Dec 16

On Absurdity: William Lane Craig and Actual Infinites

Assuming creation, what is God’s relationship to time? There are two popular views—God is infinite (existing everlastingly, but within time) and God is eternal (existing changelessly with no relation to time). In both cases, God is uncaused, never begins to exist, and never ceases to exist. William Lane Craig, interestingly, adopts what you might call a hybrid of these two views to make sense of some philosophical problems.

There have been many responses to Craig’s arguments about time and infinity. I consider many of these to be successful, but I hope to take a new approach, or at least new to me. I feel that Craig’s arguments regarding the relationship of God and time fall victim to the same absurdities as the arguments he rejects. I plan to show this through an analogous hypothetical situation.



Kalam Cosmological Argument

Craig presents some difficult arguments in favor of theism. Probably his best known argument is a defense of the Kalam Cosmological Argument, which says[1]:

  1. Whatever begins to exist has a cause.
  2. The Universe began to exist.
  3. Therefore, the Universe has a cause

Some have countered that the Universe could perhaps be infinite. With regard to modern physics, we might say there have been an infinite number of big bangs and big crunches to create a sort of cyclical Universe.

For premises (1) and (2) to be true, though, the Universe cannot be infinite. It must have a finite beginning in order for the statement “begins to exist” to have any meaning. If the cyclical model, or similar model, is true, then Craig’s argument has a problem. So Craig counters that actual infinites are not possible and create metaphysical absurdities.



Infinite Absurdities

I should briefly explain what is meant by an actual infinite. If you think of time as a traditional timeline, with the present being located at time t0 right in the middle, then time would extend endlessly in both directions. There would be an infinite number of moments in the past and in the future. This is in contrast to a potential infinite. One example of a potential infinite is something that has a definite beginning and then can stretch infinitely into the future.[2] It is the actual infinite that Craig addresses.

Craig’s argument, a variation of Hilbert’s Hotel, is succinctly described by the Stanford Encyclopedia of Philosophy as follows:

Craig argues that if actual infinites that neither increase nor decrease in the number of members they contain were to exist, we would have rather absurd consequences. For example, imagine a library with an actually infinite number of books. Suppose that the library also contains an infinite number of red and an infinite number of black books, so that for every red book there is a black book, and vice versa. It follows that the library contains as many red books as the total books in its collection, and as many red books as red and black books combined. But this is absurd; in reality the subset cannot be equivalent to the entire set. Hence, actual infinites cannot exist in reality.[3]


In other words, since we know there are black books in addition to red books, how can it be the case that there are as many red books (a subset of the whole) as total books (both red and black)? We seem to have a compelling paradox on our hands.[4]



Craig’s Resolution

Now we are faced with an interesting problem. Craig has tried to show that actual infinites are absurd, yet some hold the view that God is infinite within time. This would make God absurd. So, he must find a new home for God. The obvious choice is the eternal position.

The other way in which a being could exist eternally would be by existing timelessly. In this case God would completely transcend time, having neither temporal location nor temporal extension. He would simply exist in an undifferentiated, timeless state.[5]


What do we make, then, of creation? It seems to be a temporal event. Craig’s resolution is to say that God exists eternally in a changeless state except for the duration of the Universe, in relation to which he is temporal.

With the creation of the universe, time began, and God entered into time at the moment of creation in virtue of His real relations with the created order. It follows that God must therefore be timeless without the universe and temporal with the universe.[6]


How can this be? It appears problematic to assert that God fits into both categories of time. Craig himself sees the difficulty in this argument.

Now this conclusion is startling and not a little odd. For on such a view, there seem to be two phases of God’s life, a timeless phase and a temporal phase, and the timeless phase seems to have existed earlier than the temporal phase. But this is logically incoherent, since to stand in a relation of earlier than is by all accounts to be temporal. How are we to escape this apparent antinomy?[7]


Craig goes on to briefly describe his response to this problem.

What must be done is to dissolve the linear geometrical structure of pre-creation time. One must maintain that “prior” to creation there literally are no intervals of time at all. There would be no earlier and later, no enduring through successive intervals and, hence, no waiting, no temporal becoming. This state would pass away, not successively, but as a whole, at the moment of creation, when time begins.

But such a changeless, undifferentiated state looks suspiciously like a state of timelessness! It seems to me, therefore, that it is not only coherent but also plausible that God existing changelessly alone without creation is timeless and that He enters time at the moment of creation in virtue of His real relation to the temporal universe. The image of God existing idly before creation is just that: a figment of the imagination. Given that time began to exist, the most plausible view of God’s relationship to time is that He is timeless without creation and temporal subsequent to creation.[8]


The way we get here is essentially as follows. Actual infinites are not possible, according to Craig, so God cannot exist infinitely in a temporal state. To avoid this problem, God is considered essentially outside of time. Yet, God created the world, so that means God has relation to the world. This relation has to be temporal in order for creation to happen. So, God is temporal in reference to the Universe. Both ideas have to be true – one in reference to the non-existence of the Universe and one in reference to the existence of the Universe. As of this moment, and for all the history of the Universe, God is temporal and can act within time. Without the Universe, God is timeless and changeless. God cannot act in this latter state because that would imply a passing of time for the action to take place.



Compounding Absurdities

I find this dualistic argument to also be absurd. I’d like to offer a similar analogy to Craig’s library.

Let’s suppose there is a library that exists. This library is necessarily changeless; it is impossible for the library to change in any way. Thus, the library cannot loan any books because its collection must remain unchanged. Yet, the library has a will and is also omnipotent, and it is the library’s will that it should loan out some books. So, the library’s will is done and books are loaned. Books leave the shelves of the library even though by definition that cannot be the case.

How can the unshakable rule of not loaning books be reconciled with the fact that books are loaned? Even an omnipotent being cannot do what is impossible. For example, an omnipotent being could not be a married bachelor, since by definition a bachelor is unmarried.

In the same way, how can a being that is necessarily changeless and timeless become changing and temporal? It is a counterintuitive absurdity.




If you agree with me that I have created absurdities similar to those of Craig on infinity, then it seems you are forced into one of two conclusions. Either you reject the idea of God as presented because of the absurdity or you reject that an apparent absurdity derails the argument. If you favor the first, then you think the paradox approach is a good argument, but then you still have to reconcile the notion of God and time. If you favor the second, then you think the approach is a bad argument and an apparent absurdity does not discount the possibility of an infinite Universe.

I tend to agree with the second approach – I don’t think Craig’s apparent absurdities mean there can be no actual infinites. Thus, the Universe could be said to have no beginning. I don’t think it has ever been adequately shown that counter-intuitive results, like those demonstrated by Craig, must mean the proposition is false. Furthermore, if Craig holds a counterintuitive position himself, then it appears apparent absurdities only matter to him when they do not affirm his view.

[1] In Defense of the Kalam Cosmological Argument

[2] Another interesting example of a potential infinite is expressed by the distance between two points. Let’s say you throw a ball at a wall. At some point, the ball will be exactly halfway between the two original points. Then, the distance can be cut in half again, again, again, and so on. You can divide a line segment in half an infinite number of times and the two points will never touch. Given that there are an infinite number of line segments between the ball and the wall, how does the ball ever make contact with its destination? How can it traverse an infinite number of spaces between itself and the wall? Of course, it does reach the wall. The paradox does not make it untrue, as I believe is the case with actual infinites too.

[3] Craig’s entire argument can be found in his 1979 book The Kalam Cosmological Argument

[4] There are mathematical responses to this critique from set theorists, but I am trying to meet Craig on his own grounds. For the same reason, I am also assuming an A-theory of time.

[5] Divine Eternity

[6] Timelessness and Omnitemporality

[7] T and O

[8] T and O

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  1. Triptych

    This is a well thought out post and I’m glad to have the opportunity to talk to you. There are at least two problems I see in this post.

    1) In relation to the bookstore, if God has willing from eternity to say, loan out books, than no change has taken place. He has temporal decided to do something because it had been willed from eternity and God is merely staying consistent with His will.

    2) You assume that God’s eternalness is necessary. This in fact is not the view that Dr. Craig holds. He holds that God’s value of infinity is a contingent value and not a necessary one.

    I hope this creates some interesting ideas for you and others to think about. Merry Christmas and Happy New Year by the way!

  2. Mike

    Thanks for the feedback Triptych.

    Regarding 2, my assumption (and hopefully it comes through in the writing) is that God’s changelessness is necessary if God is eternal. This seems to be Craig’s position in Divine Eternity and elsewhere.

    Regarding 1, I’m trying to make sense of how something from a timeless eternity can then become a temporal reality. I’m still reading through Craig’s work on the subject, but it seems contradictory to me.

