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Infinite regress of causes
Posted: 14 March 2009 08:00 AM   [ Ignore ]   [ # 16 ]
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omnibus09 - 13 March 2009 08:13 PM

These types of metaphysical meanderings must use ‘time’ as a concept, and in addition ‘infinity’ as another concept.

I believe that time is a human construct to explain the actions of the physical observable world, the laws of thermodynamics and the ‘arrow of time’ notwithstanding.

Infinity or infinite describes something that is beyond the pale of human understanding, and human understanding has limitations.

Having said the above, many scientists now consider the concept of an infinite series of forming and expanding universes.

The terms used in these types of discussions become rather squishy and hard to pin down.

We need not refer to time in order to address infinite regress.  We’re stuck with infinities, on the other hand—but infinities aren’t that squishy if we keep our wits about us.  smile

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Posted: 14 March 2009 02:02 PM   [ Ignore ]   [ # 17 ]
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Bryan - 14 March 2009 07:33 AM

I’ve explained to you why that isn’t the case.  Will you deal with the substance of the objection to an infinite regress or not?


Successive addition cannot cross an actual infinite?  This is misleading.

Not only is ‘infinite’ not a line that can or cannot be crossed in that sense, but there is nothing particular about addition with this regard.

Though, regardless, this does not present a solution to this problem in the Kalam argument.

I’m not averse to starting at the beginning.  Are you?

By all means, lets.

By definition, the universe we live in is infinite, it is expanding without apparent end, and there are no signs or reasons to properly assert that it will or must.

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Posted: 14 March 2009 05:29 PM   [ Ignore ]   [ # 18 ]
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Mathenaut - 14 March 2009 02:02 PM
Bryan - 14 March 2009 07:33 AM

I’ve explained to you why that isn’t the case.  Will you deal with the substance of the objection to an infinite regress or not?


Successive addition cannot cross an actual infinite?  This is misleading.

Not only is ‘infinite’ not a line that can or cannot be crossed in that sense, but there is nothing particular about addition with this regard.

I did not refer to it as a line.  An infinite is typically described as a series in a set.  You can’t get through the set via successive addition.  Which one of us is misleading?  Me or thee?

Though, regardless, this does not present a solution to this problem in the Kalam argument.

Why not?  The only problem you’ve suggested, AFAICT, is that the problem alleged by the Kalam argument does not exist.  If you intend to deal with the objection of the Kalam argument to crossing an actual infinite (not a line, but a series), then you’ll need to improve your argument, IMHO.

I’m not averse to starting at the beginning.  Are you?

By all means, lets.

By definition, the universe we live in is infinite, it is expanding without apparent end, and there are no signs or reasons to properly assert that it will or must.

And therefore we can cross the infinite universe via successive addition?  Or am I missing something in your logic?

Seriously, the universe is generally held to be finite as to its constituent parts.  If it is finite then we could hope to cross a set of those parts via successive addition.  If, on the other hand, you refer to the expanse of space which might forever extend itself then you would seem to be talking about a potential infinite rather than an actual infinite—and you analogy makes my point for me in a different way (do we ever reach a point at which the expansion of the universe must stop for lack of being able to successively add on additional space?).

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Posted: 14 March 2009 09:17 PM   [ Ignore ]   [ # 19 ]
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Bryan - 14 March 2009 07:42 AM

I’ll zero straight in on they key graph:

Time isn’t the issue.  The issue is crossing an actual infinite via successive addition, which appears to be impossible regardless of time. 

Regress arguments from epistemology seem of dubious value when we’re talking about causation rather than justification; in any case it’s not apparent how one could cross an actual infinite via successive addition in justifying a statement any more than once could produce a cause via the crossing of an actual infinite via successive addition.


Saying “Ta-da!” at the end doesn’t fully account for the phenomenon.

Time or a temporal concept is one of the issues, besides the issue of an actual infinite.

I refer you to this article, “Cosmological Kalamity”:

http://www.infidels.org/library/modern/dan_barker/kalamity.html

Theists regularly talk about a place “beyond” the universe, a transcendent realm where God exists “outside of time.”

  “. . . the universe has a cause. This conclusion ought to stagger us, to fill us with awe, for it means that the universe was brought into existence by something which is greater than and beyond it.”[10] [emphasis in original]

Of course, if you live “outside of time,” whatever that means, then you don’t need a beginning in time. A transcendent being, living “beyond” nature, is conveniently exempt from the limitations of natural law, and all complaints that God himself must have had a cause or a designer (using the same natural reasoning that tries to call for his existence) can be dismissed by theists who insist that God is outside the loop, unaffected by natural causality, beyond time.

Yet theists continue to describe this “timeless” being in temporal terms. Phrases such as “God decided to create the universe” are taken by us mere mortals to be analogous to such natural phrases as “Annie Laurie decided to bake a pie.” If such phrases are not equal or analogous to normal human language, and if they are not redefined coherently, then they are useless. We may as well say “God blopwaddled to scrumpwitch the universe.”

