Friday, February 15, 2013

Countering the Modal Ontological Argument

Note: What follows below is a transcription of the video

Ahh the Ontological Argument, where philosophers try to define god into existence. 

This video is going to be about the modern, Modal Ontological Argument put forward by apologists like Alvin Plantinga and defended by William Lane Craig. 

This is because the original Ontological Argument put forward by St. Anselm and philosophers like Rene Descartes was refuted by philosophers like David Hume and Immanuel Kant since the original argument assumed that “existence” was a property.   You can Google that, but almost all modern apologists won’t attempt to defend that version of the argument.

So here’s the “Modal Ontological Argument” put forward by Plantinga:

  1. A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
  2. A being has maximal greatness if it has maximal excellence in every possible world.
  3. It is possible that there is a being that has maximal greatness. (Premise)
  4. Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
  5. Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
  6. Therefore, an omniscient, omnipotent and perfectly good being exists

Before I continue, I want to acknowledge that the first part of my criticism here is largely taken from the atheist blogger Chris Hallquist.  He writes an excellent blog I highly recommend checking out.

What makes this argument so annoying is that it’s easy to tell that there’s something wrong with it, but it’s so very hard to point out exactly what it is, and Chris was the first person I read online who highlighted exactly what was wrong with the argument and why.  I’m including a link to his refutation in the description box.

The modal argument hinges on “axiom S5” which is from a system of formal logic.  Basically, if you’re going to do formal logic, you can pick which system of it to work under, and so long as you stay consistent in that system and obey its axioms, all is well. 

For the record, there’s no problem with S5 axioms of modal logic, this is the logic of possibility and necessity.  You just have to be aware of what you’re dealing with before you draw conclusions from an argument.

The problem here is that once you start operating under S5, making certain assumptions and running with it is frankly absurd.  The argument relies on granting what sounds like a reasonable assumption that “X is metaphysically necessary” and “X possibly exists”.  The issue here is that under S5, this logically equivalent to saying “X exists necessarily “.

This is problematic because in normal argumentation we can say that yes, “for all we know, it’s possible X exists”, where X can be Leprechauns, Unicorns, Fairies, or a god.  The problem is that when in S5, if you say that something defined as “necessary” possibly exists, you may as well start this silly argument:
  1. God is defined as omniscient, omnipotent, wholly good, and as something that exists in any possible world. 
  2. An actual world exists.
  3. Therefore god exists!
This is logically valid, but tells us nothing!

This is why Alvin Plantinga, the guy who came up with the modal version of the argument, admits that while the argument is logically valid, it doesn’t prove anything, to quote:

“Our verdict on these reformulated versions of St. Anselm's argument must be as follows. They cannot, perhaps, be said to prove or establish their conclusion. But since it is rational to accept their central premise, they do show that it is rational to accept that conclusion”

-Alvin Plantinga, "The Nature of Necessity" (1974), pg 221

Now that last bit about the argument showing it’s rational to accept the conclusion is still way off the mark, but we’ll deal with that later. What I want to highlight here is the difference in honesty between Alvin Plantinga and William Lane Craig.  At least Plantinga acknowledges this major issue and admits it.  Craig on the other hand just presents the argument and acts as if it were somehow a valid proof of a god necessarily existing in all metaphysically possible worlds.  It shows the difference between someone doing philosophy of religion, and someone trying use arguments to evangelize.

Here’s a great example to show why granting the possibility of something that is metaphysically necessary under S5 modal logic is absurd:

Most philosophers hold that mathematical truths are metaphysically necessary.  There’s something called “Goldbach’s Conjecture” in mathematics which is an unsolved problem in number theory. 

It states that “Every even integer greater than 2 can be expressed as the sum of two primes”.

It appears to be true, and has shown to hold through 4x1018 but it’s not been proven.  However, if it is true, then it would be a metaphysically necessary mathematical rule.  Because of this, we can use the modal ontological argument to show that it must be true:
  1. If Goldbach’s conjecture is correct, then it is necessarily true.
  2. It is possible that Goldbach’s conjecture is correct.
  3. Therefore, possibly, it is necessarily true that Goldbach’s Conjecture is correct.
  4. Therefore (by axiom S5) it is necessarily true that Goldbach’s Conjecture is correct.
  5. Therefore Goldbach’s Conjecture is correct.
This turns any “unproven” area of mathematics that “might be true” into something that “must be true.”  That’s frankly absurd, even mathematical theories must be proven to be true, not assumed to be true until proven false.

