(Cross-posted at Thinking Matters Talk)
Welcome to the third of my nine part series on the kalam cosmological argument. Last time, we examined the plausibility of the first premise. Today, we’ll examine the second premise of the argument. I’ve decided to speed the publication of this post up because of some trigger-happy commenters who simply can’t wait.
Defenders of the KCA muster several different arguments in support of the premise that the universe began to exist. These arguments are both philosophical and scientific in nature. Arguments under the former category involve showing that the existence of an actually infinite number of things is metaphysically impossible. If the universe never began to exist, then its past duration would be actually infinite. Since actual infinities cannot exist, then the past duration of the universe must have been finite, implying that the universe must have begun to exist. Even if one grants that it is possible for an actual infinite to exist, it still cannot be formed by successive addition, and henceforth the past duration of the universe must still be finite. From a scientific perspective, the beginning of the universe is strongly supported by modern big bang cosmology. The proponent of the KCA thus finds himself comfortably seated in the midst of mainstream cosmology. Combined, these two reasons lend strong support to the truth of the second premise.
The Impossibility of Actual Infinities
It’s helpful to distinguish between actual and potential infinities. Potential infinities are sets that are constantly increasing toward infinity as a limit, but never attain infinite status. A more accurate description would be to say that their members are indefinite. An actual infinite, by contrast, is a set x that contains a subset x’ that is equivalent to x. That is, they are denumerable. Phrased in layman’s terms, a set is actually infinite if a part of the set is as big as the whole set. A potentially infinite set would thus be a set in which a part is less than the whole. “The crucial difference between an infinite set and an indefinite collection would be that the former is conceived as a determinate whole actually possessing an infinite number of members, while the latter never actually attains infinity, although it increases perpetually. We have, then, three types of collection that we must keep conceptually distinct: finite, infinite, and indefinite.1 Because it leads to contradictions and absurdities, an actually infinite set cannot exist in reality.
There are several examples which illustrate the absurdity of the existence of an actually infinite number of things, the most famous of which is known as Hilbert’s paradox of the grand hotel. For the sake of clarity, however, I’ll use a simple example used by Craig:
Imagine I had an infinite number of marbles in my possession, and that I wanted to give you some. In fact, suppose I wanted to give you an infinite number of marbles. In that case I would have zero marbles left for myself.
However, another way to do it would be to give you all of the odd numbered marbles. Then I would still have an infinite left over for myself, and you would have an infinite too. You’d have just as many as I would — and, in fact, each of us would have just as many as I originally had before we divided into odd and even! Or another approach would be for me to give you all the marbles numbered four and higher. That way, you would have an infinite of marbles, but I would have only three marbles left.
What these illustrates demonstrate is that the notion of an actual infinite number of things leads to contradictory results. In my first case in which I gave you all the marbles, infinity minus infinity is zero, in the second case in which I gave you all the odd-numbered marbles, infinity minus infinity is infinity; and in the third case in which I gave you all the marbles numbered four and greater, infinity minus infinity is three. In each case, we have subtracted the identical number from the identical number, but we have come up with non-identical results.2
The point of this example is that arithmetical operations with actually infinite quantities yield contradictory answers, and thus it is metaphysically impossible for actual infinites to exist. The notion of an actually infinite set is purely conceptual and has no relation to reality. It should be noted here that while one is able to work with actual infinities in set theory and calculus, they existence in re is metaphysically impossible. Their existence is only permitted in mathematics because mathematical operations involving infinite quantities are prohibited. In reality, however, there is nothing stopping someone from adding or subtracting from an infinite quantity of marbles.
Suppose however, that actual infinities could exist in reality. Would this serve as a defeater for the second premise? It seems not, for even if actual infinities could exist in reality, they could not be formed by successive addition nor could they be navigated successfully. It is impossible to form an actually infinite quantity by successive addition, as one can always add another number to what they have counted. No matter how many times one adds a number to a finite quantity, one will never yield an infinite quantity.
Even if actual infinities were possible, it is unclear that they could be traversed. Consider Bertrand Russell’s example of Tristram Shandy, who writes his autobiography at such a slow pace that it takes him a whole year to write about a single day. If Shandy had been writing for eternity past, then he would be infinitely far behind.3 Since it is impossible to traverse an actually infinite past, then we should not have arrived at this point. But since we have, we can conclude that the past duration of the universe was finite.
