• Infinite Dreams

     William Lane Craig on the infinite – Part I

     

    During my path out of Christianity, I read and watched a lot of material from the Christian philosopher and theologian William Lane Craig: lectures, debates, books and journal articles.  As I began to think critically about the logical underpinnings of Christianity, I came to realise that the arguments Craig presented were not sound (even if many of his opponents in live debates were unable to adequately point this out).  I intend to explore Craig’s main arguments at length in future posts.  But one particular aspect of Craig’s thinking struck me as especially problematic, and that was his rejection of the infinite.

    Craig’s motivation for rejecting the infinite1 is that some of his central arguments attempt to establish the existence of a divine First Cause of the universe, something that “started it all off”.  Of course, if the universe didn’t actually have a beginning, then it couldn’t have a first cause.  So a beginningless universe seems like a problem for Craig.  One way a universe could be beginningless is for time to stretch infinitely into the past,2 and it is this that Craig seeks to show is impossible.

    Someone familiar with other aspects of his work might wonder why Craig would bother attempting this via philosophical arguments, as in other places he relies on the Big Bang Theory, which he takes to imply that the universe (including space and time itself) had a beginning.  But some modern cosmological theories3 interpret the Big Bang as an event leading from some state of another universe to ours (possibly in a black hole of some other universe).  So, with his First Cause arguments in mind, it seems sensible for Craig to argue that even if our universe was caused to exist (in some sense) by some other universe, which itself might have been caused by another, which was caused by yet another, then this process could not go back forever.  Craig wants to show that time itself, even if it transcends our own universe, could not be infinite in the past.

    In what follows, it will be convenient to formally refer to the proposition

    (P1)  Time could not be infinite in the past.

    This is the specific claim that Craig wishes to demonstrate.  To do this, Craig argues for the stronger proposition

    (P2)  Nothing could be infinite.

    Since (P1) is a special case of (P2), it is clear that (P2) entails (P1).  Conversely, (P2) clearly cannot be deduced from (P1), or from any single special case (or even from a handful special cases) – at least not without some extra argumentation.  But it seems that Craig’s attempts to demonstrate (P2) revolve around appeals to several special cases that he takes to be problematic.  For example, in his debate with Stephen Law, he dismissed the possibility of an infinite collections of coins, or of Jupiter and Saturn orbiting the sun since eternity past.  Elsewhere, he objects to the possibility of infinite hotels and libraries, counting backwards from infinity and other oddities.

    I do plan to address these special cases, and many others, in a subsequent post.  However, while this is an interesting path to take, it is nevertheless tangential to a critique of Craig’s main objective of establishing (P1).  As I have already said, (P2) cannot be established simply by pointing to a collection of special cases.  Such a method could only be successful if one was able to consider all special cases.  And, since (P1) itself is one of those special cases, it seems a rather futile way of proving (P2), as it is really (P1) that Craig wishes to establish in the first place!  Furthermore, the task of considering all special cases of (P2) must seem hopelessly impossible to Craig, since there are infinitely many special cases to consider.  Even if Craig objected that the special cases of (P2) form a merely potential infinite collection, I’m sure he’d agree it had turned into an actual infinite once the task had been completed.

    But with that said, I do actually think there is a reason for theistic philosophers like Craig to consider special cases of (P2).  For example, if I was suspicious of (P2), I might suggest scenarios that seem to be problematic for its proponents, and say that I could only consider accepting the proposition if such potential counterexamples could be adequately resolved.  I would not be doing this in an attempt to prove that (P2) is false.  Rather, I would be doing it to remind Craig of his burden of proof.   Since he has asserted (P2), and has not offered a general argument in its support, but instead attempted to prove it by considering various special cases, he must be prepared to refute any potential counterexample he is presented with.

    As it happens, there are many potential counterexamples to (P2), and I intend to present just one (which I don’t claim is original, as I’m aware of many similar scenarios floating around in the philosophical journals).  Consider a world in which God exists in some spatially unbounded heavenly realm.  Rather than creating a universe, God instead decides to create an infinite number of angels to keep him company.