So even on Plantinga’s much more modest claim of the ontological argument making belief in god rational or reasonable, it doesn’t actually add any extra justification to the original idea.  You may as well say that “the idea that god exists isn’t inherently contradictory, so it’s rational to believe it.”

Of course, all of this may not be enough when dealing with apologists.  Some of them are so desperate for a valid reason to believe that they may even bite the bullet on the mathematical problem and assume theories are true until proven false.  So for those folks, I have a much more fun response to the ontological argument: The Great Demon!

Note that I’m specifically using a “Great Demon” as my example for a few reasons. If we were to use the classic maximally Great Island or maximally great lion, then apologists can say that material things can't be "necessary" since we know that outside of our space-time they couldn't really exist.  I also specifically call it a "great demon" since if we called it the "evil god" then apologists throw up a semantic smokescreen and say a "god by definition is something that is worthy of being worshipped."  So we call it a great demon.

So here’s the syllogism:
  1. A being has maximal depravity in a given possible world W if and only if it is omnipotent, omniscient and wholly evil in W; and
  2. A being has maximal evilness if it has maximal depravity in every possible world.
  3. It is possible that there is a being that has maximal evilness. (Premise)
  4. Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly evil being exists.
  5. Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly evil being exists.
  6. Therefore, an omniscient, omnipotent and perfectly evil being exists.
This is a pretty strong "reductio ad absurdum" defeater of the modal ontological argument, but there are a few weak objections apologists can throw at this that I want to refute before moving on.

The first objection claims that a maximally evil being is impossible since only "good" exists, and evil is defined as the "absence of good".  But this is obviously wrong for two reasons.  First is that it gets rid of the idea of morally neutral actions, which we know exist from our experience.  But more importantly, it fails because its nothing more than a bald assertion.  We could just as easily say that only evil exists and good is the "absence of evil" and have as much justification for it.

The second objection is that an omniscient being would have knowledge of an absolute "Moral Law" and as such would be incapable of evil, since it would feel "convicted" by the law, or that all beings aren't really evil, they just rationalize evil actions, but when doing something evil, they actually believe it's the right thing to do.  This objection is defeated fairly easily since we can say that evil is grounded in the nature of the great demon, so that it isn't "convicted" by an absolute "Moral Law", if it existed, but driven to violate it.  In fact we would go further to say that the perfect selfishness of the great demon means that it wouldn't be compelled to "do what is right" but rather to do what brings itself pleasure, which according to its nature is evil.  Finally we can reject the notion that people always do what they think is right, since we've seen examples of people doing things they know to be wrong and going through with it anyway.

Now if all that wasn't enough, the final point we can make is that if the modal ontological argument is sound, then we have shown that at least two omniscient, omnipotent beings exists.  But in this case, it would be the as if neither existed!

Let's start with the premise that a maximally good being would make sure that ultimately only good things would result in any actual world. Let's also start with the idea that a maximally evil being would make sure that ultimately only evil things would result in any actual world.

So if both a maximally good add a maximally evil being exist necessarily then they would cancel each other out. This is because they would both be omniscient and omnipotent, each knowing the others thoughts at all possible outcomes of any action the other would take. Because of this they would use their omnipotence to stop any action that the other being tried to enact. As a result if both beings existed necessarily than the actual world would be it as if neither existed since neither one could act in our actual world.

One way out of this problem is for an apologist to insist that only one omnipotent, omniscient being exists, but if that is the case, then the ontological argument can't be sound since it equally demonstrates that two very different kinds of omnipotent/omniscient beings could exist with no way to identify which one it is.

So that's going to conclude my counter to the ontological argument.  I hope viewers find this useful in being able to show exactly WHY the modal ontological argument is wrong, and be able to provide some entertaining rebuttals to those apologists who stubbornly try to defend this laughably bad argument.

Thanks for watching!