Regarding an actual infinite:

This means that there must exist a series of antecedent causal events in the mind of a time-transcendent creator, if such a being exists. Since the Kalam argument claims that “an actual infinity cannot exist in reality,” it shoots itself in the foot: although Kalam deals with temporal succession, the same logic applies to non-temporal antecedent events, if such things are a part of reality. If the series were infinite, then God never could have traversed the totality of his own antecedent mental causes to arrive at his decision to say “Let there be light.” Therefore, sticking with Kalam, there must have been a “first antecedent” in the mind of an actual God, which means that God “began” to exist. (This means “began causally,” but theists have conceded the appropriateness of expressing non-temporal actions in temporal language.)

If theists counter that the Kalam argument applies only to the impossibility of an actual mathematical infinity within the material universe and that the transcendent, timeless domain of the Creator is an entirely different kind of “infinity” that is not subject to the same laws, then they are begging the question, again. Exempting the conclusion, by definition, from the premises by excluding the supernatural (the very thing theists are trying to prove) is circular reasoning. If it is true that an “actual infinity cannot exist in reality,” then a being who is actually infinite cannot be a part of reality. In other words, the Kalam disproves the reality of a beginning-less God. If infinity is just a concept, as Kalam insists, then an infinite God is just a concept.

If we take Kalam seriously, there is no escaping the fact that God (if he exists) had a beginning, either in or out of time[13]. Since this is true, the phrase “Everything that begins to exist” includes God, and sticking with the cosmological argument, it follows that God has a cause.

Regarding the creator (mother) of the universe:

Bertrand Russell, in his 1948 debate with Copleston, touched on the matter:

  “I should say that the universe is just there, and that’s all. . . . I can illustrate what seems to me your fallacy. Every man who exists has a mother, and it seems to me your argument is that therefore the human race must have a mother, but obviously the human race hasn’t a mother—that’s a different logical sphere.”

Copleston, responding to Russell, asked: “But are you going to say that we can’t, or we shouldn’t even raise the question of the existence of the whole of this sorry scheme of things—of the whole universe?”

“Yes,” Russell replied. “I don’t think there’s any meaning in it at all. I think the word ‘universe’ is a handy word in some connections, but I don’t think it stands for anything that has a meaning.”

Conclusion:

In order for the Kalam Cosmological Argument to be salvaged, theists must answer these questions, at least:

  1. Is God the only object accommodated by the set of things that do not begin to exist?
      * If yes, then why is the cosmological argument not begging the question?
      * If no, then what are the other candidates for the cause of the universe, and how have they been eliminated?
  2. Does the logic of Kalam apply only to temporal antecedents in the real world?
      * If yes, this assumes the existence of nontemporal antecedents in the real world, so why is this not begging the question?
      * If no, then why doesn’t the impossibility of an actual infinity disprove the existence of an actually infinite God?
  3. Is the universe (cosmos) a member of itself?
      * If not, then how can its “beginning” be compared with other beginnings?

The problem with theist arguments is that they assume there must be a deity right from the start, which is begging the question. A valid argument should start from the premise that there is no deity and proceed to show evidence of a deity.

The philosophical concept of an absolute might be more useful:

http://en.wikipedia.org/wiki/The_Ultimate

The Absolute is the concept of an unconditional reality which transcends limited, conditional, everyday existence. It is often used as an alternate term for “God” or “the Divine”, especially, but by no means exclusively, by those who feel that the term “God” lends itself too easily to anthropomorphic presumptions. The concept of The Absolute may or may not (depending on one’s specific doctrine) possess discrete will, intelligence, awareness or even a personal nature. It contrasts with finite things, considered individually, and known collectively as the relative.

Roughly, the Absolute may be distinguished from the following concepts, although there is debate of the synonymity between them:

  * Thing-in-itself, an actual object and its properties independent of any observer.
  * Noumenon, an object as it is in itself independent of the mind.[1]

However, rather than distinguishing from the relative, the thing in itself is used to distinguish an actual object from phenomenon (the appearance of things-in-themselves to the senses).

Or Spinoza’s naturalistic pantheism:

http://en.wikipedia.org/wiki/Baruch_Spinoza

The consequences of Spinoza’s system also envisage a God that does not rule over the universe by providence, but a God which itself is the deterministic system of which everything in nature is a part. Thus, God is the natural world and has no personality.

Ta-da grin

[ Edited: 14 March 2009 09:22 PM by kkwan ]
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Posted: 15 March 2009 05:50 AM   [ Ignore ]   [ # 20 ]
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kkwan - 14 March 2009 09:17 PM
Bryan - 14 March 2009 07:42 AM

I’ll zero straight in on they key graph:

Time isn’t the issue.  The issue is crossing an actual infinite via successive addition, which appears to be impossible regardless of time. 

Regress arguments from epistemology seem of dubious value when we’re talking about causation rather than justification; in any case it’s not apparent how one could cross an actual infinite via successive addition in justifying a statement any more than once could produce a cause via the crossing of an actual infinite via successive addition.


Saying “Ta-da!” at the end doesn’t fully account for the phenomenon.

Time or a temporal concept is one of the issues, besides the issue of an actual infinite.

I refer you to this article, “Cosmological Kalamity”:

http://www.infidels.org/library/modern/dan_barker/kalamity.html

Dan Barker?  Are you serious?  Give us Graham Oppy instead, any day.