    Now what is wrong with this possibility?  I don’t see why, if there really is a God that is as powerful as the one the Bible speaks of, he could not accomplish such a task.  Does it lead to logical absurdities?  I don’t really see how.  Perhaps we could grant that strange things might happen.  For example, if God could communicate telepathically with the angels, and if they could teleport instantaneously (neither of which seems unlikely, from reading various Biblical passages), then God could cause the angels to arrange themselves into an infinitely long line.  He could then cause them to rearrange themselves into two infinitely long lines, or three, or even infinitely many infinitely long lines.  But what is wrong with this?  On another day, God could choose to send infinitely many of the angels out of his throne room in such a way that there would still be infinitely many left with him.  Or he could have dismissed a different infinite collection of angels so that only three remained with him.  Sure, we don’t have experience of infinitely long lines of people in our everyday lives, or of varying answers to “subtraction problems”,4 but what is to say that such scenarios are impossible even for an omniscient and omnipotent God to accomplish?  There just doesn’t seem to be any glaring logical impossibilities.  A proponent of (P2) has the burden of demonstrating conclusively that such a scenario really is logically impossible before anyone else should even consider accepting (P2).

    In conclusion, I don’t know whether or not time extends infinitely in the past – in our universe, or a multiverse, or even just some logically possible world.  And I don’t think anybody else does either.  But it seems clear that Craig has not successfully demonstrated that time does not (or cannot) extend infinitely in the past.  It seems to me that neither a finite nor infinite past leads obviously to logical absurdities.  In fact, I would be more surprised if we could resolve such questions than if they remained unanswered forever (whatever “forever” might mean).

     

    Footnotes

    1.  Going back to Plato and Aristotle (look up), Craig distinguishes between two kinds of infinities: “actual infinities” and “potential infinities”.  I won’t go into too much detail here, but the former is meant to correspond to some kind of real existent infinite collection of things (such as an infinite number of books), while the latter merely reflects infinite possibilities (such as a universe or heavenly realm that extends indefinitely into the future, even though all the “days” have not happened yet).  There are blurry edges and, for example, some philosophers disagree on whether a (real or hypothetical) infinite past and/or future would constitute an actual or potential infinity; for example, see Wes Morriston’s article Beginningless Past, Endless Future, and the Actual Infinite.

    2.  Another way would be for time to be an “open interval”.  In this scenario, there would be a point in the past beyond which time did not reach, but there would not be an actual moment of time at this point.  By way of analogy, let S denote the set of all real numbers x such that 0<x<1.  Although the number 0 is less than every element of S, 0 is not itself an element of S.  In fact, S does not possess a minimum element.  So, for every element of S, there is a smaller element of S.  For considerations like this relating to the logical possibility of a beginningless universe that only extends finitely in the past, see Quentin Smith’s article A Cosmological Argument for a Self-Caused Universe.

    3.  Smolin Selection Theory or Chaotic Inflation Theory or Cyclical Models, to name just a few.

    4.  These examples respectively correspond to the fact that any infinite set may be partitioned into a finite or countably infinite number of equinumerous subsets, or that any infinite set has various equinumerous subsets with complements of varying cardinalities.  While these properties are not shared by finite sets, one should not be surprised that infinite sets behave differently to their finite counterparts.

     

    Category: Cosmological argumentGodInfinityMathematicsWilliam Lane Craig

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    Article by: Reasonably Faithless

    Mathematician and former Christian

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    • Ian Powell

      Hi RF – seems like a solid argument here – though discussions of the infinite tend to wear out my brain more quickly than i like.
      Regarding the the multiverse and other pre-big bang theories – they seem to me be “dogma”driven rather than “data” driven. I mean by this distinction that the scientific community was (with some reluctance) driven to embrace the big bang scenario because of the data.
      But the drive to play with multiverses etc seems, i stress seems as my reading is far from exhaustive to not come form some nasty data that doesn;t fit – but becasue of the philosophic discomift this theory produces.
      IS that fair or is there some data i am unaware of.
      This is a different question to your blog so no expecteation of a quick answer.
      thanks ian p

      • Reasonably Faithless

        Thanks Ian. Don’t worry – most people don’t have to deal with infinity in their day jobs 😉

        As to your question, I’m a mathematician, not a physicist, so I can’t really comment on motivation. But I did once see a nice talk by Paul Tod (Oxford) on Cyclical Cosmology, where he said that patterns in the background radiation seemed to suggest the big bang was the second half of a crunch/bang pair. There’s also the double slit experiment, which was explained really nicely in The Grand Design (Hawking/Mlodinow) – this lends some support to the idea of summing over all histories, and if one sums over histories close to the big bang, one ends up predicting (infinitely?) many universes with different physical laws. There’s also the question of where stuff goes when it disappears into a black hole.