  1. You inspired me to write my own:

    Jolly Elf Syllogism
    1. A being has maximal jolliness in a given possible world W if and only if it is omnipotent, omniscient and wholly jolly in W; and
    2. A being has maximal jolliness if it has maximal joviality in every possible world.
    2. It is possible that there is a being that has maximal joviality.(Premise)
    4. Therefore, possibly, it is necessarily true that an omniscient, omnipotent and perfectly jolly being exists.
    5. Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly jolly being exists.
    6. Therefore, an omniscient, omnipotent and perfectly jolly being exists.

    I actually thought long and hard about the distinction between "maximal excellence" and "maximal greatness" and how to translate these words into terms representing the characteristics of being maximally jolly, but ended up just going with what sounded right because it was just for fun. Besides, I think Christians could say that their God is a maximally jolly being, but I still thought it was fun. It's interesting how trying to coming up with parodies and reductio ad absurdums forces you to truly try and understand an argument in a way that even simply trying to debunk the argument doesn't.

    Upon further consideration maybe I should have gone with my second idea, namely the "maximally sexy nymph."

  2. Personally, I think one of the strongest (non-logical) arguments against the ontological argument is that any god that has to be defined into existence is rather pathetically useless.

    Even shorter: "so show me this god!".

    An informal Ockham's razor approach to the ontological argument:
    (1) ok, I (for the sake of argument) cannot see anything wrong with the logic of the ontological argument
    (2) therefore either (A) the argument is valid and defines into existence this super-being, or (B) I have failed to identify the fault in this argument
    (3) assuming (A) creates something huge and universally significant and all sorts of other issues, so is a major step, whereas (B) assumes I am imperfect in my knowledge and logical skills
    (4) the simpler of these is to assume my ignorance and logical fallibility (both of which I know to be plausible and proven many times!), therefore I reject the ontological argument

  3. As I wrote on Chris Hallquist's blog: good stuff and thanks. I especially like the Great Demon parody as it leads to a clear contradiction (namely two supernatural entities which cannot be omnipotent at the same time).

  4. Completely off topic:I am the Dutchman who emailed you a few months ago about your two questions for creationists:

    It took me quite a while to find you back.

    1. Heya! Nice to see someone I know from commenting on other blogs.

      That said, I'm not sure you've found the right guy. I didn't write what you've linked there, and I don't recall getting an email from you. Almost all correspondence I've had so far after launching this has been on YouTube.

  5. The problem appears much earlier than even an invocation of S5: it is not possible for anyone or anything to be both omniscient and omnipotent.

    How can an omniscient being find the omnipotence to change that which he already knows?

    If he can create a rock so heavy that even he cannot lift it, the rock is now unliftable and therefore, no omnipotence, If he cannot, then he is still not omnipotent, but one step earlier.

    Omniscient? From whence then free will? However, this "free will" bit is really sticky philosophically and becomes more difficult to discuss every day as we learn more about brain physiology.

    1. I agree that there are serious problems with omnipotence and omniscience, though I'd seriously avoid the whole "rock" argument.

      The problem with taking this approach to refute the modal ontological argument (MOA) is that it gives the apologists way too many outs or counter arguments.

      I prefer to go directly to the problem with the MOA since it gives them so few options to counter, or potential areas where they can say "if X is true, then this argument hold and I can reasonably hold X".

  6. I agree almost entirely with what you have posted here with respect to this foolish argument. Would it not be a far better use of your time to explore the possibility that some omniscient, omnipotent being does in fact exist? What do you gain by showing that it is not logically necessary that He exist? Why would you not take great joy in the fact that it is possible He does exist? Why fixate on the position that since He might not exist, then I will live like He does not unless He comes down here and physically pulls me out from under this rock I have hidden myself under? Why harden your heart so that it would be true of you: “"He said to him, 'If they do not listen to Moses and the Prophets, they will not be convinced even if someone rises from the dead.'"”? Is this blog your boat to Tarshish?

    1. I have explored the possability of it existing, and I've concluded that there's as much evidence to believe in that as there is to believe in Leprechauns, Unicorns, and UFO Abductions. In fact, I've very specifically considered whether or not Yahweh, the Christian god exists, and I've concluded that it very likely doesn't.

