God, Yachts and Bitches

Aliosha VII Yacht

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Stephen Colbert recently raised an important theological and philosophical question, namely,”Could God create a yacht so big that he could not fill it with bitches?” This sort of question, obviously enough, parallels some of the classic questions about the nature of God’s omnipotence, such as “can God create a rock that He cannot lift?”

The specific question of whether or not God can create such a yacht would seem to involve considering the specifics of the scenario, such as the size limits of yachts (would a ship of a certain size be too big to be classified as a yacht?) and bitches as well as what would count as being full of bitches (does this mean that the bitches are comfortably occupying the vessel or stacked and stuffed in all the spaces?). However, these complications can be set aside (along with the offensive term “bitches”) in favor of a more general sort of question: can God create a container that He cannot fill?

On the face of it, this would seem to create what appears to be a paradox. If God is omnipotent, then it would seem to follow that He could create a container (such as a yacht) of any size-even one that would be so big that He could not fill it (even given an infinite supply of created bitches). However, His omnipotence would also seem to entail that He could fill any container, no matter how big. After all, He could just create enough things to fill the container.

One potential way out of this problem is to play games with the notion of infinity. Presumably the largest container that God could create would be infinite in size. Presumably the largest number and volume of things (such as bitches) that God could create would also be infinite. Leibniz, in his Theodicy,  writes “and infinity, that is to say, the accumulation of an infinite number of substances, is, properly speaking, not a whole any more than the infinite number itself, whereof one cannot say whether it is even or uneven.” Stealing from Leibniz, perhaps it could be said that when talking about an infinite yacht and an infinite number of bitches it would not be possible to say whether it is full or not. Of course, this seems vaguely (or not so vaguely) unsatisfying.

Perhaps a better approach would be to look at the matter a bit differently. The problem arises from taking the ability to create something so big that He cannot fill it as a positive ability of God. As such, if God did not have that ability, then He would be lacking. But, of course, if he could not fill the object, then he would also be lacking.

However, the idea of an ability to create an object so big that He cannot fill it seems to involve an absurdity. After all, if God could create a hollow object of X size and Y interior volume, then it would seem that He could simply create an object marginally smaller than X with a volume of Y. Thus, the question is actually asking “could God create an object and not be able to create a smaller object (or objects) that would fill the larger object” and the answer would seem to be “no.” After all, objects have volumes and sizes, but so big that it cannot be filled does not seem to be a legitimate property that God could just give to an object. Rather, this property is a relational property between the object and all other things that exist or could exist. Thus, the supposition that God can create objects entails that He can fill any object He creates.

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  1. Can God create a container he cannot fill? This question makes no provision for what type of container or what size it is. Its only necessary quality is containership. It seems to me then all he has to do is to create an ever expanding container which will, similar to, a rubber bag, absorb anything he puts into it.
    Maybe he has already done it, and we, and the whole of creation, are a part of its contents. The Universe so far as we currently know, is in a process of continuous expansion.

  2. The answer to the question, I believe is YES. And God has already done that.

    The Universe, as we are told, is expanding all the time so it is infinity.

    The expanding Universe is fully filled with Matter and Energy (Dark energy too etc).

    I’m not sure I’ll call Matter and Dark Energy, Bitches – but it makes interesting reading and graps attension.

  3. To create a rock so massive that it cannot be lifted ‘simply’ requires creating a rock on its own. With no frame of reference for the lifting to take place it cannot be lifted. I think.

  4. Pod,

    Good points. But, I would get Medieval and say that the question is not “did God do so” but “could He do so?” The actual universe might be so big that it is not full (unless the emptiness is not really void). Presumably God could just create some infinitely expanding matter (let us call it Bitches) that exactly matches the interior infinity of the universe. Assuming that “interior of the universe” is even meaningful.

  5. Mike, sure, I Understand. So “could He do so?

    I would once again suggest yes he could.

    There are some Bitches that we know, we know.

    There are some Bitches, that we know, we don’t know. and

    There are some Bitches, we don’t know, we don’t know.