        But I’d be grateful if someone more scientifically literate than I would comment further.

    • Jonathan MS Pearce

      RF,

      outside of thought experiment conception, do you think there is an actual infinite?

      I dislike Craig’s arguments a lot. However, I think infinites, he might be right on. Actual infinites are seemingly impossible – incoherent even before they get off the ground. I just don’t think you can have them because the term infinite is conceptual and does not refer to an actual set, but things usually tending toward. They can work as a potential set, such as in maths, but in a concrete sense, I cannot see them as coherent.

      Where I would say it gets interesting is in Big Bounce scenarios where time starts again. Here, it seems incoherent to have infinite time backwards since time would start again. Could you have infinite startings again?

      • Reasonably Faithless

        Hi JP,

        Thanks for your interesting comment. About your question, I don’t know if there *is* an actual infinite, as in a collection of concrete things that is infinite in extent.

        I have never seen an infinite collection with my own eyes, and I tend to think that since we are finite, we could never conclusively check that something is infinite – how long do you count the members of the collection before you are allowed to conclude it is infinite?

        In practice, you can sometimes check that a finite collection is indeed finite, since if you got to the end of it, you’d know! But if you found a collection of a trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion coins, you would be dead before you finished counting – what could you conclude in your dying breath? All the information gathered so far is consistent with the collection being infinite or finite. I tend to think we are not equipped to check things like this, and this lends support to the idea that we should probably be agnostic about this.

        (Some astronomers regard it as an open question of whether there is an infinite number of stars. The fact that more and more of our universe is becoming invisible to us should make us humbly agnostic about what lies beyond the visible universe.)

        So, Craig’s *conclusion* may or may not be correct – there might be actual infinities, or there might not be – but his argument is far from valid. In fact, I have never seen any convincing argument either way. You’d either have to prove that a certain collection of objects was infinite (which seems very difficult, to say the least – see above), or else show that no collection of objects could possibly be infinite.

        The only arguments I’ve heard for the latter boil down to either (i) assertions that actual infinities are incoherent or logically absurd, or (ii) appeals to counterintuitive scenarios like Hilbert’s Hotel and the like. The latter just demonstrate the fact that infinite sets (whether they exist in reality or just in the minds of mathematicians) behave differently to finite sets. Mathematicians who deal with these kinds of things every day are comfortable with the ideas involved, and are used to counterintuitive notions (as are quantum physicists, for different reasons).

        So I’d be genuinely interested if you could flesh out your reasons for thinking actual infinites are incoherent. I prefer to hear reasons from people like you, as you are objecting to infinities because you just don’t think they make sense, not because you’re trying to prove God exists 😉

        (Speaking of which, it’s interesting that the theist who wants to prove there are no infinities in order to prove God exists must then try and come up with ways that God’s knowledge, which they assume encompasses everything, is somehow not an actual infinite.)

        • Jonathan MS Pearce

          Hey RF. I would have replied earlier but had not subscribed – it’s difficult to keep on top of everything.

          So I think actual infinites are impossible since the very nature of them is incoherent. The definition of an infinite can almost entail never-endingness, such that it is a number without limit. You can just keep adding one. That concept is (seemingly) simple enough for me to accept that they cannot exist in actuality. I just can’t see how a set could exist, irrespective as to whether we could know or not.

          • Reasonably Faithless

            Thanks JP for your reply. I guess what I’m asking for is an argument to back up your assertions like: “actual infinites are impossible since the very nature of them is incoherent”. I’m not sure if the next sentence is meant to be such an argument, but if it helps, infinities are not “numbers” – numbers are finite by definition. You could have an infinite set of numbers, and you can add things to an infinite set without making it bigger, but this is simply a property that infinite sets have and finite sets do not. There shouldn’t be any surprise that infinite sets have different properties to finite ones. Being different doesn’t automatically entail meaninglessness.

