Does an Actual Infinite Exist in the Universe?

by Luke Muehlhauser on August 12, 2009 in Kalam Argument

Part 7 of my Mapping the Kalam series.
It is rumored that Puff Daddy owns an infinite limousine.

It is rumored that Puff Daddy owns an infinite limousine.

We are examining Craig & Sinclair’s defense of premise 2.11 in their Kalam Cosmological Argument: “An actual infinite cannot exist.” They use the thought experiment of Hilbert’s Hotel to show that an actual infinite would lead to certain absurdities that could not exist in the real world.

But if we have evidence that an actual infinity exists in the universe, then perhaps we can embrace the absurdities of Hilbert’s Hotel, much as we have embraced the absurdities of quantum mechanics because of strong evidence.

For example, Walter Sinnott-Armstrong asserts that “the continuity of space and time entails the existence of an actually infinite number of points and instants.”1 So the continuity of spacetime provides evidence of an actual infinite in our universe.

But this “assumes that space and time are composed of real points and instants, which has never been proven,” say Craig & Sinclair.

Moreover, say Craig & Sinclair, the objection may be met mathematically:

While one can continue indefinitely to divide conceptually any distance, the series of subintervals thereby generated is merely potentially infinite, in that infinit serves as a limit that one endlessly approaches but never reaches… If one thinks of a geometrical line as logically prior to any points which one may care to specify on it rather than as a construction built up out of points (itself a paradoxical notion), then one’s ability to specify certain points… does not imply that such points actually exist independently of our specification of them… If one simply assumes that any distance is already composed out of an actually infinite number of points, then one is begging the question.

But does not the potential infinite in these cases presuppose the existence of an actual infinite? How would you potentially divide something into infinitely many parts if there are not infinitely many parts already there to be divided?2

Craig & Sinclair charge that:

The objection is not successful. For the claim that a physical distance is… potentially infinitely divisible does not entail that the distance is potentially divisible here and here and here… The argument that it does is guilty of a modal operator shift, inferring from the true claim

(1) Possibly, there is some point at which x is divided

to the disputed claim

(2) There is some point at which x is possibly divided

But it is coherent to deny the validity of such an inference.

Unfortunately, I have not yet made it to modal logic in my Intro to Logic course. But for now I am only presenting the claims of Craig & Sinclair’s paper, and will analyze and criticize them later. Hopefully by then I will have covered modal logic!

In any case, one need not master modal logic to see that Craig seems to be right in denying the above inference. As cartesian writes:

I think Craig and Sinclair are right to deny the validity of this inference. It looks a lot like this inference:

(1*) Possibly, there is a golden mountain on which I build a house.
(2*) There is a golden mountain on which I possibly build a house.

That’s pretty obviously invalid. There actually are no golden mountains, though there clearly could have been. So (1*) is true, yet (2*) is false. So I bet the same thing goes with (1) and (2). So I guess the only remaining question is whether the objection actually relies on this inference.

Craig & Sinclair conclude:

The sober fact is that there is just no evidence that actual infinities are anywhere instantiated in the physical world. It is therefore futile to seek to rebut [premise 2.11, "An actual infinite cannot exist"] by appealing to clear counterexamples drawn from physical science.

Next, we consider premise 2.12: “An infinite temporal regress of events is an actual infinite.”

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  1. See God?: A Debate between a Christian and an Atheist, page 43. []
  2. See Rucker’s “The actual infinite” in Speculations in Science and Technology 3, p. 66 and Sorabji’s Time, Creation and the Continuum (1983), pp. 210-3, 322-4. []

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{ 39 comments… read them below or add one }

Lorkas August 12, 2009 at 5:55 am

It is rumored that Puff Daddy owns an infinite limousine.

That must be a bitch to park.

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cartesian August 12, 2009 at 6:55 am

(1) Possibly, there is some point at which x is divided
(2) There is some point at which x is possibly divided
 
I think Craig and Sinclair are right to deny the validity of this inference. It looks a lot like this inference:
 
(1*) Possibly, there is a golden mountain on which I build a house.
(2*) There is a golden mountain on which I possibly build a house.
 
That’s pretty obviously invalid. There actually are no golden mountains, though there clearly could have been. So (1*) is true, yet (2*) is false. So I bet the same thing goes with (1) and (2). So I guess the only remaining question is whether the objection actually relies on this inference.