Critics have sometimes compared the impossibility of forming an actual infinite to Zeno’s paradoxes of motion, which, though tricky and stubborn, are obviously wrongheaded. But these comparisons are not accurate for several reasons: First, the distances traversed in an infinite past are actual and equal, as opposed to being potential and unequal in Zeno’s paradoxes. Second, the distances traversed in Zeno’s paradoxes sum to a finite distance, whereas the distances traversed in an infinite paste sum to an infinite distance. Finally, it begs the question by presupposing the distance traversed as being composed of an infinite amount of points. Critics of Zeno held that the existence of the line itself is prior to any divisions that are made in it. Moreover, in regards to an infinite past, divisions such as a halfway, a quarter of a way, and a third of the way are unintelligible because there is no beginning, unlike in Zeno’s paradoxes.4
Scientific Pointers to a Beginning of the Universe
Due to the heavy influence of Aristotelianism, scientists and philosophers from the medieval periods up until the early 1900’s firmly believed in the eternality of the universe. The first indications that the universe was not eternal started to surface in 1917 with the advent of Albert Einstein’s general theory of relativity. Einstein himself was a believer in an eternal universe, and when he saw that his theory of general relativity did not permit such a model, he introduced a “fudge factor” into his equations to maintain an eternal universe. By exploiting the shortcomings of Einstein’s model, the Russian mathematician Alexander Friedman and the Belgian astronomer Georges Lemaitre independently developed an expanding model of the universe. Further evidence came in 1929, when astronomer Edwin Hubble confirmed the expanding universe predicted by the Friedman-Lemaitre model through his discovery of redshift. The fact that the universe was expanding implied that in some point in the past, it was compacted together tightly, for if one reverses the expansion of the universe backwards in time, the universe becomes more and more dense until it reaches a state of infinite density. This had the jolting conclusion that the universe, over 14 billion years ago, had once been compressed to a size of an infinitely dense point known as a singularity. Since space and time themselves came into existence at this singularity, it served as a boundary for space-time, as there was no moment “before” the big bang. Hence, the origin posited by the standard big bang model is that of an absolute origin ex nihilo.
- William Lane Craig and James D. Sinclair in William Lane Craig and J. P. Moreland (eds), The Blackwell Companion to Natural Theology (Blackwell: 2009) p.105 [↩]
- William Lane Craig, as interviewed by Lee Strobel in The Case for a Creator (Grand Rapids, MI: Zondervan 2004) p.103 [↩]
- For more on this, see Paul Copan and William Lane Craig, Creation Out of Nothing: A Biblical, Philosophical, and Scientific Exploration (Grand Rapids, MI: Baker Academic 2004) p.213-216 [↩]
- Craig and Sinclair, “The Kalam Cosmological Argument”, in TBCNT, pp. 119 [↩]
Tags: cosmology, KCA, natural theology, universe began to exist
Well, before I respond, I want to have incentive to respond :/. Since I have a few days off, I probably won’t till either tomorrow or the day after.
Anyway, congrats at being a guest blogger at ‘Thinking Matters Talk’. elgoog
HA!! I totally called this in before you even wrote this… You can’t treat infinity as a number and expect to prove your point. Infinity is a CONCEPT. As for whether infinity can be traversed… you’re assuming it has a beginning.
Complete bollocks. Einstein’s theory of relativity and Hubble falsified the STATIC UNIVERSE.
ANOTHER bollocks.
Alan Guth has been stated to say “So far, it’s been made to sound, I think for the purposes of simplifying things, that until the cyclic model, all scientists had believed that the big bang was the origin of time itself. That idea is certainly part of the classic theory of the big bang, but it’s an idea which I think most cosmologists have not taken seriously in quite a while.”
Also, even IF we were to take that idea seriously, it STILL shoots the argument in the foot, since creation REQUIRES TIME. You forget- thinking requires time.
Finally, it has NOT been established the universe ever had a beginning. The Big Bang points to a COSMIC EXPANSION of space. It does not show that time began with it- rather, the singularity itself does not experience time, much like black holes. Joe
Joe, let’s not get too confident.
