The Ontological Argument Against God

Many atheists seem to hate all metaphysics; perhaps the hatred is motivated by the notion that all metaphysics eventually leads to God.  Of course, that is entirely false – there is a long tradition of purely atheistic metaphysics, which is as deep and abstract as theistic metaphysics.  Any atheism that embraces rigorous metaphysical thinking is far more powerful than an atheism that rejects metaphysics.

Consider the classical arguments for the existence of God.  Far too many atheists actually agree with the theists that they are arguments that go to God.  Thus the theists say that they are good arguments while the atheists say that they are bad arguments.  And that’s deeply unfortunate.  A metaphysically trained atheist can look at the classical arguments in an entirely novel way – they aren’t arguments to God at all.  This way of looking at them offers atheists a powerful new strategy for dealing with theists.  Rather than engage in the tired back-and-forth about whether the arguments are good or not, atheists can just agree that the arguments prove the existence of something that is not God.  That’s a much, much harder strategy for theists to defeat.   Let’s look at the Ontological Argument this way.

The Ontological Argument has its roots in Stoic theology – some precursors to it appear in the second book of Cicero’s De Natura Deorum.  Anselm presents one of the most famous versions of the argument in The Proslogion (Chapter 2).  More modern versions have been developed by Malcolm (1960) and Plantinga (1974).

All versions of the Ontological Argument go something like this: (1) The property of being maximally perfect does not entail any contradiction.  It is therefore consistent.  But consistency is possible existence.  So it is possible that there exists some x such that x is maximally perfect.  Let us refer to this x as the Maximally Perfect Being (MPB).  The MPB is a possible object.  It possibly exists.  (2) For any possible objects x and y, if x is actual and y is merely possible, then x is more perfect than y.  (3) There are some actual objects.  (4) So, if the MPB is merely possible, then there are some things that are more perfect than it.  (5) Hence it is not maximally perfect.   (6) But that is a contradiction.   (7) Consequently, the MPB is also an actual object.  The MPB actually exists.  (8) The MPB is God.  Hence God is not merely possible – God actually exists.

Assume that the Ontological Argument is sound through step (7): the MPB actually exists.  Now focus the attack on step (8): The MPB is God.  Of course, if “God” is merely being offered as another name for the MPB, there’s little reason to object.  But that’s never the intention.  For those who make the Ontological Argument are almost always Christians, and their intention is to say that the MPB is the theistic deity, the Christian God, and ultimately the God of Abraham (as defined by the Bible).  Focus the attack on step (8) by considering the alternatives to identifying the MPB with God.

Since the Stoics were the first to use the concept of maximal perfection, it is reasonable to start with them.  According to Cicero (in Book 2 of De Natura Deorum), the Stoics declared that the universe is the MPB.  And, consistently, they used the term “God” to refer to the universe.  So the Ontological Argument merely motivates a kind of pantheistic view of the universe – the universe is sacred or divine.

Johnston (2009: 11) writes that “It is conceivable that mathematical reality taken as a whole is the Most Perfect Being, because it is utterly complete, beautiful, self-contained, and inherently intelligible, in a way that cannot be approximated by anything in the spatio-temporal realm.”  On this hypothesis, step (8) should end with God.  Perhaps the MPB is the maximally wide and high iterative hierarchy of pure sets.

Or maybe the MPB is the best of all possible worlds, not in the Leibnizian sense, but in the more recent sense in which the best world contains all universes needed to realize all the positive potentials of all possible things.  The best world is a multiverse in which every proposition that ought to be true is true at some universe in that multiverse.  It thus serves as a model for some structures in deontic logic.  This is a grander sort of pantheism, but there is no personal God of any kind; the best world is utterly godless.

Another hypothesis is that the MPB is the theistic deity – it is God.  However, the definition of the theistic deity is fraught with logical conflicts (Martin & Monnier, 2003).  And since the MPB cannot be internally inconsistent, the MPB cannot possibly be God.