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Penneyworth August 12, 2009 at 8:37 am

Take the distance between 0 and 1 on the number line. There are many countably infinite sets within this range (actually, an infinite number). How about 1/2n where n is any positive integer. We know there are infinitely many positive integers, so there are infinitely many “potential” points between 0 and 1… unless one objects to there being infinitely many positive integers. Is it coherent to say the number 6 didn’t exist until I pointed it out? The issue here is the fact that the term “exist” will be redefined whenever it suits the attempted proof. On one of Craig’s debates, I feel like I remember him trying to explain the difference between essential and contingent aspects of the universe, and that we know essential, immutable things do exist; for example, numbers. Yet I still suspect that a complaint about the infinite number of points would be that spacetime may be discrete, and those points may not exist in the physical universe. If the definitions are not consistent and well defined, the proof is dead before it starts.

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Lorkas August 12, 2009 at 8:49 am

So Craig and Sinclair are arguing that it has to be an infinite series of discrete units to count as an actual infinity? In other words, they say an infinity of zero-dimensional points doesn’t count?
 
Has anyone just put forward the argument that since the universe is unbounded, it is potentially infinite in volume? I mean, we say that the universe is finite but unbounded, but what we mean by that is that one could travel infinitely in any direction, which strikes me as an actual infinite (just not an actual infinite of objects, like hotel rooms).

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Lorkas August 12, 2009 at 8:50 am

In other words, rather than setting a distance in the universe, like 1 meter, and saying that there are infinite points in that 1 meter, why not just say that there are an infinite number of meters on a line in the universe. It’s much more straightforward and less controversial.

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Reginald Selkirk August 12, 2009 at 10:33 am

 

Penneyworth: Yet I still suspect that a complaint about the infinite number of points would be that spacetime may be discrete, and those points may not exist in the physical universe.

Planck length

The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, Planck’s constant, and the gravitational constant. Current theory suggests that one Planck length is the smallest distance or size about which anything can be known.

Note the disconnect between “about which anything can be known” and “exists.”
 

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IntelligentDasein August 12, 2009 at 10:49 am

I wouldn’t take Craig too seriously. Logical proofs can not actually prove anything. They are just fun “word problems” and they can not do anything corresponding to reality, sort of like incredibly abstract unapplicable math. The only real use logic has is to check validity of an argument, but it can not step past that barrier into real-world correspondance (soundness), which can only be checked through observational data. Aristotle used logic to come to the conclusion the universe is geogentric and a women has porportionatley less teeth than a man. That is about the jist of logic.

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Timo August 12, 2009 at 11:29 am

Reginald, I was about to make the exact same point.  Beat me to it!  We can imagine a number line and come up with the conclusion that there are infinitely many potential points between any two given numbers.  But in the real world, there would be a finite number of points between them because we cannot go any further down than the level of quarks and gluons and such.
All that said, I think that if you except this premise of Craig’s argument then it will come back and bite you in the ass when you start getting into the potential causes of the universe because of Craig’s slide of hand in using notions of absolute and relative time interchangibly in the second phase of his argument.  But I’ll save that for when you post about that.
And good post, by the way.  Good shit, Luke!
 
Peace

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Lorkas August 12, 2009 at 11:52 am

Reginald Selkirk: Note the disconnect between “about which anything can be known” and “exists.”

Strange to think of the universe as being pixelated if you zoom in enough.

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tdd August 12, 2009 at 12:10 pm

The sober fact is that there is just no evidence that actual gods are anywhere instantiated in the physical world. It is therefore futile to seek to rebut [premise 2.11, "An actual god cannot exist"] by appealing to clear counterexamples drawn from physical science.

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toweltowel August 12, 2009 at 1:49 pm

Insisting on the gap between (1) and (2) raises some puzzling questions.
 
Suppose it’s possible that there’s some point at which x can be divided. Or, since x is supposed to actually exist, perhaps we should say: suppose of x that it’s possible that there’s some point at which it can be divided. What grounds this possibility? What is it about x as it actually is that makes it possible that there’s some point at which it can be divided?
 
Perhaps x actually has a point, but it can’t actually be divided at that point, though it can possibly be divided at that point. So what explains the difference between the point as it actually is and the point as it possibly could be? Why is the actual point possibly division-suitable but not actually division-suitable?
 
