Sunday, December 18, 2011

Greene on Nozick on nothing

Brian Greene’s The Hidden Reality surveys the various speculations about parallel universes on offer in contemporary physics.  Toward the end of the book, Greene discusses a proposal put forward by Robert Nozick in chapter 2 of his book Philosophical Explanations.  (Turns out that Greene took a course with Nozick at the time Nozick was writing the book.)  Greene notes that even if any of the multiverse theories currently discussed by physicists -- those inspired by quantum mechanics, string theory, inflationary cosmology, or what have you -- turned out to be correct, one could always ask why the world is as the theory describes it, rather than some other way.  (This is one reason why it is no good to appeal to such theories as a way of blocking arguments for God as an Uncaused Cause of the world.  We had occasion recently to note some other problems with this atheist strategy.)  But Nozick put forward a version that Greene regards as not subject to this question -- what Greene calls the Ultimate Multiverse theory.

On the Ultimate Multiverse theory, all possible universes exist, including a universe consisting of nothing.  To the questions “Why does this universe exist rather than some other?” and “Why does any universe at all exist rather than nothing?”, the Ultimate Multiverse theory responds: “There is no ‘rather than’ about it.  This universe and every other possible universe all exist; indeed, this universe and a universe consisting of nothing both exist.  So there is no special explanation of our universe required, because it isn’t in the first place only one of many possibilities to have been actualized.”  (It should be added that neither Nozick nor Greene actually endorses this theory; they merely float it as a possibility.  David Lewis famously did defend a similar view, though.)

Now, the proposal that every possible universe exists does not, by itself, actually explain anything.  In fact -- again, at least by itself -- it makes things more mysterious rather than less.  Suppose I ask “Why is there a cup on the table?”  It is no good to answer “Actually, there are in fact two cups on the table; hence there is no special reason to ask where the one cup came from!”  This hardly defuses the original question; indeed, there is now more to explain than there was originally.  And the problem would rather obviously only be made worse if it turned out that ten or twenty cups were on the table, and certainly if every possible cup were on the table.  Similarly, that every possible universe exists hardly explains why anything exists at all; it just adds to the explanandum rather than providing an explanans.

But Nozick’s Ultimate Multiverse theory involves more than merely the suggestion that every possible world exists.  Nozick tells us that this “fecundity assumption,” as he calls it (and which he compares to the traditional “principle of plenitude,” which I had reason to discuss in an aesthetic context), follows from a metaphysical “egalitarianism.”  But what does he mean by “egalitarianism,” and why does he think it defensible?  The answers to these questions constitute the heart of Nozicks’ treatment of the question “Why is there something rather than nothing?”  And they reveal, I think, that Nozick misses the point both of the question and of the traditional theistic answer to the question, at least as these are understood within classical (Platonic, Aristotelian, and Scholastic) philosophy.

Recall that in the Platonic/Neo-Platonic tradition, whatever is in any way composite must be explained by reference to what is absolutely simple or non-composite; that in the Thomistic tradition, whatever has an essence distinct from its act of existence must be explained by reference to something whose essence just is subsistent existence; and that these points ultimately reflect the Aristotelian principle that whatever contains potentiality of any sort must ultimately be explained by reference to that which is pure actuality, devoid of potentiality (since that which is a composite of an essence and an act of existence, or indeed composite in any way, is merely potential until the composition of its parts into a whole is actualized by something else).  These points are, of course, very abstract, and as always I presuppose that the reader has some familiarity with the basic concepts given that I’ve spelled them out in detail elsewhere.  (The Aristotelian and Thomistic ideas in question are developed at length in The Last Superstition, Aquinas, and my article “Existential Inertia and the Five Ways” and, more briefly, here and there in various blog posts such as this one or this one; and I had reason to discuss the Neo-Platonic conception of divine simplicity in another earlier post.)  The point for now is to emphasize that it is because the things in the world of our experience are composite, because there is in them a distinction between essence and existence, and because they are mixtures of actuality and potentiality, that they necessarily require a cause.  And it is because God is none of these things -- where what we mean by “God” is that which is none of these things -- that He does not and cannot in principle require a cause.  Precisely because he can actualize without having to be actualized, precisely because He is being or existence itself rather than something which merely participates in existence, and precisely because He is absolutely simple and not in need of composition of any sort, He and He alone can serve as the ultimate terminus of explanation.