    • Rizdek

      I’m just as puzzled by various forms of “Zeno’s paradoxes” as I am when considering a universe that extends backward infinitely. IOW how can something get from point A to point B when it has to traverse an infinite number of halfway points. And how do we ever get from, say 2 oclock to 3 oclock when an infinite number of halfway times must tick by. And it’s not just “halfway” points, there are an infinite number of sets of interim points, EG 1/4, 1/5, 1/6, etc. Looking at it that way, how can things even move at all, because before something can go halfway, it must go 1/4 the distance. But before that it must go 1/5, and 1/6 and 1/7 …1/10,000,000 the distance…etc.

      Also, I have thought of this in regard to considering whether the universe is finite, spatially. I recently read where they have found a galaxy 10 billion light years away. Let’s imagine there is an advanced civilization in that galaxy that can also look out into space with equipment equivalent to ours. They should be able to look out in all directions and see objects 10 billions light years away. This means they could look off in the opposite direction away from us and would they not also be able to see objects ~10 billion light years away? If they spotted a galaxy 10 billion light years away in that direction, we could imagine a civilization on THAT galaxy doing the same….etc. IOW, where does it end? Now, I realize that in addition to looking out across space, we are looking back in time. So, the galaxy we see 10 billion light years away has receded away from us (space is expanding) and NOW, it is actually much further away from us and the hypothetical galaxy it spots while looking out away from us has also receded.

      I get lost even trying to explain this, but how can we imagine an end to that. Where do we arbitrarily say a given civilization can no longer look out in all directions and see things 10 billion light years away?

      Finally, if there IS a logical/philosophical problem with infinites, then that problem also would apply to a god in whatever realm/state of existence it occupies, figuratively speaking. It does no good for the theist to beg their god off this generalization of impossible infinites. Because if they can, then so can I. I can arbitrarily claim there is a natural “non-god” state/realm/existence that is not subject this rule of impossible infinites. And this state/realm/existence “spawns” universes…the problem is solved.

      • DRC

        A few points about Zeno’s paradoxes:
        -Yes it seems there are an infinite number of locations to visit between A and B, but the person is moving through *an infinite number* of these locations each second. If we were to assume that we must spend a finite time at each location, then of course we’ll never move, but in this example, each time you halve the distance, you’re also halving the time spent in each interval. The total time is: infinity/infinity and this can be a finite number. This makes it possible for things to move. The field of calculus formalises this argument, and says that you can spend an infinitesimal time at an infinite number of locations, and the overall effect is “continuous movement”.

        -Secondly, our best physical theories imply that there’s probably a smallest unit of space. Anything smaller is meaningless, so it’s probably untrue that there are an infinite number of locations between A and B. Just like you can halve a block of gold, and halve it again and again… but eventually you’ll have one atom of gold, and if you halve that, you won’t have gold anymore. The universe seems not to be infinitely divisible.

        -Lastly, quantum mechanics shows there’s an uncertainty pair of position and momentum. So an object between A and B does not even have an exact location and momentum. It’s probably meaningless to say the object must first visit an infinite number of locations in order, if its position is not uniquely defined.

        • Rizdek

          Not being good at mathematics I don’t understand the calculus solution though I have tried to in the past. Does the calculus solution involve positing a “transfinite” fraction that arbitrarily “reaches” the goal instead of depending on the additions of a series of ever decreasing fractions…i.e.
          1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + transfinte fraction = 1?

          If your second and third points are true, then the calculus solution is not really necessary is it?

          • Reasonably Faithless

            Sorry I haven’t been able to properly respond to your earlier post, Rizdek, but I will hopefully in the next week. But it’s probably worth mentioning that while some sums involving decreasing terms do have actual answers, others don’t. For example,

            1 + 1/2 + 1/4 + 1/8 + 1/16 + … = 2

            while

            1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + … = infinity.