    I think his out might have to do with an intrinsic change versus an extrensic one. I have some more work to do to flesh out these arguments and bring in Craig’s counterpoints. Your feedback is much appreciated.

  3. Mike

    Per my last comment, I suppose you could say that changelessness is a property of being eternal. I’ll have to think about it.

  4. Triptych

    I’m glad to see that my reply went through! This was my first time visiting your website and so I wasn’t sure if it was going to work.

    Let me just say that it is refreshing to talk to someone like yourself. Most of the people that I discuss these issues with, usually Atheist or Agnostic, are arrogant and rude. It’s refreshing to have this type of discussion with someone as sincere as yourself.

    1) It seems that if God’s timelessness is necessary, than like you said, it follows that His changeless-ness is necessary as well. However, if His timelessness is contingent, than perhaps so is His changeless-ness.

    2) I like your wording of intrinsic values vs extrinsic one’s. I’ve been thinking about it too, and there doesn’t seem to be any contradiction with God being timeless and intrinsically changeless. However, I’m still thinking about the latter; can He be extrinsically changeless if He is timeless? I’m starting to lean towards no, He can’t, but I have some more thinking to do. Moreover, is it necessary for Him to be extrinsically changeless if He is intrinsically changeless? I’m not so sure it is.

    I’ll check back in a day or two. I look forward to talking with you.

  5. Mike

    Hello again Triptych. Glad to talk to you too; I’ve experienced much of the same. Unfortunately, there are a lot of people out there on both sides who don’t do much to support their cause.

    I just thought of an interesting critique. I’ll be curious to hear your thoughts. I am thinking that something existing in a timeless eternal state cannot even have extrinsic properties. David Lewis and others talk about extrinsic properties being those held in relation to what is going on outside the thing in question. In the eternity Craig has proposed to escape the inifity problem, there are no space/time dimensions. So, it would appear the notion of properties outside of God’s own existence in this state become nonsensical. Lewis also defines extrinsic as wholly or partly dependant on something else. This latter definition epecially will clearly not work for God.

    Regarding your first point, I think you’re right about contingency, but it still just seems weird, for lack of a better term. I can’t shake thinking that God being eternal and changeless along with also being temporal and changing brings about absurdities at least as great as those in Hilbert’s Hotel. I’m just struggling to spell out why (but intuitively I think we can all recognize it as odd).

  6. Triptych

    Hey Mike,

    Sorry it took me so long to respond. I don’t get any response updates for when you reply, so I forgot to check back in. I think you are exactly right in that. There’s plenty of “blame” on both sides.

    1) On Dr. Craig’s website he explains it well. He states on there that “If God is timeless, is He incapable of creating a universe? Is He somehow imprisoned in timelessness, frozen into immobility? I see no reason to think so. The claim that if God is timeless, it is impossible for Him to create the universe is based upon the assumption that timelessness is an essential, rather than contingent, property of God. But as in the case of the color of the house, I see no reason to think that God’s being timeless or temporal cannot be a contingent property of God, dependent upon His will. Existing timelessly alone without the universe, He can will to refrain from creation and so remain timeless; or He can will to create the universe and become temporal at the first exercise of His causal power. It’s up to Him.” It’s question #7 on his website.
    So there doesn’t seem to be any contradiction with this. Perhaps the only reason it might be seen as odd is because we are talking in terms of a being that is a contingently potentially-infinite creator. Unlike anything else that does/could exist.

    2) I’ve still been thinking about this as well. Again, I like the thought provoking question you ask. Now, if 1) is correct, than it seems that there is no reason that God can not have intrinsic as well as extrinsic properties given His relationship with the world. So I’m going to assume that you are talking about the “time” before His creation of the world. Again, there doesn’t seem to be any problem with Him having intrinsic properties at this time. But what about extrinsic one’s? It’s a good question you ask and I’m not entirely sure of the answer. But the answer that I have been thinking about is “Is it necessary for God to have extrinsic properties before creation?” I’m not starting to think that, no, it isn’t. The only time this would come into play would be in the case of Christian Theology regarding the Trinity. If God, Christ, and the Holy Spirit have lived from eternity past, and the three were sharing in community, wouldn’t there be a necessity to have extrinsic properties, or interaction? However, if the three are 1, as the Trinity is defined, than it seems that they can share in community with each other intrinsically.

    Let me know what you think and if you think there is any problems with this! I look forward to talking to you!

  7. Mike


    There is supposed to be a comments subscription option, but it may not be working. It wouldn’t be the first bug on this site.

    I have to say that I do see a contradiction with 1) because of the timelessness aspect. So, Craig says “God can will to refrain from creation and so remain timeless; or He can will to create the universe and become temporal at the first exercise of His causal power.” I’ve made bold the statements that worry me because I can’t see those statements making any sense without reference to time. I’m particularly bothered by the notion of becoming temporal, since the very idea of becoming would imply there is already a temporal state. The same goes for refraining from, remaining, or creating anything.

    Perhaps this is more of a problem with our language; the argument could go something like, “We simply don’t have the terminology to describe something in this state so we use the nearest language we can.” But that doesn’t really seem satisfying.

  8. Triptych

    I’ve really enjoyed our conversation Mike! You’ve posted some of the strongest contentions against the Kalam Argument that I have had the privilege of discussion.

    I think some of what we are now talking about is coming down to mere linguistics, but only a small part.

    “I’m particularly bothered by the notion of becoming temporal, since the very idea of becoming would imply there is already a temporal state.”
    -I don’t think this is true. If God’s creating time is simultaneous with His becoming temporal, than this doesn’t imply that there must be a previous temporal state before God chooses to become temporal.

    “The same goes for refraining from, remaining, or creating anything.”
    I think the argument from what God wills from eternity would also apply to this as well. If God had willed to refrain or to create something from eternity, than there is no change no matter which path you take.

    But if you were to say that “what about the ‘time’ between God’s remaining timeless without the universe and temporal with the universe. Isn’t there a laps of time going on there for which God changed?” I think this might be mere linguistics. And I don’t think I would know how to comprehend that hah. I’ll dig into it a little more and see what I can find.

  9. Triptych

    I think I figured it out Mike, that is, your apprehenion about the state of God prior to creating. (His refraining from, remaining, or creating anything.)

    I think the reason that this was giving me (and possibly you) so much problem, was because we were taking into account God’s first causal action, His creating. And thus, everything prior to that, seems like God was existing in a past eternal state. However, I do not think it’s correct to take into account His creation, because at this point He is in a temporal state in relationship with the universe.
    So if we eliminate this point, as it seems correct to do so, than there is no state at which God was simply “refraining from, remaining, or creating anything.” To even mention the word “time” seems nonsensical as God is existing timelessly at this point.

    Hope to hear from you!

  10. Mike

    Hi Triptych, sorry it took me a while. I had surgery (nothing major). I don’t think I can really consider this under sedation, so I’ll throw a softball out there.

    Do you think this can really be a best explanation? I just don’t see how Craig can claim this is the best explanation of the existence of the Universe. It seems like an argument from ignorance dressed up in a tuxedo. That’s probably th real way to address this argument. Yes, we can probably create a God that escapes this variety of criticisms by placing all these constraints, but can that ever be a best explanation? It seems like the only way it could is in the approximate words of Sherlock Holmes, “Once we’ve eliminated all other possibilities, whatever remains, however unlikely, must be true.” It doesn’t seem to me like we’re to that point, though, of having eliminated all competitors. I’ll have to go back and watch some of Craig’s YouTube videos where he makes this best explanation claim and see how he justifies it (I may be mixing it up with his resurrection claims – I’ll blame the drugs, if so).

    Look forward to hearing your thoughts.

  11. Triptych

    No problem Mike, there’s no rush we’re just having a causal conversation hah. Whoa, are you alright? All surgery can be pretty serious.

    I think it might sound like all these constraints are being placed on God due to my continual learning. I’m learning a lot of things as we continue to talk, so it probably sounds like I just keep adding stuff hah. However, for someone who already knows the answers, like Dr. Craig or someone, it probably wouldn’t seem like this. That being said, it does seem to me that this is the best explanation.
    Yeah, check out some more videos, there’s a ton of them out there.

    The drugs lol, that made me laugh.

  12. Mike


    Sorry it took me a while, but I did want to respond.

    You said that God’s existence without the act of creation is timeless so it doesn’t make sense to apply tensed terms to his action. This is Craig’s view as well. I just don’t buy it.