Now at the beginning of his discussion, Nozick tells us, plausibly enough, that the alternative to an infinite regress of explanations is that there is some truth to which no further truth stands as an explanation.  But he regards the latter possibility as entailing that there is some truth or truths “without any explanation.”  And this claim, in turn, is one he says can be interpreted in either of two ways:

About such truths p lacking further explanation, there also appear to be two possibilities.  First, that such truths are necessarily true, and could not have been otherwise.  (Aristotle, as standardly interpreted, maintained this.)  But it is difficult to see how this would be true.  It is not enough merely for it to be of the essence of the things which exist (and so necessarily true of them) that p.  There would remain the question of why those and only those sorts of things (subject to p) exist; only if p must be true of everything possible would this question be avoided.

The second possibility is that p is a brute fact.  It just happens that things are that way.  There is no explanation (or reason) why they are that way rather than another way, no (hint of) necessity to remove the arbitrariness. (p. 117)

Here, it seems to me, Nozick’s account already goes awry in several respects.  For one thing, the notion of what is “necessary” needs to be more carefully unpacked than he (and many other contemporary philosophers) unpack it.  For instance, there is in Aristotelian-Thomistic (A-T) metaphysics a sense in which a necessary being might derive its necessity from some other necessary being.  That a derivatively necessary being exists (if it does exist) is thus a truth which will have a “further explanation,” in terms of a further necessary being from which the one in question derives its own necessity.  (See my discussion of the Third Way in Aquinas for more details.)  Moreover, even with respect to an absolutely necessary being -- one which does not in any way derive its necessity from another, but has it in itself -- it will not be correct to say that its existence is “without any explanation.”  Rather, its existence is self-explanatory.  For that which is absolutely necessary is (for A-T) absolutely necessary precisely because it is pure actuality or subsistent being itself.  Hence it doesn’t “have” or merely “participate in” being or existence in the way contingent and derivatively necessary things do, and it doesn’t have a potential for contingent or derivatively necessary existence which needs in some way to be made actual.  Again, it “already” is being or existence itself; it “already” is pure actuality.  That does not make its existence less intelligible than that of other things, but more intelligible.  Contingent and derivatively necessary things are contingent or derivatively necessary precisely because their existence is merely participated existence, and is in one way or another merely potential until actualized.  Their explanation must accordingly lie in something outside them.  The being or actuality of an absolutely necessary being, by contrast, is like the goodness of Plato’s Form of the Good -- it is intrinsic, intelligible in itself and the source and standard of the intelligibility of all other things.

(Note that the notion of being self-explanatory is not to be confused with the notion of being self-caused, which is incoherent.  Causation is a metaphysical notion, having to do with the source from which a thing derives some aspect of its being.  But explanation is a logical notion, having to do with the way in which we understand or make sense of some aspect of a thing’s being.  We cannot coherently say that a thing derives its existence from itself or its nature, for that would entail, absurdly, that the thing or its nature exists prior to itself, in an ontological sense even if not a temporal sense.  But we can coherently say that a thing’s existence can be made sense of in terms of its nature, for that has to do, not with where a thing “gets” its existence from -- an absolutely necessary being doesn’t get it from anywhere -- but rather with how we can make intelligible or understand its existence.)

This brings us to the second part of the passage from Nozick just quoted, wherein (to repeat) he says:

It is not enough merely for it to be of the essence of the things [lacking further explanation] which exist (and so necessarily true of them) that p.  There would remain the question of why those and only those sorts of things (subject to p) exist…

Nozick seems to mean by this that we would have to ask, with respect to any purportedly necessary terminus of explanation, whence it derived its necessity and why only the thing or things that constitute the terminus have derived it, and that we would have to ask this even if this necessity were “of the essence” of these things -- as if the necessity of the terminus of all explanation were merely a “participated” or “instantiated” necessity, in the way that the four-leggedness of a dog, though “of the essence” of being a dog, is still a “participated” or “instantiated” four-leggedness.  But this misses the whole point of the idea of God as an absolutely necessary being, at least as that is understood in classical metaphysics (i.e. in terms of pure actuality, subsistent being itself, and so forth).

Nozick may have been misled here by the way modern philosophers of religion often speak of God, under the influence of what Brian Davies has called a “theistic personalist” conception of God that is very different from the classical theism of Augustine, Anselm, Aquinas, and other ancient and medieval thinkers.  (I have addressed the difference between classical theism and theistic personalism in a number of posts, such as this one, this one, and this one.)  Proponents of Leibnizian cosmological arguments and Cartesian ontological arguments often say that God’s essence “includes” existence -- as if existence (or perhaps “necessary existence”) was merely one among a number of “great-making properties” that God “instantiates.”  But that is not at all what Aquinas (and, I would say, Anselm) are saying.  God doesn’t “instantiate” properties.  That would make of God merely “a being” among other beings, and the God of classical theism is not that.  Aquinas, Anselm, and other classical theists are saying something far more radical.  For them (and to repeat) God does not “have” existence but is existence itself; and He doesn’t “instantiate” or “participate in” anything, but is rather that in which everything else participates.  