Theists regularly talk about a place “beyond” the universe, a transcendent realm where God exists “outside of time.”

  “. . . the universe has a cause. This conclusion ought to stagger us, to fill us with awe, for it means that the universe was brought into existence by something which is greater than and beyond it.”[10] [emphasis in original]

Of course, if you live “outside of time,” whatever that means, then you don’t need a beginning in time. A transcendent being, living “beyond” nature, is conveniently exempt from the limitations of natural law, and all complaints that God himself must have had a cause or a designer (using the same natural reasoning that tries to call for his existence) can be dismissed by theists who insist that God is outside the loop, unaffected by natural causality, beyond time.

Yet theists continue to describe this “timeless” being in temporal terms. Phrases such as “God decided to create the universe” are taken by us mere mortals to be analogous to such natural phrases as “Annie Laurie decided to bake a pie.” If such phrases are not equal or analogous to normal human language, and if they are not redefined coherently, then they are useless. We may as well say “God blopwaddled to scrumpwitch the universe.”

So far, Barker is not dealing with the basics of the Kalam argument.  Should we wonder whether or not he knows what it is?

Regarding an actual infinite:

This means that there must exist a series of antecedent causal events in the mind of a time-transcendent creator, if such a being exists. Since the Kalam argument claims that “an actual infinity cannot exist in reality,” it shoots itself in the foot: although Kalam deals with temporal succession, the same logic applies to non-temporal antecedent events, if such things are a part of reality. If the series were infinite, then God never could have traversed the totality of his own antecedent mental causes to arrive at his decision to say “Let there be light.” Therefore, sticking with Kalam, there must have been a “first antecedent” in the mind of an actual God, which means that God “began” to exist. (This means “began causally,” but theists have conceded the appropriateness of expressing non-temporal actions in temporal language.)

If theists counter that the Kalam argument applies only to the impossibility of an actual mathematical infinity within the material universe and that the transcendent, timeless domain of the Creator is an entirely different kind of “infinity” that is not subject to the same laws, then they are begging the question, again. Exempting the conclusion, by definition, from the premises by excluding the supernatural (the very thing theists are trying to prove) is circular reasoning. If it is true that an “actual infinity cannot exist in reality,” then a being who is actually infinite cannot be a part of reality. In other words, the Kalam disproves the reality of a beginning-less God. If infinity is just a concept, as Kalam insists, then an infinite God is just a concept.

If we take Kalam seriously, there is no escaping the fact that God (if he exists) had a beginning, either in or out of time[13]. Since this is true, the phrase “Everything that begins to exist” includes God, and sticking with the cosmological argument, it follows that God has a cause.

Now Barker is engaged with trying to suggest that the first cause somehow needs a first cause in turn in order to act—or something like that.  Apparently he mistakes the notion of being “outside of time” for a critical aspect of the Kalam argument.  He misses the point.  His talk of God having to cross an actual infinite is ridiculous, amounting to an ad hoc tu quoque.  On the contrary, the theistic solution is not to appeal to God’s ability to cross an actual infinite but instead to God’s ability to serve as an uncaused cause not only with respect to existence but with respect to action.

Regarding the creator (mother) of the universe:

Bertrand Russell, in his 1948 debate with Copleston, touched on the matter:

  “I should say that the universe is just there, and that’s all. . . . I can illustrate what seems to me your fallacy. Every man who exists has a mother, and it seems to me your argument is that therefore the human race must have a mother, but obviously the human race hasn’t a mother—that’s a different logical sphere.”

Why would you think that touches on the matter?

Copleston, responding to Russell, asked: “But are you going to say that we can’t, or we shouldn’t even raise the question of the existence of the whole of this sorry scheme of things—of the whole universe?”

“Yes,” Russell replied. “I don’t think there’s any meaning in it at all. I think the word ‘universe’ is a handy word in some connections, but I don’t think it stands for anything that has a meaning.”

http://www.bringyou.to/apologetics/p20.htm

It turns out that you left out quite a bit between the two exchanges.  It seems to me that Russell was rather evasive on the whole.

Conclusion:

In order for the Kalam Cosmological Argument to be salvaged, theists must answer these questions, at least:

  1. Is God the only object accommodated by the set of things that do not begin to exist?
      * If yes, then why is the cosmological argument not begging the question?
      * If no, then what are the other candidates for the cause of the universe, and how have they been eliminated?
  2. Does the logic of Kalam apply only to temporal antecedents in the real world?
      * If yes, this assumes the existence of nontemporal antecedents in the real world, so why is this not begging the question?
      * If no, then why doesn’t the impossibility of an actual infinity disprove the existence of an actually infinite God?
  3. Is the universe (cosmos) a member of itself?
      * If not, then how can its “beginning” be compared with other beginnings?

1)  No.
* other candidates for causation have not been eliminated at the basic stage of the Kalam argument.  Wm Lane Craig uses a separate set of arguments for that, arguments that Barker does not engage.  The first stage deals with having a beginning

2)  No.  As I pointed out above, it isn’t even necessary to appeal to time as such.  We can deal with series in or out of time or with series imagined for the sake of argument.
*The Kalam argument does not disprove the existence of an actually infinite God because we are not talking about crossing an actual infinite in that case—unless we accept something like Barker’s idea that God needs to cross an actual infinite in terms of the causes of the thought process involved in a given action.  Barker doesn’t seem to offer much rationale for accepting that notion.