Additionally, keep your posts civil.
Here it seems you are confusing qualitative infinities with quantitative infinities. When I speak of infinity, I mean it in the qualitative (numerical sense). I do not mean it in a qualitative sense. Secondly, I make no such assumption, it’s completely irrelevant to whether or not it can be traversed. In fact, I made it clear that actual infinites do not have a beginning.
Yes, it did. Einstein himself, however, didn’t like these conclusions, so he introduced a “fudge factor” into his equations. He later came to admit his mistake, much to his own chagrin.
This is an accidental generalization. Thinking may include time, but it does not require time. In the absence of time, God would have just had all his thoughts in one eternal “now.”
The very definition of a singularity, according to Quentin Smith, entails a beginning. The initial singularity served as the boundary for the space-time manifold, such that there was no moment prior to it. Thus, it is in this sense that the universe had an absolute beginning. Tim H
Of course. Nobody holds the steady state theory seriously anymore. However, the inflationary theory does not speak of an actual “beginning”.
Please elucidate. The typo here makes it rather contradictory.
How do you think in an “eternal now”? You can’t have an “eternal” without time. You can’t have “thought” without time, since to “think” which REQUIRES consequential events, already has the underpinning of time. Without time, there is no “now”.
Sorry, but Quentin Smith is no physicist. I don’t care how he defines the “beginning”, because he is wrong. It’s nothing more than a blind assertion on his, and your part. The ONLY thing that cosmologists and physicists have been able to agree on thus far is that there was an inflation of space approximately 14 years ago. Joe
14 BILLION… sorry. Joe
Prove? Uh, no. Not even close. All this shows is that that universe “began” has not been established.
The universe need not have existed in the current observable state, prior to the Big Bang. Joe
i am seriously tempted to quote from Everitt again simply because he is one of the few atheist writers who actually tries to deal with this topic in depth.
You wrote:
“The point of this example is that arithmetical operations with actually infinite quantities yield contradictory answers, and thus it is metaphysically impossible for actual infinites to exist.”
Everitt replies to this:
“To illustrate the contradictions implicit in the concept of an actual infinity, he [William Lane Craig] asks us to imagine a library with an infinite collection of books where every book was coloured either black or red. He then continues:
‘We would probably not balk if we were told that the number of black books and the number of red books is the same. But would we believe someone who told us that the number of red books in the library is the same as the number of red books plus the number of black books? For in that latter collection there are all the red books – just as many as in the former collection, since they are identical – plus an infinite number of black books as well.’
We are meant to agree here that the assumption that there are infinitely many books leads to absurdity, and hence that the assumption must be absurd itself. But Craig has unfairly loaded the dice. Of course, we know antecedently that no library contains infinitely many books because we know that books take a finite time to write, and there have only been finitely many people in the history of the universe who have written a book. So of course there have only ever been finitely many books in the universe. But this is a fact about books, and the conditions of their production. It tells us nothing at all about infinity. If it were telling us an important truth about infinity, then the following argument ought to have equal force against the infinity of the set of natural numbers:
‘We would not balk at being told that the number of even numbers and the number of odd numbers is the same. But would we believe someone who told us that the number of even numbers is the same as the number of even numbers plus the number of odd numbers? For in that latter collection there are all the even numbers – just as many as in the former collection, since they are identical – plus an infinite number of odd numbers as well.’
In fact, this argument and Craig’s do have equal force, i.e. none at all, as an objection to the very idea of infinite collections. While recognising that Craig’s library, and other homely examples which he produces, have an intuitive appeal, from a logical point of view they have no force.”
Everitt is basically saying that examples such as this and Hilbert’s Hotel cannot be applied to infinity because they deal with finite things such as books and hotel rooms, making their application to infinities unjustified. If numbers are used instead as examples, then there is no contradiction.
Next, you wrote:
“It seems not, for even if actual infinities could exist in reality, they could not be formed by successive addition nor could they be navigated successfully.”
As for the problems involving successive addition, it seems to me that it presupposes that the infinite set has a beginning, which, of course, is logically impossible. If successive addition is taken to mean continually adding some number x to another number y, the argument falls apart, since y is the initial number, which cannot happen if we are dealing with infinities.
