goes.
<SIGNATURE CENSORED> nac
Sidewalker
Posts: 3,713
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3/3/2013 4:22:51 PM
Posted: 3 years ago
At 3/3/2013 2:43:18 PM, 000ike wrote:
On an intuitively logical level, I can't see any reason for infinity to be impossible. If numbers are infinite, then surely all things which may be quantified have a capacity for infinity. If there can be an infinite future, then there can be an infinite past. But of course, this is only layman reasoning. It seems that in many debates, people point to either an infinite regress or infinity in general and use that alone as a refutation. For the most part I've just accepted that infinity is impossible, since it seems to be the accepted view. However, just for the sake of understanding it, It'd be nice if someone could explain why this is true.

It was Aristotle that said actual infinities couldn"t exist, so the idea has been around for quite some time. Infinity is a theoretical abstraction as are philosophical constructs relating to infinities and I think the real philosophical problem of the existence of actual infinities is that they are logically inconceivable. If they did exist we could not confirm it through observation because there would be no way to measure them. If an actual infinity were to exist there is no way for us to know it.

A temporal infinity is said to be impossible because you can never traverse an infinite so theoretically, we could never arrive at today from an infinite past. That assumes a linear progression of time, a cyclical model could be considered infinite.
The possibility of a spatial infinity is harder to logically refute. If space in conceived of as flat in all directions then a space that is finite in size is logically problematic because the question of what is beyond it arises. The general theory combines the temporal and spatial into a single fabric of space-time and says it has a shape, and if it has a shape then it is not infinite, space is also said to be expanding and it couldn"t be expanding if it were infinite.

Modern science produces a lot of mathematical infinities but I tend to think they represent places where the mathematical formulas break down rather than actual infinities. In quantum electrodynamics renormalization is the process used to eliminate infinities from equations.

There are supposedly infinite densities at the center of black holes, along with infinite curvature of space-time, but again, a black hole is unobservable because there is an event horizon that makes any observation impossible.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
Apeiron
Posts: 2,446
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3/3/2013 4:36:39 PM
Posted: 3 years ago
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.
unitedandy
Posts: 1,173
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3/3/2013 5:04:33 PM
Posted: 3 years ago
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.
Apeiron
Posts: 2,446
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3/3/2013 5:07:27 PM
Posted: 3 years ago
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.
Cyrano
Posts: 33
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3/3/2013 5:10:52 PM
Posted: 3 years ago
Am I right in thinking it is only infinite past that is absurd and therefore thought to be impossible?
An infinite future, while it can never in practice be reached because you can always add one more, is not absurd... because you CAN always add one more.

WLC uses examples of a static infinite number then shows its absurdity using math examples like "infinity minus all the odd numbers equals... infinity".

And Hilbert"s hotel also deals with a static infinite number.

But starting from now, there is no reason (as far as I know) to think that time cannot stretch on to theoretical infinity, because it will just keep going.
Sidewalker
Posts: 3,713
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3/3/2013 5:16:44 PM
Posted: 3 years ago
At 3/3/2013 5:10:52 PM, Cyrano wrote:
Am I right in thinking it is only infinite past that is absurd and therefore thought to be impossible?
An infinite future, while it can never in practice be reached because you can always add one more, is not absurd... because you CAN always add one more.

WLC uses examples of a static infinite number then shows its absurdity using math examples like "infinity minus all the odd numbers equals... infinity".

And Hilbert"s hotel also deals with a static infinite number.

But starting from now, there is no reason (as far as I know) to think that time cannot stretch on to theoretical infinity, because it will just keep going.

That would still be a theoretical infinity.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
unitedandy
Posts: 1,173
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3/3/2013 5:30:31 PM
Posted: 3 years ago
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.
Apeiron
Posts: 2,446
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3/3/2013 5:46:53 PM
Posted: 3 years ago
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?
Sidewalker
Posts: 3,713
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3/3/2013 6:05:00 PM
Posted: 3 years ago
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

Nope, you can't traverse an infinite, so the potential would never be actualized.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
unitedandy
Posts: 1,173
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3/3/2013 6:26:17 PM
Posted: 3 years ago
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?
unitedandy
Posts: 1,173
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3/3/2013 6:34:40 PM
Posted: 3 years ago
At 3/3/2013 6:05:00 PM, Sidewalker wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

Nope, you can't traverse an infinite, so the potential would never be actualized.

Not only does such a response beg the question, it misses the point.

