Considering the Ontological Argument

Like Bertrand Russell, I have always kind of felt that, while I can’t directly refute Anselm’s famous ontological argument for the existence of God, I am also not convinced by it.  It feels to me like I am being subtly manipulated with words.

Nevertheless, I find the God that the ontological argument leads to, i.e., one who is not any greater even with all of creation added to it, very appealing for much work in theology because it keeps God out of the system of “things.”

I would like to state this as a resolution to be discussed, because I’d like to know how others think and feel about this:

Resolved:  Anselm’s ontological argument is inadequate as proof of God’s existence, but helpful in understanding just what we mean by the word “God.”

Discuss.

About Brett Salkeld
  • LM

    I don’t think that the ontological argument tells us anything about God at all. It merely tells us that God exists and is the greatest thing that can be conceived of. Living in a Christian super-majority country, we assume that the God in question must be the Christian version of God but there’s no reason why it couldn’t be Brahama, Amun-Ra, Zeus, Odin, Amaterasu or any number of divine beings that are considered the top deity in their respective cultures, all of whom have very different attributes.

  • HopefullyHopeless

    I think the ontological argument boils down to: if God exists, then He certainly does.

  • Melody

    Could you briefly summarize Anselm’s ontologicial argument for those of us not familiar with it?

    • David Cruz-Uribe, SFO

      From Wikipedia, a summary of the argument in Chapters 2 and 3 of the Prologion

      Anselm’s argument in Chapter 2 can be summarized as follows:

      It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).

      God exists as an idea in the mind.

      A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.

      Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).

      But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)

      Therefore, God exists.

      In Chapter 3, Anselm presented a further argument in the same vein:

      By definition, God is a being than which none greater can be imagined.

      A being that necessarily exists in reality is greater than a being that does not necessarily exist.

      Thus, by definition, if God exists as an idea in the mind but does not necessarily exist in reality, then we can imagine something that is greater than God.

      But we cannot imagine something that is greater than God.

      Thus, if God exists in the mind as an idea, then God necessarily exists in reality.

      God exists in the mind as an idea.

      Therefore, God necessarily exists in reality.

      • Opie

        Yeah it doesn’t really tell us much. Of course the greatest thing imaginable must be imagined AS existing. That doesn’t mean it actually does. It just means that IF a “greatest possible being” existed…it would exist. Tautology. It doesn’t prove that the greatest possible being is the greatest actual being. There may be unrealized possibilities that would be greater than anything that exists IF they existed, and we know this when we imagine them existing, but they still don’t really exist.

        The fastest possible car must be imagined as existing, because if it’s imagined as not existing, if it’s merely an “idea of an idea”…well, ideas have no speed. Doesn’t mean the fastest possible car imaginable exists. Just that when we posit it as “fastest possible” we are saying IF it existed, that existence is a condition of the hypotheticals “possibility” describes.

        So does it tell us anything about God? I don’t know. What it does lay out is something like the relationship between mind and existence, which is to say: that when we imagine something, we are imagining it existing. That when we posit something as “possible,” we are referencing (counterfactually) the world of the actual and not some other plane or category.

        So I guess it reveals that Being itself is the basic or foundational category of thought. But…didn’t we already know that?

  • Melody

    Sorry, that should be ontological. That’s what happens when I try to type on a Kindle.

  • Jack Hartjes

    I like your thought that adding the idea of all creation to the idea of God doesn’t make the idea of God any greater. But I’m inclined to think we’re not really getting any closer to understanding God. After all, what do we mean by “great”? Jesus says the least in the Kingdom of Heaven is greater than John the Baptist. Could God’s greatness be like the greatness of the least of us? Could the word “great” be misleading us?

  • http://gravatar.com/tausign Tausign

    I agree with your proposition. It seems that the argument simply shows that the existence of God is consistent with logic or not illogical. But at any rate, a ‘proof’ that relies on ‘what the mind can comprehend’ is inadequate for what is acknowledged (a priori) to be ‘beyond our comprehension’. For this we rely on what must remain a mystery…namely ‘the gift of faith’.