    That surely, could mean, Bitches could “exactly match the interior of the universe”

  6. “Stealing from Leibniz, perhaps it could be said that when talking about an infinite yacht and an infinite number of bitches it would not be possible to say whether it is full or not. Of course, this seems vaguely (or not so vaguely) unsatisfying.”

    i don’t know what you mean by vague. in mathematics, one can presuppose n=the number of bitches queuing to get inside the yatch, and then god builds a yacht with space big enough to contain n+1, for all kinds of n excited to jump on board. n+1 is not a vague concept at all, mathematically.

  7. It seems the paradox invites a clearer conception of what it means for a being to be “omnipotent” (see, for example, the article “maximal power”). Suppose we stipulate that an “omnipotent” being has as much power as is possible for a being to have and that it’s not possible for a being to bring about an impossibility (given modal axiom S4). Then we may reply to the paradox as follows: Either an unfillable container is possible, or it is not. If it is possible, then an omnipotent being can create it but cannot fill it (because it’s being filled is not possible, by definition). On the other hand, if an unfillible container is not possible, then an omnipotent being cannot create such a thing (being doing so is impossible). Either way, we avoid contradiction.

  8. Josh puts it more concisely than I would have, but my thinking is along similar lines.

    An omnipotent being is able to do anything that can, in principle, be coherently described. It can do anything that it is logically possible to do. It cannot do things that are not things at at all, e.g. if the relevant sentence simply makes no sense or if it purports to describe something logically inconsistent.

    If, as Josh puts it, creating unfillable container is logically impossible, then even an omnipotent being cannot do it.

    It seems to me that anything that we’d count as “a container” must have a limited – however vast – volume. I.e., this is part of our concept of what it is for something to be a container. Thus any container is fillable in the relevant sense, i.e. it could be filled by a being or thing that can create an arbitrarily large volume of stuff.

    Thus, an unfillable yacht is logically impossible. Thus, God (if such a being existed) could not make one. This would not detract from God’s omnipotence, since it is not an example of something that (1) God cannot do, but (2) is logically possible.

    (As Josh says, the alternative is that an unfillable yacht is logically possible. I don’t see how that could be so, but imagine it is for the sake of argument. The question is then whether it is logically possible to fill an unfillable yacht. If it isn’t then it does not detract from the omnipotence of an omnipotent being that it is unable to fill an unfillable yacht.)

  9. Can someone tell me if we can have a class which has infinite membership? If this is possible then we do have a mathematical example of a container which cannot be filled. I appreciate it is not an actual object in the world, which I assume, we we wonder if God can create. I am just speculating as to whether this idea has any relevance to the discussion, or is in any way helpful

  10. “An omnipotent being is able to do anything that can, in principle, be coherently described. It can do anything that it is logically possible to do.” – R. Blackford

    No, for instance, God is essentially eternal, which means that he cannot commit suicide, because once he exists, he cannot cease to exist. God’s committing suicide is doubtless a coherently describable, logically possible state of affairs; but given his indestructible nature, it is ontologically impossible for him to cause himself to cease to exist.

  11. Re Myron 23 Nov:-
    That is interesting. There is something I could do which God Cannot.

  12. Is it logically possible to destroy an “essentially eternal” thing? I find the idea of being “essentially eternal” hard to grasp, and I wonder whether it is even meaningful. But maybe I’m wrong about that. If our concept of “essentially eternal” includes “cannot be destroyed” (as opposed to just “very difficult to destroy”) then surely even an omnipotent being cannot destroy anything that counts as being “essentially eternal”. An omnipotent being can destroy something that is as arbitrarily difficult to destroy as you like, but that’s a different issue.

