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aleph naught

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Re: Argument against Infinity
« Reply #45 on: May 21, 2015, 02:21:21 pm »
Quote from: aleph naught
So it must be possible to perform an infinite many tasks instantaniously, and produce an actual infinity through successive addition.
 

No this is nonsense as you cannot arrive at infinite instances from potentially infinite no matter how many successive additions one does.

For example even if you were to construct a computer that calculate algorithm  i =1; (i++) instantaneously you would never arrive at a point wherein the variable i is not an actual finite number. To say otherwise is nonsensical i.e. wherein does the algorithm actually produce i = infinite and not a finite number?

Hate to break it to you, but if you've done an infinite many successive additions, then you've 'arrived at infinity'. You're confusing an infinite many objects within a collection, and an infinite numerical value. I never said amything about infinite numerical value, so this is a straw man.

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kurros

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Re: Argument against Infinity
« Reply #46 on: May 21, 2015, 02:25:07 pm »
Quote from: aleph naught
So it must be possible to perform an infinite many tasks instantaniously, and produce an actual infinity through successive addition.
 

No this is nonsense as you cannot arrive at infinite instances from potentially infinite no matter how many successive additions one does.

For example even if you were to construct a computer that calculate algorithm  i =1; (i++) instantaneously you would never arrive at a point wherein the variable i is not an actual finite number. To say otherwise is nonsensical i.e. wherein does the algorithm actually produce i = infinite and not a finite number?

Infinity is not an integer, so of course "i" will never "equal" infinity. It is logically impossible due to the definition of infinity, not due to the algorithm. Nevertheless you will get an infinite collection of integers if you perform this iterative process infinitely many times.

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innerbling

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Re: Argument against Infinity
« Reply #47 on: May 21, 2015, 02:54:29 pm »
Quote from: kurros
Infinity is not an integer, so of course "i" will never "equal" infinity. It is logically impossible due to the definition of infinity, not due to the algorithm. Nevertheless you will get an infinite collection of integers if you perform this iterative process infinitely many times.

Now tell me what value does the variable i attain if you are able to run the algorithm infinite times? Does it suddenly become a infinite collection of integers as you seem to assume? Obviously not as the variable i can only have one finite number and this number will never be "infinite" but a specific number.

It is simply nonsensical to say that this algorithm could be run infinite times and one could get some other result rather than a finite number. This is why processes like these are always potentially infinite never actually infinite.


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innerbling

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Re: Argument against Infinity
« Reply #48 on: May 21, 2015, 03:06:26 pm »
Quote from: aleph naught
Hate to break it to you, but if you've done an infinite many successive additions, then you've 'arrived at infinity'. You're confusing an infinite many objects within a collection, and an infinite numerical value. I never said amything about infinite numerical value, so this is a straw man.

The point of my simple illustration was that you cannot ever logically do "infinite many successive additions" with the algorithm so your point is moot. That is variable i will never coherently "arrive at infinity" whatever that means in this context as the result will always be a finite number no matter how many times it is run.



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kurros

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Re: Argument against Infinity
« Reply #49 on: May 21, 2015, 03:29:22 pm »
Quote from: kurros
Infinity is not an integer, so of course "i" will never "equal" infinity. It is logically impossible due to the definition of infinity, not due to the algorithm. Nevertheless you will get an infinite collection of integers if you perform this iterative process infinitely many times.

Now tell me what value does the variable i attain if you are able to run the algorithm infinite times? Does it suddenly become a infinite collection of integers as you seem to assume? Obviously not as the variable i can only have one finite number and this number will never be "infinite" but a specific number.

It is simply nonsensical to say that this algorithm could be run infinite times and one could get some other result rather than a finite number. This is why processes like these are always potentially infinite never actually infinite.

The "final value" which "i" has is undefined, because there is no "final value".

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Emuse

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Re: Argument against Infinity
« Reply #50 on: May 21, 2015, 05:00:46 pm »
If no world contains a timeless cause then no world contains a timeless cause.

Right.

Not quite.

Let's grant that there is a necessary being N and that N exists timelessly in all possible worlds.  Let's also grant the KCA ...

P1. For any X, if X began to exist then there exists some cause C, such that C caused X.
P2. The universe began to exist.
C. Therefore, there exists some cause C, such that C caused the universe.