So here’s the strategy: First, agree with the theist that the Ontological Argument is a sound argument for the existence of the MPB.  Second, show that the MPB cannot possibly be the theistic deity.  Hence the Ontological Argument becomes an anti-theistic argument: it is a wonderful argument for showing that God does not exist.  But by all means, use the Ontological Argument to justify the existence of the universe, or mathematical reality taken as a whole, or the best of all possible worlds, or some other godless reality.

The same strategy can be applied to the classical cosmological arguments and the universe-level design arguments.  For instance, the same strategy can be applied to the so-called fine-tuning argument, to show that any apparent fine-tuning of our universe for life (or, if you prefer, the anthropic coincidences) is an argument against the existence of God.

References

Johnston, M. (2009) Saving God: Religion after Idolatry.  Princeton, NJ: Princeton University Press.

Malcolm, N. (1960) Anselm’s ontological arguments.  The Philosophical Review 69 (1), 41-62.

Martin, M. & Monnier, R. (Eds.) (2003) The Impossibility of God.  Amherst, NY: Prometheus Books.

Plantinga, A. (1974) The Nature of Necessity.  New York: Oxford University Press.

About Daniel Fincke

Dr. Daniel Fincke  has his PhD in philosophy from Fordham University and spent 11 years teaching in college classrooms. He wrote his dissertation on Ethics and the philosophy of Friedrich Nietzsche. On Camels With Hammers, the careful philosophy blog he writes for a popular audience, Dan argues for atheism and develops a humanistic ethical theory he calls “Empowerment Ethics”. Dan also teaches affordable, non-matriculated, video-conferencing philosophy classes on ethics, Nietzsche, historical philosophy, and philosophy for atheists that anyone around the world can sign up for. (You can learn more about Dan’s online classes here.) Dan is an APPA  (American Philosophical Practitioners Association) certified philosophical counselor who offers philosophical advice services to help people work through the philosophical aspects of their practical problems or to work out their views on philosophical issues. (You can read examples of Dan’s advice here.) Through his blogging, his online teaching, and his philosophical advice services each, Dan specializes in helping people who have recently left a religious tradition work out their constructive answers to questions of ethics, metaphysics, the meaning of life, etc. as part of their process of radical worldview change.

  • had3

    3 things: 1) is “more perfect” as much more perfect as “infinity plus one” is more than infinity? 2) why is reality presumed superior to imaginary? And 3) if no 2 people can agree on the characteristics that a perfect being would have, as it is subjective, wouldn’t this require and prove there’s a god for each individual?

  • Physicalist

    Here’s my preferred ontological argument:

    1. It’s possible that god doesn’t exist.
    2. By definition, god is a necessary being.
    3. Therefore, god does not actually exist.

    • pngwn

      Point 1, although I believe in it, you did not prove it.

      Point 2 comes down to, by definition, god must exist, if he exists. It is a pointless statement.

      This makes conclusion 3 invalid.

      Notice that I could apply your logic to any concrete being. It is possible that you do not exist (you have not proven otherwise). By definition, you must exist. Therefore you do not exist.

      Bravo sir, you have made a circular and contradicting argument. That takes some skill.

    • sqlrob

      Why does he need to prove point 1? It’s a statement of probability, not of fact.

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      If it’s a statement of probability and not fact, then it can’t be used to contradict the idea that God must be a necessary being and so must exist. It has to be REALLY possible that God does not exist, not possible that God does not exist based on our current knowledge of the world; it cannot merely be the case that there might not be such an agent as far as we know, but really the case that such an agent might not exist.

  • http://www.russellturpin.com/ Russell

    What I want to know is where the maximally perfect island lies. The ontological argument shows it exists!