As for traversing infinities, Everitt replies as such:
“As an example consider the ‘proof’ by Moreland that an infinite set of past times is impossible. ‘[This] series cannot even get started. This is because it has no first member!’ (Moreland 1987: 29). The implication is that a series which cannot ‘get started’ and which has ‘no first member’ is not one which can terminate in the present. But this is impotent to show that an infinite regress is vicious. Of course an infinite series that terminates in the present does not have ‘a first member’ (assuming that ‘first’ means ‘earliest in time’). If it did, it would clearly be only a finite series of times. Some of the elementary implications of saying that the past series of times is infinite are that the series did not begin, that it did not have an earliest member, that for every member there is an earlier member, and so on. Moreland does not show that there is anything vicious about the idea of an infinite regress merely by pointing to such implications – what he needs to do is to show why any of them is supposed to be objectionable.”
Of course, none of this shows that the universe IS infinite. All these objections show that the universe COULD BE infinite; all they can show is that infinities are merely possible. Interestingly, however, it seems that Everitt actually provides a positive, inductive argument for the infinitude of the universe:
“By contrast, in all our experience of series of events, we have never experienced an event which did not depend on a predecessor, and if we try to think of what an event might depend on other than a predecessor, no answer comes to mind.”
This would imply that infinite regresses are not only possible but are indeed actual, since any event would have to be temporally preceded by another event. How might the Christian respond to such objections and arguments? Midas Vuik
His whole “infinity” argument boils down to
“given an infinite distance, there can be no such things as a location anywhere on it.” Joe
The actual infinite argument does not really affect the KCA, it just proves that actual infinities are not possible. Which no sane person believes in anyway.
P2: The Universe began to exist.
Oh really? This seems a little vague. You think that the big bang was the beginning of the universe, but why? Because it created time, matter, ect? When exactly does a car begin to exist? When I put on the frame, and add the engine? What happens when I simply remove the engine? Does it cease to exist? What happens when you remove me from the universe? Does it cease to exist? No, it doesn’t. It just means that the universe is in a constant state of change. Including when the big bang happened. Nothing really ‘begins to exist’, everything is in a constant state of change. Including the big bang. It was in a state of change from a singularity. And I see no laws why anything in a state of change needs a cause.
If you respond to me, I will respond only once. Because I don’t want to consume my time here. elgoog
Um, Tim hasn’t actually shown how “actual infinities” is impossible. He uses infinity as a number, and treats it as a finite number to “prove” his point, when infinity is a concept. Aren’t numbers “actually infinite”?
It hasn’t been established at all that either time nor the universe “began” at the Big Bang. It’s thought that the singularity itself did not experience time, but that doesn’t mean time did not exist.
Alan Guth has been stated to say “So far, it’s been made to sound, I think for the purposes of simplifying things, that until the cyclic model, all scientists had believed that the big bang was the origin of time itself. That idea is certainly part of the classic theory of the big bang, but it’s an idea which I think most cosmologists have not taken seriously in quite a while.”
Finally, without a beginning means it’s just an event of infinite regress, of which really there’s no problem. It’s odd, yes. But not absurd. Joe
Joe,
Sure, I’m speaking of infinity in terms of quantity (A set which contains a denumerable subset), and not in terms of quality (Which would be more conceptual as you have stated). The KCA treats an actual infinite in terms of the former, and not the latter.
I did not literally mean an eternal “now” (I thought my use of quotation marks made that clear). In the absence of time, God would simply have all his thoughts tenselessly. His consciousness would simply be made out of changeless beliefs such as “2+2=4,” “The Prime Minister is not a prime number,” etc…
You have yet to show that thought is essentially temporal. From all indications, temporality is merely a common property of thought. So your argument just seems to be based on an accidental generalization.
Smith is one of the leading philosophers of time and physics (And an atheist who has published significantly on the KCA), and as such he is extremely well qualified to speak on such matters. Maybe it’s you should stop with the blind assertions. I saw no supporting evidence other than a mere assertion in your above statement. The fact is that on the standard model, the singularity entails a beginning of the universe.