So now we have a necessary and timeless being N and a cause of the universe C.  These are both granted.  Now we have to demonstrate that they are the same being (eg, that N = C) in worlds where universes are caused.  But, there is a problem ..

P1. For any Y, if Y has a timeless cause then Y is a timeless effect.
P2. The universe is a temporal effect.
C. Therefore, the universe has a temporal cause.

So given that P1 and P2 are true (and Craig grants P1 which is why he has God becoming temporal with a universe ... if P1 wasn't true he wouldn't need to) we now know that C is temporal.  So we have a necessary and timeless being N and a temporal being C.   Given that N is timeless and C is temporal we can no longer arbitrarily declare that they are the same being.  But we need them to be the same entity (C is N as a consequence of N undergoing a change) otherwise premise 1 of Kalam is false.

But there is another problem.  Given the second argument, it is necessarily the case that the cause of the universe is temporal which entails it is necessarily the case that the cause of the universe isn't timeless.  But this means that although N exists timelessly in all possible worlds it is still the case that there is no possible world in which N is the cause of a universe (the cause of the universe must be temporal and N is timeless). 

If there is no possible world in which an entity does X, then by definition that entity is incapable of X.  For example, God is incapable of evil by virtue of the fact that he is omnibenevolent in all possible worlds.  A two year old human is incapable of being father for the very reason that there is no possible world in which a two year old human fathers a child.  So, if there is no possible world in which N causes a universe then N is incapable of causing a universe.  It follows from this that N can't be omnipotent ...

P1. For any X, if it is metaphysically impossible for X to cause Y then X is incapable of causing Y.
P2. It is metaphysically impossible for N to cause a universe.
C. Therefore, N is incapable of causing a universe.
P3. For any Y, if Y is incapable of causing a universe then Y is not God.
C1. Therefore, N is not God.

In order for an entity to be God, there must be a possible world where that entity causes a universe and there is no possible world in which a timeless being causes a universe.
« Last Edit: May 21, 2015, 05:59:40 pm by Emuse »

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innerbling

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Re: Argument against Infinity
« Reply #51 on: May 21, 2015, 05:52:05 pm »
Quote from: kurros
The "final value" which "i" has is undefined, because there is no "final value".

I said nothing about the final value but pointed out a simple fact that any value variable i attains is necessarily finite. So there is no logical way wherein variable "i" becomes something else rather than a finite number thus coherently the process itself is at most potentially infinite.

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aleph naught

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Re: Argument against Infinity
« Reply #52 on: May 21, 2015, 08:37:49 pm »
Quote from: kurros
Infinity is not an integer, so of course "i" will never "equal" infinity. It is logically impossible due to the definition of infinity, not due to the algorithm. Nevertheless you will get an infinite collection of integers if you perform this iterative process infinitely many times.

Now tell me what value does the variable i attain if you are able to run the algorithm infinite times? Does it suddenly become a infinite collection of integers as you seem to assume? Obviously not as the variable i can only have one finite number and this number will never be "infinite" but a specific number.

It is simply nonsensical to say that this algorithm could be run infinite times and one could get some other result rather than a finite number. This is why processes like these are always potentially infinite never actually infinite.

Why think i must have numerical value?

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ParaclitosLogos

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Re: Argument against Infinity
« Reply #53 on: May 21, 2015, 09:36:03 pm »
Argument against Infinity:

1.) If you could obtain the actual value of infinity you could not add one more
2.) You can always add one more
3.) Therefore you cannot obtain the actual value of infinity


There are thought experiments that demonstrate that infinity is impossible, but I wanted to express it as a syllogism to hopefully give it some clarification. Would be nice to give it a fancy title but Argument against Infinity works.

I would defend P1 by saying it would be a self contradiction to claim the value of infinity and then add one more to it. By adding one more to infinity you've proven it was at least one short of infinity.

Some Atheists have claimed the universe is infinite in the past, meaning yesterday we obtained the actual value of infinity and added one more today. Few atheists still hold to this but you still hear it now and then.

Seems to me, The conclusion should be you can not obtain an actual infinity by consecutive addition of finite numbers of elements, so the argument is valid.

That wouldn't follow from his premises, though. And, that just wouldn't be true. If we added members to a set instantaneously, we could add an infinite members to the set instantaneously (because each addition would require no time). It seems theists, especially those who use the Kalam, are committed to the possibility of instantanious causation.