      Given that this god of yours supposedly WANTS me to believe in him so badly, he could "pull me from under the rock". And I can't tell whether to listen to Moses and the Prophets, or Muhammed, Joseph Smith, Buddah, the Hindu Mystics, or the wide variety of other gods. Now if this god of yours could raise up someone I knew from the dead and they could tell me about the afterlife, then maybe we'd have something.

      But your god conspicuously refuses to do that in a way that would compel belief from people alive today, since miracle stories from your holy book are as plausible as the miracle stories from other "prophets".

    2. Leprechauns? Are you really saying that the evidence for Leprechauns is equal to the evidence for the God of the Bible? You must be using some rhetorical device to make a point. Why the amount of testimony alone; has there been even one person who would rather die than to renounce their faith in Leprechauns? Is there even one pot of gold at the end of a rainbow to stack up against the array of physical scars on the earth from the world wide – Noah’s – flood? No, it sounds to me that you have some sour grapes. You feel God has let you down in some way; not lived up to your perfectly reasoned expectations. I have news for you. God does not answer to you and is not impressed with your boosting. I suggest you take another look at the book of Job; chapter 40 and beyond. A fool says in his heart “There is no God.”

    3. As the god of the bible? Yes, absolutely. There’s nothing but subjective accounts from people who lived a long time ago. How am I supposed to tell between the subjective accounts of Yahweh’s existence vs. the ones of Allah, or of people who believe in Leprechauns? Are we supposed to go by the number of people giving similar styled accounts? Fact is that there’s only one kind of evidence for the god of your bible, and it’s the same kind of evidence we’ve got for all the other mystical creatures.

      The comment about Noah’s Ark and the flood is a dead giveaway that continuing this conversation is going to be pretty fruitless. There is mountains of evidence that there was no such thing as a global flood, let alone the possibility that two or seven of each species of animal could have fit into a ship of the dimensions given, let alone be cared for by 8 people for a year. I suggest you go to The main questions of where did the water come from, and where did it go? Can’t really be answered except by a miracle.

      If you’re a Young Earth Creationist, then almost every modern apologist thinks you’re wrong. I should have another article/video on that in the next few weeks.

    4. The historicity of eye witness testimony is generally accepted by scholars and direct testimony is accepted in every court of which I am aware. The more testimony and the more the witness is commited to that testimony, the more reliable. That you will concede nothing is again sophmoric. I will look forward to your upcomming treatment of YEC, I am well versed on the subject.

    5. This comment has been removed by the author.

    6. "Accepted by courts everywhere" is true, but it's regarded as some of the least reliable evidence.

      But of course, none of that has anything, at all, to do with the point I'm making.

      There's eye witness testimony to Leprechauns, Unicorns, UFO's, the miracles of Joseph Smith, Sathya Sai Baba, and countless others.

      Do you accept those too?

    7. I accept, where the testimony is serious, they have had some encounter (there are fakes and hoaxes for all observed phenomena – just ask Ernst Haeckel). What is obvious but you will not concede is that the body of evidence for the God of the Bible far exceeds, in breadth, depth, density, volume, and consistency any of these other examples. I am not saying it is objectively proved. I am saying to compare Leprechauns or Unicorns with Jesus is absurd = wildly illogical.

    8. Considering you think that there is actual evidence for a world-wide-flood, which is at odds with a wide variety of empirical evidence that says otherwise, I'm not going to take your objection very seriously.

      All you've got is testimony of people who claim to have experienced god, and then had their stories written down many years after the fact. Like most other religions.

      That's pretty much on par with Leprechauns and Unicorns, and at least we currently have living people who very seriously claim to have been abducted by UFO's, or seen the miracles of Sathya Sai Baba.

    9. "... then had their stories written down many years after the fact." Like all of history you mean? Look it is fairly obvious that something super natural is going. Or, like 95% of all the people that ever lived were and are crazy. What you are doing is giving ultimate authority to human logic and human reason. That is a mistake. Why? Well because of human bias and human selfishness. You can have the first without the later. You speak of empirical evidence that says there was no world-wide flood. That only shows your bias. Most of the evidence can go either way. There are some physics problems to overcome, but, these occur on both sides of the fence. Again, I await your treatment of the subject.