I’m not sure how this is supposed to refute my argument. According to the BVG theorem, any universe in the state of cosmic expansion (Such as ours) must have had a beginning. I saw no evidence against this.
This is irrelevant. Regardless of what state the universe existed in, it must have attained maximum entropy if it is eternally existent.
This is completely off. Firstly, I am not treating actual infinites as numbers, but as sets. I made it very clear that my definition of an actual infinite is a set which contains a denumerable subset.
On the standard model, the very definition of a singularity entails a beginning. It served as the boundary to the space-time manifold, such that there was no prior moment before it. So, time began at this singularity.
This is a mere assertion, and I have not seen any justification for it.
________________
Midas,
It seems to me that Everitt completely misses the point of the examples. Yes, in reality things such as hotels and libraries deal with only a finite amount of rooms and books, but there is no problem at all with proposing a thought experiment in which the number of rooms in a hotel/books in a library are actually infinite. This is only for the sake of clarity. The same absurdities result even if we use numbers in place for rooms/books. If we subtract all the even numbers from the set of all positive natural numbers, we are left an infinite difference. If we subtract all the positive natural numbers from the set of positive natural numbers, then we are left with zero. In both cases, infinity minus infinity yields contradictory answers, illustrating the absurdity of an actual infinite. It makes no difference if we substitute numbers for rooms or books.
That’s exactly where the contradiction is supposed to lie. It’s impossible to form an actual infinite through through successive addition because an actual infinite has no beginning.
This doesn’t seem convincing at all. Everitt seems to be saying that because we have never experienced beginnings on the causal chain, it’s reasonable to suppose that the causal chain as a whole does not have a beginning. This seems to commit the compositional fallacy (Since we have not observed a beginning to parts of the causal chain, the causal chain as a whole must not have had one).
_____________
Elgoog, I have responded to that criticism already in the previous segment of this series. Tim H
What’s “qualitatively infinite” supposed to mean? As for “quantitatively infinite” things, there can be infinite different subdivisions between integers, or between any two numbers.
What they believe is of no consequence. What I’m interested is what has actually been established.
This is pure bollocks. The fact that NONE of their “theories” whether it be Smith, BVG or Hawking have any empirical evidence. The only thing that all cosmologists agree on is the inflation. There is NO consensus on the mechanisms behind it.
This is because there are NO evidence whatsoever for ANY of the theories regarding the mechanisms of the Big Bang, hence why it’s not established. What one model dictates does not a consensus make.
Uh, why? Only if it is eternally existent in the current form, where it has the extended space would it have achieved the maximum entropy.
simply put, creation and “beginning to exist” REQUIRES time. Otherwise, how can you say it ever “did not exist”? Joe
Hey guys, sorry I haven’t been able to respond personally. I’m currently on a trip for an academic competition and will be back by the weekend to answer some of the comments. Timothy
Gravitation force (Newtonian) is the creator and sustain er of the universe. Einstein’s work is intuition based. His work is less empirical. e=mc^2 is purely an intuition of Einstein. Anirudh Kumar Satsangi
When one speaks of infinity in qualitative terms, they are not referring to an actual quantity (Ie: God is infinitely strong). Quantitative infinities, however, refer to a quantity of things (Numbers, for instance). The KCA uses infinity in a quantitative sense, since it argues that the past duration of the universe cannot be actually infinite.
It’s pretty much consensus that the universe began to exist, so the burden of proof is on you. I’m interested in seeing some hard evidence from you, not just a “Not all scientists agree, therefore your point is refuted!”
This is an unsubstantiated assertion. I additionally cited three lines of evidence for the standard big bang model: redshift, cosmic background radiation, and relativity theory. For the BVG theorem, empirically evidence isn’t necessarily required. Borde, Vilenkin, and Guth were able to generalize some of their earlier findings into such that ANY universe in a state of cosmic expansion must have a beginning. it is purely mathematical.
Even if I were to admit the lack of consensus, you still need to show how I’m wrong, instead of using “People disagree with you! Therefore you are wrong” as your argument.
Simple, according to the second law, the amount of energy in closed systems tends toward maximum entropy. That is, the amount of energy available to do work is constantly decreasing. If the universe were eternally old, then there would be no energy to do work. The only way to circumvent this is to find a way in which the entropy buildup could be reset.