    I see this as a move by Craig to simply try and avoid his own criticism of actual infinites. He is trying to make a home for God that is something other than infinite. But there are so many problems. What does it even mean to exist without time? How can anything possibly exist in such a manner? It would have to be nothing – a changeless nothing. But then even that is problematic because even nothing is something and “nothing” ironically requires spatial dimensions (another thing Craig says does not exist for this timeless God). I think this might be the biggest problem. Can something exist with neither time nor space? Does God think in this state? Does God sleep? Is God awake? Can you say anything about this God? If you can, then I would contend you need to bring in at least time, and maybe space, to make sense of it. If you can’t, then how does such a being ever create? This gets us back to my intuition that this is a contradiction.

  13. Triptych

    Hey Mike!

    It’s all good! You didn’t respond for a while and so I kind of forgot about our discussion hah. But I’m glad you’re back! How is the healing from your surgery going?

    I wouldn’t say this is a type of strategic move to avoid something, like an actual infinite. Rather, it seems to me that it logically follows that in order for a cause to create time, it must transcend time, i.e. be timeless. Not some arbitrary quality that is applied to the cause.

    Long quote from reasonablefaith.org:

    “An entity exists temporally just in case it has a temporal location and temporal extension. To have a temporal location is to exist at a time, so as to stand in temporal relations of simultaneity with other entities existing at that time and posteriority or priority to any entities that either have existed or will exist relative to that time. Temporal extension is an entity’s duration, roughly, how long it exists. Even an entity which exists for only an instant has an extension, the measure of which is, in this case, zero. As such it differs from an atemporal entity, for the category of temporal extension does not even apply to a timeless entity, whereas any temporal entity has an extension, even if the measure of that extension happens to be zero.”

    So a being which exists timelessly is a being which has no temporal location and no temporal extension. So all those activities that you named, (ponder things[under the Christian view God is omniscient] and sleeping) this cause would not do. So it seems to me that it logically follows that the cause of the universe must have at least 6 properties. Timeless, spaceless, changeless, immaterial, unimaginably power, and personal.

    Indeed, as you seem to be implying, timelessness is a complex thing to fit our minds around! But there doesn’t seem to be anything incoherent or contradictory about it.

    Hope all is well!

  14. Mike

    Hi Triptych. I’m doing much better, thanks.

    My feeling about it being a strategic move of “finding a home for God” is just more of a sense I get. It’s not like Craig was persuaded by this argument. He had a pre-existing theological commitment and he has spent his entire professional life defending that. He is as much apologist as he is philosopher – maybe more. Now, of course there isn’t anything wrong with that. We can’t dismiss his argument simply on the grounds that he already believed it. Yet, it should set off a yellow flag when someone comes to the conclusion they already held. (Example: “Think Tanks” releasing studies that always support the interests of their funding sources) So, certainly not enough to reject, but something to consider on the periphery.

    Now, the bigger problem is I’m really uncertain about this conclusion. We may have even reached an impasse here. So, of your six properties, the first four – timeless, spaceless, changeless, and immaterial – seem to be the perfect defintion of perfect nothingness; this state might put a vacuum to shame. Now, we add to this nothingness two properties that are very much something – power and personal nature. This nothingness has agency somehow and the means to bring about something. Now you might say that it’s really not nothing because of the last two properties. So, there is supposed to be some sort of mind floating (ok, not realy floating because there is nothing) in this void. It just doesn’t register for me how you find this comprehensible. Why should we believe such a state of affairs actually existed?

    I’m talking about more than mere possibility here. In metaphysics, we are often drawn into discussions of possible states of affairs, like metaphysical zombies on a possible world. With these constraints, almost anything is possible. But I’m wondering in this actual world/universe, why are we to believe that this is possible? Why would we conclude mind can exist without body? Why should we add these personal traits to nothingness?

    Regarding the activities I mentioned, I think God would need to have thought attributed to him in order to change from eternal to temporal. What else would spark the change? Now, if there is thought, I think you can argue there is extension. I know that Craig discusses God having a will that brings about this change. But what is will? Can it be had without thought, without desire? These things cannot make any sense without temporal extension.

    I want to go back to my original conclusion. I said that apparent absurdities don’t have to mean impossibility. So, I don’t want you to think I’m saying there could be no possible state of affairs where this type of God could exist. Rather, I want to know how we are justified in saying this state of affairs actually happened. You could sick any number of “possible” conclusions into the causal role. But why should we? I wrote a post about us coming from a cosmic sneeze that is consistent with the known facts. But is consistency enough for this type of suspect conclusion? I don’t think it should be.

    I think we can both agree that what we need is plausibility. So, as I see it, there are a few main issues which have very suspect plausibility. 1 – Whether a mind can exist apart from physicality. There are no shortage of people who think this is the case, but they have no evidence, only unexplained gaps. 2 – Whether “nothing” can have the attributes you say (presumably the mind from the first point) and not have temporal extension. I don’t think you can make sense of things like thought or will without time, as I’ve said.

  15. Mike

    I also want to bring in another point from my original conclusion. You seem to think that some of these intuitive oddities are only apparent absurdities – that they don’t entail impossibility. Well, I would agree that our intuitions about such things can be flawed. So, I don’t think Hilbert’s Hotel means an actual infinite is impossible. Plenty of mathematicians and physicists would agree and there are solutions to the paradox.

    So my original conclusion was not that god is impossible, but that intuitive absurdities do not derail an argument; and what’s good for the goose is good for the gander.

  16. Triptych

    I’m glad to hear you’re doing better Mike!

    The first four properties of this cause:
    I think first we need to look at this idea of nothingness. How is it that we can say those 4 properties have the same as nothingness, as nothingness has no properties to compare it to. So I’m having a hard time coming to terms with the idea that those first 4, is exactly what nothingness is (just as side thought).
    But my main point is, if that’s true, still those properties aren’t necessarily the definition of nothingness. We know at least two things that fit that description of timeless, spaceless, changeless, and immaterial. Those two things would be abstract objects (like numbers for example) or minds. And if you want to say that nothingness is like this too, than we have three examples of things that have that description. But abstract objects and nothingness don’t have causal powers; they don’t cause anything.

    But like you mention, once we include those last two properties, than abstract objects and nothingness are definitely ruled out. I think we should believe that such a state of fairs exists for at least two reasons. First, because such an explanation is not a logical contradiction. And Second, because it seems to me that those properties necessarily flow out of what a cause of the universe would have to be like. It has those properties necessarily.

    I agree with you though, it’s difficult to comprehend! One way that might help to comprehend timeless is by saying that this cause transcends time. That helped me understand it a little better. But I don’t think mere difficulty of comprehension counts as evidence against something (I’m not saying you were saying this, just something I thought about). For example, I literally can not comprehend the universe. I mean billions and billions of galaxies and trillions and trillions of stars! How do you comprehend something like that?! But that of course doesn’t mean that the universe doesn’t exist. It’s very mind boggling!

    Why should we believe that a mind can exist without body? Well, I think one reason is because it’s the best candidate we have for a timeless, spaceless, immaterial, changeless, uncaused and unimaginably powerful cause of the universe.
    I think another reason is that there are some strong arguments for dualism. A couple which you could look into would be the Argument from Extension, Argument divisibility, and maybe even the Argument From Feigning. Also, you might be interested in this:
    But notice here that I’m not going into great detail. This is because that the burden of proof is not on the theist at this point. I think I’ve shown, as a proponent of this argument, that an abstract mind fits these attributes. I.e. there isn’t anything logically incoherent about it. If an opponent wishes to refute this claim, he needs to give us some reason for why an unembodied mind is incoherent. He needs to show that it is somehow logically impossible. If he doesn’t, than I think we’re justified in thinking that this is not only just an explanation, but the best explanation.

    I think you’re right. If God is thinking/considering things, not only could you argue that time exists, I would say that time absolutely exists. But why would God need to think? If He is a maximally great being, He would have the quality of Omniscience and so would just know all things. He wouldn’t need to consider or think about things. Just like it doesn’t take time for you and I to know that 2+2=4. We can think about it if we want, but temporal extension isn’t necessary to know something. So in this sense, God would know from eternity that He wants to create the universe.

    Just as a final point about Hilbert’s Hotel. I don’t think I’ve said that any these certain attributes are absurd. I think they can be difficult to comprehend, but there isn’t anything absurd about them. Whereas Hilbert’s hotel produces mathematical absurdities. There are also a couple of arguments against an actual infinite, here would be another one. Maybe you’ll like this one better:

    The series of past events has been formed by adding one event after another. The series of past events is like a sequence of dominoes falling one after another until the last domino, today, is reached. But no series that is formed by adding one member after another can be actually infinite. For you cannot pass through an infinite number of elements one at a time.
    This is easy to see in the case of trying to count to infinity. No matter how high you count, there’s always an infinity of numbers left to count.
    But if you can’t count to infinity, how could you count down from infinity? This would be like trying to count down all the negative numbers, ending at zero: …,-3,-2,-1,0!. This seems crazy. For before you could count 0, you’d have to count -1, and before you could count -1, you’d have to count -2, and so on, back to infinity. Before any number could be counted an infinity of numbers will have to have been counted first. You just get driven back and back into the past, so that no number could ever be counted.
    But then the final domino could never fall if an infinite number of dominoes had to fall first. So today could never be reached. But obviously here we are! The shows that the series of past events must be finite and have a beginning.