Of course, one might object on various grounds to classical theism and its classical (Platonic, Aristotelian, and Scholastic) metaphysical underpinnings.  The point is just that Nozick’s discussion of the question of why there is something rather than nothing simply fails even to take account of this entire classical tradition -- no small lacuna given that it is, historically, the mainstream approach to the question.  And it is his failure to take account of it that leads him quickly to jump to the conclusion that any answer to the question is to some extent going to have to appeal to an inexplicable “brute fact” -- a position the classical tradition vehemently rejects.  One can intelligibly deny that the God of classical theism exists.  But one cannot intelligibly say that even if He did exist, His existence would be a “brute fact,” or that “there would remain the question of why that and only that sort of thing” does not require further explanation.   As I have noted before, suggestions of this kind completely miss the point of classical theism.

This brings us to Nozick’s metaphysical “egalitarianism,” which undergirds his Ultimate Multiverse scenario and which is best understood in contrast with what he calls “inegalitarian” views:

An inegalitarian theory partitions states into two classes: those requiring explanation, and those neither needing nor admitting of explanation.  Inegalitarian theories are especially well geared to answer questions of the form “why is there X rather than Y?”  There is a non-N state rather than an N state because of the forces F that acted to bring the system away from N.  When there is an N state, this is because there were no unbalanced forces acting to bring the system away from N.

Inegalitarian theories unavoidably leave two questions unanswered.  First, why is it N that is the natural state which occurs in the absence of unbalanced external forces, rather than some other (type of) state N’?  Second, given that N is a natural or privileged state, why is it forces of type F, not of some other type F’, that produce deviations from N?  If our fundamental theory has an inegalitarian structure, it will leave as brute and unexplained the fact that N rather than something else is a natural state, and that F rather than something else is the deviation force. (p. 121)

Perhaps it is obvious from the foregoing what is wrong with all this, at least if intended as an analysis of classical metaphysical approaches to the question of why anything exists rather than nothing.  As the classical tradition understands it, the N from which there are “deviations” would be (say) a potency or potential, such as the potential redness of skin (before it has become sunburned), the potential squishiness of an ice cream cone (before it has been left out to melt), or indeed the potential existence of a universe.  And there is nothing “brute,” “unexplained,” or “unanswered” about why these or any other potentials need some “external factor” or “force” to bring about a “deviation from N” -- being merely potential rather than actual, the Ns in question quite obviously cannot do anything at all.  In particular, potential redness, potential squishiness, potential universes, etc. cannot actualize themselves.  The relevant F which does actualize them is something which is itself already actual (such as the sun in the case of the sunburn and the melted ice cream cone), and there is nothing remotely “brute” or “unexplained” about why F has to be something already actual -- nothing non-actual could be F, because being non-actual, it (obviously) couldn’t do anything at all.  

Nozick makes the whole issue sound more mysterious than it really is precisely because of his use of formalisms of the sort fetishized by analytic philosophers, and he thereby provides a good illustration of how this method can generate obfuscation rather than rigor.  For the formalisms simply ignore the actual content of the principles classical writers appeal to when addressing questions of ultimate explanation, and thereby miss the entire point.  When, for example, a Scholastic writer says that no potential can actualize itself, but has to be actualized by something already actual, he is not postulating some mysterious “force of type F” whose power to “produce deviations from N” is left “brute” and “unexplained.”  For he is not talking about “a” force among other forces in the first place, not even a special kind of force; he is rather making the extremely obvious point -- indeed, one almost wants to say the trivial point, except that some decidedly non-trivial consequences follow from it -- that only what is actual can serve as any kind of force at all.  And neither is the Scholastic postulating some mysterious “natural state N which occurs in the absence of unbalanced external forces.”  He is rather making another obvious point, viz. that what is merely potential -- whether it is “natural” or not is not relevant -- cannot do anything, precisely because it is merely potential and not actual.