Obviously, there would be no point God reaches infinity as a number and stops. But that's not what I'm asking. I'm asking how many numbers WOULD be counted, if God counted forever.
Apeiron
Posts: 2,446
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3/3/2013 6:36:33 PM
Posted: 3 years ago
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.
Illegalcombatant
Posts: 4,008
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3/3/2013 6:42:51 PM
Posted: 3 years ago
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

I recall once from my extensive research into infinities, and by research I mean flipping through the tv channels. And it mentioned some guy who's view was that you could have different size ? set ? infinities.

The guy apparently went crazy.
"Seems like another attempt to insert God into areas our knowledge has yet to penetrate. You figure God would be bigger than the gaps of our ignorance." Drafterman 19/5/12
unitedandy
Posts: 1,173
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3/3/2013 6:44:07 PM
Posted: 3 years ago
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

No, there's no such thing as forever plus 1. Forever includes the plus one and the one after that literally ad infinitium (or at least so it seems).
Apeiron
Posts: 2,446
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3/3/2013 6:47:34 PM
Posted: 3 years ago
At 3/3/2013 6:44:07 PM, unitedandy wrote:
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

No, there's no such thing as forever plus 1. Forever includes the plus one and the one after that literally ad infinitium (or at least so it seems).

If there's no such thing as forever plus 1, then why think there's "forever"? ... Again, this ignores the distinction Aristotle made.

Potential infinities exist. As evidenced by what you're getting at, but actual infinities, that's just an imagination.
Apeiron
Posts: 2,446
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3/3/2013 6:48:29 PM
Posted: 3 years ago
At 3/3/2013 6:42:51 PM, Illegalcombatant wrote:
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

I recall once from my extensive research into infinities, and by research I mean flipping through the tv channels. And it mentioned some guy who's view was that you could have different size ? set ? infinities.

The guy apparently went crazy.

I want to say cool story bro so bad right now..
Kinesis
Posts: 3,667
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3/3/2013 6:59:18 PM
Posted: 3 years ago
My thoughts on this basically are: there are no contradictions in supposing that actual infinities exist. 'Metaphysically impossible' seems to just be another way of saying 'it would be fucking weird if it existed'. Since it would be so weird I'd prefer we only used infinities as explanations if that explanation was the best out of a very bad bunch. But in that case I'd prefer to remain agnostic anyway.
Apeiron
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3/3/2013 7:00:20 PM
Posted: 3 years ago
At 3/3/2013 6:59:18 PM, Kinesis wrote:
My thoughts on this basically are: there are no contradictions in supposing that actual infinities exist. 'Metaphysically impossible' seems to just be another way of saying 'it would be fucking weird if it existed'. Since it would be so weird I'd prefer we only used infinities as explanations if that explanation was the best out of a very bad bunch. But in that case I'd prefer to remain agnostic anyway.

COOL STORY BRO!!
unitedandy
Posts: 1,173
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3/3/2013 7:01:10 PM
Posted: 3 years ago
At 3/3/2013 6:47:34 PM, Apeiron wrote:
At 3/3/2013 6:44:07 PM, unitedandy wrote:
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

No, there's no such thing as forever plus 1. Forever includes the plus one and the one after that literally ad infinitium (or at least so it seems).

If there's no such thing as forever plus 1, then why think there's "forever"? ...

Because forever would incorporate the plus one.

Again, this ignores the distinction Aristotle made.

Don't theists typically believe in eternal life and such? An eternally typing monkey would be exact same thought experiment and the question would still apply.

How many letters would an eternally typing monkey type?


Potential infinities exist. As evidenced by what you're getting at, but actual infinities, that's just an imagination.
Sidewalker
Posts: 3,713
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3/3/2013 7:04:06 PM
Posted: 3 years ago
At 3/3/2013 6:48:29 PM, Apeiron wrote:
At 3/3/2013 6:42:51 PM, Illegalcombatant wrote:
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

I recall once from my extensive research into infinities, and by research I mean flipping through the tv channels. And it mentioned some guy who's view was that you could have different size ? set ? infinities.

The guy apparently went crazy.

I want to say cool story bro so bad right now..

He's talking a Georg Cantor, invented set theory and transfinite numbers, he died in a sanatorium.

Pondering infinity will do that.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
Apeiron
Posts: 2,446
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3/3/2013 7:04:25 PM
Posted: 3 years ago
At 3/3/2013 7:01:10 PM, unitedandy wrote:



If there's no such thing as forever plus 1, then why think there's "forever"? ...

Because forever would incorporate the plus one.

Why's that so special?

Again, this ignores the distinction Aristotle made.

Don't theists typically believe in eternal life and such? An eternally typing monkey would be exact same thought experiment and the question would still apply.

