Defining Away the Ontological Argument

The ontological argument for the existence of God is a famous one, being one of the first arguments made. It still exists today in quite a variety of forms.

The first version came from St. Anselm in Proslogion, written in 1078. His argument has a lot of twists and turns about an idea existing in our minds and in reality, but the argument can be neatly summarized without that, as follows:

  1. God is defined to be the greatest possible being.
  2. Existence is necessary to be the greatest possible being.
  3. Therefore from 1 and 2, God exists.

 

Many philosophers after Anselm continued to shape this argument, but it remained in roughly the same form. Even Descartes in Meditations (1637) used the same argument 500 years later, saying that “God’s perfection logically implies existence the same way two mountains logically imply a valley”.

Nearly a millenium after Anselm, a second version of the argument comes from Alvin Plantinga in The Nature of Necessity, written in 1974. It keeps to roughly the same structure, but also makes use of possible worlds.

  1. A possible world is defined to be any world that can be imagined to exist, including our own.
  2. God is defined to be the greatest possible being.
  3. If a greatest possible being exists in a possible world, it must exist in all possible worlds.
  4. The greatest possible being exists in a possible world.
  5. Therefore from 4-7, God exists in our possible world.

 

 

A Reduction to Absurdity

A few years after Anselm’s argument was published, a monk named Gaunilo (or Gaunilon) of Marmoutier responded to the argument through what is called a reducto ad absurdum (reduction to absurdity), which defeats an argument not by showing that it contains an unsound premise or an invalid conclusion, but by showing that it produces absurd conclusions when applied to different scenarios.

An summary of his argument:

  1. The Lost Island is defined to be the greatest possible island.
  2. Existence is necessary to be the greatest possible island.
  3. Therefore from 9 and 10, the Lost Island exists.
  4. Obviously, the Lost Island does not exist.
  5. Therefore from 11 and 12, conclusion 3 is invalid.

Initially this seems strange, because what qualities make an island greater than another? Are we to imagine that the Lost Island has the most ideal tropical weather and the best ratio of palm trees to beaches? It seems like for every island we can imagine, we can always imagine a better island. But it seems like if this is the case, then it must also hold true for God: either we can imagine the perfect version of a thing or we can’t, being stuck in an infinite series.

Also, perhaps we could bite the bullet and suggest that the greatest possible island does exist. However, simply replace “the Lost Island” with “the greatest possible unicorn” or “the greatest possible Santa” to prove other outlandish things.

Or even, consider a retort of my own invention:

  1. It is possible for a being to be the greatest possible atheist.
  2. Existence is necessary to be the greatest possible atheist.
  3. Knowing a conclusive disproof of God is necessary to be the greatest possible atheist.
  4. Therefore from 14 and 15, the greatest possible atheist exists.
  5. Therefore from 16 and 17, a conclusive disproof of God exists.
  6. Therefore from 18, God does not exist.

 

Super Atheist Man has the super power of being able to disprove God

 

Exposing the Circular Logic

So how is it that these arguments manage to prove the existence of anything we want them to? It seems to rest with the idea of calling something perfect by definition, and then suggesting existence is part of perfection.

Let’s look at 1-3 again:

  1. God is defined to be the greatest possible being.
  2. Existence is necessary to be the greatest possible being.
  3. Therefore from 1 and 2, God exists.

What happens when we replace “greatest possible being” with what we mean by that term?

  1. God is defined to be all-powerful, all-knowing, all-loving, and in existence.
  2. Existence is necessary be all-powerful, all-knowing, all-loving, and in existence.
  3. Therefore from 1 and 2, God exists.

When we look at this, we see that 1 defines God to exist, and 2 says you must exist to exist, and 3 concludes that therefore God must exist. This is circular: God exists because he is defined to exist. This means we must reject 3 as being logically invalid (also meaning we must reject 11, 16, 17, 18).