Thus, when Nozick asks “Why is it forces of type F, not of some other type F’, that produce deviations from N?” he is not asking a profound question, but a very silly question, at least if he intends to raise problems for an account like that of Aquinas or some other Scholastic.  You might as well ask: “Why is it only actual forces that act as forces?”  To ask the question is to answer it.  Nor is it profound to ask “Why is it N that is the natural state which occurs in the absence of unbalanced external forces?”, again, at least not if this is intended to raise problems for views of the sort defended by ancient and medieval philosophers.  You might as well ask: “Why do potentials remain potential until actualized?”  When we put things the way traditional writers actually put them, instead of in terms of Nozick’s pseudo-rigorous formalisms, the answers are obvious, and obviously hard to deny.  

It is also obvious why there is nothing the least bit “brute” or “unexplained” about the classical metaphysician’s “inegalitarian” “privileging” of actuality over non-actuality.  Nozick’s own discussion presupposes that actuality is “privileged” in this way, insofar as he is keen to explore various possible answers to the question of what “states” and “forces” might account for this or that aspect of reality.  For to raise the question of whether this or that “state” or “force” is the correct explanation of anything is precisely to ask whether this or that “state” or “force” actually obtains or is operative, and is thus available to serve as an explanans.  (This is true even of Nozick’s rather farcical discussion of the idea of a “nothingness force” which “nothings” other things, and even “nothings itself” -- see pp. 122-24, complete with the obligatory variables, and even a graph for extra “rigor.”  To ask whether there is such a force is precisely to ask whether it is actual and thus an available explanans.  It is, by the way, standard Nozick shtick to devote many pages to exploring ideas that are obviously non-starters and which he does not even believe himself.  Some of Nozick’s fans seem to find this kind of mental onanism entertaining.  I find that it gets tiresome pretty fast, especially in a book of over 700 pages.)

Now, Nozick’s Ultimate Multiverse proposal crucially depends on the suggestion that there is something fishy about “inegalitarian” theories.  The idea is that if no state of affairs is special or “privileged” in the way “inegalitarian” theories suppose, then there is no reason not to regard all possible worlds as equally actual.  In this way, Nozick’s “egalitarianism” -- which is just a rejection of “inegalitarian” theories -- underwrites the “fecundity assumption.”  But what Nozick does not realize is that what the classical, “inegalitarian” metaphysician regards as “privileged” is not this or that state of affairs or possible world, and not even the actual world per se, but rather actuality itself -- something that, as I have said, Nozick too implicitly “privileges” no less than the classical metaphysician does.  The classical metaphysician simply pushes this “privileging” out to its logical conclusion: Since actuality is more fundamental than potentiality, the ultimate explanation of things must be purely actual, without potentiality; for anything less than that would itself require actualization in some respect, and thus not be the ultimate explanation.

To be sure, Nozick suggests that his “principle of fecundity… den[ies] special status to actuality” insofar as it makes every possible world as real as the actual world (p. 131).  But what it really denies special status to is the actual world, not actuality itself.  That is to say, it denies that there is anything special about a universe which (say) includes human beings, began with a Big Bang 13.7 billion years ago, is governed by the laws of quantum mechanics and relativity, and so forth.  It does not deny that being actual is privileged over being non-actual; on the contrary, rather than denying this privilege to any possible universe, it extends it to all of them.  Indeed, its attribution of actuality to all of them is precisely what is supposed to be doing the theory’s explanatory work vis-à-vis answering the question “Why is there something rather than nothing?”

That Nozick does not understand the way ancient and medieval philosophers would approach that question is especially evident from the following passage:

To ask ‘why is there something rather than nothing?’ assumes that nothing(ness) is the natural state that does not need to be explained, while deviations or divergences from nothingness have to be explained by the introduction of special causal factors.  There is, so to speak, a presumption in favor of nothingness.  The problem is so intractable because any special causal factor that could explain a deviation from nothingness is itself a divergence from nothingness, and so the question seeks its explanation also. (p. 122)

This is, in fact, the reverse of what the classical metaphysician thinks.  For the classical metaphysician, God -- understood as pure actuality, subsistent being itself, and absolute simplicity -- could not have failed to exist, precisely because He is pure actuality, etc.  Hence His existence -- the existence of that which is the opposite of “nothingness” -- is the “natural state” of things, in the relevant sense.  When the classical metaphysician claims to explain why there is something rather than nothing, then, he doesn’t mean that sheer nothingness is the natural state of things and that we need to find out why it doesn’t obtain.  He means that the world of our experience, since it is a mixture of actuality and potentiality, composite rather than simple, etc., could have failed to exist, so that its explanation must lie in something distinct from it, something which actualizes its potentials, which composes its parts, and so forth.  And when we arrive at that explanation, we find that it lay in something whose existence is self-explanatory, precisely because it is pure actuality without any admixture of potentiality, absolutely simple, and subsistent being itself.  Rightly understood, then, the question “Why is there something rather than nothing?” leads us to conclude that nothingness is not the natural state of things and that there is nothing without an explanation -- precisely the opposite of where Nozick seems to think the question leads.  And we are led to these conclusions however many possible universes -- one, two, or all of them -- exist.  For that they could have failed to exist -- that they are mixtures of actuality and potentiality -- is what leads to those conclusions.