  • David Cruz-Uribe, SFO

    I think that Anselm’s argument does not prove the existence of God and I am really not sure that it tells us a lot about the nature of God as well. The problem is that Anselm, like other medieval theologians, has a hard time dealing with the infinite and the argument seems to implicitly rejecting the notion of an infinite progression.

    The problem is what does “greater than” mean in this context? And once we define this, what does this really tell us about God?

    • Opie

      Well what it seems to reveal is that existence is essential to any other evaluation. You can have a possibility with every possible perfection, but if it doesn’t have Being, if the possibility doesn’t have actuality, it’s less valuable than even the most imperfect Real thing. Existence is the foundation of every other ranking or evaluation. If a possibility doesn’t have actuality…who cares what else it has?

      So it tells us that when considering God…what matters (or would matter) most is that He exists. Being almighty or omniscient or eternal are less important than Being, because without existence they’d be worthless.

      This isn’t just true for God but for everyone and everything: what matters most is that they ARE. We can resent a broken lamp and imagine its unbroken hypothetical counterpart in an alternate history. But that lamp isn’t, and the broken lamp IS. So the non-existent lamp has less value than ours (however broken) so why are we devaluing something that at least exists while coveting something that literally has no value because it has no Being?

      • David Cruz-Uribe, SFO

        “If a possibility doesn’t have actuality…who cares what else it has?”

        Do unicorns exist? And if not, should I care whether a fantasy author declares that the six-legged, purple reptilian creatures in his novel are unicorns because they have a horn in the middle of their forehead?

        A silly argument I realize, but my point is that things which may not exist can still have relevance if not importance. So existence, as a predicate, is important, but I don’t think it is quite as fundamental as you make it out to be.

  • http://www.scribd.com/johnboy_philothea Johnboy

    This reminds me of Charles Sanders Peirce’s distinction between the formulation of an argument and argumentation, the latter which he considered a fetish where so-called proofs of God are concerned. Peirce formulated what he called the Neglected Argument for the Reality of God, very mindfully employing “reality” rather than some other root metaphor, like being.

    It has always seemed to me that the formulation of various God arguments are philosophically indispensable, precisely to establish the logical consistency and internal coherence of our God-concepts, themselves. They thus demonstrate how eminently reasonable a belief in God can be, that the reality of God is modally possible.

    Over against, for example, the problems posed by evil, it’s no longer controversial, even among those who primarily traffic in atheological critiques, to hold that, sufficiently nuanced, certain God concepts are not incompatible with the reality of evil. The possibility of God has, indeed, been established in several modal logics.

    What we have accomplished in all of this, philosophically, is a great deal of dutiful disambiguation and rigorous definition of our God-concepts, precisely, clarifying what we mean by “God.”

    What we cannot do, methodologically, is also demonstrate that such arguments are logically sound, because, lacking probabilistic access, we cannot establish whether or not our God-concepts successfully refer, much less describe, the Reality of God.

    It is precisely for this reason that atheological critiques have largely abandoned the so-called logical problem of evil and fallen back to a weaker position to argue an evidential problem of evil. While there are indeed evidential problems, atheologians cannot probe the Reality of God in a robustly inferential way, limited as they are to the weakest of inferential modes, abductive inference, which, when endlessly cycled with deductive clarifications without the benefit of inductive probes, traffics in im/plausibilities not im/probabilities. The same weaknesses afflict most theodicies, which, in addition to being considered blasphemous by some are considered callous by many others in light of the enormity of human pain, the immensity of human suffering. Bravo, then, for Pope Francis who, asked why children suffer, said that the 12 year old, alone, had asked a question without an answer.