It seems that the Ontological Argument is based on circular logic which lurks within the premises, not clearly visible to people reading the argument for the first time. This is why the Argument strikes many people as some sort of magic trick, like you are looking at a mathematical proof that 1 = 2.

 

This is the bait and switch that makes the argument seem plausible: there are great beings we can imagine and great beings that exist, and that the beings who we can imagine would be greater than the existing ones, should they exist. But we don’t know that they do.

Our concepts of God are thus conditional: if this being were to exist, it would be the greatest possible being. But if it doesn’t, it is just the greatest being among all those we can conceive in our minds, but we will have to look elsewhere to find the greatest possible being.

If existence is a necessary part of being great, we can only search the things we know to exist to find the greatest among them, and that is the greatest possible being.

 

 

Finding God in Possible Worlds

Possible worlds are any worlds we can imagine, so basically anything that is logically possible (does not entail a contradiction). To further complicate things, world is used in the expansive sense not in a planetary sense, so perhaps it would be better to say “possible universe”.

Close to anything can be a possible world: a world populated only by monkeys, or a world identical to ours except everyone speaks Spanish, or a world where people are capable of interstellar flight. The only things that can’t be possible worlds are worlds with contradictions, like a world where one does not equal one, or a world with an object that simultaneously has a property and lacks that same property.

Plantinga suggests that we imagine a world with a god in it, a world where perhaps Christianity is true. Such a world appears to be imaginable without contradiction, though if we’re imagining a world like ours, it may imply stubbornly hidden and confusing God that allows people to suffer needlessly, and it couldn’t be a world with prayer.

However, Plantinga is not asking us to imagine any ol’ god, but a greatest possible being, and he thinks that this greatest possible being must possess the property “exists in all possible worlds”. But as soon as we frame the argument like this, we see that Plantinga’s argument is also circular:

  1. God is defined to exist in all possible worlds, among other perfect qualities.
  2. If a being which exists in all possible worlds exists in any possible world, it must exist in all possible worlds.
  3. A being which exists in all possible worlds exists in a possible world.
  4. Therefore from 4-7, a being which exists in all possible worlds exists in our possible world.

 

So Plantinga is really asking us to imagine the existence of “being which exists in all possible worlds”. However, imagining such a being does create contradiction, because we can clearly imagine a world with no such being — a world with nothing at all, or the atheist world. The fact that we can imagine a world with no God means that this God does not exist in all possible worlds.

If this isn’t clear, also imagine a world that contains a “being that destroys all possible worlds” or a “being that if it exists in one possible world, it will prevent consciousness from existing in all worlds”. Like the “being which exists in all possible worlds”, these properties aren’t contradictory on their face, but contradictory to what the idea of a possible world is. Clearly, if these beings existed, we could not exist, but we do.

 

Thus these beings aren’t even possible, and thus Platinga’s conclusion 8 does not establish the existence of God. And considering Anselm’s and Descartes’s conclusion 3 also ends up unjustified, we can safely rule out the ontological argument as a reason why we should believe in God, and instead look elsewhere.

Those arguments will be left for another day.

See also: Chris Hallquist’s “Plantinga’s Ontological Argument, Take Three

-

I now blog at EverydayUtilitarian.com. I hope you'll join me at my new blog! This page has been left as an archive.

On 7 Oct 2011 in All, Atheism, Counter-apologetics. 10 Comments.

10 Comments

  1. #1 M.S. says:
    15 Jul 2012, 1:11 pm  

    When I say that “X possibly exists”, I mean “I do not know whether there is a thing with the properties ascribed to X”. I do not mean “there is a potential realm in which an X is actual”, but that is the sense we must assume for “if X exists in a possible universe” to make sense. Potential existence is not existence ; X cannot potentially actually exist. Either X is present in the only actual universe there is or it is not.

    If you get rid of the self-contradictory “(actually) exists in all [potential] universes” to make it clear that only one universe can actually exists you get “the greatest possible entity exists in any actual universe” and it becomes clear that this is question begging.