Or perhaps x doesn’t even actually have a point, but it could possibly have a point, and if it did, it could possibly be divided at that point. But then what’s the difference between x as it actually is and x as it possibly could be?

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Lamplighter Jones August 12, 2009 at 1:57 pm

But does not the potential infinite in these cases presuppose the existence of an actual infinite? How would you potentially divide something into infinitely many parts if there are not infinitely many parts already there to be divided?

The answer depends on what you mean by ‘finite.’  This is why it’s so annoying that the word ‘finite’ is never defined in the Blackwell Companion.  For the rest of this post, I’ll use a definition of ‘finite’ that doesn’t automatically make Crag & Sinclair’s argument against the existence of an actual infinite an instance of begging the question.

Let’s say a thing T is finite if there is a positive integer n such that no multitude contained in T has more than n parts.*

With this definition, the potential to divide a thing into an arbitrarily large (finite) number of parts implies that said thing is not finite.
So under the assumption of the continuity of time, we’re left with two possibilities: (i) time is potentially infinite, or (ii) time is actually infinite.  Perhaps there is a third possibility I’m not aware of.
 
 
If Craig & Sinclair are correct in arguing that the infinitude of the past implies that the past is actually infinite, then they have shown that, assuming time is continuous, the past is actually infinite.  But the aforementioned argument makes the following (implicit) unjustified assumption:

(A) If the past is infinite, then there is a denumerably infinite collection of past events.  (That is, a collection of events such that each event in the collection can be labeled with a distinct positive integer, and every event in the collection is labeled with at a positive integer.)

A very similar unjustified assumption is also made in the Hilbert’s Hotel argument, namely:

(B) If an actual infinite is possible, then an actual denumerable infinite is possible.

I don’t know whether (A) and (B) are true.  I would be very interested to see sound arguments for either one.
 
 
* – I have reservations about using the concept of numbers to define the word ‘finite’, since that seems to imply some form of mathematical realism, and it raises the question of just what one means by ‘number.’  But the only common definitions of ‘finite’ that I know either use numbers or make Craig & Sinclair’s argument against the existence of an actual infinite an instance of begging the question.

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lukeprog August 12, 2009 at 2:04 pm

cartesian,

Some of your comments here are masterpieces of both precision and concision. Please write books.

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lukeprog August 12, 2009 at 2:29 pm

Lamplighter Jones,

Can you give an example of a definition of ‘finite’ that would cause one of Craig & Sinclair’s arguments to be question-begging?

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Lamplighter Jones August 12, 2009 at 2:54 pm

 

lukeprog: Lamplighter Jones,Can you give an example of a definition of ‘finite’ that would cause one of Craig & Sinclair’s arguments to be question-begging?

The definition I have in mind is
 

Call a multitude M finite if no submultitude contained in M can be placed into one-to-one correspondence with M.

With this definition, the question-begging arises when one says that an actual infinite is impossible because it brings the following two principles into conflict:

(i) There are not more things in a multitude M than there are in a multitude M′ if there is a one-to-one correspondence of their members.
(ii) There are more things in M than there are in M′ if M′ is a proper submultitude of M.
(From this post)

But under the current definition of finite, saying that a multitude M violates (ii) is simply a restatement of “M is not finite.”  So the argument is something like, “an actual infinite is impossible because every multitude is finite.”

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lukeprog August 12, 2009 at 5:24 pm

Thanks, Lamplighter Jones.

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Ben August 12, 2009 at 9:02 pm

I don’t see how we could ever hope to present evidence of the infinite to a finite being.  It’s a logical impossibility given the natural constraints of any knowledge base.  Agnosticism on the issue doesn’t leave theism with its proof negative against materialism, however.  So it really doesn’t matter.  WLC and company simply want too much from what they have to work with.
 
Ben

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Yair August 13, 2009 at 7:19 am

It is somewhere between sad and amusing that Craig et al drag up the old metaphysical “certainties” as if they have any merit at all.
 
Space and time has been shown to be composed of real points and instances, in the only way such things can be proven: theories assuming that they are work. Specifically, classical mechanics assumes a real continuum of space and time. Things are murkier in quantum mechanics, but it doesn’t really matter. There mere possible truth of classical mechanics exposes the metaphysical assertion as empty speculation.
 
There is no contradiction in an actual infinite past or future (or whatever). (No, having a certain process (counting) not work like you expect is not a contradiction.) Therefore, it is possible. It’s as simple as that. Next.
 