  • http://branemrys.blogspot.com Brandon Watson

    I suppose a question would partly be what’s meant by ‘inadequate as a proof’. There’s a fairly decent argument that it’s sound — no logical error and true premises — but that the premises are such that at least the most likely reason someone would affirm them is that they are theists already. And, indeed, one way of reading what Anselm actually says is not as an argument for why atheists should become theists but an argument clarifying to theists what atheists get wrong — it establishes God’s existence with a diagnostic aim rather than a persuasive one. The Proslogion, after all, is explicitly structured as a prayer, and it is from Christian practice of prayer that the description ‘that than which no greater can be conceived’ is originally derived. He never addresses the atheist, only God.

    The idea that the argument, at least as presented by Anselm, might not establish the existence of God but does say something about the divine nature has a long and respectable history, though; both Bonaventure and Scotus essentially take this view (although both of them also think that you can modify Anselm’s argument somewhat to get a viable argument for God’s existence).

  • http://www.scribd.com/johnboy_philothea Johnboy

    “Greater than which” is vague, fraught with
    implicit divine attributes. While we might retrieve Anselm’s implied attributes, we might also take a b.y.o.a. approach, bringing our own conceptions?

    This reminds me of Charles Sanders Peirce’s distinction between the formulation of an argument and argumentation, the latter which he considered a fetish where so-called proofs of God are concerned. Peirce formulated what he called the Neglected Argument for the Reality of God, very mindfully employing “reality” rather than some other root metaphor, like being.

     It has always seemed to me that the formulation of various God arguments are philosophically indispensable, precisely to establish the logical consistency and internal coherence of our God-concepts, themselves. They thus demonstrate how eminently reasonable a belief in God can be, that the reality of God is modally possible.

     Over against, for example, the problems posed by evil, it’s no longer controversial, even among those who primarily traffic in atheological critiques, to hold that, sufficiently nuanced, certain God concepts are not incompatible with the reality of evil. The possibility of God has, indeed, been established in several modal logics.

     What we have accomplished in all of this, philosophically, is a great deal of dutiful disambiguation and rigorous definition of our God-concepts, precisely, clarifying what we mean by “God.”

     What we cannot do, methodologically, is also demonstrate that such arguments are logically sound, because, lacking probabilistic access, we cannot establish whether or not our God-concepts successfully refer, much less describe, the Reality of God.

     It is precisely for this reason that atheological critiques have largely abandoned the so-called logical problem of evil and fallen back to a weaker position to argue an evidential problem of evil. While there are indeed evidential problems, atheologians cannot probe the Reality of God in a robustly inferential way, limited as they are to the weakest of inferential modes, abductive inference, which, when endlessly cycled with deductive clarifications without the benefit of inductive probes, traffics in im/plausibilities not im/probabilities. The same weaknesses afflict most theodicies, which, in addition to being considered blasphemous by some are considered callous by many others in light of the enormity of human pain, the immensity of human suffering. Bravo, then, for Pope Francis who, asked why children suffer, said that the 12 year old, alone, had asked a question without an answer.

  • Mark VA

    Anselm’s argument doesn’t grab me logically. As has been demonstrated, it can be applied to many things, for example, to the existence of “the greatest island”, and the results of such tests seem ambiguous.

    On a more humorous note, I like the (apocryphal) proof for the existence of God by Leonhard Euler, given to the philosophe Diderot:

    http://en.wikipedia.org/wiki/Leonhard_Euler#Personal_philosophy_and_religious_beliefs

    Perhaps there is something of substance to this story, since Diderot promptly left Russia afterward.

  • David Cruz-Uribe, SFO

    I want to return to the problem with Anselm’s argument where he talks about the greatest thing imaginable. I want to present a simple example from mathematics which shows how this idea is not as self-evident as it seems at first glance.