  1. Excellent set of points, Ed.

    Nozick also appears to equivocate on "universe" pretty badly: what we use to mean is "the sum total of all the 'beings' that have existence or can have existence", more or less. That "sum total" does not include God, because God is not "a being" that "has existence". But clearly there cannot be many "sum totals", that's pure silliness. So the idea of Nozick and the other multiversers is a "universe" that is a limited portion of all of the beings that exist.

    The idiocy of a "universe" of nothing kind of shows up the equivocation. What would that even mean? A universe empty of beings but still having "laws", maybe? But we already know that the laws that a universe exhibits are not independent of the stuff that is the stuff of that universe. You would end up saying it is a universe devoid of beings and also of laws and of any whereness for these to be absent from: it would't be a universe. Ok, so maybe he is equivocating on being as well.

    It is also a philosophical cop-out to say that all possible universes exist, in two ways. First, in this universe I have not yet gone to sleep tonight, but I will - at least that is possible. Are there an infinitude of other universes in which I have already gone to sleep tonight even though there is no "tonight" yet? The notion of "possible" is so ill-defined as to defy any usefulness.

    More seriously, the supposition does not solve the problem: explaining WHY things are. The fact that in this universe Oswald killed Kennedy and in another one Oswald did not does nothing whatsoever to explain why in this universe Oswald did it. I think Ed pointed this out in another way, I am just pushing at it from a slightly different angle. To say that all possible universes occur in order to "explain" is, effectively, to say that there is no such thing as an explanation. Every "this rather than that" really has happened, so you can never really distinguish or state a rationale for the "rather than" supposedly. But that is to say that the supposition of the ultimate multiverse is, finally, a self-defeating supposition: it is made in order to explain, but if one supposes it one ceases to believe in explanations about anything. (A lot like the materialist notions of thinking.)

  2. I'd be tempted to answer the 'all possible universes' argument like this:

    If all possible universes exist, then a universe exists that points to Aquinas' God as its source.

    If Aquinas' God is the source of one universe, then he must be the source of all possible universes.

    There are, most likely, innumerable problems with my answer - but most atheists probably wouldn't know the difference!

  3. "There are, most likely, innumerable problems with my answer - but most atheists probably wouldn't know the difference!"

    There are problems with it. The same innumerable problems that applies to your answer when applied to 'this' universe.

    Same problem. Over confidence in 'words'.

  4. "First, in this universe I have not yet gone to sleep tonight, but I will - at least that is possible. Are there an infinitude of other universes in which I have already gone to sleep tonight even though there is no "tonight" yet? The notion of "possible" is so ill-defined as to defy any usefulness."

    Not only that, but I'm not sure what another "universe" would tell you about YOU exactly. A person in another part of this multiverse that looks, acts, and thinks like you but doesn't share your unity and continuity of consciousness... well, what does that tell you about YOU exactly? In what sense is this alternate you even you? It is still a mystery why "you" are here and not there. Appealing to doppelgangers in other universes doesn't do anything to explain your current state of existence in this universe.

  5. "...most atheists probably wouldn't know the difference!"

    That's because divine pedagogy resonates at frequencies unavailable to mere infidels.

  6. Most infidels couldn't care less about philosophy, reason or even science. All this goes over their heads. What they know is they dislike what they see as Christian morality, politics and culture, so they parrot whatever they think speaks against it. Understanding what they're saying isn't priority.

    Great post, Ed.

  7. Anonymous said...

    Most infidels couldn't care less about philosophy.

    There, fixed it for you.

  8. How do you catch a lion, Ed? You catch two lions, and let one go.

  9. May I just say that one of my favourite parts of Ed's blog are the people that show up in the comboxes?

  10. E. H. Munro,

    Would you care to elaborate?

  11. How could a "universe consisting of nothing" be said to exist at all? If it's nothing, then it doesn't exist. And if it exists, then it's not nothing. And if "nothing" "exists," than "something" can't simultaneously "exist." There's either nothing or something. You can't have both.