    Speaking as the token nominalist here, what I object to is not every thought that might be labelled “metaphysics,” but to arguments based on suspicious rhetoric. Take any property at all, say, the quality of “being a female who speaks fluent Swedish, Nahuatl, and Arabic, and is the spitting image of Ernest Hemingway when he was living in Cuba.” Let’s call this property P, and pretend it defines an order Q over both real and imaginary people. Now, define the ordering Q’ where Q’ is identical to Q if the two people compared either are both imaginary or both exist, but Q’ ranks higher anyone who exists than anyone imaginary. Now, define the property perfect-P, which applies to the x that is maximal on the relationship Q. Lo! By the ontological argument above, somewhere there is a woman who is perfectly fluent in the three languages named, and who is the spitting image of Ernest Hemingway.

    And I can prove this from my armchair.

    • http://www.facebook.com/profile.php?id=1127827774 neleabels

      And I can prove this from my armchair.

      Sir, I envy you! I am obviously in the wrong business, actually having to go out and do some this-world work to get my results. :)

  • Pierce R. Butler

    The property of being maximally perfect…

    … is close to maximal undefinedness; hence, asymptotically approaches maximal meaninglessness.

    … consistency is possible existence.

    Only by the narrow logic of reversing “not-consistent = impossible”. No doubt philosophizers have a word for such nimble sleight-of-brains; being less precise, I’m forced to call it sophomoric sophistry.

    By this argument, the Harry Potter books are of much higher probability than, say, the Judeo-Xian bible; and Faulkner’s Yoknapatawpha stories would qualify as hard historical reality.

    For any possible objects x and y, if x is actual and y is merely possible, then x is more perfect than y.

    That non-definition of “perfect” just did another Olympic-class backwards somersault, while simultaneously cramming its head up its own rectum. That’s why this sort of competition never gets on tv, kids.

    But that is a contradiction. (7) Consequently, the MPB is also an actual object.

    Now the non-definition of “actual” is competing to win, leaving mere reality eating dust and staring at “actual”‘s ass. But wait! Johnston’s space-warping it ahead by a lap with this “mathematical reality” gambit, rarely seen since Keats won a match by declaring “beauty = truth” to sweep the field about 16 decades ago.

    Stay turned for the exciting conclusion of the Magical Metaphysics Mega-Meet, after these important messages!

    • consciousness razor

      Stay turned for the exciting conclusion of the Magical Metaphysics Mega-Meet, after these important messages!

      Damn, I was sure this was just a commercial, seeing him peddle all of that bullshit. I’m not even going to bother fast-forwarding through the rest.

  • Adam

    I like metaphysics, and I actually like a few of the arguments for God. They are wrong, but I like what we can learn from how exactly they fail to prove what they purport to. The ontological argument, for instance, fails because existence is not a real predicate. After all of the argument and debate, I feel we gain something by figuring this out. And looking at the Kalam cosmological argument allows us to note that there was no time prior to the universe, and that predicates satisfied by everything in the universe (e.g. “has a cause,” though the applicability of that predicate to everything in the universe is rather dubious to begin with) do not necessarily apply to the universe as a whole (since the universe is not a member of that class).

    There is of course a lot more to it, too.

  • grung0r

    Eric:

    When you say things like: “First, agree with the theist that the Ontological Argument is a sound argument…”, are you endorsing that premise, or is this just a statement regarding lying about one’s belief’s strategically?

    • http://freethoughtblogs.com/camelswithhammers Daniel Fincke

      There is a third option—you can grant the premises of your opponent and show that on their own terms they should conclude atheism. Even if you do not yourself share their premises and might want to dispute them another time, you can at least argue on their own terms in the way Eric describes.

      I tend to suspect though that Eric does accept the premises and the conclusions drawn from it above but then I’m confused by the impression he gives that the maximally perfect being can be argued to be numerous different beings. I’m curious if he thinks a case can be made for any one of them or if the point is that as long as there are numerous obviously greater beings than the theistic god that that’s all the atheist has to prove.

    • grung0r

      you can grant the premises of your opponent and show that on their own terms they should conclude atheism.

      That’s true. But in such cases, I would expect such an statement to be prefaced with a “for the sake of argument” or something else along those lines. If such a preface is lacking, it seems to me that it implies an agreement with the premises up to whatever point is in dispute, which is dishonest, if one does not agree that the previous premises are sound.