    Even if we were to posit multiple disjoint universes, since the formulation calls for a unique greatest entity, it must mean that this single greatest entity is shared between all possible universes simultaneously, and not that each universe has its own greatest entity. Therefore, these universes are not disjoint, so there is only one universal grouping of things in which the greatest entity exists. Again “exists in all universes” must reduce to the degenerate case of zero or one universes.

  2. #2 Peter Hurford (author) says:
    22 Jul 2012, 9:06 pm  

    When I say that “X possibly exists”, I mean “I do not know whether there is a thing with the properties ascribed to X”. [...] X cannot potentially actually exist. Either X is present in the only actual universe there is or it is not.

    Here, I think you end up a bit confused by accidentally equivocating between a variety of different types of existence.

    Saying “I do not know whether there is a thing with the properties ascribed to X” is saying that X is epistemically possible, possible for as far as you know.

    Saying X actually exists is saying that it exists in our (actual) world.

    Saying X potentially exists, means that it could exist in our (actual) world, but it doesn’t.

    Saying X possibly exists, means that it does exist not in our (actual) world, but in a possible world.

    When you account for all this terminology, I think Plantinga’s possible world’s ontological argument makes more sense, but I agree that it ends up confused at the end, because it makes no sense to talk about things being in one possible world affecting other possible worlds.

  3. #3 Stephen R. Diamond says:
    5 Aug 2012, 11:13 pm  

    I think the simplest answer to the ontological argument is to accept take the dilemma by the second horn. The deity as defined is either necessary or impossible. It’s impossible because no being can possibly be necessary.

  4. #4 Peter Hurford (author) says:
    6 Aug 2012, 1:40 am  

    If the theist wants to define God as a logically necessary being, then I’m going to definitely say that god concept is logically impossible.

  5. #5 M.S. says:
    7 Aug 2012, 12:07 am  

    Peter, thanks for explaining. I’m still confused about the meaning of “possible” since “Saying X possibly exists, means that it does exist not in our (actual) world, but in a possible world” seems circular. I tried enumerating definitions based on different logics to come up with possible meanings but ended up stalled. Do any of the below correspond to your understanding of the word as using in the ontological argument? (1) from probabilistic logic, there exist prior occurrences of X so the unconditional probability is non-zero; (2) from fuzzy logic, we can point to an extant entity with most of the defining attributes of X; (3) from intuitionist logic, we can point to a sound constructive process by which X could come to exist; or (4) from propositional logic that X exists because I can point to some combination of (recursively) possible premises and sound inferences that leads to that conclusion. What I (or my inner closet intuitionist) does not accept is that possible & impossible are a proper dichotomy — since possibility deals with knowledge, one option is always unable to quantify. It seems to me that Dr. Plantinga cannot have (1) in mind since we have no priors for other universes; is unlikely to have (2) in mind since fuzziness is incompatible with absolutist arguments — mostly omnipotent is not omnipotent; is unlikely to have (3) in mind since if there exists a constructive proof for X, then X must be derivable from natural laws; and is unlikely to have (4) in mind because if he had one, it would moot the need for the ontological argument which is itself a propositional argument. Is Plantinga using some other definition of “possible”?

  6. #6 Stephen R. Diamond says:
    7 Aug 2012, 12:42 am  

    To say something possibly exists or exists in some possible worlds (exactly the same meaning) is just to say it involves no logical contradiction.

    To say it is necessary is just to say denying it is logically contradictory. If it is necessary, is exactly the same thing as existing in all possible worlds. The fancy possible-worlds language is sheer window dressing; this isn’t a problem that requires invoking any properties of possible worlds that don’t apply strictly to the formal logic of contradiction.

    But you’re right to question the meaning as used by Platinga. If god necessarily exists, it exists as a matter of definition: that’s what “necessary” truths are these days. But definition can’t create an entity! That’s not necessary the concept of necessity used by the medieval philosophers.