    Moreover, the whole multiverse idea is a sham. If the universe is infinite, then pretending that "in another dimension" there's ANOTHER infinite universe is just trickery, a way to have two simultaneous infinite things, which is impossible -- as is, needless to say, an infinity of infinite universes. And if they're not infinite, then they are just a bunch of parts of one big (or perhaps infinite) thing. So, as Tony so aptly pointed out, you are still stuck with the problem of explaining everything except that you have just made your concept of "everything" include more things.

    Making things bigger or more numerous or more complex doesn't negate discussion about them, but I have noticed that a lot of people think it does. Recently I've heard the claim that there are actually tens of millions of planets like the earth but that they are so far away that it would take 50,000 light years to get to the nearest one. This supposed to prove something about man or God or reality, but I'm not sure what. We already thought the universe was infinite, didn't we? Starting to number things and distances has not changed the concept of "infinite."

  12. Gail Finke - "If the universe is infinite, then pretending that "in another dimension" there's ANOTHER infinite universe is just trickery, a way to have two simultaneous infinite things, which is impossible -- as is, needless to say, an infinity of infinite universes."

    The number of integers (whole numbers, 1, 2, 3, etc.) is infinite. The number of real numbers (1.5, 2.66667, 3.14159...) is also infinite.

    But in some sense there are more real numbers than integers. See Cantor's diagonal argument for the reasoning. It's possible for there to be 'countable' and 'uncountable' infinities.

    There's no logical contradiction in having an infinitely-long line in one direction, and another infinitely-long line in a perpendicular direction. (Picture X and Y axes in a graph. And then you can add a Z axis coming vertically up from the 'paper'...)

    "So, as Tony so aptly pointed out, you are still stuck with the problem of explaining everything except that you have just made your concept of "everything" include more things."

    True, a multiverse simply expands the "set of all things that exist".

  13. I think there is something rather than nothing because the state of "nothing" is UNSTABLE. According to the Heisenberg Uncertainty Principle of Quantum Physics,” nothing” does not stay “nothing” for long. A true nothing means no energy, no space and no time. Nothing is a little like a sphere of zero radius. Once a quantum event occurs and the radius of this sphere expands slightly, the pressure ratio of the inside pressure of the sphere to the nothing "outside" of the sphere (zero pressure) is infinite or near infinite. Remember that a number divided by zero is infinity. This infinite pressure ratio causes a rapid expansion as in a Big Bang type explosion - a bit like putting a balloon in a vacuum chamber. Since less pressure exists outside of the balloon, it expands rapidly and bursts. Download and read "The Origin of the Universe - Case Closed". It's easy to understand and will explain in greater detail. It also explains how the mass and gravitational energy in the universe is created from nothing without violating the Law of Conservation of Energy. It explains how we can have a universe from nothing.

    1. It seems to me that nothing cannot have a property such as:

      "Nothing" does not stay "nothing" for long.

      If there is a property such as the above, then that property has to be tied to something, doesn't it?

      The same goes for instability. What is it that is unstable? Doesn't something have to exist in order for it to have the property of being unstable?

      Nothing can have no properties.

  14. @Ray
    You may be confounding "infinite" as to quantity with "infinite" as to extension. That is, there is a difference between an infinite number of things and a thing with infinite extent.

    Nor is there any mystery that two dimensions of one thing may both extend infinitely, as the X and Y axes of an infinite Euclidean plane. (The universe does not seem to be one; a closed, curved Riemannian space seems a better fit so far.) It is the space E^2 that is infinite, the axes are simply a frame on the space.

    Ditto, the rationals and the reals. The former are a subset of the latter (and in fact are dense in the latter) and it is no great mystery that an infinite set might be divided into infinite subsets.

    However for two universes X and Y to be infinite in extent, each must be in every place; but if they are distinct, then one must be in places (on the purported manifold of space-time continua) where the other is not, and hence the other is not infinite in extent. (This is over and above the empirical paradoxes of a physically realized infinity.)

  15. Don't you guys ever listen to Ed? What part of "do not feed the trolls" do you not understand? Honestly, this is starting to go well beyond ridiculous.

  16. Thanks, Anonymous. Yes, guys, please. If you're not going to ignore even the most obviously psychotic trolls, don't complain when the combox gets crapped up with their drivel and your responses to it, and serious people stop commenting.