3)  This question seems confused.  The “universe” is spoken of as “all that exists” or as the space-time continuum.  Barker appears to confuse the two meanings.  Obviously if we take “the universe” as all that exists then a god would simply be another name for the universe or part of the universe.  So obviously, within the context of the Kalam argument, “the universe” means the space-time continuum.  I don’t see any sense in referring to “the universe” being a member of itself in terms of the space-time continuum.  I can only conclude that Barker has equivocated.

The problem with theist arguments is that they assume there must be a deity right from the start, which is begging the question. A valid argument should start from the premise that there is no deity and proceed to show evidence of a deity.

The problem with Barker’s argument is that he assumes that the Kalam argument assumes a deity right from the start, which is incorrect.  The Kalam argument attempts to demonstrate the impossibility of crossing an actual infinite and from there posits a beginning which is then identified as god.  Later stages of the argument attempt to identify god as God.

I suggest we stick with the first portion of the argument.  We should discuss whether or not we have a first cause before worrying about the identification of the first cause.

The philosophical concept of an absolute might be more useful:

http://en.wikipedia.org/wiki/The_Ultimate

The Absolute is the concept of an unconditional reality which transcends limited, conditional, everyday existence. It is often used as an alternate term for “God” or “the Divine”, especially, but by no means exclusively, by those who feel that the term “God” lends itself too easily to anthropomorphic presumptions. The concept of The Absolute may or may not (depending on one’s specific doctrine) possess discrete will, intelligence, awareness or even a personal nature. It contrasts with finite things, considered individually, and known collectively as the relative.

Roughly, the Absolute may be distinguished from the following concepts, although there is debate of the synonymity between them:

  * Thing-in-itself, an actual object and its properties independent of any observer.
  * Noumenon, an object as it is in itself independent of the mind.[1]

However, rather than distinguishing from the relative, the thing in itself is used to distinguish an actual object from phenomenon (the appearance of things-in-themselves to the senses).

Or Spinoza’s naturalistic pantheism:

http://en.wikipedia.org/wiki/Baruch_Spinoza

The consequences of Spinoza’s system also envisage a God that does not rule over the universe by providence, but a God which itself is the deterministic system of which everything in nature is a part. Thus, God is the natural world and has no personality.

Ta-da grin

Uh, yeah.  Like I said.  You’ll note that Barker never provides us a means of crossing an actual infinite—unless he was exceptionally successful in providing distractions.  Basically, he skipped the first stage of the Kalam argument and attempted to deal with later stages but without apparently knowing what they are.

In fact, your response above hints that you accept that first stage of the Kalam argument, as you are apparently offering up candidates for the role of the first cause.

Seriously, we’re much better off with either Graham Oppy or Quentin Smith.  Spare me the Dan Barker.

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Posted: 15 March 2009 08:24 AM   [ Ignore ]   [ # 21 ]
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Bryan - 14 March 2009 05:29 PM

I did not refer to it as a line.  An infinite is typically described as a series in a set.  You can’t get through the set via successive addition.  Which one of us is misleading?  Me or thee?

Last I heard, infinity was specific to ‘increasing without bound’.  By all means, we can keep it down to a series within a specific set, but as a christian, you’ll have trouble with regard to everything outside of that set.

Why not?  The only problem you’ve suggested, AFAICT, is that the problem alleged by the Kalam argument does not exist.  If you intend to deal with the objection of the Kalam argument to crossing an actual infinite (not a line, but a series), then you’ll need to improve your argument, IMHO.

Either I am missing something, or you’ll need to go into detail about how the concept of crossing an infinite is tied to an objection to this argument.

Seriously, the universe is generally held to be finite as to its constituent parts.  If it is finite then we could hope to cross a set of those parts via successive addition.  If, on the other hand, you refer to the expanse of space which might forever extend itself then you would seem to be talking about a potential infinite rather than an actual infinite—and you analogy makes my point for me in a different way (do we ever reach a point at which the expansion of the universe must stop for lack of being able to successively add on additional space?).

Anything can be held to be finite if you define bounds and hold it to a constituent part.  That does not address the issue of the universe increasing without bound.  While you pose an interesting enough question with regard to it’s expansion, you present nothing to weigh on the question.  You’re insisting that the universe must arbitrarily stop it’s expansion at some point with no explanation why.  You’ll need an explanation specific to this universe regarding how and why it must be if you want to insist that; otherwise you will be speaking of limits that could easily be applied to your god concept.

So…what is it about your god, specifically, that makes him immune to being caused?

Additionally, let’s also understand that, even if the Kalam argument is taken and accepted, there are other issues abound with respect to positing your specific diety…but we’ll cross that bridge when we get to it.

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Posted: 15 March 2009 11:47 AM   [ Ignore ]   [ # 22 ]
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Mathenaut - 15 March 2009 08:24 AM
Bryan - 14 March 2009 05:29 PM

I did not refer to it as a line.  An infinite is typically described as a series in a set.  You can’t get through the set via successive addition.  Which one of us is misleading?  Me or thee?