  13. Re Russell Blackford Nov 23:-
    Personally I do not find this idea difficult to grasp. The essence of the thing, whatever that is, is eternality, that is ceaselessness, everlastingness, permanence, perpetuation, perpetuity, timelessness ; It will persist for ever, it is accordingly invulnerable. There is nothing within, or without it, which can diminish or otherwise alter this essence. I cannot point to or imagine the composition of this thing. All we know is that it is eternal. It has connotation but no denotation intension but no extension so far as I can tell. Possibly the reality which embraces us and all other matter, space, and time, or matter space and time, themselves are in essence eternal.
    I have problems with the expression omnipotent being. It is most often anthropomorphised such that we imagine it to have human characteristics. If such an entity does exist, I doubt it is concerned with the actions of human beings, any more than matter space and time are.

  14. Myron,

    You have quite ably shown that God’s suicide is not something that can be coherently described (at least giving your assumptions). After all, saying God has committed suicide is to say that the unkillable has been killed, which would seem to at least entail a contradiction. So, God cannot commit suicide.

  15. Don,

    Spinoza’s God seems to be just that of entity.

  16. “Is it logically possible to destroy an ‘essentially eternal’ thing? I find the idea of being ‘essentially eternal’ hard to grasp, and I wonder whether it is even meaningful.” (R. Blackford)

    X is an essential property of y.
    For all possible worlds w, if y exists in w, then y is X.

    This is the standard definition.
    (By the way, it implies that existence is an essential property of all existents, since nothing can exist without existing. But essential existence in this sense certainly isn’t the same as necessary existence. Contingent beings are essentially existent but not necessarily existent.)

    Accordingly, “x is essentially eternal” means “x is eternal in all possible worlds in which it exists”.

    Unfortunately, the concept of eternity is ambiguous, meaning either timelessness or everlastingness.
    In the first sense “God is essentially eternal” means “God exists timelessly in all possible worlds in which he exists”; and in the second sense it means “God has always existed and will always exist in all possible worlds in which he exists”, which is synonymous with “God has neither a first/earliest nor a last/latest temporal part in all possible worlds in which he exists.” It is obvious that a being that is essentially eternal in the second temporal sense lacks both a beginning and an end of its existence in those possible worlds in which it exists, which implies that it cannot be created or destroyed, since nothing can be created or destroyed whose existence is necessarily beginningless and endless.

    Whether or not God is temporally or atemporally eternal is still a contentious issue among theologians. There are even hybrid positions such as William Craig’s, who holds that God exists atemporally without creation, but by creating a spacetime world his timeless existence became existence in time, such that he exists temporally as long as the spatiotemporal universe exists.
    (In my opinion, the concept of a timelessly existing mind is nonsensical, and it is incomprehensible how a timeless being could “enter” time.)

    Given the assumption that God exists temporally eternal, the question arises as to what it is about God’s temporally eternal being that makes it impossible for him to commit suicide despite his omnipotence.
    Well, he is said to be an “immaterial/spiritual substance”. But not all such substances are per se uncreatable and indestructible, since we are told that God can create and destroy human souls (and other spiritual beings such as angels and demons). So the divine immaterial substance must be uniquely special, of course not in the sense of being a special kind of imperishable stuff or matter, since pure minds/souls/spirits such as God do not consist of any stuff. It seems that the theologians cannot present any intelligible explanation of the temporal eternity of the divine spiritual substance, and thus cannot help but assert that it is an “ultimate brute fact”.

    By the way, the concept of essential (temporal) eternity largely overlaps or is virtually identical with the concept of factual necessity:

    “To say that ‘God exists’ is necessary is, I believe, to say that the existence of God is a brute fact that is inexplicable—not in the sense that we do not know its explanation, but in the sense that it does not have one. …[A]ny terminus to explanation of things logically contingent must be itself something logically contingent. …[T]here are two ways in which God’s existence being an inexplicable brute fact can be spelt out. The first position is to say that God’s essence is an eternal essence. God is a being of a kind such that if he exists at any time he exists at all times; his existence at all remains the one logically contingent fact. The alternative position is to say that the divine essence is a temporal essence; the ultimate brute fact is not God’s existing as such, but his existing for a period of time without beginning. His subsequent existence would be due to his intentional choice at each moment of time to continue to exist subsequently. Theism has traditionally taken the former position, … . In that case God will have the strongest kind of necessity compatible with his being a logically contingent being. Such necessary existence we may term factually necessary existence (in contrast to logically necessary existence).”