  17. @Anonymous:

    I think there is something rather than nothing because the state of "nothing" is UNSTABLE. According to the Heisenberg Uncertainty Principle of Quantum Physics,” nothing” does not stay “nothing” for long. A true nothing means no energy, no space and no time.

    True, but insufficient. A true nothing also means none of the zero-point energy which is required for quantum events to occur; and not even a single point for such an event to occur in. As soon as you admit the conditions in which all quantum events actually do occur, you have energy in a space-time manifold, which is not ‘nothing’ at all. Indeed, the very laws of quantum mechanics, which are meaningless unless there is at least one quantum event for them to describe, are not ‘nothing’. Dr. Feser has made this point repeatedly in other posts.

  18. Anonymous said...

    Don't you guys ever listen to Ed? What part of "do not feed the trolls" do you not understand? Honestly, this is starting to go well beyond ridiculous. ..."

    But ... but ... but ... OK

    On the topic, I'm not sure I can even make any sense of the idea, that,

    "On the Ultimate Multiverse theory, all possible universes exist, including a universe consisting of nothing."

    What is the statement that all possible universes exist, supposed to mean? That any state of affairs not inherently contradictory to some larger frame of reference must exist?

    Obviously some definition of "not possible" must be stipulated along with its domain.

    If a universe with the cup on the table is possible, because it is seen to exist and there is no inherent contradiction in it so existing, then is another universe with the cup moved over one millimeter, but identical in almost all other ways, implied as existing? How about another universe yet, to accommodate a state of affairs with two cups. Or one with one cup in the same position, but arriving at it's placement a fraction of a second earlier or later?

    Geez, and we haven't even gotten to the flying monkeys, yet.

    It seems to me that this cannot be what Nozick has in mind as a possible universe unless he were willing to grant that when it comes down to it, from a
    God's-eye view, everything not non-possible exists more or less simultaneously in one universe or another, within a larger system of infinite universes. But what could that possibly mean? Other than something Whitehead might think up about everything being preserved in the Mind of ....

  19. TheOFloinn - "However for two universes X and Y to be infinite in extent, each must be in every place"

    Well, in effect, for the concept of a 'multiverse' to make sense, the term 'universe' must necessarily denote a subset of the multiverse. Just as a Euclidean plane (which can be 'infinite in two-dimensional extent') would be a subset of a Euclidean 3-space.

    So there is a sense that one could use those terms in non-contradictory way. Of course, from the perspective of the philosophical question Feser is pursuing, I agree that usage isn't really relevant.

  20. Potency and act. Potency and act.

    Every philosopher should find himself continually referring to potency and act. And if he doesn't, he should start. And if he can't, he should quit.

  21. DNW, you have touched on only the merest beginning of the infinities needed. The cup may be at this exact location, or one inch away, or the uncountably infinite different locations in between. The cup may be this specific shade of blue, or a shade of green, or an infinite list of shades in between. The cup may have one atom less, or two less, or 3 more... The cup can have one molecule of water in it, or two, or three... The cup can arrive intact, or slightly dented, or dented just a fraction more... There are an infinite number of axes of distortion of the denting. There are an infinitude of different ways that cup can be different in an uncountable infinitude of different degrees WHILE STILL being a cup on the table.

    Worse yet, if a cup can be on the table now, it can be there yesterday, or last week, or a year ago, or 10 years from now - and at ALL of the infinite times in between. What Nozick is assuming is a multiverse not merely where every state of affairs happens once, but it happens (in some universe) in every possible moment it could happen - so it happens an uncountable infinity of times throughout the multiverse, and will continue to do so forever. Indeed, for each and every thing that can occur, there are an infinity of universes in which it is occurring at EACH moment: (at least) once in each slightly different way it can happen. Since each of them CAN happen now, there is somewhere where it IS happening now.

    The whole notion falls apart in sheer silliness. While still failing to accomplish an iota of useful explaining of a single fact.

  22. The whole notion falls apart in sheer silliness.

    Not only that, but it was precisely this notion - that all things that can happen have happened and will happen in every possible configuration - that strangled natural science in the cradle in every society but three.

  23. When a JJC Smart, Quintin Smith or a Thomas Nagel,dies the world will have lost Atheists worth having. Persons who contributed greatly to the discussion.

    Hitchens was good at politics nothing more.

    Sadly fanatical Gnus like him see no difference between arguing politics vs arguing religion or philosophy.

    What a wasted life.

  24. Blasted! Posted on the wrong thread!

  25. Ultimate Multiverse theory?

    Does this teach that somewhere in some universe somewhere the events of the Book of Mormon are actually playing out?