Last I heard, infinity was specific to ‘increasing without bound’.  By all means, we can keep it down to a series within a specific set, but as a christian, you’ll have trouble with regard to everything outside of that set.

You’re such a tease.  wink
What specific problem will I have, IYO?

Why not?  The only problem you’ve suggested, AFAICT, is that the problem alleged by the Kalam argument does not exist.  If you intend to deal with the objection of the Kalam argument to crossing an actual infinite (not a line, but a series), then you’ll need to improve your argument, IMHO.

Either I am missing something, or you’ll need to go into detail about how the concept of crossing an infinite is tied to an objection to this argument.

I do????  The concept of crossing an actual infinite is the most basic aspect of the Kalam argument.  If you don’t understand that then you’ll never be able to mount an effective criticism of that aspect of the argument—and as that is our topic ...

An infinite regress requires the crossing of the an actual infinite.  That is the point of the Kalam argument.

Seriously, the universe is generally held to be finite as to its constituent parts.  If it is finite then we could hope to cross a set of those parts via successive addition.  If, on the other hand, you refer to the expanse of space which might forever extend itself then you would seem to be talking about a potential infinite rather than an actual infinite—and you analogy makes my point for me in a different way (do we ever reach a point at which the expansion of the universe must stop for lack of being able to successively add on additional space?).

Anything can be held to be finite if you define bounds and hold it to a constituent part.

OK, but I talked about the whole of the constituent parts.  If something is made of a finite set of constituent parts (as the universe is thought to be), then it is finite.

That does not address the issue of the universe increasing without bound.

That’s why I addressed the two things separately (“on the other hand, you refer to the expanse of space which might forever extend itself then you would seem to be talking about a potential infinite rather than an actual infinite”).

While you pose an interesting enough question with regard to it’s expansion, you present nothing to weigh on the question.

Only pending your acknowledgment of the difference between an actual infinite and a potential infinite.  We’ll get there, I think.

You’re insisting that the universe must arbitrarily stop it’s expansion at some point with no explanation why.

:LOL:
No, that’s not what I’m doing at all.  I’m explaining to you that infinite expansion represents a potential infinite rather than an actual infinite.  Unless you agree that the universe has completed its expansion (thus completing the set and crossing an actual infinite), then appealing to the potentially infinite expansion of the universe does nothing to address the Kalam argument.

You’ll need an explanation specific to this universe regarding how and why it must be if you want to insist that; otherwise you will be speaking of limits that could easily be applied to your god concept.

No need for that.  I think the infinities of God are potential infinites.  Plus I’m not about to let you wriggle away from the thrust of the Kalam argument with a tu quoque or anything of like nature.

So…what is it about your god, specifically, that makes him immune to being caused?

Immutability and eternality—but let’s not change the topic, eh?

Additionally, let’s also understand that, even if the Kalam argument is taken and accepted, there are other issues abound with respect to positing your specific diety…but we’ll cross that bridge when we get to it.

Great.  Admit the point of the initial step of the Kalam argument we can proceed to the next one.  smile

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Posted: 15 March 2009 12:32 PM   [ Ignore ]   [ # 23 ]
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Bryan - 15 March 2009 11:47 AM
Mathenaut - 15 March 2009 08:24 AM
Bryan - 14 March 2009 05:29 PM

You’re such a tease.  wink
What specific problem will I have, IYO?

I would say that the problem would lie with defining what exists outside of the set, but in hindsight, you already have your mind made up about that.  It’s a different can of worms trying to define what lies outside of the universe, how, and (or if) why.

I do????  The concept of crossing an actual infinite is the most basic aspect of the Kalam argument.  If you don’t understand that then you’ll never be able to mount an effective criticism of that aspect of the argument—and as that is our topic ...

An infinite regress requires the crossing of the an actual infinite.  That is the point of the Kalam argument.

How does an infinite regress require crossing an actual infinite?  What does not make sense is that, given how this is worded, it is sounding like you are defining ‘infinite’ as a point which can or cannot be crossed, which you denied in an earlier post.  It is sounding impossible, not in the sense of an amazing feat that cannot be done, but more in that it just doesn’t make sense to begin with.

When you regress infinitely, you don’t ‘reach’ infinity, as if it were a marked goalpost along a distant path.  It implies that you simply do not stop.  In that sense, it is a ‘potential infinite’, not that it really changes much.

OK, but I talked about the whole of the constituent parts.  If something is made of a finite set of constituent parts (as the universe is thought to be), then it is finite.

It’s finite, despite the fact that it is constantly increasing in size?  It’s not really a matter of opinion or different viewpoint that the universe is expanding, with no signs of slowing down or ending.

Only pending your acknowledgment of the difference between an actual infinite and a potential infinite.  We’ll get there, I think.

I suppose that I am failing to see the specific difference you are pointing out here.

:LOL:
No, that’s not what I’m doing at all.  I’m explaining to you that infinite expansion represents a potential infinite rather than an actual infinite.  Unless you agree that the universe has completed its expansion (thus completing the set and crossing an actual infinite), then appealing to the potentially infinite expansion of the universe does nothing to address the Kalam argument.