            The sense is that if you add the first n terms of either sequence, you get a partial sum you could denote S(n). As n tends towards infinity, S(n) tends towards 2 in the first one, but grows without bound in the second one. You could easily check this yourself, by calculating, say, S(10) in the first one, and observing it is very close to 2. It’s a bit harder to see the second one, but there are simple arguments showing that it diverges.

            I’ll say more about Zeno I have a chance.

            • Rizdek

              I made a mistake in my post. I meant to write:

              1/2+1/4+1/8+1/16 etc <1

              And I wondered if the "solution" per calculus was to invent a "transfinite" fraction that "gets us there?" IE, just make it up because we all know things move and get form point a to point b.

            • Jonathan MS Pearce

              Good to see you over here, Rizdek. Pop round to ATP, too, if you fancy!

      • About Zeno-style paradoxes…..

        Say you’re walking to a wall. First you have to go half the distance, then half the remaining distance, then half the remaining distance, etc. It seems you won’t be able to get there. But in fact, each successive “task” takes half as long. And it is easy to prove that 1/2 + 1/4 + 1/8 + … = 1.

        The same thing happens even if you’re not doing anything. Sit still for a minute. To get to the end of the minute, first half a minute has to pass, then another quarter minute, then another eighth, etc. But the minute passes just fine.

        It’s an interesting question to ask whether there are “atoms” of space and time – ie whether space and time are built out of indivisible blocks. This is an open question, and it might be impossible to answer. The planck length refers to the minimum distance we can have any hope of measuring – not necessarily to the limit to how small things can be, or something like that.

      • About your other question (what things might look like to someone in a galaxy 10 billion light years away)….

        This is a fascinating question. From what I have read, I understand that rate of expansion of the universe is faster than the speed of light. That means that the furthest thing away from us that we can see now will be invisible to us soon. It also means that there is a lot of our universe that we are unable to see. From our vantage point, we feel as if we are in the centre of the universe, but really we are just at the centre of *our visible universe*. You can’t be at or even near the edge of the universe, as if you could see for 1 light year in one direction, and a billion in another. The universe is not like a solid sphere, expanding into empty space. It’s more like the surface of a sphere expanding into empty space, so that wherever you stand on it, it extends the same in every direction. (Of course, the surface of a sphere is 2D, and our universe is at least 4D, so the analogy is just to help us get our heads around very complicated higher dimentional geometry and topology.)

        This is all a very roundabout way of saying that I expect an alien living in a galaxy 10 billion light years away from us would see something very similar to us if he/she/it looked out in any direction – i don’t think they would have us 10 billion light years in one direction, and the edge of the universe 3.7 billion light years in another direction.

        This kind of thought experiment lends support to the possibility that the universe could actually be spatially infinite.

      • About your last observation, it is very interesting listening to philosophers like William Lane Craig speaking about God’s omnipotence, given that they object to all “actual infinities”. The lengths they go to to allow God to somehow know everything (which automatically includes infinitely many things) is extraordinary. I will probably devote a whole blog to it one day.

    • JohnM

      We don’t live in an infinite universe.

      Our universe is expanding. Something infinite, cannot expand. In what direction would it expand?

      Our universe had a beginning, regardless of whether or not there were *something* before it. And it will end, in the so-called ”fiery-heat-death” of the universe.

      So both in time and scale, we live in a finite universe. A universe that had a beginning. And whatever begins to exist, has a cause 😉

      RF said:
      “Some astronomers regard it as an open question of whether there is an infinite number of stars”

      We don’t live in an infinite universe. The universe is expanding, so it must have a present space/time border. And therefore, the number of stars must be finite.

      RF said:
      “Furthermore, the task of considering all special cases of (P2) must seem hopelessly impossible to Craig, since there are infinitely many special cases to consider. Even if Craig objected that the special cases of (P2) form a merely potential infinite collection, I’m sure he’d agree it had turned into an actual infinite once the task had been completed.”

      And when would the task be complete? After considering 10222021221 special cases? Or after 21897456464897676448464564 special cases? Or after 4564564646545646424324545645213546456422248686846846524 special cases?

      You can consider special cases from this point onwards, to the end of the universes. You’re never going to reach an infinite number, by adding +1 to a finite number. It will continue to be, just be a really really big, finite number. And that just goes to show, that infinity, is just an idea in your head.