    Hope I answered everything! There was one thing that you said that I don’t think I understood. What was this about the cosmic sneeze?

  17. Mike

    RE: The cosmic sneeze, check out a little creation myth I wrote here: http://foxholeatheism.com/creating-a-myth/

    I’ll get back on your other points tonight or tomorrow. Thanks for the response.

  18. Mike

    Hi Triptych; I’ve enjoyed our conversation. So to avoid confusion I’ll try to quote you and then respond underneath as we’re getting into a lot of points.

    “We know at least two things that fit that description of timeless, spaceless, changeless, and immaterial. Those two things would be abstract objects (like numbers for example) or minds. And if you want to say that nothingness is like this too, than we have three examples of things that have that description. But abstract objects and nothingness don’t have causal powers; they don’t cause anything.”

    So, I want to get to a couple of points here. First, we can probably let go of my nothingness comment because I think it would actually be quite difficult to describe nothingness. It seems the only way we can comprehend such a state is to not add properties at all to our mentalization of it. Now, the reason I think it fits is because the first four properties seem to actually be the absence of a property, like saying something is non-physical. It doesn’t actually tell us anything about what it is – more like what it isn’t. But that’s more of an interesting side discussion about nothingness.

    Now, it gets a little more tricky. You say numbers don’t have causal powers, but minds do. I’m not sure if we can say this. First, if you want to say the burden of proof is on me to show that minds can’t exist without bodies, then I think the burden is on you for an impossibility claim that other abstract objects lack causal power. Dan Dennet has an example of one possible “cause” from such a property, but I don’t remember it offhand and I’m at work so I don’t have the YouTube link available (maybe search Dan Dennett and William Lane Craig). I recall thinking it wasn’t a particularly good example, but the issue still remains of “Why can’t numbers, etc. cause something?” Second, you say minds can cause. Do you have an example of a mind explicitly causing something that can’t be reduced to brain activity that leads to a physical response? This gets pretty muddled, but I’ll say more about minds below.

    “But I don’t think mere difficulty of comprehension counts as evidence against something (I’m not saying you were saying this, just something I thought about).”

    I wholeheartedly agree.

    “Why should we believe that a mind can exist without body? Well, I think one reason is because it’s the best candidate we have for a timeless, spaceless, immaterial, changeless, uncaused and unimaginably powerful cause of the universe. I think another reason is that there are some strong arguments for dualism.”

    I think it’s questionable that these traits follow necessarily from what we know about the universe, but that discussion would probably take us too far from the issue. That would be really more of a general KCA complaint.

    Regarding the arguments for dualism – let’s say they are persuasive for the sake of argument. What would we be justified in concluding? Would it be that minds actually exist apart from physicality? I’m not sure it would. It seems like you would be justified in saying that minds seem to emanate from brains, but that they have features and functionality apart from brains. But we still are left with the problem of whether they can actually arise and exist apart from some physical grounding (even A.I. would need circuits, etc.). We just don’t know of any such example even if you were justified in saying mind and body are not the same thing. Of course, I’m not sure they are convincing. In Plantinga’s thought experiement we have the problem of intuition, which psychlogical studies show are notoriously flimsy and faulty. So, I’m not really moved by the thought experiments.

    The best neuroscience on the subject of things like free will is inconclusive at best right now, so it’s really difficult to say much. As one researcher recently said, “There isn’t much evidence against free will, but there isn’t much evidence for it either.”

    “But notice here that I’m not going into great detail. This is because that the burden of proof is not on the theist at this point. I think I’ve shown, as a proponent of this argument, that an abstract mind fits these attributes. I.e. there isn’t anything logically incoherent about it. If an opponent wishes to refute this claim, he needs to give us some reason for why an unembodied mind is incoherent. He needs to show that it is somehow logically impossible. If he doesn’t, than I think we’re justified in thinking that this is not only just an explanation, but the best explanation.”

    So, this is a tough one for me. On the one hand, I agree that an impossibility claim bears burden of proof (and I brought that back around a little bit regarding numbers above). On the other hand, it seems unfair to request such a proof. Let’s consider Craig’s first premise that everything has a cause. That’s sort of a common sense notion, and I would imagine his justification for saying it is that everything we can point to has been caused by something else (we’ll ignore the quantum particles problem). Well, couldn’t I say every single instance of mind is associated with brain? Do I really bear the burden here? This is why I mentioned metaphysical zombies in my earlier comment. Impossibility claims are very tough to show unless there is a logical contradiction. But I think if you are willing to grant that our experience of cause is enough to support the first premise, then you should also be willing to say that our experience of minds is enough to support my premise.

    I think we should actually be able to reach agreement here that logical possibility is simply not good enough. Of course, the reason you still feel justified is because you think it’s entailed by what the cause must be like, as you said. But I don’t particularly want to get into that – maybe it will get it’s own post someday so it can be properly discussed.

    So, hopefully we can agree that I’m justified using the evidence available to say minds only exist along with brains and you are similarly justified in saying that things are caused and that numbers don’t cause things.

    “Just as a final point about Hilbert’s Hotel. I don’t think I’ve said that any these certain attributes are absurd. I think they can be difficult to comprehend, but there isn’t anything absurd about them. Whereas Hilbert’s hotel produces mathematical absurdities.”

    There are mathematical solutions to the problem, just like Newton’s calculus enabled us to solve Zeno’s paradoxes. So, I disagree that they are absurdities.

    My real solution to HH and to your other problem about traversing an infinite to get to the present would invoke a B-Theory of time. In my post, I promised I would stick to A-Theory. Under A-Theory, I’m not sure I can solve the paradoxes. But again, to get into a discussion of time would be a beast. So, like the other argument above that’s probably best saved for its own post some day.

  19. Triptych

    I like the idea of the quotes as our conversation is expanding now hah. I’ll try and do the same.

    “Now, the reason I think it fits is because the first four properties seem to actually be the absence of a property, like saying something is non-physical. It Doesn’t…”
    I just checked this out yesterday by random hah, this might help (Sorry I’m sending you to all these videos, but at least it’s short 🙂 )

    (I’ll put the URL in another post if embeded doesn’t work)

    “So, this is a tough one for me. On the one hand, I agree that an impossibility claim bears burden of proof (and I brought that back around a little bit regarding numbers above). On the other hand, it seems unfair to request such a proof. Let’s consider Craig’s first premise that everything has a cause. That’s sort of a common sense notion, and I would imagine his justification for saying it is that everything we can point to has been caused by something else (we’ll ignore the quantum particles problem). Well, couldn’t I say every single instance of mind is associated with brain? Do I really bear the burden here? This is why I mentioned metaphysical zombies in my earlier comment. Impossibility claims are very tough to show unless there is a logical contradiction. But I think if you are willing to grant that our experience of cause is enough to support the first premise, then you should also be willing to say that our experience of minds is enough to support my premise.”

    This is actually a great point which I had been thinking about a little over a month ago, until I thought about it some more. So we both agree that the burden of proof does in fact lie with the opponent of this argument, but the question is, is it fair or justified to do so? When we take a look at the causal principle, the reason we believe in the causal principle is not just because it is universally verified and never falsified, not even because it is a fundamental principle of metaphysics (although I think these are good reasons) but because 1) It becomes inexplicable why anything and everything doesn’t just come into existence. Why don’t we see cable TV, honey badgers, and fried rice pop into being? And 2) It’s opposite is a logical contradiction; that something can come from nothing. Nothing has no properties, nor causal power. Neither can anything constrain nothingness, because there isn’t anything to be constrained. So this isn’t the same as the idea of other minds, and I think it’s enough to show that the burden of proof does in fact lie with the opponent of the other minds hypothesis and that it is fair for them to provide some explanation for what it is logically impossible. But it was an extremely good objection!

    Daniel Dennett’s view is, as remarkable as this is, that the universe actually created itself! That the universe brought itself into being! What he calls the “ultimate boot-strapping trick” the universe created itself. I think this response though is quite embarrassing. Notice that Dennett is not saying the universe is self caused, that it is eternal so to speak. He is saying that the universe began to exist, that it came into being, but it created itself, it came into being by creating itself. But this is just nonsense, because in order for it to create itself, the universe would have to already exist. It would have to exist, before it existed, in order to bring itself into existence. So that Dennett’s view is just a self contradiction and is logically impossible.