    I begin with a story told by Saunders Maclane, a great algebraist at the University of Chicago in the mid 20th century. A farmer, in order to attract attention to his farm stand, wants to paint the largest number possible on the side of his barn visible to the highway. So he gets a can of paint, puts a “1” in the upper left hand corner, and then proceeds to fill the rest of the side with row upon row of zeros. The first person to stop suggests that if he repaints it with smaller zeros, he can get even more on the barn, making it an even bigger number. So the farmer laboriously repaints his barn with zeros that were as small as he could make them with a paintbrush. The next person to stop was an engineer, and he explains exponential notation to the farmer. So the farmer deletes a few rows at the bottom and paints a 10 in the lower left hand corner, getting 10 raised to some immeasurably huge number. The next person to stop is a mathematician who explains towers of exponentials. So the farmer paints over his barn and paints 10^10^10^10…. rising from the lower left to upper right. The next person to stop is a logician. He thinks for a moment and writes a suggestion on a piece of paper, telling the farmer to copy it exactly. So the next day the farmer repaints the side of the barn to say “One more than the largest number that can appear on the side of this barn.”

    This gives the key to showing that at least in the sense of sets, it is always possible to create a “greater” set, in the sense of proper inclusion. Given any set E, form a new set F which consists of all the elements of E and the set E itself. F is greater than E since it contains everything which is in E, but also something which is not in E. One could try to construct a set E, a universal set, which contains itself as an element of itself. However this quickly leads to paradoxes in standard ZFC set theory (Russell’s paradox), and so no such universal set can exist. (One can try to create more general objects called “classes” but I am going to stick with classical set theory.)

    One could argue that F is “bigger” but not “greater” since E and F are still the same size—if E is an infinite set, then everything in F can be but into a one-to-one correspondence with everything in E. (To see how, google Hilbert’s hotel.) However, by a different construction, we can construct a new set, G, called the power set of E, that is strictly bigger in the sense that you cannot use the elements of E to count the elements of G. Let G be the set whose elements are the subsets of E. To show this is bigger than E, you need to use the Cantor diagonalization argument. So this gives a set “greater” than E. And clearly this process can be repeated indefinitely, creating an infinite tower of sets, each “greater” than the previous one.

    So at least in the sandbox of ZFC set theory, one cannot conceive of a “greatest” set. We could pass to the universe of all sets constructed in this way (via transfinite induction) but I imagine that given any universe, one could construct yet another one “greater” than it in some way.

    This does not disprove Anselm’s argument, but it does call into question one of his preconceived notions, that “the greatest possible thing we can imagine” is a meaningful statement.

    • http://branemrys.blogspot.com Brandon Watson

      Well, in fairness, Anselm’s actual concept is “that than which a greater cannot be conceived”, and he would be stickler that it is this, and only this, that is in view. For instance, one of his key claims — namely, that-than-which-no-greater-can-be-conceived is necessarily greater than we can conceive — doesn’t follow from ‘greatest thing conceivable’; the two are not synonymous. It comes up in the Reply to Gaunilo, and Anselm firmly rejects any commitment to an argument using the latter.

      • David Cruz-Uribe, SFO

        Thanks for this clarification: I was being a bit sloppy, which is incredibly dangerous in these kinds of arguments. However, I think my example is still relevant as a cautionary note.

  • http://www.scribd.com/johnboy_philothea Johnboy

    I appreciate Christopher McHugh’s modal ontological argument:

    http://infidels.org/library/modern/doug_krueger/krueger-mchugh/mchugh1.html

    Rather than “greater than” one employs the concepts of deficiency and perfection. Rather than kataphatic and analogical predications, which are subject to parody and other inconsistencies, one uses apophatic predications, like nondeficient.

    • http://www.scribd.com/johnboy_philothea Johnboy

      I also found it curious that Kurt Godel authored both his Incompleteness Theorems, which Hawking recently came to realize and Stanley Jaki realized decades ago, suggest Theories of Everything cannot be proved within closed symbol systems (like math and formal syllogistic logic), and a Modal Ontological Argument for God.

      Of course, Godel, better than most, understood that one could, indeed, write down a sound argument, nevertheless. One just wouldn’t know it was true via a formal proof. That always evokes for me the sentiment: “Taste and see …” For example, one would have to travel with Russell and Whitehead halfway through the Principia to arrive at a proof of the axioms for 2+2=4. Or one could simply, as I do, SEE that it is true and TASTE whether or not apples and/or oranges are being counted. Hawking, for his part, at least asked where the “fire” might come from in his equations.