    Or as one internet comedian once quipped does this mean in some universe somewhere Batman exists? Which could mean in some other reality somewhere you are Batman?

    Also the other BenYachovs in the other realities....are they really me or am I alone me?

    It seems only I am me since the other BenYachovs are no better then twins only more identical in the materialistic sense.

    Of course then we have questions such as why a multiverse?

  26. OK. STRICTLY in "devil's advocate" mode:

    (1) On the omniverse account, to exist MEANS to be possible - i.e. to be capable of being coherently described.

    (2) Asking why all possibilities exist is therefore nonsensical - they exist by virtue of the fact that they're possible. In that sense, they're self-explanatory.

    (3) An omniverse is descriptively and hence metaphysically simple: to say that an omniverse exists is to say that all possibilities are realized.

    (4) The universes that are "inside" the omniverse are not parts of it, but consequences of it; their relationship to the omniverse is like that of the corollaries to the theorem they follow from.

    (5) The essence-existence distinction would not apply to the omniverse, because it's self-explanatory.

    How did I do? Obvious flaws, anyone?

    (If you asked me what was wrong with the preceding account, I would say it fails the agency test. To act is to rule out a possibility; but if all possibilities obtain, the rationale for agency collapses.)

  27. The so-called "omniverse" is a manifold with quantum states. One quantum state is k=0, meaning that no "universe" exists. If k≥1, then one or more universes exist. These can be thought of as "bubbles" that have been "pinched off" the manifold.

    The "omniverse" is thus the "universe" and the "universes" are simply distinct "space-time continua" that "patch" the manifold. Lemaitre himself pointed out to the Pope that the beginning of a space-time continuum was not the same thing as a moment of creation.

    The omniverse is a "spatial" re-imagining of the ancient vision of continually-recurring cyclic universes.

  28. According to Jewish Tradition God created and destroyed whole worlds before he settled on this one.

  29. Bobcat, not only are Ed's comboxes filled with the wisdom of its own all-star roster (Untenured, DNW, dguller, grodrigues, et al) but it also gets hit up by the likes of Michael Flynn, Stephen Law and Gene Callahan. It really is one of the hippest spots in town.

  30. It seems that if one embraces the omniverse, one concedes theism automatically. Gods of every type and name exist, have existed, and will exist. Not only that, but since you can stack (via simulation) universes to infinite, we would expect to live in a created universe ourselves.

    TheOFloinn is right about what sort of problems this leads to for science, regardless of whatever philosophical meat it lacks.

  31. @TheOFloinn:

    "The omniverse is a "spatial" re-imagining of the ancient vision of continually-recurring cyclic universes."

    This reminds me of a story of the Argentinian fabulist J. L. Borges. It is called "The Theologians" and it is part of his 1949 "Aleph" book (cyclic theories of the universe is actually one of Broges' recurring themes; he discusses it at length in his 1936 book "History of Eternity" and it resurfaces later in other stories in different guises). The story centers around the intellectual struggle of two theologians with the pretext being the sect of the monotonous or the anulars, that held that history is a circle and there is nothing that is that was not or that it will not be. The two theologians prepare refutations and Euphorbus the heresiarch is condemned to the fire. He pronounces "This has happened and it will happen again. You do not light pyre a but a labyrinth of fire. If here and now all the fires that I have been were united, the world could not contain them and all the angels would go blind. This I have said many times." Then J. L. Borges ends with: "Then he screamed, because the flames reached him."

    Note: the translation into English is my responsibility. J. L. Borges is considerably more eloquent than my mangled and paltry translation lets on.

  32. Translated from the Greek a long time ago by somebody.

    “I will destroy the wisdom of the wise, and the cleverness of the clever I will set aside.” ...

    Where is the wise man? ... For since in the wisdom of God the world through its wisdom did not come to know God, God was well-pleased through the foolishness of the message preached to save those who believe.

  33. By coincidence, this:

  34. Flynn said, "it was precisely this notion ... that strangled natural science in the cradle in every society but three."

    Don't leave us in suspense. Who were the three?

  35. Don't leave us in suspense. Who were the three?

    1. The Latin West, where it did blossom.
    2. The Byzantine East, which was extinguished before it could blossom.
    3. The House of Submission, which strangled natural science with a different garrote; viz., occasionalism, rather than the infinitely recurring universes.

  36. Could it have been the case that all potentials could have been un-actualized? Could "pure act" exist without "acting" on a potential at all?

  37. What a gift you have, Ed. Thank you for your work!