    I don’t know if I got this across, maybe I forgot, but what I was trying to convey is that it’s not enough to say the only minds we know are, for example, occur with physicality. Because it doesn’t eliminate the possibility that a mind could exist like this. But lets not stop there, lets even take it one step further. Is there good reason to posit a unembodied mind as the cause of the universe? Let me give three forms of evidence why I think it is:
    1) The argument from dilemma; either an abstract number or a mind>not an abstract number>therefore a mind
    2) Only by a personal agent, how an effect with a beginning (us) could arise from an eternal cause. If the cause is timeless, why aren’t we timeless?
    3) There are two types of explanations, either scientific or personal. There can not be a scientific explanation of the first state of the universe, because there aren’t any laws of nature or initial conditions for which that first state could be explained. Therefore it must be a personal agent.

    I’m still researching more indepthly about Hilbert’s Hotel, as it requires great math knowledge, and I’m still on cosmology lol. But I haven’t heard of any refutations of it so far. However, I’m a little more experienced with the, quite separate, example of the dominoes that I gave. In some senses, I think that is even stronger of an example.
    We can get into the discussion of time at a later point. We are talking about quite a bit as of now. I would like to at some point though, as to the best of my knowledge, a tenseless theory of time does not eliminate the beginning of the universe, nor the absurdity of an actual infinite. But maybe later! 😀

    Sorry, this was a lot to talk about, I hope I didn’t skip anything hah. Just let me know.

  20. Triptych


  21. Mike


    Re: the causal principle point 1 – Well some things actually do pop in and out of existence; namely, particle and anti-particle pairs. It does not follow from questioning the causal principle that we should see all sorts of things behaving this way. Rather, it undercuts the notion that everything is caused in this way. Of course, perhaps there is a true cause for these particles and we just don’t understand it. That’s why it undercuts, rather than defeats. Re: causal point 2 – If the particle pairs can come into existence in a vacuum without cause, and that is the best we can actually say right now, then it can’t be a logical contradiction. It actually happens, if we are interpreting the events correctly. So, I do still think the main force of arguing in favor of the causal principle falls back on folk wisdom, in a sense. The beauty of the KCA is the simplicity of its premises and the common sense notions they contain.

    Re: Dennett – I was actually referring to his questioning of whether abstract objects cannot cause something. This is fairly counterintuitive, but, if we are placing burden of proof on impossibility claims, then we should also place it for claiming abstract objects cannot cause something. I’m not sure such a task can be done, other than appealing to our common sense notions. According to the Stanford Encyclopedia of Philosophy, “The challenge is therefore to characterize the distinctive manner of “participation in the causal order” which distinguishes the concrete entities. This problem has received relatively little attention. There is no reason to believe that it cannot be solved. But in the absence of a solution, this standard version of the Way of Negation must be reckoned unsatisfactory.” Part of the Way of Negation, referenced in this quote, is the causal inneficacy criteria in trying to define abstract objects. (Interesting overall discussion of abstract objects, if you’re interested: http://plato.stanford.edu/entries/abstract-objects/#3)

    Re: Minds – Yes, I also want to get at whether there is good reason to think this, not just whether it is strictly possible. I was trying to convey that as well, perhaps not successfully. On the argument from dilemma, I would point to the abstract objects discussion above and I would ask a question I posed in my previous post. Is there an example of a mind explicitly causing something that can’t be reduced to brain activity that leads to a physical response?

    I’m not sure what you mean by your second argument. Perhaps you could explain further.

    On your third argument, I would disagree that there cannot be a scientific explanation. This seems premature since there are actually many scientific explanations on the table, but they are not currently verified. Stephen Hawking’s latest book is one such example. Guth’s inflationary model would also resolve a number of problems. So, while there may not be a verified explanation at this point, I don’t think we are justified to say there can’t be one. And given the several candidates currently on the table this is more than just a retreat to possibility. We are actually fairly close to testability with the findings of the WMAP. This will shed new light on the multiverse and similar issues.

    Re: Time – The B-theory would refute the Kalam and Craig acknowledges this. Quoting Craig, “For any entity e and time t, e comes into being at t if and only if (i) e exists at t, (ii) t is the first time at which e exists, (iii) there is no state of affairs in the actual world in which e exists timelessly, and (iv) e’s existing at t is a tensed fact.” Given (iv), the second premise of the Kalam (the universe began to exist) fails under a B-theory. Of course, Craig is an A-theorist so he doesn’t view it as a problem. But many believe that physics entails the B-theory.

    I believe the domino paradox would also fail because it relies on the notion of a moving present.

    Re: Hilbert’s Hotel – For your enjoyment, Cantor’s diagonal argument is a solution to the paradox (http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument).

    Quoting from diveintomark.org, “The gist of it is this: two infinite sets are considered the same size (technically the same “cardinality”) if you can map each element of one set to an element of the other set with none left over on either side (technically called a “bijection”). That’s why there as many even numbers as there are natural numbers: you can map one to the other with the function F(N) = 2 × N, and you’ll hit all of them eventually. Mapping the rationals to the natural numbers is a little trickier, and mapping the primes is even trickier, but both are doable. But mapping the real numbers to the natural numbers is not doable, because no matter how hard you try, there will always be reals left over. That’s what Cantor’s diagonal argument proves. Mathematicians express this by saying that the natural numbers are countable, but the reals are uncountable. They have a name for the size of the set of natural numbers: “aleph-null”, written as ℵ0. There are ℵ0 natural numbers, ℵ0 even numbers, ℵ0 odd numbers, ℵ0 prime numbers, ℵ0 rational numbers, and ℵ0 perfect squares.”

    Exploring this will take you into some very complex math and the issues related to bijection. If you choose to do so, good luck!

  22. Mike

    More on Hilbert’s Hotel. From the Wikipedia entry:

    “Hilbert’s paradox of the Grand Hotel is a mathematical veridical paradox (a non-contradictory speculation that is strongly counter-intuitive) about infinite sets presented by German mathematician David Hilbert (1862–1943).”

    “These cases demonstrate the ‘paradox’, by which we mean not that it is contradictory, but rather that a counter-intuitive result is probably true: The situations “there is a guest to every room” and “no more guests can be accommodated” are not equivalent when there are infinitely many rooms.

    Some find this state of affairs profoundly counterintuitive. The properties of infinite “collections of things” are quite different from those of finite “collections of things”. In an ordinary (finite) hotel with more than one room, the number of odd-numbered rooms is obviously smaller than the total number of rooms. However, in Hilbert’s aptly named Grand Hotel, the quantity of odd-numbered rooms is as many as the total quantity of rooms. In mathematical terms, the cardinality of the subset containing the odd-numbered rooms is the same as the cardinality of the set of all rooms. Indeed, infinite sets are characterized as sets that have proper subsets of the same cardinality. For countable sets, this cardinality is called (aleph-null).

    Rephrased, for any countably infinite set, there exists a bijective function which maps the countably infinite set to the set of natural numbers, even if the countably infinite set contains the natural numbers. For example, the set of rational numbers – those numbers which can be written as a quotient of integers – contains the natural numbers as a subset, but is no bigger than the set of natural numbers since the rationals are countable: There is a bijection from the naturals to the rationals.”

  23. Triptych

    Re: Casual Principle 1): Often time skeptics will say that in physics, subatomic particles (virtual particles as they’re called) come into being from nothing. And therefore, in subatomic physics you did get something from nothing, these particles come from nothing! Or certain theories of the origin of the universe are sometimes described as getting something from nothing (often times in popular books or television shows). However, this is a deliberate abuse of science. The theories in question have to do with particles originating as a fluctuation of energy in the vacuum. But in physics, the vacuum is not what we mean by the vacuum (aka nothing). In physics, the vacuum is a sea of fluctuating energy, having a physical structure and governed by physical laws. Similarly with these models of the origin of the universe where the universe comes into being out of the vacuum, it doesn’t come into being from nothing. The vacuum is not nothing.
    Re: Causal Principle 2: So even if we are still trying to understand the laws the govern the vacuum in physics, etc, it is not the same thing as nothing. So it does still seem to me that it is a logical contradiction

    Re: Dennet: I have no doubt that they are trying to see if it’s possible for abstract objects to cause things. If this question can be followed back to as far as Plato, they’ve been trying to do it for while i guess hah. However, all these attempts seem to be destined to failer. Abstract objects like numbers, or sets of things, don’t exist in casual relationships. And there is just no evidence to show or think that they do or could. The number “3” doesn’t cause anything. I do think it’s a pretty rational view too. As you said, a lot of what makes the KCA so interesting, and even strong, is its simplicity and common sense claims. (however, if you want to go deeper like we are doing, there is plenty of room to do so hah)

    Re: Minds: “Is there an example of a mind explicitly causing something that can’t be reduced to brain activity that leads to a physical response?” If you are asking, do we experience immaterial unembodied minds, than I’d say no lol. But that was the point of the three forms of evidence, we can not rule of the possibility just because we don’t experience it that way. But even more (as both of us would agree, it’s not very convincing to leave “possibility” as the best explanation when it comes to the idea of an unembodied mind) I think those 3 forms of evidence give good reason to why we should believe at least one exists.