When Gallileo was to be put on trial, the pope was quoted as saying “do not necessitate god”. I’m tempted to say “do not necessitate reality”. Reality is whatever it is, and all we can do is postulate a non-contradicting structure to it and check whether it pans out.

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Dace August 13, 2009 at 10:50 pm

cartesian: (1) Possibly, there is some point at which x is divided (2) There is some point at which x is possibly divided   I think Craig and Sinclair are right to deny the validity of this inference. It looks a lot like this inference:   (1*) Possibly, there is a golden mountain on which I build a house. (2*) There is a golden mountain on which I possibly build a house.   That’s pretty obviously invalid.

(1) ◊∃x (Fx∧Gx)
(2) ∃x(Fx)∧◊(Gx)
Yep, I agree. But Craig and Co.may still be in trouble. Their attack on actual infinites is supposed to show us that they are metaphysically impossible. So, not only are they claiming that this possible world doesn’t contain an actual infinite, but they are claiming that all possible worlds fail to contain an actual infinite. So, if they agree with (1), then they agree that there is some possible world in which (2) is true, and if (2) would falsify “actual infinites exist” at that world, then actual infinites can’t be metaphysically impossible, and Craig and Co. fail.
But does (2) falsify their claims? Does the fact that there is some point at which a physical distance is possibly divided entail that an actual infinite exists? Something’s missing here. It doesn’t look like Craig and Co. have represented their opponents argument properly (perhaps that’s not their fault).

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Jeff May 26, 2010 at 10:54 am

I don’t know a lot about logic or higher math so maybe I am viewing this wrong but just how do you really prove the statement “An actual infinite cannot exist.”?
It seems to me they are saying it is true only because our definitions and intuitions make it true, can one exist and we don’t know it, if space is truly infinite how would you prove it?

It seems to me that something can be infinite and finite, such as going around the Earth , there is no end or start of the journey but the Earth is finite

I can envision something similar with the universe itself.
Something along the lines of there will be a big crunch followed by a big bang. The big crunch from what I understand will cause time as we understand to cease to exist and a big bang will cause it to exist again

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Mike December 17, 2010 at 6:58 am

I recognize I’m a little late to the commenting party on this post, but I’m looking for some help on this argument. I made a recent post on this subject:

http://foxholeatheism.com/on-absurdity-william-lane-craig-and-actual-infinites/

I’m still working through the details of the argument and would appreaciate your feedback on my blog or here in this thread. For anyone who doesn’t want to read the whole thing, it goes essentially as follows:

Craig wants to escape an infinite universe from defeating the premises of the KCA. So, he argues an actual infinite is not possible. Then, where does God fit? God must be outside of time to escape the same problem. But God created the universe, so God must have some temporal relationship to it. So, Craig concludes, God is timeless without the universe and temporal with the universe. It seems to be a hybrid approach. But I argue that Craig is also committing to a counterintuitive absurdity (his charge against actual infinites). If God being outside of time means God is necessarily changeless, then to say that God in relation to something else is both changing and temporal seems absurd.

If Craig’s position is also absurd, then it would seem he must either agree that arguing from counterintuitiveness is valid and abandon his argument about God’s relationship to time – or – agree that an apparent absurdity does not derail an argument (which would mean an infinite past could exist to defeat the KCA). I think the latter is true, that this is just a bad way to argue the point.

Before anyone jumps on me, let me also say I realize there are many other ways to approach this argument, but I wanted to try something new (at least it’s new to me) and I wanted to approach Craig on his own terms, including assuming an A-theory of time.

Thanks for any input!

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Paul Prescod April 14, 2011 at 7:31 pm

The actual universe we live in is believed by most astrophysicists to be infinite. This was not the leading model in 1979 but it is now.