    • http://freethoughtblogs.com/camelswithhammers Daniel Fincke

      Sure. But I think Eric is laying out the logic for either case—both for those who accept the premises and those who will merely grant them for the sake of argument. (Hence his ambiguity.)

    • grung0r

      Eric isn’t just asking us to grant the premises of the ontological argument for the sake of argument, he’s asking us to grant his conclusion too:the Immanent ultimate creative power of being in place of god. This is not like Bertrand Russel or the countless other atheists who have pointed out that all philosophical arguments for God are not arguments for a specific god, but just arguments for Deism, pantheism or panpsychism. This is someone ambiguously stating the logic behind an argument who’s conclusion he believes to be true and has a stake in proving. To refuse to state if he thinks the premises of the ontological argument are true allows him to further his agenda is establishing the Immanent ultimate creative power of being while not having to defend the well known and debunked argument itself. It’s dishonest, plain and simple, and the fact that he could clear it up in 5 seconds, yet hasn’t, demonstrates this fact far beyond my power to.

    • http://www.ericsteinhart.com Eric Steinhart

      There’s no harm in going along with the arguments up until the last step, which is where “God” enters the picture. So, for this arg, it’s fine to agree with steps (1-7). It’s step (8) that’s troublesome for the atheist.

      One point is that theists get a free pass on these arguments – atheists agree that if the arguments work, then they prove God. So my point is much stronger against theism than most atheists. I say that even if the arguments work, they don’t prove God. They prove something else.

    • grung0r

      There’s no harm in going along with the arguments up until the last step, which is where “God” enters the picture. So, for this arg, it’s fine to agree with steps (1-7).

      Wrong. Gaunilo, Hume, Kant, etc. all debunk the ontological argument without really referencing god. Gaunilo’s maximally perfect island for instance specificity shows that the unsoundness of the this argument once god(and thus people’s emotional wish for his existence to be proved) is removed.I don’t see how you argument escapes this or the other famous critiques of the ontological argument. So yes, there is harm in going along with these arguments, at least if one wishes to remain intellectually honest.

      I’ll ask again: Do you agree with the with the premise of the ontological argument, or are you suggesting strategic lying?

  • http://www.ericsteinhart.com Eric Steinhart

    Outside of pure math, most arguments are only shades of gray.

    • http://www.legionofreason.com/ HJ Hornbeck

      The Ontological argument is pure logic, and math and logic are the same beast. Where the fuzziness creeps in is via sloppy definitions and unsound or incomplete thinking.

      This argument isn’t my favorite demonstration, but it’ll do. It claims that existence is better than non-existence, but I can think of one obvious exception. Ask most artists which version of their art is better, and the majority will claim the version within their heads beats out the physical product. In crafting the final work, compromises of time, energy and physics had to be made; in their heads, no such compromise is needed, and in fact they can invent or change the entire work at will.

      Adam and others (hat tip: Kant) have pointed out that existence is a-posteriori to existence and cannot be treated as an arbitrarily-assigned attribute. Only the deities seem to arrive in our mind as if by magic; kittens, kites, and karts have to be sensed or explained first before existence can be granted to them. And yet, no person has started babbling about Jesus before someone else talked about it in their prescence. Even Descartes’s God feelings came long after he’d been first exposed to the idea. This suggests the “magic” trick is nothing more than post-hoc rationalization. Further evidence is how the deity being felt so nicely aligns with assertions about that deity made by others.

      I don’t reject the classical arguments because they are “bad,” I reject them because on examination I discovered they were unsound.

      HJ Hornbeck

    • Steve Schuler

      This argument isn’t my favorite demonstration, but it’ll do. It claims that existence is better than non-existence, but I can think of one obvious exception. Ask most artists which version of their art is better, and the majority will claim the version within their heads beats out the physical product. In crafting the final work, compromises of time, energy and physics had to be made; in their heads, no such compromise is needed, and in fact they can invent or change the entire work at will.