    #2 on Minds: Perhaps you have heard Dr. Craig give the analogy of water freezing. The cause of water freezing is the temperature dropping below 32°C. But if the temperature had been below 32°C from eternity, than any water present would be frozen. The only way for God to be timeless, and the effect (the universe) to begin in time is if the cause is a personal agent who freely chooses to create the universe at some point in the finite past.

    #3 on Minds: I might have expressed this third consideration in an unhelpful way. What I mean by “there can not be a scientific explanation” is that prior to the universe, there were no physical laws or scientific properties. There just wasn’t anything at t0, because it is the first state. So it’s impossible to say that a scientific property caused the universe, because there were none. This is the argument that is purposed by the Oxford philosopher Richard Swinburne and which seems to me to be a good argument. However, I still have a lot of studying to do on it before I could say that it is as good as arguments 1 & 2 :P.
    If you are talking about Hawking’s newest model of instead of the universe coming down to a point, and is rounded off, I’m afraid this still fails. What Hawking’s model is able to show, if it is true, is that there was no singularity. That time and space didn’t begin at a singular point. But notice that the 2nd premise of the KCA is not “The universe began to exist at a singularity” but, “the universe began to exist.” This is because even though Hawking’s model doesn’t have a beginning Point, time and space still have a beginning. So I’m afraid this model doesn’t work.
    I’m aware of Linde’s inflationary model, but not Guth’s. However, all inflationary models have been put to death for quite some time. This is due to the BVG Theorem that Borde, Guth, and Vilenkin comprised together in 2003. That any universe which is in a constant rate of expansion, on average, must have had a past space-time boundary.

    Re: Time: I guess we are getting into it lol :P. This is why it doesn’t seem to me that the KCA fails under B-theory. B-theory does not state that the universe never began to exist. It merely says that past, present, and future are all equally real. That they aren’t coming in and out of existence; the past is gone, the future doesn’t yet exist, the present is all there is (like on the A-Theory that you, I, and the general public tend to experience). So time can be all equally real, but that doesn’t eliminate the need for a beginning, which I what it meant by Craig’s statement: “e’s existing at t is a tensed fact.” That even if all time is equal real, the universe still had a beginning. Or as a B-Theorist might say, the universe came into existence at a first point.
    But the domino explanation isn’t exactly what you think it is. It doesn’t rely on a moving past, present, and future. Rather that previous (I’ll use that word instead of past to accommodate for a tenseless theory) events are real, and not just ideas in our minds; they actually exist. That before we could get to today, an infinite amount of days would have had to of happened. But of course you could not count an infinite amount of days. Even given an infinite amount of time, we would have to ask “How come the person counting just finished NOW? Why not yesterday or a year before?” Now, under a B-theory, one would just say that ALL days are equally real, and so not just ideas in our minds. But the problem is, that seems to me that this is where the B-theorist runs into some issues. What reason is there to believe that our experience of past, present, and future is false? What reason is there to doubt that our intuition is false given no evidence?

    Wow, all that on numbers is very interesting! I am definitely going to have to look into that more as that is my weakest area in defending the Kalam; Hilbert’s Hotel.
    I’ll for sure have to check back with you on that one some time in the future! lol

  24. Mike

    I’ll have to respond to a few points now and save the rest for later.

    Re: Causal Principle 1 – The point in mentioning these particle/anti-particle pairs was to undermine the notion of cause. These pairs have no “apparent or intelligible cause,” as Victor Stenger puts it. So, it serves as an example to undercut the notion that everything is caused in the way defended by the KCA. I don’t really know whether something like this could explain the universe, but that’s not my intent anyway. You had said we didn’t have to just rely on folk principles to support this notion of cause, and I disagree. If this were clear, I don’t think we would have sharply divided camps of Humeans and Anti-Humeans about causality, supervenience, etc.

    Your first argument in favor of not having to rely on empiricist types of arguments for cause was that, “It becomes inexplicable why anything and everything doesn’t just come into existence. Why don’t we see cable TV, honey badgers, and fried rice pop into being?” My point is that some things do come into being without us knowing why, and it doesn’t follow that TVs and other things should act the same way. So, I don’t find that objection convincing.

    Re: Causal Principle 2 – I actually said without cause, not from nothing, though I think a vacuum is as close as we can actually get to nothing. Perhaps you can give an argument showing it’s a logical contradiction that something can come from nothing? It doesn’t seem logically impossible to me. Maybe it wouldn’t be permitted by our current physics or something like that, but that wouldn’t mean logically impossible. Again, if this argument is predicated on our experience of the universe and the nature of causation, then that supports my initial point about the real basis for this being experience.

    Re: Dennet – I happen to agree with you and that was the point I wanted to make. You don’t have a rationalist type of argument agaisnt my abstract objects claim – rather, you have an empiricist type argument. I could say the same thing about minds or I could use the same type of logic to say there are only natural causes for things.

    I’ll provide some more responses later.

  25. Mike

    Ok, back at it!

    Re: Minds – Ok, so let’s take another look at the three forms of evidence.

    1) The dilemma of either a mind or an abstract number, not a number, therefore a mind.

    So, I have a number of problems here. First, it may be a false dilemma since it could be neither, but that would require some more discussion on how we arrived to that dilemma so I’ll leave that one. Instead, let’s consider why we rule out abstract numbers. You’ve said there is just no evidence that they exist in causal relationships. Likewise, I’ve said there is no evidence that minds exist in causal relationships. You’ve agreed there is no epmirical evidence of this (or even that minds exist). Instead, it will depend on the success or failure of rationalist arguments. Both alternatives are questionable, so I think this argument only reaches a standoff. I’m questioning whether mind can cause and you are asserting it here under the assumption that it can, so it begs the question. Likewise, if I were to use this argument in support of abstract objects being causes, that would also beg the question. We have to first determine whether there is reason to think either can be a cause (or can even exist, since both are questionable) to ever even reach the point where we can propose this dilemma. While it’s asserted as a dilemma, it should really be a conditional for the purpose of this discussion: If minds can exist and perform causes, then [dilemma].

    2) So, the argument is that the cause had to be temporal. Does this entail mind? Well, I suppose you are saying that for the cause to be personal, then it would have to be a mind. But this is an argument for how God would have to be given a number of assumptions. It’s not at all clear that God is necessary for the universe, so this doesn’t seem like good reason. If I were granting that God existed and was the cause of the universe, then I probably wouldn’t be raising these issues with mind. Rather, I can simply assert that some natural temporal thing caused the Big Bang.

    3) I was simply giving a few examples that were on my mind, but there is a better example – M-Theory. The interesting thing about M-Theory is that it not only takes us to the Big Bang, but it takes us before the Big Bang. It asserts that something existed prior to the Big Bang. So, if we are considering the universe to be our own universe, then that solves a number of issues we’ve been discussing.

    I suspect that instead you will want to state that the universe is all of physical reality, as Craig does (and maybe Leibniz did too). But I can at least show that there can be a scientific explanation for the Big Bang and our own universe. That would make some of the simple premises and common sense notions less so. Craig often uses Big Bang cosmology to support his argument that space/time had a beginning. M-Theory renders that example useless. Please note that I’m not asserting M-Theory is true. I’m not in a good position to fully understand the theory. But, according to the people who support it, those are the things it entails.

    Re: Time – Let me start with a disclaimer. This is an issue in which I’m very interested in, but still studying. I don’t fully understand the theories of time, but I’ve got a few books on my wish list (hint, hint), like Quine’s for example.

    But, as I understand it, the phrase “began to exist” no longer has any meaning. The notion of beginning is a very intuitive A-Theory type of notion.

    I think the bigger issue here is what Craig thinks, since he probably understands both theories better than i do. Craig says that the KCA fails under B-Theory and depends on A-Theory. Given that Craig has spent his whole professional life defending this argument, I tend to believe him. I don’t think he would offer an escape route if he thought it was defensible. I don’t have any quotes from him to know why exactly he thinks it fails under B-Theory, but I suspect it is for the reason I gave about beginning. You might also be interested in this paper by Wes Morriston about the possibility of an infinite series where he gets into something closer to your domino example: http://stripe.colorado.edu/~morristo/infpast.html

    I wish I could say more, but I just don’t know yet and I’m not in a position to defend B-theory adequately. I’m in the process of learning, though, and will do a post with whatever conclusion I reach (I’m also planning a post on what effects M-Theory would have on cosmology if it were true – should be coming up within the next few weeks, if interested).