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

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Utkarsh October 18, 2011 at 5:10 am

Actually I posted a question regarding the existence of actual infinites on Dr Craig’s website reasonablefaith.org and so far he has not responded(perhaps he doesn’t have the time to or simply didn’t notice or there were so many questions that mine got sidelined.Who knows?) .
However , an actual infinite DOES EXIST . In fact I know 2 such infinites :
1. the infinite electrical conductivity of a superconductors
and,
2.the infinite number of reflections produced when an object is placed between 2 mirrors of equal shape and size facing opposite each other.
Not to mention that the singularity at the start of the big bang (and black hole gravitational singularities) are calculated to be infinitely dense . However since the area of singularities is not without controversy , I’ll leave anything further about them out of my post
The way I see it , Dr Craig can respond to this in 3 ways :
1.Distorting the scientific facts about my 2 prime examples(the superconductors and mirrors) to fit his response.
2.Ignoring this question (and the serious challenge it presents to the KCA) altogether .
3.Denying that my 2 examples can be regarded as “actual infinites” because they somehow don’t fit the criteria to be regarded as one.
He is very much capable doing this . I have seen many of his debates and, though an intelligent man that he is ,he is not above using dirty tricks to bring validity to his points in a debate (after all what else is a debate about).

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Mike October 18, 2011 at 6:21 am

Utkarsh,

I don’t know much about superconductors, but the mirror example seems to just be two potential infinites, which does not make an actual infinite. I think the appeal is that it seems like an actually infinite line but it’s really more like two potentially infinite ones . What do you think?

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Zeb October 18, 2011 at 8:19 am

1. the infinite electrical conductivity of a superconductors

Don’t know about this one.

and,
2.the infinite number of reflections produced when an object is placed between 2 mirrors of equal shape and size facing opposite each other.

You are ignoring all the physics involved here. Infinite reflections would imply that the photons reflected and travleled between the mirrors and infinite number of times. And since each reflection gets smaller, it would imply that they get infinitely small without dissappearing. Obviously the smallest possible reflection must be at least as big as a few atoms of the reflective material. And you assume perfectly reflective mirrors and a perfect medium between them, which are impossible.

Not to mention that the singularity at the start of the big bang (and black hole gravitational singularities) are calculated to be infinitely dense .

Density is a ratio, and no ratio can count as an actual infinite. I mean literally, you cannot count the infinite units in a ratio. You could count the mass which would never be infinite, or you could count the volume which would approach zero, but even at the moment when the volume reaches zero would not have an infinity of anything, and at that point deciding to divide the mass by the volume to get infinity would be both mathematically and semantically invalid.

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Utkarsh October 18, 2011 at 12:15 pm

You are ignoring all the physics involved here. Infinite reflections would imply that the photons reflected and travleled between the mirrors and infinite number of times. And since each reflection gets smaller, it would imply that they get infinitely small without dissappearing. Obviously the smallest possible reflection must be at least as big as a few atoms of the reflective material. And you assume perfectly reflective mirrors and a perfect medium between them, which are impossible.

Please go and read the optics section in your high school physics textbook if you think that an infinite regress of reflected images between 2 oppositely facing mirrors is impossible, so that you can better understand the optics going on around here before telling me that I am “ignoring all the physics involved.
Or simply google the term “infinite mirror effect” if you don’t find it your textbook (I am sure that you will be able to find it at least in the problems section of your textbook if not in the main theory part).

Density is a ratio, and no ratio can count as an actual infinite. I mean literally, you cannot count the infinite units in a ratio. You could count the mass which would never be infinite, or you could count the volume which would approach zero, but even at the moment when the volume reaches zero would not have an infinity of anything, and at that point deciding to divide the mass by the volume to get infinity would be both mathematically and semantically invalid

Read the whole paragraph in my previous post . In the next sentence I state that “since the area of singularities is not without controversy , I’ll leave anything further about them out of my post”. What part of it did you not understand for you to ignore this sentence altogether?

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Utkarsh October 18, 2011 at 12:22 pm

Zeb,
Here is link to physics website which discusses the reflection of light(indirectly including the infinite mirror effect):
http://www.physicsclassroom.com/class/refln/u13l2f.cfm

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Utkarsh October 18, 2011 at 12:33 pm

Utkarsh,

I don’t know much about superconductors, but the mirror example seems to just be two potential infinites, which does not make an actual infinite. I think the appeal is that it seems like an actually infinite linebut it’s really more like two potentially infinite ones . What do you think?

Here is the part of the wiki article titled “Mirror” which deals with the infinite mirror effect:
“Face-to-face mirrors
Two or more mirrors placed exactly face to face can give an infinite regress of reflections. Some devices use this to generate multiple reflections:
Fabry–Pérot interferometer
Laser (which contains an optical cavity)
3D Kaleidoscope to concentrate light [24]
momentum-enhanced solar sail”

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Utkarsh October 18, 2011 at 12:49 pm

Zeb,
Also , in a way photons do travel” an infinite number of times” between the 2 mirrors because when you place an object between them , light is simply “bouncing” between the 2 mirrors indefinitely , thereby creating an infinite regress of reflected images on both the mirrors. And this in no way contradicts or invalidates ANY OF THE LAWS OF PHYSICS . If it were so, then they would’n't be teaching this in basic high school physics.