      Works for me, Dude! That is entirely consistent with my experience with any number of imagined outcomes as compared to the realized results. However, I’ve never been accused of being particularly philosophically sophisticated, so I may still be ‘missing the boat’.

    • http://www.facebook.com/profile.php?id=1127827774 neleabels

      BTW, I do not hate metaphysics. The discipline has its place in the history of human thought and in the past it may very well have served its purpose in the ongoing developement of human understanding. But time has stepped over this branch of philosophy (and perhaps over philosophy in general) and it is as outdated and antiquated as humoralism, ether-science, or the “great chain of being” of early modern times.

      Generally, metaphysics could perhaps serve as an entertaining exercise of mind, perhaps a bit like sudoku. At best, it could perhaps be taken as some kind of language art. If in all seriousness considered as a viable approach to enhance the body of human knowledge, it’s a lamentable waste of resources and money.

      Eric: Outside of pure math, most arguments are only shades of gray.

      If meant seriously, this statement would be an act of intellectual self-castration. But I take it more as resignated gesture that you are ready to leave behind the clash with reality, which you have suffered in this comment section, and are going to pump a fresh load of empty phrases into the poor blogosphere?

      Ah, I see you have already done that…

  • NewEnglandBob

    Assume that the Ontological Argument is sound through step (7)…

    I don’t even agree that step one is sound. Nothing can be perfect. We are done here.

  • danielrudolph

    I can see doing this with the cosmological argument, which is mostly valid, but fuzzes some definitions and has one sketchy premise. The Ontological argument is just a bad argument. People don’t say it’s a bad argument because they don’t like what it’s arguing for. They say it’s a bad argument because it hinges on the idea that existence is better than existence, which makes no sense. Trying to use it to argue for a conclusion one agrees with doesn’t make it any more sound.

  • http://stochasticscientist.blogspot.com kathyo

    I’m not sure I see the point of conceding anything. Yes, the theist cannot connect the MPB with God, but neither can he prove that existence is more perfect than nonexistence. As HJ Hornbeck notes, the image in my mind may very well be more perfect than the one I put on paper (especially since I can’t draw). The ontological argument is trying to make the case that nonexistence is a flaw. I think unicorns would disagree.

  • http://www.facebook.com/profile.php?id=1127827774 neleabels

    Eric: (1) The property of being maximally perfect does not entail any contradiction.

    Another problem with the ontological argument is the assumption that something like absolute perfectness actually does exist. The thought implies some universal scale of degrees with the “property of being maximally perfect” at its upper end. But this is not true – the state of being perfect is not absolute but relative. The property of being maximally perfect is only thinkable with two points of reference. First, the object it describes, second, the understanding of the human being applying the term. A trivial example is the question “what is the perfect sausage?” A perfectly fried pork sausage may be the answer for many Germans, the overwhelming majority of Muslims and Jews would kindly disagree. A less trivial example: “what is perfect beauty?” Taking the term “perfect” out of a context simply renders it meaninglesss.

    The property of being maximally perfect obviously does not entail an absolute hierarchy but must be regarded as a dynamic denotation used in specific contexts which may very well entail a contradiction. Since the whole ontological argument is based on a faulty absolute understanding of the concept, it is already flawed in step one. HJ Hornbeck says that this makes the argument unsound but not bad. I disagree, an unsound argument does not fulfil its discoursive purpose and an argument that does not work, is a bad argument. I see no difference.

    David: There is a third option—you can grant the premises of your opponent and show that on their own terms they should conclude atheism. Even if you do not yourself share their premises and might want to dispute them another time, you can at least argue on their own terms in the way Eric describes.

    I don’t agree. Some other commentator has pointed out that the ontological argument itself has been disproved several times by philosophers. But if not only the premises but also the method of inquiry is flawed, then there is no reason to repeat the faulty exercise just to arrive at a different result which is as meaningless as the first result because it was achieved in the same faulty way. Why should anybody waste time on this? There is no reason in wasting time and energy by going through useless motions.