If an infinite regress represents a potential infinite, then what is the deal in crossing an actual infinite?  You’ve established them both to be distinct from one another, so how does crossing the potential relate to crossing the actual?

If the universe stopped expanding, it would be finite.  Unless you’re defining ‘crossing an actual infinite’ as the end of a potentially infinite increase, I don’t see how that second sentence makes any sense.

No need for that.  I think the infinities of God are potential infinites.  Plus I’m not about to let you wriggle away from the thrust of the Kalam argument with a tu quoque or anything of like nature.

Immutability and eternality—but let’s not change the topic, eh?

rolleyes

Great.  Admit the point of the initial step of the Kalam argument we can proceed to the next one.  smile

I’d be willing to humor it, sure.  Though the concept does not sound as solid as you’d think it does, nor does the conclusion imply what you insist it does (there is still a big leap between positing a cause of the universe, and your god).

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Posted: 15 March 2009 01:39 PM   [ Ignore ]   [ # 24 ]
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Mathenaut - 15 March 2009 12:32 PM
Bryan - 15 March 2009 11:47 AM

You’re such a tease.  wink
What specific problem will I have, IYO?

I would say that the problem would lie with defining what exists outside of the set, but in hindsight, you already have your mind made up about that.  It’s a different can of worms trying to define what lies outside of the universe, how, and (or if) why.

It’s tough enough defining what lies inside the set.  I don’t see that my problem is any bigger than yours based on the first of the Kalam steps.  And I can’t say that I found your answer as specific as I might have hoped.

I do????  The concept of crossing an actual infinite is the most basic aspect of the Kalam argument.  If you don’t understand that then you’ll never be able to mount an effective criticism of that aspect of the argument—and as that is our topic ...

An infinite regress requires the crossing of the an actual infinite.  That is the point of the Kalam argument.

How does an infinite regress require crossing an actual infinite?

Are you not familiar with the Kalam argument?

If we posit an infinite regress of causes (regardless of time, though it’s hard to imagine events without some sort of time involved), then our existence in the present implies that we exist at the end of an infinite series of causes—one that goes back infinitely far into the past.  Under that assumption, our existence in the present implies that we have somehow crossed an actual infinite.

What does not make sense is that, given how this is worded, it is sounding like you are defining ‘infinite’ as a point which can or cannot be crossed, which you denied in an earlier post.  It is sounding impossible, not in the sense of an amazing feat that cannot be done, but more in that it just doesn’t make sense to begin with.

If you think of it as a bridge rather than a finish line then perhaps the semantic confusion will clear for you.

If you think it doesn’t make sense to begin with to suppose that one can reach an end to an actual infinite in the first place, then you would appear to have conceded at least the prima facie appeal of the Kalam argument.

When you regress infinitely, you don’t ‘reach’ infinity, as if it were a marked goalpost along a distant path.  It implies that you simply do not stop.  In that sense, it is a ‘potential infinite’, not that it really changes much.

Right.  We stopped at the other end (the present).  So how did we get here other than by crossing an actual infinite or starting with some discrete event?

OK, but I talked about the whole of the constituent parts.  If something is made of a finite set of constituent parts (as the universe is thought to be), then it is finite.

It’s finite, despite the fact that it is constantly increasing in size?

Yes, for we can describe the universe in terms of a finite number of constituent parts that would fit a non-infinite set.  And the size at any given moment is also finite. since it grew to its present point via a form of successive addition and can still be added to via successive addition.  That is, the size of the universe is potentially infinite (not actually infinite).

It’s not really a matter of opinion or different viewpoint that the universe is expanding, with no signs of slowing down or ending.

Of course.  Neither is it a matter of opinion whether the size of the universe is an actual infinite or merely a potential infinite.

Only pending your acknowledgment of the difference between an actual infinite and a potential infinite.  We’ll get there, I think.

I suppose that I am failing to see the specific difference you are pointing out here.

I’ll do what I can.

Imagine a ladder ascending from your current location (ignore the roofs and ceilings).  Suppose the ladder extends upward as far as you can see.  You begin climbing the ladder at 3,000 rungs per second (wow!), but after 10,000 years the ladder continues to appear to go on as far as you can see.  Just for the heck of it, you climb for 10,000,000 more years, but still the ladder ascends out of your sight.

The ladder may be infinitely high.  It’s hard for you to say since you don’t know for sure that you wouldn’t reach the top after another billion years or so.  But we can at least treat the ladder as though it is infinite for the sake of argument.  If the ladder is actually infinite, then you’re not going to reach the top.  If the ladder is only potentially infinite and not actually infinite, then you might reach the top to find that you can pull out a telescoping section that extends further upward to double the height of the existing ladder, and given an infinite number of such telescoping sections we could call the ladder potentially infinite.  It simply waits on the intrepid climber to extend the next segment.

That is the difference between an actual infinite and a potential infinite.

Now, the Kalam argument points out that, by analogy, you’re on the ladder.  Regardless of whether the ladder is actually infinite going up, the infinite regress implies that the ladder goes infinitely down.  The argument asks how the universe came to be at any point on that infinite ladder without crossing an actual infinite, which we reasonably expect to constitute an impossibility.