Yes, eternal life as in potential infinity. No one actually thinks that one day in heaven, boom, actual infinity by noon and everyone parties.

How many letters would an eternally typing monkey type?

Like soo many, but he / she / it can always type one more.
Apeiron
Posts: 2,446
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3/3/2013 7:05:28 PM
Posted: 3 years ago
At 3/3/2013 7:04:06 PM, Sidewalker wrote:
At 3/3/2013 6:48:29 PM, Apeiron wrote:
At 3/3/2013 6:42:51 PM, Illegalcombatant wrote:
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

I recall once from my extensive research into infinities, and by research I mean flipping through the tv channels. And it mentioned some guy who's view was that you could have different size ? set ? infinities.

The guy apparently went crazy.

I want to say cool story bro so bad right now..

He's talking a Georg Cantor, invented set theory and transfinite numbers, he died in a sanatorium.

Pondering infinity will do that.

Oh I just think that was the nature of the beast, look at Tesla, Newton too that guy nearly gouged his eye out looking for different spectra. SCIENCE!
Kinesis
Posts: 3,667
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3/3/2013 7:09:04 PM
Posted: 3 years ago
At 3/3/2013 7:00:20 PM, Apeiron wrote:
At 3/3/2013 6:59:18 PM, Kinesis wrote:
My thoughts on this basically are: there are no contradictions in supposing that actual infinities exist. 'Metaphysically impossible' seems to just be another way of saying 'it would be fucking weird if it existed'. Since it would be so weird I'd prefer we only used infinities as explanations if that explanation was the best out of a very bad bunch. But in that case I'd prefer to remain agnostic anyway.

COOL STORY BRO!!

http://media.tumblr.com...
Apeiron
Posts: 2,446
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3/3/2013 7:13:41 PM
Posted: 3 years ago
At 3/3/2013 7:09:04 PM, Kinesis wrote:
At 3/3/2013 7:00:20 PM, Apeiron wrote:
At 3/3/2013 6:59:18 PM, Kinesis wrote:
My thoughts on this basically are: there are no contradictions in supposing that actual infinities exist. 'Metaphysically impossible' seems to just be another way of saying 'it would be fucking weird if it existed'. Since it would be so weird I'd prefer we only used infinities as explanations if that explanation was the best out of a very bad bunch. But in that case I'd prefer to remain agnostic anyway.

COOL STORY BRO!!

http://media.tumblr.com...

hell ya, fvcking love baby parrots!
Sidewalker
Posts: 3,713
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3/3/2013 7:18:00 PM
Posted: 3 years ago
At 3/3/2013 7:05:28 PM, Apeiron wrote:
At 3/3/2013 7:04:06 PM, Sidewalker wrote:
At 3/3/2013 6:48:29 PM, Apeiron wrote:
At 3/3/2013 6:42:51 PM, Illegalcombatant wrote:
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

I recall once from my extensive research into infinities, and by research I mean flipping through the tv channels. And it mentioned some guy who's view was that you could have different size ? set ? infinities.

The guy apparently went crazy.

I want to say cool story bro so bad right now..

He's talking a Georg Cantor, invented set theory and transfinite numbers, he died in a sanatorium.

Pondering infinity will do that.

Oh I just think that was the nature of the beast, look at Tesla, Newton too that guy nearly gouged his eye out looking for different spectra. SCIENCE!

I think Newton was autistic...and Tesla's behavior was probably normal for whatever planet he was from.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
Apeiron
Posts: 2,446
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3/3/2013 7:21:41 PM
Posted: 3 years ago
At 3/3/2013 7:18:00 PM, Sidewalker wrote:
At 3/3/2013 7:05:28 PM, Apeiron wrote:
At 3/3/2013 7:04:06 PM, Sidewalker wrote:
At 3/3/2013 6:48:29 PM, Apeiron wrote:
At 3/3/2013 6:42:51 PM, Illegalcombatant wrote:
At 3/3/2013 6:36:33 PM, Apeiron wrote:
At 3/3/2013 6:26:17 PM, unitedandy wrote:
At 3/3/2013 5:46:53 PM, Apeiron wrote:
At 3/3/2013 5:30:31 PM, unitedandy wrote:
At 3/3/2013 5:07:27 PM, Apeiron wrote:
At 3/3/2013 5:04:33 PM, unitedandy wrote:
At 3/3/2013 4:36:39 PM, Apeiron wrote:
Infinity just serves as an idealization in math. It's a limit just like in science PV=nRT serves as an ideal limit for gas, the ideal gas law. But everyone knows there is no ideal gas out there.