    10. I would go as far to say that leprechauns and unicorns are much, much more likely to exist. A unicorn is not much different from animals we already know exist, and a leprechaun is still some sort of human. Both have odds much better than an omniscient, omnipotent, omnipresent deity who exists in some magical nether realm.

    11. "That you will concede nothing is again sophmoric."

      BWAHAHAH! The intellectual dishonestly of godbots never fails.

  7. I recommend using the following premises instead of "it is possible that the Goldbach Conjecture is true":

    1) It is possible that the googolth prime is 1 mod 4
    2) It is possible that the googolth prime is 3 mod 4

    This way you don't just get a bogus proof for something that is probably true anyway, you get an outright contradiction. Further, since both of these claims are exhaustive and equally plausible given our present state of knowledge and limited computational capacity, it is very hard to reject either in the "possibly true for all we know" sense. This highlights that "possibly true for all we know", and "logically possible" in the formal sense are not synonyms, which is the core of what's wrong with the modal ontological argument.

    1. ""possibly true for all we know", and "logically possible" in the formal sense are not synonyms, which is the core of what's wrong with the modal ontological argument."

      Quite so. Like all of religion, the argument is a dishonest cheat, an intentional bait-and-switch.

  8. I'm not sure that Anselm's argument IS dead. Plantinga says:

    "If this is what [Kant] means [about existence not being a property], he's certainly right. But is it relevant to the ontological argument? Couldn't Anselm thank Kant for this interesting point and proceed merrily on his way? Where did he try to define God into being by adding existence to a list of properties that defined some concept?...If this were Anselm's procedure -- if he had simply added existence to a concept that has application contingently if at all -- then indeed his argument would be subject to the Kantian criticism. But he didn't, and it isn't."

    1. There are many attempts to try and formalize Anselm's argument into something we'd be used to, and Plantinga's is one attempt at that specific argument (that's not the Ontological argument I dealt with in this video).

      The Stanford Encyclopedia's of Philosophy's entry on this is pretty good as a resource:

      The specific entry I'd refer to for Anselm's argument is here:

      The relevant section that deals with the way Plantinga spins Anselm's argument is in section 8.6, under the objection about the "Smallest Conceivable Martian", which is where we can see how the idea of existence gets smuggled into the concept.

      Even with that though, Anselm's argument is very much vulnerable to the Great Demon Objection I put out in my video, just modify it to go from the modal version to the same form Anselm uses.

      In terms of being "dead", Plantinga himself admits that there is no "proof" for the existence of a god in natural theology, he does this as I quoted in the video, and in his works on "Warranted Christian Belief" and Reformed Epistemology.

      Second why would he make a Modal Ontological argument if Anselm's version works? There are no defenders of Anselm's argument today, any apologist who will even attempt to defend the Ontological Argument that I've read or listened to always go for the modal version.

  9. Here's a thorough refutation of the Ontological Argument by Rayndeon, including a series of youtube videos.

  10. Hmm, don't know if anyone has said this: while the key premise is derivable in S5, it is also derivable in the weaker logic B, whose axiom is A --> []<>A:
    1. ~A --> []<>~A (B)
    2. ~[]<>~A --> ~~A (contra. 1)
    3. <>~<>~A --> A (~[], 2)
    4. <>[]A --> A (def. [], 3)

    I agree that the modal ontological argument is spurious. But it relies on a weaker (and perhaps more intuitive) axiom in alethic logic: namely, that anything that is the case is necessarily possibly the case.

  11. Excellent article. Minor nit: the power was missing for Goldbach's conjecture: it has been proven for up to 4 x 10^18.

  12. Excuse me; you are wrong in regard of your understanding of modal logic. Your modal argument proving that Goldbach’s conjecture is true is absolutely incorrect under S5 logic. Here is why: your premise "It is possible that Goldbach’s conjecture is correct" is not justified in S5 because saying that Goldbach’s conjecture is possibly true means that this conjecture is logically coherent and hence true! You cannot say that "It is possible that Goldbach’s conjecture is correct" if you don't have a valid formal proof of it.