    But on a related yet slightly different topic: have you two guys ever heard about the thing called the “linguistic turn”? Just wondering…

    • John Morales

      Ahem.

      Perhaps Eric refers to arguendo, no?

    • http://www.facebook.com/profile.php?id=1127827774 neleabels

      I don’t think so. Judging from his articles so far, Eric has got a pretty prefixed expectation of the positive results of his argument. I don’t see any indication of tentative exploration from his side.

  • csrster

    “The property of being maximally perfect does not entail any contradiction.”

    … or any meaning. Is “perfection” objectively defined? measurable? comparable? well-ordered?

    I have two mobile phones on my desk right now. Which one of them is closer to maximal perfection? How would even go about answering that question?

  • http://marniemaclean.com Marnie

    Many atheists seem to hate all metaphysics; perhaps the hatred is motivated by the notion that all metaphysics eventually leads to God.

    I don’t hate metaphysics, but I reject arguments (metaphysical or otherwise) that start with faulty logic.

    Any atheism that embraces rigorous metaphysical thinking is far more powerful than an atheism that rejects metaphysics.

    I can no more decide to embrace a metaphysical view than I can decide to embrace a sincere belief in Vishnu. I need to be convinced of it.

    Rather than engage in the tired back-and-forth about whether the arguments are good or not, atheists can just agree that the arguments prove the existence of something that is not God. That’s a much, much harder strategy for theists to defeat.

    If an argument is unsound, it is unsound. It is a tired argument because it’s an obvious fallacy. That doesn’t mean one cannot come to a similar argument to the one you’ve stated. Most atheists, regardless of their view on metaphysics, point out exactly that specific argument. Even if the theist were right and the argument were sound, we sat, “that doesn’t prove your god.” We can have it both ways, we can understand their argument, see the fallacy and still make the same argument that the atheist who embraces metaphysics does.

    But of course, the real problem is that we are playing semantic games here. What is “perfect”? By what standard? For whom? And how do we determine what it is? It actually makes the entire ontological argument faulty from the start if you can’t even determine what this means:

    (1) The property of being maximally perfect does not entail any contradiction. It is therefore consistent. But consistency is possible existence. So it is possible that there exists some x such that x is maximally perfect. Let us refer to this x as the Maximally Perfect Being (MPB). The MPB is a possible object. It possibly exists.

    We cannot determine if there is a contradiction if we don’t yet know what we mean by “perfect”. We are at a dead stop from the first sentence.

    So I go back to my previous point. Someone can reject the ontological argument as faulty logic but still point out that even if true, the argument does not prove the believer’s assertion. I don’t have to believe there can be a perfect being to see how the argument can be misinterpreted.

  • http://qpr.ca/blogs/ Alan Cooper

    If *every* step in an argument is completely meaningless BS, why should we pretend to agree with all but the last in order to deny the conclusion?

    I would start at the beginning with “The property of being maximally perfect does not entail any contradiction.” and ask WTF does *that* mean?

    Maybe the translation from Latin is poor, but in English “perfect” is an absolute condition representing a (usually non-existent) extreme of some value. So even with just one value variable the phrase “maximally perfect” implies the existence of different suprema for the same real variable which *is* a contradiction. Or on the other hand there may be many equally valuable but mutually incompatible characteristics such that the perfections of each are mutually non comparable. If after 2000 more years of chewing it over we can finally make sense of that silly sentence, only *then* may it finally be time to move on to the second half of your step1.

  • csrster

    Exam Question:
    “Does there exist a maximally poor argument for the existence of God and, if so, what are the chances that it has ever been seriously proposed by a professional theologian? “

  • The Vicar

    Sorry for the late follow-up to this post — I actually had trouble finding it after so many days; thankfully Planet Atheism has a good search function — but I was looking for a fault in the logic without looking up a solution, and without reading through every single comment above (I read a bunch of them), I think I found one you haven’t seen yet — a reductio ad absurdum.