Like SideWalker said, actual infinity may be used in mathematics, but when you apply it to reality you get contradictory results. Even in math you do, for identical quantities minus identical quantities leads to contradictory answers as Craig, Hilbert, etc have all shown.

So it's not that infinity is some mysterious thing that we're ignorant on, rather it's that we know about infinity! Hilbert was a great mathematician and a genius, he knew just what made infinity metaphysically absurd, and he showed this by various thought experiments.

One of the criticisms is that they misuse infinity though, in the same way as one does when they divide by zero. Also, Hilbert's hotel and Craig's library take objects and rearrange them to get contradictions, which obviously just can't be done with events.

If God were to count for all eternity, how many numbers would He count? It seems to me the answer would have to be infinitely many, even though we know at no point does He reach infinity.

Yup, that's all potential infinity.

How can it be a potential infinity? Unless God ceases to exist, he'll be counting forever. In other words, the "potential" would be actualised.

When it's said that God is eternal it's meant in a qualitative sense, not quantitative. What would it even mean for God to be quantitatively eternal?

Whether God is eternal or not isn't the issue. If it helps, think of a monkey typing forever. How many letters would he type?

A lot of letters. But he could always have typed one more.

I recall once from my extensive research into infinities, and by research I mean flipping through the tv channels. And it mentioned some guy who's view was that you could have different size ? set ? infinities.

The guy apparently went crazy.

I want to say cool story bro so bad right now..

He's talking a Georg Cantor, invented set theory and transfinite numbers, he died in a sanatorium.

Pondering infinity will do that.

Oh I just think that was the nature of the beast, look at Tesla, Newton too that guy nearly gouged his eye out looking for different spectra. SCIENCE!

I think Newton was autistic...and Tesla's behavior was probably normal for whatever planet he was from.

You're probably right about Newton. All of his painting's look autsy ZING!
unitedandy
Posts: 1,173
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3/3/2013 7:28:43 PM
Posted: 3 years ago
At 3/3/2013 7:04:25 PM, Apeiron wrote:
At 3/3/2013 7:01:10 PM, unitedandy wrote:



If there's no such thing as forever plus 1, then why think there's "forever"? ...

Because forever would incorporate the plus one.

Why's that so special?

Because it cuts off your response.

Again, this ignores the distinction Aristotle made.

Don't theists typically believe in eternal life and such? An eternally typing monkey would be exact same thought experiment and the question would still apply.

Yes, eternal life as in potential infinity. No one actually thinks that one day in heaven, boom, actual infinity by noon and everyone parties.

And eternal life is actualised, presumably. Even if it weren't, it's a thought experiment. .

Again, Infinity isn't like a destination in the road map, where one eventually reaches. But if we ask, how many numbers will we count, the answer will have to be infinitely many.


How many letters would an eternally typing monkey type?

Like soo many, but he / she / it can always type one more.

Again, eternity includes this plus one and everything that comes after and before it. So how many would this be?
Apeiron
Posts: 2,446
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3/3/2013 7:36:24 PM
Posted: 3 years ago
At 3/3/2013 7:28:43 PM, unitedandy wrote:
At 3/3/2013 7:04:25 PM, Apeiron wrote:
At 3/3/2013 7:01:10 PM, unitedandy wrote:



If there's no such thing as forever plus 1, then why think there's "forever"? ...

Because forever would incorporate the plus one.

Why's that so special?

Because it cuts off your response.

Not really, there's nothing obvious about there being a set called "forever" which can't be added to.

Again, this ignores the distinction Aristotle made.

Don't theists typically believe in eternal life and such? An eternally typing monkey would be exact same thought experiment and the question would still apply.

Yes, eternal life as in potential infinity. No one actually thinks that one day in heaven, boom, actual infinity by noon and everyone parties.

And eternal life is actualised, presumably. Even if it weren't, it's a thought experiment. .

It's an imagination, that there's this instance where before it there was only working towards infinity, but now it's reached it's goal, by if we're now in infinity, why did we reach it yesterday? Why has it been a finite time until now? What made it switch?


Again, Infinity isn't like a destination in the road map, where one eventually reaches. But if we ask, how many numbers will we count, the answer will have to be infinitely many.

Counting... think about it, you're counting towards a number from another, that wall between finitude and actual infinitude is as yet without any content. I haven't any idea what you're talking about.



How many letters would an eternally typing monkey type?

Like soo many, but he / she / it can always type one more.

Again, eternity includes this plus one and everything that comes after and before it. So how many would this be?

THat's just a meaningless question which presupposes the existence of an actual infinitude rather than potential..