If an infinite regress represents a potential infinite, then what is the deal in crossing an actual infinite?

An infinite regress does not represent a potential infinite.

You’ve established them both to be distinct from one another, so how does crossing the potential relate to crossing the actual?

Crossing a potential infinite isn’t hard.  You do it every time you move, in effect (I’ll be happy to explain, if necessary).  You’re making my point for me.  Appealing to the expansion of the universe does not touch the Kalam argument, for the former refers to a potential infinite while the latter deals with an actual infinite.  When you make the infinite regress only potentially infinite, it implies that you reach a particular point in the past where you might go further back.  A distinct beginning in time, if such we suppose the Big Bang to be, represents such a point in a potentially infinite past.  But clearly it also represents a finite point in the past.  The point of the Kalam argument is that if history is an actual infinite then we can no more reach the present moment than you can reach the top of an infinitely high ladder.

If the universe stopped expanding, it would be finite.

More than that, at any given point in the expansion of the universe its expansion is finite.  Unless you somehow cross the actual infinite via successive addition.

Unless you’re defining ‘crossing an actual infinite’ as the end of a potentially infinite increase, I don’t see how that second sentence makes any sense.

That’s exactly it.  We’re on our way.

Great.  Admit the point of the initial step of the Kalam argument we can proceed to the next one.  smile

I’d be willing to humor it, sure.  Though the concept does not sound as solid as you’d think it does, nor does the conclusion imply what you insist it does (there is still a big leap between positing a cause of the universe, and your god).

I hope you’ll judge my arguments according to their content rather than what you imagine they must be.  I don’t think the proof of the impossibility of crossing an actual infinite is absolutely airtight (lacking a logical contradiction with which to illustrate the absurdity).  Nor do I think the Kalam argument is sufficiently developed to prove the existence of the God of Abraham, Isaac, and Israel.  The topic of this thread was established around the notion of the infinite regress of causes.  It’s perfectly fair to utilize the relevant portion of the Kalam argument without getting burdened down with the other steps of the argument.

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Posted: 15 March 2009 04:59 PM   [ Ignore ]   [ # 25 ]
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Alright, I’m breaking the quote track.  Don’t feel like editing.

I’m familiar with the Kalam argument, but I will admit that this is the first time this particular issue was brought forth in my criticism of it.  However, for the sake of how it is being defined, then the problem facing the Kalam argument should be ‘potentially infinite regress’ instead of an outright infinite regress. wink

Regardless, you’re still left with the same problem.  You’re saying that there must be an end because it must be.  Sure, there can be an end, it’s possible (and I will admit that the Kalam argument plays upon this point), however the problem lies with necessity, which you’re still a bit short of the mark on.  You may think that you’re set enough just playing upon the role of possibility, but at least in my experience, most christians are inconsistent with it.

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Posted: 15 March 2009 06:21 PM   [ Ignore ]   [ # 26 ]
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Mathenaut - 15 March 2009 04:59 PM

Alright, I’m breaking the quote track.  Don’t feel like editing.

I’m familiar with the Kalam argument, but I will admit that this is the first time this particular issue was brought forth in my criticism of it.  However, for the sake of how it is being defined, then the problem facing the Kalam argument should be ‘potentially infinite regress’ instead of an outright infinite regress. wink

Anything less than an actually infinite regress is not an infinite regress but instead a first cause at some point.  Remember the ladder you cannot climb.  There’s no putting on an extension to our past.

Regardless, you’re still left with the same problem.  You’re saying that there must be an end because it must be.  Sure, there can be an end, it’s possible (and I will admit that the Kalam argument plays upon this point), however the problem lies with necessity, which you’re still a bit short of the mark on.

No, I don’t think so.  If you climb down the ladder there’s no way to add an extension if you should reach the end of it (the past is unalterable).  An infinite regress necessitates an actual infinite.

You may think that you’re set enough just playing upon the role of possibility, but at least in my experience, most christians are inconsistent with it.

That could be a weakness in your approach to this argument.  smile

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Posted: 15 March 2009 09:27 PM   [ Ignore ]   [ # 27 ]
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Seriously, we’re much better off with either Graham Oppy or Quentin Smith.  Spare me the Dan Barker.

Here is Graham Oppy:

http://www.infidels.org/library/modern/graham_oppy/gifford.html

In this paper, I have argued, in effect, that proponents of kalam cosmological arguments presuppose Strict Finitist metaphysics: they presuppose that the world is fundamentally discrete in all respects. Speaking for myself, I think that there is a pretty good inference from the success of current physics to the conclusion that the world is not fundamentally discrete in all respects. However, since I recognise that this instance of inference to the best explanation is a little contentious, I have only argued for the weaker claim that the controversial nature of this Strict Finitist presupposition creates substantial problems for proponents of kalam cosmological arguments. I do not find it plausible to think that there are many theists for whom the Strict Finitist presupposition is more doxastically secure than their belief in God. Nor do I find it plausible to think that there are many people at all who are very securely persuaded of the Strict Finitist presupposition. Consequently, it seems to me that kalam cosmological arguments are bound to be pretty useless things.