    1. If this argument is true, then god is the greatest possible thing, greater than any real or imaginary being.
    2. It is demonstrably possible to imagine a being greater than god. (“The tentacular demon Vlorflax, who conquered the universe one thousand years ago using his unlimited diabolic abilities to neutralize god, enslaved the inhabitants of heaven, and uses god’s bones to pick the teeth of his many ravening maws.”)
    3. By (1), god is greater than the being imagined in (2), which is a contradiction. Therefore one of the axioms in this argument is false. Since (2) is demonstrable, (1) must be false, which means that the original argument is false.

    I came up with this because the form of the argument brought to mind the arguments involving the unlimited abstraction principle.

    (For non-mathematics-aware readers: the unlimited abstraction principle is a rejected axiom in set theory, which basically says that if you name a property, you have defined a set of all the things which have that property. “Blue” conjures up “the set of all things which are blue”, for example. This axiom leads to paradox — “set which is not a member of itself” leads to “the set of all sets which are not members of themselves”, which must be a member of itself and therefore must not be a member of itself. Unlimited abstraction was basically replaced by the much more cautious “if you have a set and a property, then you can define the subset of the original set which contains all the elements which have that property”, which prevents this particular paradox from happening.)

    Once I saw that connection, I realized that Anselm requires not only that “the set of all things which it is possible to imagine” be well-ordered, but that it have a maximum (named “god”). If you look at it that way, constructing a contradiction is fairly easy.

    Besides which: this argument relies on there being an abstracted set of “everything it is possible to imagine”. Since humans have already thought of “the set of all sets which are not members of themselves”, once you bring in “anything it is possible to imagine” you have automatically roped in a contradiction and therefore your proof is not logically valid.

    Yet another example of how actual math and logic is too hard for theologists, so they should avoid trying to borrow terms from them. (Remember, the word “dunce” comes from the name of a theologist who thought he was teaching logic.)

  • http://www.ericsteinhart.com Eric Steinhart

    This isn’t an argument for god, it’s an argument against god.

    But that hardly matters.

    Suppose X is the greatest possible thing.

    To imagine something greater than X is to imagine something greater than the greatest possible thing, which is impossible.

    You can’t imagine anything greater than X.

  • The Vicar

    Certainly you can — provided the thing greater than X is imaginary. To claim that there is a greatest possible thing of any type ever anywhere cross-your-heart-and-kiss-your-elbow no-takebacks and without exception requires the unlimited abstraction principle, which cannot be assumed without inserting paradox and therefore rendering the proof invalid. The only thing you can do without causing this invalidity is to say “of the things we know exist, there is some greatest thing” (which requires a solid definition of “greatest”, by the way). Since we don’t know god exists, the proof then falls apart.

    But part of the constructive element of the original argument requires a blurring between things which can be imagined and things which have real existence — a trick which has been used for at least one other “proof” of god’s existence. (The “proof” runs like this: “you claim not to believe in god, and yet you ascribe attributes to god. Non-real things don’t have attributes so therefore you are implicitly admitting god exists!” You’d think this proof was so childish that nobody would ever seriously use it, yet I have seen priests pull it out as though they were being clever. This, of course, means that the million dollars I lent you in a black briefcase must also exist, because otherwise the briefcase couldn’t be black and there couldn’t be a precise amount, so you must repay me that million dollars right now or I’ll call the police. :P )

  • The Vicar

    Oh, in case it wasn’t totally obvious: my arguments are intended against the argument for the existence of god, although they will work just as well against an argument against the existence of god which also relies on unlimited abstraction.