      RF said:
      “Rather than creating a universe, God instead decides to create an infinite number of angels to keep him company. Now what is wrong with this possibility? I don’t see why, if there really is a God that is as powerful as the one the Bible speaks of, he could not accomplish such a task. Does it lead to logical absurdities?”

      Omni-potency has always been understood as anything that is logically possible. Creating an infinite number of something is logically absurd. Something created, will always be of finite number. You have to show, that it is possible, to have create an infinite number of something, for it to count against God. Something that you cannot do.

      “Speaking of which, it’s interesting that the theist who wants to prove there are no infinities in order to prove God exists must…”

      He’s not trying to prove that God exists.

      ..must then try and come up with ways that God’s knowledge, which they assume encompasses everything, is somehow not an actual infinite. )

      We don’t believe in an infinite number of gods. We believe in one eternal God.

      Random internet atheist said:
      “Nothing ever begins to exist.. “

      Oh boy… Let’s leave this one to the man himself..
      http://www.youtube.com/watch?v=6gpJuztzOH4

      • Rizdek

        “We don’t live in an infinite universe. The universe is expanding, so it must have a present space/time border.”

        Consider we are looking out 10 billion LY and see a galaxy. Since it has been receding from us during the time the light from it took to reach us, it is now, let’s say 15 billion LY away. On it, let’s say there is a civilization that is also looking out in all directions. They look back and see our area of space as it was 10 billions years ago. They also can look out the other way 10 billion LY and could, theoretically see a galaxy that itself is receding from them. It is now 15 billion LY from them and 30 billion LY from us. On that distand galaxy there is a civilization that ALSO can look out and see areas of space/galaxies 10 billion LY away…etc. By your reasoning, at some point there is a civilization that woould look out and see the edge of space…i.e. nothing…no stars, nothing. Now does that sound reasonable?

      • “We don’t live in an infinite universe.”

        how do you know this?

        “Our universe is expanding. Something infinite, cannot expand. In what direction would it expand?”

        that is not true. consider the set R of all real numbers, and the function f:R->R defined by f(x)=2x. when f is applied, each point becomes twice as far from the origin as before the function was applied. but f maps R onto itself. it is expanding, yet is not expanding “into” anything other than itself.

        if the universe is infinite, then that is precisely the kind of expansion that is happening (but obviously in a more complex way). we don’t know if the universe is infinite or not, but the fact that it is expanding in no way rules out the possibility that it is infinite.

        “Our universe had a beginning, regardless of whether or not there were *something* before it.”

        even this is not known. we know that if we trace the history of the universe back in certain models, we reach a point beyond which those models do not stay relevant. we do not know what happened at the point where the models break down. *by definition*, those models do not tell us what happened. it might be that our universe has been going forever, or maybe not. it might be that our universe began to exist with nothing “before” it. and it might be that our universe began to exist with something before it – and this “something” could be finite or infinite. we don’t know. the humble thing is to admit we don’t know – don’t you agree?

        “And it will end, in the so-called ”fiery-heat-death” of the universe.”

        “end” is an interesting word for the heat-death of the universe. it is expected that the universe will wind up in a never-changing wasteland of radiation (with even black holes decayed into nothingness). but it’s hard to say that this is the “end” of the universe, rather its final state. it might also be that this state is a kind of limit that is never reached, so that things become slower and slower, but never quite reaching zero (in a similar way in which nothing can reach absolute zero in temperature). we don’t know for certain what the eventual fate of the universe is.

        again, it seems best to be humble the possibilities. don’t you agree? it also seems best to let the research in cosmology be done by people that are suitably qualified.

        “So both in time and scale, we live in a finite universe. A universe that had a beginning.”

        well, you have asserted that we do anyway 😉

        “And whatever begins to exist, has a cause”

        how do you know this? can you please define what it means for *time* to begin to exist? and can you please do it in such a way that your definition does not imply that (your conception of) god did not also begin to exist?

      • “We don’t live in an infinite universe. The universe is expanding, so it must have a present space/time border.”

        again, false. in my example above, the real numbers can be thought of as expanding under the transformation x->2x, yet the set of real numbers has no border. if the universe is spatially infinite, then this is precisely the kind of expansion that would be taking place (in higher dimensional geometry).