    (Swinburne, Richard. The Existence of God. 2nd ed. Oxford: Oxford University Press, 2004. p. 96)

    “God’s necessary existence has been interpreted in two different ways. Some have understood the notion in the sense of logical necessity; others have attempted to delineate a sense of factual necessity.
    If God’s necessity is understood as logical necessity, the proposition ‘God exists’ is logically true. A logically necessary being is one that exists in every possible world. The proposition ‘three plus five equals eight’ is necessarily true; it is true in every possible world. Likewise, if God is a logically necessary being, the proposition ‘God exists’ is true in every possible world. To say that something is logically necessary is to claim that it is logically impossible for that thing not to exist. Just as it is logically impossible for a triangle to have four sides, so it is logically impossible for God not to exist.
    In recent years, many religious philosophers have given up on the notion of a logically necessary being. For reasons that will be explained shortly, they decided the concept was not only indefensible but even damaging to theism. Consequently, in order to retain a sense of necessity with respect to God, these thinkers explained God’s existence as necessary in a nonlogical sense; God’s existence, they said, is a factual necessity.
    A being who is necessary in the factual sense is one about whom three claims can be made. (1) The being is eternal, that is, it had no beginning and its existence will never end. (2) The being is self-caused, which is to say that it does not depend upon anything else for its existence. It is, in a sense already explained, a se. (3) Everything else that exists depends upon the necessary being for its existence. Here is the key difference between the notion of logical and factual necessity: a factually necessary being does not exist in all possible worlds. In the sense of factual necessity, the proposition ‘God does not exist’ is not logically false. A factually necessary being is, in a sense, accidental.”

    (Nash, Ronald H. The Concept of God. Grand Rapids, MI: Zondervan, 1983. p. 108)

    “[I]f God exists, then he is a necessary being who cannot be created or destroyed.”

    (Hoffman, Joshua, and Gary S. Rosenkrantz. The Divine Attributes. Oxford: Blackwell, 2002. p. 79)

    Is it logically possible to create or destroy a factually necessary/essentially eternal being?
    Yes, but it is ontologically/metaphysically impossible. (Logical possibility in the narrow sense is nothing more than formal consistency of propositions.) And that’s why it is ontologically/metaphysically impossible for God to commit suicide or to create a duplicate of himself.

  17. I should have added that the existence of an atemporally eternal being would have to be both beginningless and endless as well, because existence beginnings and endings are events and thus changes. But events are necessarily time-involving, which means that the concept of a timeless event (or process) is incoherent. In a timeless world, nothing could happen, and so there couldn’t occur any creation or destruction events/processes therein either.

  18. “I cannot point to or imagine the composition of this thing.” – D. Bird

    God is a (mereologically) simple being, i.e. one which lacks components or constituents. An immaterial/spiritual substance such as God is a spatially unextended, zero- or adimensional entity lacking form and internal structure.
    The question I have is how it is possible for such a simple entity to be the substrate and producer of complex or even infinitely complex mental states or events.

  19. Re Myron:-
    This simple entity you describe I would say is not the producer of ‘complex or even infinitely complex mental states or events’. I assume you refer to these states and events as those common to all humans. There is a confusion between cause and effect. The simple entity is the effect, not the cause, of creativity on the part of complex or even infinitely complex mental states.
    It seems to be an innate propensity of all humans to imagine or create by mental act, many entities which have no existence, save for the universe of discourse in which they are discussed. Somewhat like chess these provide grounds for interesting discussion at times of a high intellectual nature, rather like the question you have posed, but that is all.
    The idea of God I would say finds its origin in the fear and dread which beset all humans from time to time. It has been said there are no atheists in foxholes.

  20. Aquinas, I think, does a reasonable job of sorting out how there could be an eternal being without beginning or end. That said, my own criticisms of Platonic universals have included points about their alleged timelessness. As such, I am rather sympathetic to the idea that eternal stuff is suspicious.