    Here’s another interesting thing. I watched the first episode of Wonders of the Universe with Brian Cox the other day. The episode was about time. Cox discussed how eventually, long after the heat death of the universe, everything will be swallowed by black holes and even the black holes will eventually “evaporate.” Then, we would be left with essentially the end of time. There would be no more change and no more potential to change. That’s what he said, anyway. So, that got me thinking, if there is a definite end to time, then does it make sense to say its past is infinite? It seems problematic to me to have this kind of asymmetry. I’m not sure why, but something just feels “off” about it. Food for thought.

  26. Mike


    We’ve started to move away from the intuitive issue of whether the non-temporal can become temporal. I thought it might be helpful to reframe the debate to focus on this issue of minds. So I’ve written a new post here: http://foxholeatheism.com/the-sherlock-holmes-defense/

    You are welcome to comment there and continue the discussion within a more focused framework or you are also welcome to continue the discussion here so we don’t lose the trail of what’s already been said. I’m fine with either and look forward to continued discussion.

  27. M Gehlke

    I was reading this piece as an accompaniment to the other and wanted to say that I think you’re ceding too much by accepting the fallacious mathematics.

    He’s really committing a categoric fault when he’s talking about the relationship between the red and the black books (and their aggregate) and then switching to discussion about non-local phenomena. The reason that we balk at this is because it’s not intuitive because our universe is in fact not locally infinite. (We’re in the middle of lots of discrete blocks, so we can only impact finitely many, regardless of how many there are in total.) However, in no way does it follow that because local behavior is bounded that absolute behavior is. Look at the behavior of the ordinals.

    There’s no way, internal to a system, to justify calling it either absolute or conditionally infinite.

    A semi-proof:

    1. Events in the world are discrete in at least one measure.
    2. Infinities of can be set in bijection with subsets of the ordinals which contain 0 and omit no elements.
    3. Processes internal to the universe can be codified into a transition function and an inverse transition function.
    4. Pick any point in the middle of an actual infinity, assign it to 0 on the ordinals.
    5. Plot all backwards paths as sequences beginning at 0 through the ordinals, using the transitions function.

    You now have a model of a “absolute infinite” universe in “conditionally infinite” terms, which really just shows that it’s a contrivance of modeling language, not something substantive.

    The second and more important critique is that finite doesn’t mean it has an edge. The universe can be finite in spacetime and still be internally bounded in regards to causality, at least mathematically speaking.

    This is important, even just in the abstract, because it raises the question of what is even meant by “origin” or “cause”. We’ve allowed, for far too long, theological positions to hide their faults in ambiguity of language and the confusion of macro-level concepts in relation to distinctly not macro-level events. I think it’s time that we begin to insist that proposed models of deities must if not explain, at least relate to the physical reality of the world.

  28. Mike

    @ M Gehlke

    Thanks for the info. This gets a bit out of my expertise, but I don’t see a problem in your reasoning.

    I agree that I ceded more than I normally would. If you look at footnote four, you’ll see that I do find mathematical critiques of these notions to be persuasive, as well as B-Theories of time. But what I wanted to do here was a bit different. Rather than get caught up in all of the potential problems of the KCA, I wanted to look at this notion of apparent absurdities.

    So, I think we can probably agree that inifnity paradoxes will sound confusing to the man on the street. Issues like bijection are pretty esoteric. I wanted to say that just because something comes to a counterintuitive conclusion, that doesn’t make it false. I find that point to be pretty straightforward, but I wanted to apply it to an overused case and turn the tables on Craig a bit. I argued that Craig comes to a pretty counterintuitive conclusion himself. I find the notion of a timeless, changeless being engaging in temporal becoming to be very odd. Triptych argues in return that this doesn’t make it impossible. But my point, of course, in my conclusion was just that – counterintuitive conclusions don’t have to be impossible. Furthermore, we might have good reason to think they are the case. So, just as you can find a way out of the temporal becoming issue with God, you can also find a way out of the actual infinite issue.

    Now, what happened in the comments was that we did start to dig deeper into the premises of the KCA. So that’s why I wrote the other post to give some ideas about how I would go about responding to those premises. You’ve read it, so you know, but for anyone who hasn’t, I would challenge the impossibility of actual infinites, I would challenge the theory of time, I would challenge Big Bang cosmology as being the beginning of all space and time, and I would certainly challenge the notion of an immaterial mind with causal efficacy, as I’ve been doing here in the comments. I would also bring up some of Morriston’s points about Craig selectively picking the common sense notions that help him and ignoring others. You can see a few of those on Page 11 here, if interested: http://spot.colorado.edu/~morristo/Reply2BillCraig.pdf

  29. Steven Carr

    William Lane Craig makes a very good point about infinity.

    Infinity leads to paradoxes and downright contradictions.

    I thought I had zero money in my pocket.

    But then I realised that if zero existed, I could divide it by 2 and still have zero.

    That is not a contradiction, but what happens if I divide zero by zero.

    According to well-respected mathematicians, zero divided by zero is impossible. It cannot exist! It leads to absurdity.

    So zero cannot be something which exists. You can’t divide by it, as you can by any other number ,without producing absurdity.

    Having proved that zero could not exist, I looked in my pocket, and guess what? There was some money there!

    That is the power of logic.

  30. Mike

    Thanks for the comment, Steven. I definitely think that we should be wary of concluding too much from the infinity paradoxes.

    I think it’s relevant to think of Zeno’s several paradoxes. In those cases, we had the experience to understand something was amiss, but we didn’t have the mathematics. We knew that you could obviously cross finite distances with no trouble regardless of how it seemed in purely theoretical terms. The mathematics didn’t come until calculus was invented and we could finally put the paradox to rest.

    With actual infinites, the opposite seems to be the case. We have the mathematical understanding of inifinity. What we don’t have is the common sense experience of actual infinites. Of course, why would we expect to have it? That doesn’t seem too problematic to me. Just like we only had one piece of the puzzle in Zeno’s time, so it is today. It’s just that we have the other piece.

  31. Me

    The Kalam argument is not a valid argument because there is no way to assign a definite truth value to its major premise–“whatever begins to exist has a cause.” This is an empirical assertion. How do you know it to be true? At a minimum, you must know exhaustively what things begin to exist–now, in the past, and in the future. Have you got such a list? Do you know that off in the Andromeda galaxy something has just begun to exist? Or something began to exist a billion years ago? Or will begin to exist a billion years from now? All premises in a valid argument must have definite truth values, but there is no way to assign a truth value to Kalam’s major premise because we have no empirical method to prove or disprove it and can never have such a method either in practice or in principle. Its truth value is undetermined. Consequently, there is no valid argument.

    As for the infinite library, the word “infinite” is being misused. “Infinite” is not a quantity, so the word “many” has no application here. The library does not contain a definite quantity of books; its contents are infinite; there is no quantity because quantity is by definition finite. The correct way to express the problem is that the library consists of the union of two infinite sets–one of red books and one of black books. Remove the first infinite set and you’ve still got a second infinite set. Perfectly logical. There is no paradox.

  32. Triptych

    Hey Mike!!!

    Long time no see! LoL I almost feel embarrassed replying at this point hah. To say that this is a late reply is a wild understatement LOL. Although it wasn’t without good reason. When I stopped replying things were starting to get a little heavy with work and I was helping plan my wedding :D. I got married in June and I just got back from my one-year anniversary from Greece! Nevertheless, occasionally I would remember that we were having this discussion and I finally decided to sit myself down and force myself to continue it before I got preoccupied with other things hah. How have you been this last year? Anything new?

    Well, I can’t really think of anywhere to start than where we left off! It seems we were talking about the causal principle and whether we have good reason to accept premise 1 of the KCA as more plausibly true than false.

    Re: Causal Principle 1) The example you give in regards to electron pairs (I’m assuming in radioactive decay if you got it from Victor Stenger) is a popular example given to try and disprove the causal principle by giving an alternative example where the causal principle does not apply. The first premise of the KCA is very carefully formulated. The first premise of the KCA is not that, “Everything that exists has a cause.” The first premise is, “Everything that begins to exist has a cause”. That is, this argument is deliberately formulated so as to allow for quantum indeterminacy with regard to events. This is quite consistent with admitting that there are events that occur without a cause. So events that are say, movements of a libertarian freewill, or decay of atomic isotope, or emission of a photon; we can happily admit, at least for the sake of argument, that those are uncaused events and it wouldn’t affect the truth of the premise, which concerns whether or not things can actually begin to exist without any causes.
    However, is the radioactive decay of an atomic isotope even evidence of a general uncaused event? I don’t think so. It’s not at all proven that these events really are indeterminant. Right now, it’s said that no cause can be found. That is to say, we don’t have the ability to determine or predict when or where these events will take place. But that’s no proof that they don’t have causal conditions. There are about ten different physical interpretation of the mathematics of quantum mechanics, and some of these are fully deterministic. So that any indeterminism is purely in your mind, it’s just epistemic, it’s just our ignorance of the determining conditions, but they actually are there. So even on the quantum level, these quantum events are not proven as counter examples to casual determinism. Actually, Victor Stenger admits this, (Victor Stenger is the particle physicist who usually purports this objection) if you look in Stenger’s book “God The Failed Hypothesis” he admits that causes for these events may someday be found and we cannot assert with any kind of confidence that these events are really uncaused.