        “And therefore, the number of stars must be finite.”

        why don’t you write a paper and submit it to a cosmology journal? do you think they would find your “argument” compelling?

        “And when would the task be complete? After considering 10222021221 special cases? Or after 21897456464897676448464564 special cases? Or after 4564564646545646424324545645213546456422248686846846524 special cases?
        You can consider special cases from this point onwards, to the end of the universes. You’re never going to reach an infinite number, by adding +1 to a finite number. It will continue to be, just be a really really big, finite number.”

        you’re actually making my point for me. my point is that craig simply cannot check every special case in order to know that they all have a certain property.

        “And that just goes to show, that infinity, is just an idea in your head.”

        no, it doesn’t. it shows that craig would be unable to accomplish this particular task.

        “Omni-potency has always been understood as anything that is logically possible.”

        i understand that. that’s why i am asking for a theist to present an *argument* to show that something like the scenario i suggested is not logically possible.

        “Creating an infinite number of something is logically absurd.”

        i welcome you to present an argument to back up this assertion.

        “Something created, will always be of finite number.”

        do you have an argument to support this assertion of yours?

        “You have to show, that it is possible, to have create an infinite number of something, for it to count against God. Something that you cannot do.”

        no, i don’t. as i explained in the post, craig is the one that has claimed that actual infinites are impossible. i merely proposed one case that *might* count as an actual infinite (in a possible world). anyone that claims that actual infinites are impossible has the burden of proof to show that my suggestion is logically impossible. remember – i am not claiming that actual infinites exist – just that craig has not successfully shown that they don’t.

        you’re welcome to present an argument that shows my scenario is impossible.

        “He’s not trying to prove that God exists.”

        um, yes he is. the impossibility of actual infinites is a premise in his argument that the past is not infinite, which in turn is a premise in one of the cosmological argument forms craig uses.

        “We don’t believe in an infinite number of gods. We believe in one eternal God.”

        i was referring to the belief craig has that, even though actual infinites do not exist, god is still omniscient, and in particular, has infinite knowledge.

    • JohnM

      Well you tell me…

      http://www.youtube.com/watch?v=Tz8ithgTBj4&feature=related

      That youtube video is a standard illustration of Big bang. “In the beginning…” we see a very compact ball, containing all mass in the universe, that then starts to expand outwards.

      Had I been standing right next to it, 0.01 seconds into the video… and then turned 180 degrees around, thereby facing away from it.. What would I have seen?

      Now imagined, that right after looking around, I picked up my surfboard, and then continued to surf /ride the shockwave of the “explosion” for the next 14 billion somewhat years.

      Where would I be? And what would I see when looking around ?

      • Rizdek

        You would see an expanding universe all around you as far as you could see…which might not be that far given the concentration of material at that stage of expansion. There is no edge to the universe. Because there is no “outside” the universe.

        • JohnM

          So, I would have seen the expanding universe, located behind me, in front of me.

          Is that a fair summarization of your reply?

      • Micke

        It isn’t possible to stand “right next to it” because there is nowhere to stand. The “explosion” wasn’t an explosion of mass that moved out into a pre-existing space, but rather the rapid expansion of space itself. There isn’t anything that is “outside” the universe, not even space, so there is nowhere to stand.

        • JohnM

          I’m well aware that one cannot stand there. Leaving aside, that no humans existed at the time.

          It was a theoretical question. Therefore I wrote “Had I been standing…”

          But anyway, thanks for pointing out the obvious.

    • Micke

      First: We don’t know whether the universe is infinite or not. The measurements done so far are consistent with both an infinite universe and a really, really big universe.
      Second: An infinite universe can expand. The expansion of the universe is an expansion of the space itself, and does not imply that the galaxies are moving away from each other through space. The galaxies are separated by an increasing amount of space. They do not move (much) but the amount of space in between is increasing. This kind of expansion is possible if the universe is finite and if it is infinite.

      • JohnM

        An infinite expanding universe, is an oxymoron.

        • DRC

          No it’s not. Some infinities are bigger than others so it’s possible for an infinite universe to get “bigger”.