      So, the practical takeaway from Godel’s Theorems is not that we might not one day SEE the truth of our syllogisms, only that we cannot formally prove their soundness. I like to imagine that one day we may indeed stumble over a Theory of Everything but that it’s axioms will be as uninteresting to me as those which prove 2+2=4. I often wonder if I’ve similarly seen a sound God Argument and tasted its truth, beauty, goodness, love and freedom in Jesus of Nazareth.

  • http://turmarion.wordpress.com turmarion

    I go back and forth on Anselm. Sometimes the ontological proof seems to me to have a certain amount of profundity, and sometimes it seems totally cracked. It does serve to distinguish God, properly so-called, from gods or any other god. This is where a lot of atheists err–the old saw is that the atheist tells the believer that neither of them believes in Zeus or Astarte or Shiva or Isis; the atheist just believes in one fewer god (i.e. the Judeo-Christian God) than the theist. Thing is, though, that the One God of Judaism, Christianity, Islam, and so on is not just a quasi-anthropomorphic deity like any of those named. As St. John of the Cross pointed out, He is not even a being (as we conceive that) among beings, but “nada”–nothing, or better, “no thing”. The Abrahamic God is more like the Hindu notion of Brahman or the Neoplatonic En (“The One”), that is, the source of all being. In this regard, Anselm firmly establishes that God is not a “sky fairy” (as some anti-theists say) or one among many other possible gods, but the absolute.

    Whether that establishes His existence is another matter. He seems, as Kant argued, to make “existence” a property, which seems dubious. It’s also unclear that one can go from definitions to actual reality as Anselm tries to do.

    FWIW, in his excellent book Infinity and the Mind, Rudy Rucker argues for an ultimate infinity beyond all other infinities (I think he goes outside of ZFC, but it’s been awhile since I’ve read it), using the term that Cantor used, Ω (omega). Also, for those who are interested, the great Kurt Gödel produced his own version of the ontological proof. I’m not sure it works for him, either, but it’s more rigorous than Anselm’s, and has a lot more cool mathematical notation!

    • David Cruz-Uribe, SFO

      I think you are right and this gets back to Brett’s original post: Anselm’s proof does not tells us positively about the nature of God, but it makes clear what God is not.

      I had not seen Godel’s proof of the existence of God: thanks for the reference. Heavy duty logic going on there, all of it in a realm beyond ZFC—the sandbox where, as a practicing mathematician, I prefer to spend my days.

      • http://www.scribd.com/johnboy_philothea Johnboy

        I think you are right and this gets back to Brett’s original post: Anselm’s proof does not tells us positively about the nature of God, but it makes clear what God is not. <<<

        That sounds right. Anselm did a good job of formalizing an intuition, anticipating, if only inchoately, modern modal logics. But "greater than which" remains a fraught conceptualization, implicitly and vaguely incorporating popularly understood divine attributes. It invites exploration toward the end of helping us demonstrate the logical validity of faith's philosophical preambles and the coherency of our god-talk, over against the facile atheological critiques of our time, which unnecessarily, but with great efficacy, scandalize so many young believers.

        We tend to extremes of all or nothing and either-or in formulating arguments. There are no a priori grounds for privileging one root metaphor (metaphysic) or another, or for predicating one attribute or the next as analogical, univocal, equivocal, kataphatic or apophatic. Instead, I like to imagine that, not all the divine attributes would be 1) analogical, otherwise we'd introduce causal disjunctions 2) equivocal, or all god-talk would cease 3) univocal, or there'd be no halt to infinite regressions 4) apophatic, or what's already wholly incomprehensible would not also be partly intelligible 5) kataphatic, or we'd be telling untellable stories and proving too much.