    So I agree with you that some things may come into being without us know why (or really even how) but just because we are ignorant on the issue doesn’t mean that these things really do come into being without a cause. The reason things like Cable TV, batteries, etc should come into being is because nothing has no properties, it has no constraints. What makes nothing so discriminatory as to only allow for particles to come into being? How can anything constrain nothing to make it discriminatory when there is nothing to constrain!? The fact that these things don’t happen gives us more evidence in support of the causal premise.

    Re: Causal Principle 2) For the basis of this discussion, I believe, even in Dr. Craig’s work, “without a cause” and “from nothing” are used interchangeably. To say that something comes from nothing is just the same thing as saying it has no material or efficient cause. To say that something comes into being without any efficient or material cause is to say that it comes from nothing. They are interchangeable. So I don’t know if it is for sure logically contradictory, like the idea of a married bachelor. It just seems like that to me in some ways. But what I would say is that it is certainly metaphysically impossible (and highly counter intuitive for that matter).

    Re: I think we’ve already got started on the wrong foot here. The argument is:
    1) Either a mind or an abstract object (like a number), not abstract objects, therefore a mind.

    Second, I think you’ve misunderstand my argument. My argument is not an empiricist type argument that we simply lack evidence of abstract objects causing things (Although even if it was I don’t think you could use the same argument against an unembodied mind. For the beginning of the universe would necessitate an unembodied mind should that be the cause, because there is no space, matter, or energy. So it doesn’t seem like you can just flip the argument and say that there is no evidence for unembodied minds either) Rather, it’s simply part of the definition of what it means to be an abstract object. By definition, abstract objects don’t stand in causal relationships. For example, our knowledge that 2+2=4 is knowledge about certain abstract objects. Namely, numbers and the mathematical relations that obtain among them. But it does not seem to be correct to say that these nonphysical abstract objects cause our knowledge of them. Again, one can know that if tree A is taller than tree B and tree B is taller than tree C, then it must be the case that tree A is taller than tree C. But what is it that causes this knowledge? It is not the trees because the knowledge itself does not depend on any specific objects in space or time but on the logic of the relation called “taller than.”

    2) It’s not that “this is an argument for how God would have to be given a number of assumptions.” But that we are just following the argument to it’s logical ends. If the standard Big Bang model is true, we have an absolute beginning of space, time, matter and energy. So if the cause is timeless it must be changeless. Why? Because things require time in order to change. If there is no time there is no change. But if this cause is changeless than it must also be immaterial. Why? Because material things are constantly changing, at least on the molecular level. So we have a timeless, spaceless, changeless, immaterial cause (which has other qualities at this point but which need not be listed right now because they don’t pertain to the current discussion). There are two types of things which we know of which fit this description. Abstract objects and unembodied minds. Now sure, if neither of these work than we have a false dilemma. But that’s the very question at hand. There are three arguments for unembodied minds at this point, I’ll give two.
    1) Either abstract objects or unembodied minds. Abstract objects don’t stand in causal relationships, therefore unembodied minds.
    2) How is it that we can have a timeless cause and a temporal effect? If the necessarily and sufficient conditions for the cause have been timelessly present than the effect should be timeless present. The cause of water freezing is the temperature dropping below 0° C. Now, if the temperature had been below 0°C for all eternity, than any water that would be present would be frozen. The only way for the cause to be timeless and the effect to begin to exist in time is if the cause is a personal mind who freely wills to create.

    I don’t see how the discussion of M-Theory fits into the discussion of minds so lets just make that a different topic (you can correct me if I’m missing something here).
    Models of the Universe:
    String Theory, (M-Theory): String theory really is the far extreme end of cosmological theories out there. It states that prior to the Big Bang a black hole formed in the eternally preexisting, static vacuum space and collapsed to the maximum allowed values of such quantities before rebounding in the current expansion observed today. Aside from this being based on a non-existent theory (because the equations haven’t even been worked out yet) and it having considerable difficulties, for example, as to how to join a pre- and post- Big Bang phase, there are many other problems. I’ll give one here:
    1) Like the old Vacuum Fluctuation Models, the Pre-Big Bang Scenario postulates an eternal, static space in which our observable universe originates via a Big bang event a finite time ago. But since there is a positive probability of a black hole’s forming in any patch of pre-existing space, such an event, given infinite past time, would have happened infinitely long ago, which is inconsistent with the finite age of our observable universe.

    It’s true, there are many models of the universe that are bounced around here and there. But none of them has committed itself so strongly as the standard Big bang model. As Alexander Vilenkin said at Stephen Hawking’s 70th birthday, “All the evidence we have says that the universe had a beginning.” There is no evidence to anything else. If we are going to follow the evidence where it goes, one has to be committed to accepting the Big Bang.

    I hope we can carry on our conversation! Since its been such a long time and I didn’t go back and read every post we’ve written in the past, I may have lost some things in translation hah. It may also be the case that I’ve repeated myself as I don’t remember what has been said already lol. Go ahead and bring up anything which you feel I left out. Anyway, I hope you’re doing well!

    Btw, I haven’t read your new post on the issue of minds. I’ll try to do that a little later!

  33. Joe

    Hi there Mike, just wanted to tell you, I liked this post. It was funny. KeepPlease keep on posting!

  34. Lea

    If some one wants expert view about blogging afterward
    i propose him/her to visit this blog, Keep up the nice job.

  35. Nathan

    That’s not what potential and actual infinity are at all, what you called an actual infinity (a timeline with t(0) with time stretching infinitely forward and backward) is the perfect example of a POTENTIAL INFINITY. An actual infinity is bounded, it is a completed totality. If an actual infinity were possible, it would be like there was a bowl with an infinite number of jelly beans, where each one had slightly less mass each one having the mass of a sequential term in the Riemann sum ∞(n=0)∑(1/2)^n grams, so the entire mass would only be 2g even though there was an infinite amount of jelly beans. That would be an actual infinity. It’s defined by Aristotle in Physics, 3.6 and is the basis of the way theists are using the concept. It’s amazing that you would write an entire article about this without even understanding the most basic distinction involved. Wow, great job.

  36. igore

    The KCA argument is composed of several syllogisms that are used in attempted proofs. A syllogism is a logic construct that provides deduction of information/data that is already known. A syllogism is not proof of anything.

    In the case of the first syllogism:

    1. Whatever begins to exist has a cause of its existence.
    2. The universe began to exist.
    3. Therefore, the universe has a cause of its existence.

    The set “whatever begins to exist” is such that for each member of the set, there is “a cause of its existence”. So to use validly the second premise requires that “the universe began to exist” is already a member of the set. In that case, it has already been established that “the universe has a cause of its existence”. So a claim that “the universe has a cause of its existence” must be referred to the original argument/proof that was used when this member was added to the set.

    The 2.n arguments betray the usage of syllogism. By presenting attempts of argument that the universe began to exist but no arguments that the universe had a cause of its existence, the attempt to add “the universe began to exist” to the set “whatever begins to exist” fails.

    Similarly, these syllogisms are presented as proof but do not (because they cannot) prove anything.

    2.11. An actual infinite cannot exist.
    2.12. An infinite temporal regress of events is an actual infinite.
    2.13. Therefore, an infinite temporal regress of events cannot exist.

    2.21. A collection formed by successive addition cannot be actually infinite.
    2.22. The temporal series of past events is a collection formed by successive addition.
    2.23. Therefore, the temporal series of past events cannot be actually infinite.

    It may indeed be the case that these arguments are correct, but the usage of syllogism does not establish this – that requires other arguments/proofs.

    So the foundation arguments (these syllogisms) of the KCA are not proofs. Without reference to the actual arguments used in each case to justify inclusion into the appropriate set, the KCA as a whole is dead in the water.

  1. The Sherlock Holmes Defense | Foxhole Atheism

    […] does this make sense? This is the question I’ve been debating in the comment thread of On Absurdity: William Lane Craig and Actual Infinites. How can we realistically assert some kind of mind as the cause of the […]

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