The only way that I see it is that Dr Craig (or anyone else including you) could around this problem is by either ignoring it(which is hard to do since it is such a well known phenomenon) or by denying that it’s an actual infinite altogether .
But then Dr Craig isn’t very specific(rather very vague) on what is it that he defines as an “actual infinite” in the KCA . So the possibility of him rejecting this(IME) as an example of an actual infinite is very likely.

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Utkarsh October 18, 2011 at 1:15 pm

Zeb’

Furthermore , density is a real physical quantity . It doesn’t matter whether or not you can count the number of units in an infinite density. What does matter is that the known laws of physics break down the moment they reach the singularity . This is one of the prime reasons that Einstein refused to believe in the existence of black holes(too bad that NASA’s recent findings are causing him to turn in his grave) !

It is however by and large undisputed that a gravitational singularities have infinite density (except perhaps for guys like Bill Gaede).This is one of the main reasons that Hawking refutes the idea of a naked singularity.The singularity , located within the event horizon of the black hole , is essentially incapable of interacting with the rest of the universe and hence it doesn’t disturb the physical framework of our universe.

The problems that the singularity poses to the laws of physics is one of the main reasons why we have all these new theories (all of them by the way are TOE wannabes):
String theory,M-theory,Brane-theory,Heim’s theory etc.

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Utkarsh October 18, 2011 at 1:19 pm

Mike,

Here is the link that I gave to Zeb . Hope it clarifies any doubts that you may have.
http://www.physicsclassroom.com/class/refln/u13l2f.cfm

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Mike October 18, 2011 at 1:34 pm

Yes, the problem is that the regress is potential, not actual. I do happen to agree that Craig has not ruled out actual infinites, but I don’t think it’s the sort of thing we can point to.

I raised my own concerns with Craig’s argument here: http://foxholeatheism.com/fine-tuning-and-a-beginningless-past/

I don’t try to give an example, but instead try to save it as a counterpossible.

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Utkarsh October 18, 2011 at 9:43 pm

Yes, the problem is that the regress is potential, not actual. I do happen to agree that Craig has not ruled out actual infinites, but I don’t think it’s the sort of thing we can point to.

I raised my own concerns with Craig’s argument here: http://foxholeatheism.com/fine-tuning-and-a-beginningless-past/

I don’t try to give an example, but instead try to save it as a counterpossible.

Mike,

If an actual infinite is indeed demonstrated to exist , then how do you think Dr Craig will respond to it. Will he try to modify the Kalam argument to fit this new piece of evidence . Or do you think he will abandon the KCA altogether and assert his “evidence” for God solely on the basis of Jesus’s empty tomb(I am not very familiar with that one) and the fine tuning of the universe (which has too has been sufficiently argued against).

I am inclined to think that he would do the former.Either ways, its not really going to change his point of view regarding his God. Because , funnily enough as much as he accuses the atheists of doing this , he himself is rather rigidly fixated on the idea that God must exist and no amount of counterarguments or evidence is ever enough to convince him otherwise.

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Mike October 18, 2011 at 9:52 pm

He would not abandon it. He would focus more on what he calls scientific appeals. He has arguments about entropy that he thinks are evidence for a beginning. Heeling focus away from general infinity arguments and focus on problems (alleged) specifically about an infinite number of moments.

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Zeb October 19, 2011 at 6:59 am

Utkarsh, the sources you gave are talking about hypothetical mirrors in an imaginary world, as highschool physics normally does. It’s a world in which light is not quantum, mirrors are Euclidean surfaces rather than three dimensional objects made of atoms, reflectivity is 100% and alignment is perfect, and light travels infinite distances instantaneously. Hypothetical ‘mirrors’ could hypothetically be used to create an hypothetically infinite number of hypothetical reflections, but physical mirrors reflecting physical light in the physical world never could. Two reasons: it would take an infinite amount of time for the reflections to actualize because of the travel time of light, but early in the process reflection would stop anyway because of imperfections in the mirrors and the quantum nature of both the light and the surface of the mirrors. This reddit thread goes into a little more detail. http://www.reddit.com/r/askscience/comments/ipj7x/when_you_have_two_mirrors_facing_each_other/