This is just plain wrong. There are infinite sets. Two examples would be the set of odd numbers and the set of even numbers.
Firstly, let me warn you about plagiarism. If you do it again without citing your source, you will no longer be permitted to comment here. Second, that the standard model doesn’t deal with anything before the Planck time is trivial at best. This only means that in order to go before the Planck time, we must introduce quantum physics, since general relativity breaks down. Additionally, both the laws of thermodynamics and the BVG theorem still apply. Craig writes:
[1]
You then write,
I have dealt with this already in my previous post. Quantum fluctuations are not uncaused out of nothing, they still emerge from the framework of pre-existing particles within a quantum vacuum, which acts as a probabilistic cause.
That had nothing to do with the point you responded to. I was in fact responding to Midas’s comment about Nick Everitt’s argument.
Tim H
Huh? No. The consensus is that the Big Bang occurred. There’s no consensus the universe began at that point, or that the universe began at all.
I don’t need to- you’re the one claiming the universe began existing, and it began absolutely. The consensus is not this, at all. In fact, if it was, we wouldn’t be fiddling around with the LHC and the brane collision models, for instance.
All your evidence have are for the blood Big Bang, which, again, has not been established to be the beginning
I don’t need to. YOU were the one claiming that ONE model shows the universe began, therefore a consensus has been reached that the universe began, when this is not the case at all.
Uh, why? Only if it is eternally existent in the current form, where it has the extended space would it have achieved the maximum entropy.
Only if it is eternally existent in the current form, where it has the extended space would it have achieved the maximum entropy.
Somebody forgot the law of conservation of energy…
Only if it is eternally existent in the current form, where it has the extended space would it have achieved the maximum entropy
Sets are finite, hence your flaw. Infinity+7 isn’t infinity+7. Infinity is infinity. Hence why it’s a concept. Numerically or qualitatively it’s irrelevant.
Again, Infinity+7 isn’t infinity+7. Infinity is infinity. Hence why it’s a concept. Numerically or qualitatively it’s irrelevant.
How you can claim this to be “trivial” is just astounding.
Sorry, but Craig has no clue what he’s talking about. Firstly, the Borde-Guth-Vilenkin theorem assumes the space-time to be locally infinite, which obviously is not compatible with the KCA. To claim such incompatible theorem SUPPORTS his view is just stupid.
Read my post again. I did not claim it was “uncaused”. Firstly, we cannot point to a cause, if there is one- which doesn’t necessarily mean there are none. Secondly, I did not claim it was uncaused, but that it was a “spontaneous cause”, not requiring any “creator” for this “beginning”. Joe
As for the BVG Theorem, Here’s what Guth himself had to say about it.
and
Joe
@Tim:
Nom like you said: there are obviously objectiosn to my previous argument. Dr. Craig said: well, did I not being to exist? Even though the matter that composes my body has been around forever, that matter is not ‘me’.
But this actually has nothing to do with the argument. Because still nothing comes into existence. We are not dealing here with anything that comes into being but about a certain time or event at which a certain concept or properties can be applied to a collection of rearranged matter. So if you want to say that it is the concepts that come into existence then you have essentailly shifted away from the argument itself which is about it coming into existence and moved into metaphysical forms of concepts.
I have the same objection to the first premise of the Kalam since there is no example of anything that has come into existence. The only things that we see in the universe are reaarangements of materials into different shapes. I myself am only 16 years old but the matter that composes my body has been around since the first second after the big bang when it was formed from energy. To be mroe precise, every 7 years the matter that composes my body has been completely replaced by different particles. We observe formation, not creation.
But even if we hold the view that concepts are actually existing entities like in a platonic form, then still they do not come into existence. Especailly if you are a Christian you would have to believe that all possible concepts exist timelessly in Gods mind. You can only say that these concepts are only applicable on certain collections of matter at certain times.
You say in your blog that the universe could not exist eternally. Well, define eternally first. If you’re talking about the universe could not have an infinite past then I agree. Because actual infinities lead to a logical contradiction making them logically impossible. So I agree that the universe could not be eternal in that sense.