    Set theory is (sort of) to mathematics what quantum theory is to physics; you can’t understand the nitty-gritty small stuff without it (the natural numbers are formally defined through set theory these days), and yet it is full of traps for the unwary and surprising odd results. The unlimited abstraction principle seems so intuitively obvious to us that it is very difficult to let go of it, but logic dictates that we must do so if we want mathematics which work. (In fact, from what I recall of the histories I have read, when the problems arising from it were first discovered, mathematicians were at a loss because they had not consciously realized that they were assuming the unlimited abstraction principle in the first place. They had to sit down and reason out that they had assumed it from the nature of the problems.)

  • http://www.ericsteinhart.com Eric Steinhart

    I use Von Neumann – Godel – Bernays class theory, so, yeah, there are lots of maximal objects. They’re called proper classes. Like the proper class of all sets and the proper class of all ordinals, and on and on. And, using class theory, I’ve got no troubles at all with unlimited comprehension principles. None of which are at all relevant here. And no, you can’t imagine anything greater than that than which no greater is possible. Unless you’re imagining something impossible, which doesn’t exist, and, therefore, can’t be imagined. But hey, if you want to read my published books or papers on formal logic and set theory, you can find them.

  • The Vicar

    I use Von Neumann – Godel – Bernays class theory, so, yeah, there are lots of maximal objects. They’re called proper classes. Like the proper class of all sets and the proper class of all ordinals, and on and on. And, using class theory, I’ve got no troubles at all with unlimited comprehension principles. None of which are at all relevant here. And no, you can’t imagine anything greater than that than which no greater is possible. Unless you’re imagining something impossible, which doesn’t exist, and, therefore, can’t be imagined. But hey, if you want to read my published books or papers on formal logic and set theory, you can find them.

    Yes, you can imagine something greater than that which no greater is possible. To take an example: suppose we take the set of real numbers from 0 to 1, inclusive; there is no number larger than 1 in that set. But if I say something like “the number in that set which has a magnitude larger than one” your imagination will not be able to resist metaphorically whipping out a crowbar, inserting it just below the upper limit, opening a space up, and wedging in a number (carefully muffled in wisps of imaginary cotton so you can’t actually see what it is), no matter how much your reason protests. You did it just now while reading that sentence. Anselm’s ontological proof of the existence of god fails more or less because it insists that sets derived from imagination are closely defined and can be lined up with objects in the real world.

    Or at least, you can do this if you actually have an imagination. Saying “this can’t exist so you can’t imagine it” is a ridiculous misunderstanding of what “imagination” means, and almost suggests that you don’t have one — magic can’t exist, to give an example, but people routinely imagine magic in such detail that they write entire series of novels about it, some of them tedious enough that even an insufferable pedant might appreciate them. (And now you’re imagining that I have called you an insufferable pedant, even though I never did. You have now noticed the way your tongue fills your mouth, too — when you read, your mind is not your own.)

    As for class theory: the axioms of class theory (as opposed to mere set theory) are not suited for theological proof of the sort aimed at by Anselm. If you were to explain class theory to Anselm (which you would presumably have to do slowly, and using small words) (a process which would be, of course, impossible because Anselm lived in the 11th century and is long since dead and in any event wouldn’t speak modern English; yet once again I suspect you have imagined this impossible thing merely by reading it), he would refuse to use it and insist on set theory, insofar as he would want to use mathematical language at all.

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  • Contrarian

    Any classical argument for god’s existence falls into one of two classes: either it is (1) incoherent or ill-posed, or (2) it proves the existence of something that everybody accepts to exist, not the existence of a deistic, let alone theistic, god.

    In the post, it’s not clear that the ontological argument is well-posed; what does “perfect” mean? Does it totally order all things which can be imagined? It is further not clear that existence is more perfect than nonexistence. But if one makes these ideas precise (I wish Eric had done so) without introducing a contradiction, one must arrive at a correct argument.

    That correct argument yields the existence of something which is maximally perfect and necessarily exists. In this case, the strategy suggested is, I think, quite correct — one cannot dispute the unsoundness of, e.g., Godel’s ontological argument, because it is sound! Then the ontological argument proves the existence of something like modal logic (what is necessarily true in every universe which is logically consistent?).


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