You have not challenged my contention that even something were to have infinite density, and actual infinite would not be realized because density is not a physical quantity, but a ratio of physical quantities. If the singularity is a universe with finite mass and zero volume, the fact that you can decide to divide one by the other and call it infinity does not conjure the existence of any actually infinite thing. I could decide to divide the number of fish in existence by the amount of time left until noon Friday and correctly predict that number of fish existing per hour is going to reach infinity, but that does not mean there will be an actual infinite.

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Utkarsh October 19, 2011 at 12:51 pm

You have not challenged my contention that even something were to have infinite density, and actual infinite would not be realized because density is not a physical quantity, but a ratio of physical quantities. If the singularity is a universe with finite mass and zero volume, the fact that you can decide to divide one by the other and call it infinity does not conjure the existence of any actually infinite thing. I could decide to divide the number of fish in existence by the amount of time left until noon Friday and correctly predict that number of fish existing per hour is going to reach infinity, but that does not mean there will be an actual infinite.

It originally wasn’t my intent to challenge your contention that the existence of an infinite density doesn’t necessarily imply the existence of an actual infinite . However , if you didn’t know , then density is one of the quantities used to measure the gravitational field of a black hole . So your above idea that density is not an actual physical quantity but merely a ratio of 2 physical quantities doesn’t make much sense to me. By that logic we could say that things like velocity,pressure,flux(both electric and magnetic),momentum aren’t physical quantities. Sure you could call them “derived” physical quantities as they are derived from base quantities like mass,length,time and current by applying the appropriate laws of physics. However, that doesn’t change the fact that they ARE CLASSIFIED AS PHYSICAL QUANTITIES IN PHYSICS .So your claim that “density is not a physical quantity but merely a ratio of 2 of them” makes about as much sense as the statement that “a liger is not a big cat because its a hybrid of 2 of them”.Which is absurd.
Was it noon Friday when you posted your comment(sorry I live in India so the time zone might create a problem here)?
Since none of the TOE wannabes have managed to sufficiently resolve the problem of gravitational singularities , therefore its only logical to assume that they exist because black holes exist(NASA has proven it).
QED

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Utkarsh October 19, 2011 at 12:56 pm

Zeb,

By the way(I forgot to mention this in my previous post) density is also defined as a physical quantity in physics . If you don’t believe me , just go and check you physics textbook or simply wiki the article “Physical Quantity” .

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Zeb October 19, 2011 at 1:45 pm

You’re right, density is considered a physical quantity. I think you understand my point though – it’s not a quantity in the sense of ‘an amount of something’, such that an infinity of it could exist. I think black holes prove the point. A black hole has a certain finite mass, and that mass is concentrated in a certain finite volume of space. If that volume is or approaches zero, then the ratio of mass to volume could be considered infinite, no actual infinite is realized. No more than the ratio of fish that exist to hours until noon Friday is going to give us an actual infinite of anything.

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Utkarsh November 4, 2011 at 5:18 am

Hey Zeb,
Did you read this post of mine?

It originally wasn’tmy intent to challenge your contention that the existence of an infinite density doesn’t necessarily implythe existence of an actual infinite . However , if you didn’t know , then density is one of the quantities used to measure the gravitational field of a black hole . So your above idea that density is not an actual physical quantity but merely a ratio of 2 physical quantities doesn’t make much sense to me. By that logic we could say that things like velocity,pressure,flux(both electric and magnetic),momentum aren’t physical quantities. Sure you could call them “derived” physical quantities as they are derived from base quantities like mass,length,time and current by applying the appropriate laws of physics. However, that doesn’t change the fact that they ARE CLASSIFIED AS PHYSICAL QUANTITIES IN PHYSICS .So your claim that “density is not a physical quantity but merely a ratio of 2 of them”makes about as much sense as the statement that “a liger is not a big cat because its a hybrid of 2 of them”.Which is absurd.
Was it noon Friday when you posted your comment(sorry I live in India so the time zone might create a problem here)?
Since none of the TOE wannabes have managed to sufficiently resolve the problem of gravitational singularities , therefore its only logical to assume that they exist because black holes exist(NASA has proven it).
QED

  (Quote)

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