And Quentin Smith:

http://www.qsmithwmu.com/the_reason_the_universe_exists_is_because_it_caused_itself_to_exist.htm

Their objection is that an uncaused beginning is impossible[14]. I have now nullified that objection by explaining three ways in which the universe can cause itself to begin to exist. Deltete, Craig, Sullivan and Vallicella are now deprived of the main weapon in their arsenal of arguments against the atheistic theory of a finitely old universe. They can no longer say the atheistic theory can be rejected out of hand since it violates the ‘self-evident’ or ‘plausible’ principle that uncaused beginnings are impossible. Given this, ‘the cosmological argument for God’s existence’ is invalid for universes that begin to exist. More precisely, the kalam cosmological argument for God’s existence is invalid, since its premises are consistent with the conclusion that the universe caused itself to begin to exist. The kalam cosmological argument in one of its theistic versions is that: if the universe begins to exist, it has a cause; the universe begins to exist; therefore the universe has an external cause such as God. The invalidity is the inference of ‘an external cause’ from ‘a cause’.

Thus, the atheist is not the one who needs to fear the principle that if the universe begins to exist, it has a cause. Indeed, it is this very principle that endangers theism.

Graham Oppy again:

http://www.infidels.org/library/modern/graham_oppy/whynot.html

If asked to provide a broad outline of the history of the universe since the Big Bang, I would—to the best of my ability—outline the history that is delivered to us by our best sciences. In particular, I would insist that life appeared on Earth some billions of years ago, and that human beings are directly descended from those ancestral life forms. Moreover, I would insist that there is no need to appeal to the hypothesis of intelligent design to explain any of the features that our universe has possessed over the course of its history. Furthermore, I would say that any impulse to postulate intelligent designers to explain structural or organizational features of the universe should be matched by an impulse to postulate further intelligent designers for those intelligent designers—to explain the structural or organizational features of the beliefs, desires, and intentions of the initial intelligent designers.

BTW, thank you for introducing me to these two atheist philosophers.

LOL

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Posted: 15 March 2009 09:55 PM   [ Ignore ]   [ # 28 ]
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Bryan - 15 March 2009 06:21 PM
Mathenaut - 15 March 2009 04:59 PM

Anything less than an actually infinite regress is not an infinite regress but instead a first cause at some point.  Remember the ladder you cannot climb.  There’s no putting on an extension to our past.

No, I don’t think so.  If you climb down the ladder there’s no way to add an extension if you should reach the end of it (the past is unalterable).  An infinite regress necessitates an actual infinite.

This isn’t true.  Possibility is not necessity.  Even in an infinite set (i.e. real number line), you can stop at any point, define bounds, and define it finitely.  This does not address the issue of how and why your cause must be, much less where it must be.

Remember that events outside of our universe are not contingent upon time and specific order.  There are other implications to this, however they are irrelevant to the scope of this specific issue in the argument.

That could be a weakness in your approach to this argument.  smile

Doubtful, given that there are things within the realm of possibility that you are not willing to accept.  No…christianity is rather very specific and exclusive.  You have no room to maneuver in this without sacrificing the integrity of your faith.

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Posted: 15 March 2009 11:25 PM   [ Ignore ]   [ # 29 ]
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kkwan - 15 March 2009 09:27 PM

BTW, thank you for introducing me to these two atheist philosophers.

LOL

No problem.

Judging from your post, one would think that you think me unfamiliar with either one.

But that isn’t realistic, is it?

Shall I just refer you to William Lane Craig’s replies to Oppy and Smith, or would you care to interpret their arguments, put them in your own words, and actually invest something in the argument?

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Posted: 15 March 2009 11:42 PM   [ Ignore ]   [ # 30 ]
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Mathenaut - 15 March 2009 09:55 PM
Bryan - 15 March 2009 06:21 PM

An infinite regress necessitates an actual infinite.

This isn’t true.  Possibility is not necessity.

The person arguing for infinite regress is not simply saying that it is possible that there was no first cause in the case of an infinite regress.  They are saying that there is no first cause and that history goes back infinitely—no other possibility, for you can’t have a first cause and an infinite regress both. Thus, under the condition of an infinite regress, we have the conditional necessity of an actual infinity.

Even in an infinite set (i.e. real number line), you can stop at any point, define bounds, and define it finitely.  This does not address the issue of how and why your cause must be, much less where it must be.

True, but beside the point AFAICS.  Perhaps you can explain it so that it is no longer beside the point.  I’ll look for that with interest.

Remember that events outside of our universe are not contingent upon time and specific order.  There are other implications to this, however they are irrelevant to the scope of this specific issue in the argument.

If events outside of our universe are not contingent upon time and specific order than why on Earth would we ever appeal to an infinite regress?  Wouldn’t we have made the infinite regress unnecessary and unlikely as an explanation?

That could be a weakness in your approach to this argument.  smile

Doubtful, given that there are things within the realm of possibility that you are not willing to accept.

If you don’t flatly deny it then you imply that I’m right.  It could be a weakness in your approach to this argument.  I’m happy to see that you consider it a live possibility.  Perhaps I wouldn’t have done that in your shoes, being a Christian and all.  wink

No…christianity is rather very specific and exclusive.  You have no room to maneuver in this without sacrificing the integrity of your faith.

I love specifics in association with statements along those lines.

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