          I think you’ve assumed that there is only one infinity with a single, fixed size. You’re treating it like a finite number. We can’t have an “expanding 5”, but can have an “expanding infinity”.

          • JohnM

            What on earth are you talking about?!?!

            There’s no big and small infinity. Infinity, is infinity.

            • Bungoton

              In mathematics there are different sizes of infinity. The infinite number of integers is not the same size as the infinite number of fractions between 0 and 1. I’m sure this doesn’t apply to anything physical like the universe.

            • JohnM

              Hehe. Well sure, there are those crazy examples..

              But in my view, that’s just math gone horrible wrong.

              Infinity > Infinity
              Infinity < Infinity
              Infinity != Infinity

              That's absurd!

              So I would argue, that whenever one can say, that one is bigger or smaller than the other, one is not actually dealing with infinity. Or the other option. Infinity being nothing more than an idea in our head.

            • DRC

              It’s not absurd at all. You should read about the work of Georg Cantor who first demonstrated that there are many different infinities and some are bigger than others. This is well established mathematics.

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

              However, I do take your second option seriously. I think it’s possible that there are no “physical” infinities in the universe. Perhaps the universe is finite, however the original post was more about time being infinite in the past which seems to be a separate issue as to whether the universe is spatially infinite. It’s possible that the universe is finite in space, but infinite in time.

            • john, on my youtube video, you have lectured me again and again on how superior your mathematical knowledge is to mine. but in this thread you’ve done an outstanding job of demonstrating just how little you know about mathematics. one would think that when speaking about a topic you are not an expert in, you would at least do a little research first. (and don’t worry, i will reply to your post there once i have time.)

              yes, there are all kinds of different infinities. the set of all real numbers is bigger than the set of all integers. (for the record, bungoton’s statement below it wrong – the set of fractions between 0 and 1 is actually the same size as the set of integers.)

              there are infinitely many different infinities. given any set X, the set P(X) of all subsets of X is bigger. so if X is infinite, then P(X) is a bigger infinite set, and P(P(X)) is bigger still, and so is P(P(P(X))), and on and on. there are sets that are even bigger than all of these. there are so many different infinities that it is impossible to put them all into one set – the collection of all possible infinities forms what is called a “proper class”. you should look it up – it’s really quite fascinating.

              “But in my view, that’s just math gone horrible wrong.”

              your view is just that – a view. you have not backed it up with any kind of argument. you have simply demonstrated that you do not understand infinite set theory, and concluded that it is simply “math gone horribly wrong”.

              “Infinity > Infinity
              Infinity infinity.

              they might (and do) write inequalities like

              a>b

              where a and b are different kinds of infinities (for example, a=”aleph 1″ and b=”aleph 1”). but to lump all infinities together under the label “infinity” and write down inequalities like you did would be as absurd as noting that some numbers are bigger than other numbers and saying:

              number>number
              number<number
              number!=number
              ZOMG math is brokenz!!1!!!!

              "So I would argue, that whenever one can say, that one is bigger or smaller than the other, one is not actually dealing with infinity. Or the other option. Infinity being nothing more than an idea in our head."

              you say the word "argue" a lot for someone that has not presented a single argument. please go ahead and make an argument for the numerous assertions you have made.

    • Rosemary Lyndall Wemm

      If time does not extend infinitely in the past then why should it extend infinitely into the future, either? In the Christian world, an infinite future is assumed to be possible because it would otherwise be logically impossible to have eternal life.
      If “eternal life” were only to be experienced in “non time” and “non space” then time-dependent things like learning, memory, emotions and pain would not be possible. The lack of eternal pain would also rule out the possibility of eternal torture in “hell”.
      Apologists can’t have it both ways. If an eternal past is impossible, then an eternal future is also impossible. In other words, Christian theology is logically incoherent.

      • Wes Morriston wrote an excellent article entitled “Beginningless past, endless future, and the actual infinite” in the Faith and Philosophy journal. There he argued that if an infinite past is deemed an “actual infinite”, then an infinite future should be too. Thus, if being an “actual infinite” is enough to reject an infinite past, one should also reject an infinite future.

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