  7. #7 M.S. says:
    7 Aug 2012, 1:52 am  

    It seems reasonable to define “impossible” as “ruled out due to a logical contradiction” which is a fine operational definition. But defining possible as “involves no logical contradiction” is not an operational definition since Gödel proved that no deductive system can be sound, complete, and effective meaning that every proof of the lack of a contradiction is a one-off. Any operational definition of what is “possible” has to be based on some identifiable class of possible things for which a solver has been identified. That gets me back to the question of what does “possible” mean in this context — into what class of possible things does Plantinga’s God fall?

  8. #8 Stephen R. Diamond says:
    7 Aug 2012, 2:11 am  

    But defining possible as “involves no logical contradiction” is not an operational definition since Gödel proved that no deductive system can be sound, complete, and effective meaning that every proof of the lack of a contradiction is a one-off

    Well, it certainly isn’t intended to be an operational concept. I’m sure Platinga rejects intuitionism; well, almost sure. (I really am sure that the medievals who came up with the argument reject intuitionism too.)

  9. #9 M.S. says:
    7 Aug 2012, 2:44 am  

    I doubt medieval apologists had an opinion on intuitionism since it wasn’t an issue until fairly recently when mathematicians started trying to reason about uncountable collections :) Thanks for taking the time to explain terminology. I suspect the idea of one possible universe constraining another confuses me so much that I just flail around looking for ways to redefine other terms to make it fit.

  10. #10 Peter Hurford (author) says:
    7 Aug 2012, 3:38 pm  

    M.S.: I’m still confused about the meaning of “possible” since “Saying X possibly exists, means that it does exist not in our (actual) world, but in a possible world” seems circular.

    It’s not circular, it’s an analytic statement — true by definition. That’s just one definition of what “possible” means. Really, as Stephen pointed out, logically possible means “this entails no logical contradiction”. Possible worlds are a philosophical means to analyze logically possible truths, by thinking of worlds where these facts hypothetically take place.

    It comes from an extension of logic called “modal logic”. See the Stanford Encyclopedia of Philosophy article for more than you’ll ever need to know.

    ~

    M.S. Do any of the below correspond to your understanding of the word as using in the ontological argument? (1) from probabilistic logic, there exist prior occurrences of X so the unconditional probability is non-zero; (2) from fuzzy logic, we can point to an extant entity with most of the defining attributes of X; (3) from intuitionist logic, we can point to a sound constructive process by which X could come to exist; or (4) from propositional logic that X exists because I can point to some combination of (recursively) possible premises and sound inferences that leads to that conclusion.

    (1) or (4) would be the closest. Really, what you’re looking for is some sort of counterfactual reasoning — “had circumstances been completely different, X *could have* come into existence” — or some sort of logical reasoning — “The existence of X entails no logical contradictions”. Both of these are taken to be equivalent.

    ~

    Is Plantinga using some other definition of “possible”?

    What Plantinga is doing is using modal logic reasoning, which suggests that if something necessarily exists, it must exist and never could not exist. Therefore if God necessarily exists, he exists.

    On the other side, if it’s possible that God exists, then God possibly necessarily exists. But if God necessarily exists, he could never have failed to exist. Thus God exists.

    If you’re not convinced by this, then you’ve seen the trick of the argument. Though I think it’s possible to dress it up a bit more convincingly — see here for a bunch of explanatory YouTube videos on the Ontological argument. I’d also like to introduce to Chris Hallquist’s analysis of the argument.

    If you’ve had very little exposure to the ontological argument, it clearly sucks. Then, when you begin to understand it more, it seems compelling. Then, after having even more exposure, it clearly sucks again.

    ~

    Stephen: If god necessarily exists, it exists as a matter of definition: that’s what “necessary” truths are these days. But definition can’t create an entity!

    That’s basically the whole trick to the Ontological Argument — defining something into existence.

Leave a Reply

You must be logged in to post a comment.