You are right, it does not follow from the premises, but, that was not what I was trying to say, though admitedly, I was as unclear as can be, because I wrote in a hurry.

Also, I meant consecutive as in successive accrual.

I have no idea what the rest about Kalam and theist commitments has got to do with anything.

If God created timelessly, then he would have had to have done so instantaniously. So instantanious causation must be possible. So it must be possible to perform an infinite many tasks instantaniously, and produce an actual infinity through successive addition.

Why would God have to produce an infinite many tasks, and, not just a googleplex to the googleplex to the googleplex many tasks?

Sorry, I have been performing too many tasks myself, lately.

I didn't say he'd have to, just that he could. God could perform an infinite many tasks if he performed each one instantaneously.

Oh, ok.

Right, maybe, that could be put forward to a Thomist, but,  I don´t know enough about the position.

On Dr. Craig´s type of view, God does not create timelessly.

Then how could God be the cause of the universe? The origin of the universe is the origin of time itself. God's act of creation cannot have temporal duration.

When would the universe be created (Be it God or not) ? shouldn´t it be created at the 1st moment in time?

that's not incompatible with God creating instantaniously. (Though, we don't have any reason to think there was a first moment). Again, though, how could God's creation of time have temporal duration? Time must exist before causal relationships can have temporal duration.

If time is discrete (as some physicist seem to think) then each time event would have a duration, an event then is time intervals. The  specific 1st time interval with no equally long time interval before it, would be the 1st time event at which X brings about time and the universe.
« Last Edit: May 21, 2015, 09:37:59 pm by ontologicalme »

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aleph naught

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Re: Argument against Infinity
« Reply #54 on: May 21, 2015, 10:20:15 pm »
Argument against Infinity:

1.) If you could obtain the actual value of infinity you could not add one more
2.) You can always add one more
3.) Therefore you cannot obtain the actual value of infinity


There are thought experiments that demonstrate that infinity is impossible, but I wanted to express it as a syllogism to hopefully give it some clarification. Would be nice to give it a fancy title but Argument against Infinity works.

I would defend P1 by saying it would be a self contradiction to claim the value of infinity and then add one more to it. By adding one more to infinity you've proven it was at least one short of infinity.

Some Atheists have claimed the universe is infinite in the past, meaning yesterday we obtained the actual value of infinity and added one more today. Few atheists still hold to this but you still hear it now and then.

Seems to me, The conclusion should be you can not obtain an actual infinity by consecutive addition of finite numbers of elements, so the argument is valid.

That wouldn't follow from his premises, though. And, that just wouldn't be true. If we added members to a set instantaneously, we could add an infinite members to the set instantaneously (because each addition would require no time). It seems theists, especially those who use the Kalam, are committed to the possibility of instantanious causation.

You are right, it does not follow from the premises, but, that was not what I was trying to say, though admitedly, I was as unclear as can be, because I wrote in a hurry.

Also, I meant consecutive as in successive accrual.

I have no idea what the rest about Kalam and theist commitments has got to do with anything.

If God created timelessly, then he would have had to have done so instantaniously. So instantanious causation must be possible. So it must be possible to perform an infinite many tasks instantaniously, and produce an actual infinity through successive addition.

Why would God have to produce an infinite many tasks, and, not just a googleplex to the googleplex to the googleplex many tasks?

Sorry, I have been performing too many tasks myself, lately.

I didn't say he'd have to, just that he could. God could perform an infinite many tasks if he performed each one instantaneously.

Oh, ok.

Right, maybe, that could be put forward to a Thomist, but,  I don´t know enough about the position.

On Dr. Craig´s type of view, God does not create timelessly.

Then how could God be the cause of the universe? The origin of the universe is the origin of time itself. God's act of creation cannot have temporal duration.

When would the universe be created (Be it God or not) ? shouldn´t it be created at the 1st moment in time?

that's not incompatible with God creating instantaniously. (Though, we don't have any reason to think there was a first moment). Again, though, how could God's creation of time have temporal duration? Time must exist before causal relationships can have temporal duration.

If time is discrete (as some physicist seem to think) then each time event would have a duration, an event then is time intervals. The  specific 1st time interval with no equally long time interval before it, would be the 1st time event at which X brings about time and the universe.