But there are two versions of eternity. When it coems to a Christian God Theist’s do not hold the view that God had an eternal timeline so to say, but he is a timeless entity. So they are talkign in the case of their God about a timeless eternity and in the case of an impossibly eternal universe of an omnitemporal eternity. It is indeed impossible for the universe to be omni-temporal eternal, but the universe can exist as a timeless entity(I am talking about B-theory of time, and I won’t go in depth on that).
My best arguement for B-theory of time is that the flow of time is different in different points in space. Inside a gravity-well, the flow of time is different(this has been confirmed by experiments using atomic clocks). Time is relative to the location of the observer. There is no eternal ‘now’ as being a single moment within the universe. elgoog
@ elgoog
How is an “actual infinity” impossible? Joe
Because it is logically invalid. Infinity is only a concept, so it can’t be applied ‘actually’. elgoog
You’re going to have to clarify your position for me, Elgoog.
In any case, god being a “timeless creator” is similarly logically impossible, since in order to create the universe, there MUST have been a time prior to which there was NO universe. Also, if the universe did not begin to exist, how can you claim god is a cause, since the effect does not exist for god to cause? Joe
I don’t really see why you’re arguing my position. Is it because your main argument against the KCA is invalid? I explained my position perfectly clear. Tim means actual infinities like ‘I have an infinite amount of books’. I think you might be mixing up actual infinities with possible infinities. elgoog
I also see no point in arguing with your criticism. If yours fails, then mine might succeed. And vice-versa…. elgoog
Nah, I was just genuinely curious, because I didn’t understand what you meant…
How do you have an “infinite amount”? In this case, yes it’s a logical impossibility because infinity is a concept, while he’s trying to use it as a numerical value.
In any case, I don’t find my criticism against KCA invalid. My points, I think, have been clear. That a “timeless cause” is an incoherent view, that the universe has not been established to ever begun existing- same with time, and that to claim otherwise is simply lying. Even Craig’s fave card BVG theorem has been shown to be misrepresented in the KCA. Joe
I think we may have just misunderstood each others argument. I’m simply agreeing with him that actual infinities(numerical values) are logically impossible. But it really has no affect on my arguement… elgoog
Yeah, that sounds about right. My bad. Joe
Hi folks, due to the sheer volume of comments, I’m going to stop with the one-on-one responses. General responses will be handled in subsequent posts. Tim H
All of the evidence for Big Bang/inflationary theory merely suggests that the OBSERVABLE universe was once so incredibly small that a quantum theory of gravity would be required to describe it (a theory we currently lack in any useful form). The universe could still actually be infinite in spatial extent. Brian Greene’s book “The fabric of the cosmos” is a good read for this kind of stuff. He also deals with the entropy issue. The currently accepted mechanism for inflation is a Higgs field, and the low entropy at the start of the universe can be explained by the Higgs field “dumping” out energy during the inflation to create most of the mass/energy in the universe, to counterbalance the increase in spatial uniformity (i.e. decrease in apparent disorder). I’m not sure if this can get around the issue of entropy and an infinite past, but there are certainly subtleties.
I’m a physics research student, and while I didn’t take a cosmology course, I have done some reading and talked to colleagues. Physicists say “the universe began at the Big Bang” but they do not actually mean it literally, they really mean, the known laws of physics break down ~14 billion years in the past, based on astrophysical observations. I don’t think this argument should be used to support the premise of KCA.
I’m more intrigued by the construction of infinities argument, I haven’t wrapped my head around it yet. bdforbes
His “infinity” argument suffers from treating infinity not as a concept, but as a finite number which leads to, of course erroneous results. He then calls it victory. He also claims that because it is infinite, it is somehow not traversable, which is also twaddle. Joe
Surely the same reasoning (that on the impossibility of actual infinities) can also be applied to God.
If the universe cannot have an actually infinite past, then how can God? If were allowed to assume that God just always was, then why not the universe? Steve
A more thorough understanding of number theory would confirm that a simple misunderstanding has occurred.
It’s true that a countable infinity + a countable infinity = a countable infinity, but this doesn’t imply a contradiction. It simply reveals that basic arithmetic operators are generally limited to finite numbers. Brendan