    When Plantinga says that "It is possible that there is a being that has maximal greatness" this means simply that the concept of a Maximally Great Being is logically coherent and does not lead to a logical contradiction. You cannot say the same about Goldbach’s conjecture if you did not prove mathematically that it's correct. If you are to object to Plantinga's argument, you have to show that the concept of a Maximally Great Being is logically incoherent and this is the only way to object to the argument.

    Your Absolute Evil concept is also incoherent. You postulate an omnipotent, omniscient and wholly evil being. There are two cases; either this being is perfectly free in the sense that he acts in perfect freedom without being influenced by another being or some desires or weaknesses. In this case, as Richard Swinburne correctly argues (the details of his argument are in his book The Existence of God), he will be morally perfect and not wholly evil as you claim. If he is not perfectly free, then there are some other factors that influence his behavior and on which he has no control and then he is not omnipotent and also not wholly evil. Your parody does not refute the modal ontological argument of Plantinga as you argue for a logically incoherent concept which renders your premise "It is possible that there is a being that has maximal evilness" false.

  13. >the original Ontological Argument put forward by St. Anselm and philosophers like Rene Descartes was refuted by philosophers like David Hume and Immanuel Kant

    That never happened and Kant was too stupid to even notice that in one of his examples "God is omnipotent" the word is not ONLY states a relationship between the two terms, but also functions as an abbreviation of two words that were dropped in our economical communication: "God [exists and] is omnipotent." Secondly, since his epistemology only deals with the physical world, he cannot say anything about the metaphysical. That observation shows that his supporters don't even know Kant!

  14. I think it is worth pointing out that Christian (or just theistic) apologetics is not dependent on the validity of the modal ontological argument. It is quite possible to be sceptical about a line of reasoning that does indeed appear to be an attempt to "define God into existence", while at the same time accepting that there are strong reasons for belief in God (the argument from the objective validity of reason itself is actually more than sufficient - a huge problem within the philosophy of naturalism). We don't need the ontological argument, modal or otherwise, although it does throw up some interesting ideas concerning the necessary human appreciation for the concept of 'perfection'. In fact, it could be argued that Prof. Dawkins' frequent claim that the human body exhibits "bad design" presupposes a belief in a standard of "good design", which cannot easily be explained unless this standard of perfection actually exists in some form. Attempting to explain this standard in entirely utilitarian terms is highly subjective, of course. And then there is the idea of "moral perfection" without which talk of morality is incoherent (even if we cannot define this concept exactly). So I think there is some epistemic value in the argument, but certainly Christian / theistic apologetics does not depend on it.

  15. Theorem: The ontological argument exists.

    Proof: Consider the set of all arguments. It is partially ordered by “stupider than”: thus a <= b if argument b is stupider than argument a. (If this runs counter to intuition you can do it the other way). Now I contend that every chain C in this partial order has an upper bound. Just take the argument that is the union of all the arguments in C: this argument is clearly stupider than any of its subarguments. It may be infinite but that only contributes further to its stupidity. Thus, by Zorn’s Lemma there is an argument stupider than all other arguments. This is the ontological argument. QED.

    Corollary: Among all proofs that the ontological argument exists, this one is the cleverest.

    Proof: Exercise

  16. assess the premise:

    1. The expression "it is possible" means that the proposition is true in "at least one Possible World, and fewer than all Possible Worlds".
    2. Thus, the proposition is untrue in the remainder of Possible Worlds.
    3. So (according to the premise), "a Being that has Maximal Greatness" exists in "at least one Possible World, and fewer than all Possible Worlds".
    4. Thus, "a Being that has Maximal Greatness" does not exist in the remainder of Possible Worlds.

    So we have a problem - these are two of the solutions:

    1. replace the premise with "It is necessary that there is a being that has maximal greatness. (Premise)"

    2. use an alternative MGB definition - "A being has maximal greatness if it has maximal excellence in every possible world in which it exists."

    As it stands, the premise is oxymoron-ish.

  17. The idea of there being a great Demon as you describe is illogical. Most of us would say that there is good in this world and so this being would by nature be bound to destroy this very world. Yet we are still here. Whereas God as he is defined in the Bible, is not bound to necessarily destroy the world even though he is permitted.

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