Sure, but why would we think time is discrete?

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Booger

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Re: Argument against Infinity
« Reply #55 on: May 22, 2015, 12:46:55 am »
In discussing in infinity, I always suggest that people read Holophany: The Loop of Creation.
« Last Edit: May 22, 2015, 12:49:06 am by Booger »
-- This user has been banned for abusing forum staff --

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kurros

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Re: Argument against Infinity
« Reply #56 on: May 22, 2015, 05:14:53 am »
Quote from: kurros
The "final value" which "i" has is undefined, because there is no "final value".

I said nothing about the final value but pointed out a simple fact that any value variable i attains is necessarily finite. So there is no logical way wherein variable "i" becomes something else rather than a finite number thus coherently the process itself is at most potentially infinite.

That's silly. You can say the exact same thing about integers in general. Every integer has a finite value, but there are still infinitely many of them.

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ParaclitosLogos

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Re: Argument against Infinity
« Reply #57 on: May 22, 2015, 05:33:11 am »
Argument against Infinity:

1.) If you could obtain the actual value of infinity you could not add one more
2.) You can always add one more
3.) Therefore you cannot obtain the actual value of infinity


There are thought experiments that demonstrate that infinity is impossible, but I wanted to express it as a syllogism to hopefully give it some clarification. Would be nice to give it a fancy title but Argument against Infinity works.

I would defend P1 by saying it would be a self contradiction to claim the value of infinity and then add one more to it. By adding one more to infinity you've proven it was at least one short of infinity.

Some Atheists have claimed the universe is infinite in the past, meaning yesterday we obtained the actual value of infinity and added one more today. Few atheists still hold to this but you still hear it now and then.

Seems to me, The conclusion should be you can not obtain an actual infinity by consecutive addition of finite numbers of elements, so the argument is valid.

That wouldn't follow from his premises, though. And, that just wouldn't be true. If we added members to a set instantaneously, we could add an infinite members to the set instantaneously (because each addition would require no time). It seems theists, especially those who use the Kalam, are committed to the possibility of instantanious causation.

You are right, it does not follow from the premises, but, that was not what I was trying to say, though admitedly, I was as unclear as can be, because I wrote in a hurry.

Also, I meant consecutive as in successive accrual.

I have no idea what the rest about Kalam and theist commitments has got to do with anything.

If God created timelessly, then he would have had to have done so instantaniously. So instantanious causation must be possible. So it must be possible to perform an infinite many tasks instantaniously, and produce an actual infinity through successive addition.

Why would God have to produce an infinite many tasks, and, not just a googleplex to the googleplex to the googleplex many tasks?

Sorry, I have been performing too many tasks myself, lately.

I didn't say he'd have to, just that he could. God could perform an infinite many tasks if he performed each one instantaneously.

Oh, ok.

Right, maybe, that could be put forward to a Thomist, but,  I don´t know enough about the position.

On Dr. Craig´s type of view, God does not create timelessly.

Then how could God be the cause of the universe? The origin of the universe is the origin of time itself. God's act of creation cannot have temporal duration.

When would the universe be created (Be it God or not) ? shouldn´t it be created at the 1st moment in time?

that's not incompatible with God creating instantaniously. (Though, we don't have any reason to think there was a first moment). Again, though, how could God's creation of time have temporal duration? Time must exist before causal relationships can have temporal duration.

If time is discrete (as some physicist seem to think) then each time event would have a duration, an event then is time intervals. The  specific 1st time interval with no equally long time interval before it, would be the 1st time event at which X brings about time and the universe.

Sure, but why would we think time is discrete?

Why not?

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innerbling

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Re: Argument against Infinity
« Reply #58 on: May 22, 2015, 12:34:50 pm »
Quote from: kurros
That's silly. You can say the exact same thing about integers in general. Every integer has a finite value, but there are still infinitely many of them.

Where do you have this infinite collection of integers? You confuse potentiality, mathematical descriptions with what actually can coherently exist. It is obviously not true that someone has made an actual infinite collection of integers but that mathematical descriptions that refer to the infinite are procedural or approximations of the concept.

That is  natural numbers 1,2,3,... is conceptually infinite series but not infinite in the actual world as natural numbers describes a procedural which approaches infinity however never coherently reaching it.