        Thus, those who refer to unitary being and identify may be onto something, even while those who emphasize unitive strivings and intimacy may be onto something equally true. And so on. Same thing for our root metaphors, like substance, process, experience and such.

        I like to imagine that Anselm would have contributed much to discussions regarding the univocity vs analogy of being.

    • http://www.scribd.com/johnboy_philothea Johnboy

      Whether that establishes His existence is another matter. He seems, as Kant argued, to make “existence” a property, which seems dubious. It’s also unclear that one can go from definitions to actual reality as Anselm tries to do. <<<

      In all of these considerations, whether mathematical, set theory, modal logic and predicating existence of being, we are repeatedly running into the same "problems of beginning," which include such as circular referentialilty, infinite regressions, causal disjunctions and question begging.

      That's why, after first grasping Godel's meta-mathematical insights of his Incompleteness Theorems, I was initially puzzled as to why he, of all people, would bother with an ontological argument. I better realized, then, that one could write down an argument that's both complete and consistent, only one couldn't prove it formally. Similarly, one may indeed take existence as a predicate of being, as it may indeed be true, only one has not added any new information to one's system.

      The reason Godel and Hartshorne attempted modal ontological proofs is because they do conclude to actual reality, but only if one has successfully described – that is, dutifully disambiguated and rigorously defined – each concept. In other words, for all those who are in agreement that each term of an argument successfully describes reality, there will be agreement that, modally, the conclusion necessarily obtains in reality. There's the rub, though.
      Our apophatic predications of divine attributes are reasoning from effects to causes via weak abductive inference, specifically from effects proper to no known causes. Generally, the terms employed are making successful references to reality, so have great heuristic value. We reasoned like this in particle physics, looking for the Higgs Boson and such. What's controversial in ontological god-argumentation comes back precisely to whether or not existence really is a predicate of being, begging for a creatio ex nihilo. Or, might a neoplatonic emanation or even a Tohu Bohu origination beg for cosmological arguments and so on.

      So, basically, we are grappling with now this tautology or now that. And, whether in a godelian or kantian sense, just because they are tautological doesn't mean they aren't true, only that they aren't necessarily informative. They can still have great heuristic value, opening the way to new inquiry.

      Not all tautologies are equally taut because not all enjoy the same degree of epistemic virtue in terms of such criteria as external congruence, internal coherence, logical consistency, hypothetical consonance, abductive facility, speculative fecundity, interdisciplinary consilience and a use of concepts and terms that, at least, successfully refer, better yet, successfully describe various realities.

      Anselm got Peirce, Godel and Hartshorne, among others, thinking, for good reason.

  • Peter Paul Fuchs

    Howdy Vox Nova denizens, I am not in the mood anymore to join the fray here, but I did want to point out one thing apropos this post. My relative, the well-known Catholic theologian Anselm Stolz ( he was the cousin of my German grandfather) had some profound things to say about this. Stolz averred that in regards this matter
    logic and prayer were not distinct as regards this argument, and thus seemed to suggest that the argument itself could be understood in terms of a prayerful entreaty. Here is a book which mentions his views: https://books.google.com/books?id=rCRMAwAAQBAJ&pg=PA183&dq=Anselm+Stolz+ontological+argument&hl=en&sa=X&ei=enPIVIf5B8uqggTE6oP4Bg&ved=0CB0Q6AEwAA#v=onepage&q=Stolz&f=false

    • http://gravatar.com/tausign Tausign

      Thank’s PPF for sharing this insight and perspective. I was truly captivated in reading a substantial amount of the book preview. I was able to locate an inexpensive used copy which is now on its way to me. Fr. Stolz’s perspective seems quite compelling and spiritually fruitful. I am not a logician by any stretch, but it appears that this volume on the Proslogion (which includes but is not limited to Stolz’s view) opens up a totally new vista and perspective on how to approach what may be more prayer than most take into account. It does seem that our minds may be so preconditioned to modern biases that we need a new framework to discern what Anselm of Canterbury even intended to accomplish.