  21. God could be non spatial but also non-simple at the same time. After all, the idea of non-spatial dimensions seems sensible enough. Unless, of course, it is assumed that all dimensions are spatial.

  22. Don,

    Some notions of God do arise from fear. But, I would also contend that the belief in God can also arise from wonder at the (alleged) design and (alleged) beauty of the world (thus giving rise to the argument from design in its various forms).

  23. “God could be non spatial but also non-simple at the same time.” – M. LaBossiere

    A spatially unextended being existing in time can be said to be temporally extended in the sense of having many different temporal parts. Such a being would be spatially simple but temporally nonsimple.

  24. The philosophical discussion about the properties of eternal entities is all very interesting, but science actually has something to say about that. Namely that time is simply a dimension in space-time and therefore cannot exist independently of our universe. To postulate an eternal creature is to postulate something further north then the North Pole, it is meaningless.

    Which isn’t to say there aren’t other universes with other time dimensions, in fact this is strongly hinted at by the mathematics, but it simply moves the problem one step back and even then simply reinforces our absolute ignorance of what time is and how it functions.

    At least that’s what a physicist told me.

  25. “…Namely that time is simply a dimension in space-time and therefore cannot exist independently of our universe.” – Keddaw

    If space and time aren’t mutually independent but inseparably unified as spacetime, then the theologians (such as Swinburne) who claim that God exists extraspatially but intratemporally do have a very big problem. Some have tried to solve it by postulating a transcendent “metaphysical time” distinct from and independent of physical time, but I don’t think this makes much sense.

  26. Re Mike LaBossiere | November 25th

    “Some notions of God do arise from fear. But, I would also contend that the belief in God can also arise from wonder at the (alleged) design and (alleged) beauty of the world (thus giving rise to the argument from design in its various forms).”
    I agree. I should have mentioned that, and developed it.

  27. “The idea of God I would say finds its origin in the fear and dread which beset all humans from time to time….”

    “Granted for the sake of arguument”, says the theist “but beware the genetic fallacy.”

    I once knew a chap who broke into a church whilst on lSD and met God there.

    My own youthful adventures on magic mushrooms and the like never did lead to any such revelation = but making footprints in wet river sand and and watching them spring out of existence kept me amused for hours.

  28. Re Jim Houston Nov 25th
    The idea that I seem bound eventually, to re-enter the oblivion, which was broken by my birth I do not find appealing. The idea that I may fall one day seriously ill and suffer, for what seems no reason at all, is similarly not appealing. I do not dwell on these prospects I have one life, so try to make the best of it. How ever how wonderful it would be If there were some benevolent all powerful entity who fully understood my plight and could reassure me that all is well. This life on Earth is not the real thing. Hang on in there, Heaven awaits me, eternal bliss and satisfaction will be mine. Now if I can persuade myself that this be the case, how much easier life on Earth will be. But I cannot persuade my self, and nobody else can, I am sure. Those who subscribe to this belief I consider for want of a better word silly, but I do envy them nevertheless. A fool’s paradise has a lot going for it.

  29. Don,

    I am not indifferent to death myself, but swing as it were in the other direction from you.

    The notion of eternal existence sounds appalling to me. That I will die and that will be the end of it has been a source of great comfort to me over the years. But that I keenly want there to be no afterlife should not guide me to the absolute certainity that there is not one.

    I personally find no reason to believe in such things as gods or a hereafter – I do not seriously doubt that there are no such things – but I have become somewhat more reluctant of late to describe such notions as the sillyness of fools.

  30. Jim,

    I’d be fine with existing eternally, provided that the experience was worth having. I can, however, easily imagine an endlessly dreary eternity and non-existence might well be preferable to such a fate.

    I do think that an eternal existence is a coherent notion, but one that seems rather lacking in proof. David Hume’s writing on the immortality of the soul is a rather good discussion of this matter, as is Clarence Darrow’s classic essay.

  31. Myron,

    God could hang out in the time of another dimension in which there is no extended space. Perhaps our universe has space-time, but this might not be a matter of logical necessity. Then again, I could be wrong.

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