A Concise and Valid Ontological Argument
February 2, 2010 — 1:50

Author: Michael Almeida  Category: Christian Theology Concept of God Existence of God  Comments: 20

According to most Anselmians–and most theists–God has a special set of essential properties. Those essential properties include omniscience, omnipotence, perfect goodness and necessary existence. But how do we know this? There are just two possibilities: either we know that God has those essential properties apriori or we know aposteriori. Again, almost no theist maintains that we know the essential properties of God aposteriori. The reason this is rejected is because it entails that we might have discovered that God was less than essentially perfectly good, etc. But almost no theist thinks that’s a possible discovery. So, most Anselmians–I’d again say most theists–maintain that (A) is true.
A. A being x = God only if (i) for most essential properties P of x, it is
primarily necessary (i.e., apriori) that x has P, and (ii) the essential properties of x
include omnipotence, omniscience, perfect goodness, and necessary existence
There is a concise and valid apriori demonstration based on (A) and some well-known logical relations holding between primary necessity (aprioricity) and secondary necessity (metaphysical necessity). Let M be restricted to essential properties understood as properties objects have in every world in which they exist. Here’s a concise ontological argument.


1.0. □1∀x(□1Mx ⊃ □2Mx)
(1.0) states that, it is apriori that x instantiates essential property M, only if it is metaphysically necessary that x instantiates essential property M. For instance, if it is apriori true that the empty set instantiates the essential property of being non-membered, then it is metaphysically necessary that the empty set instantiates the essential property of being non-membered. Now instantiate (1.0).
1.1. □1(□1MG ⊃ □2MG)
(1.1) says that If it is apriori that God has essential property M, then it is metaphysically necessary that God essential property M. But we know from (A) that (1.2) is true.
1.2. □1MG
It is an apriori known conceptual truth, based on (A), that God has the essential properties of omniscience, omnipotence, perfect goodness and necessary existence. But then, obviously, (1.3).
1.3. □2MG
It is metaphysically necessary that God has the essential properties of omniscience, omnipotence, perfect goodness and necessary existence.
The argument is valid. And it makes no mistakes in moving from conceivability to necessity. The principle in (1.0) properly licenses that inference. And it would be sound if (A) were true. But I’m not sure (A) is true. Is it an apriori knowable conceptual truth that God instantiates the divine essential properties? Norman Malcolm thought so, and so did Anselm of Proslogion 3. Suppose it isn’t apriori knowable. Then it can be no more than aposteriori knowable that God instantiates the divine essential properties. That’s a pretty startling conclusion that is contrary to what most theists and certainly most Anselmians believe. It entails that we might have discovered that God had quite a different set of properties.

Comments:
  • Jeremy Pierce

    Doesn’t 1.0 require that there’s no synthetic a priori? Isn’t that a pretty controversial claim?

    February 2, 2010 — 20:32
  • Jeremy Pierce

    On second thought, maybe not, if M is restricted to essential properties. It’s hard to imagine anyone thinking those could be synthetic a priori.

    February 2, 2010 — 20:38
  • Jeremy Pierce

    I think there is a more serious problem, though. Doesn’t instantiation assume the thing you’re instantiating exists? You can’t instantiate unless you already know that there is such a thing that you’re naming.

    February 2, 2010 — 20:54
  • M.

    I’d like to know more about the “□1” operator. Is □1Fx supposed to imply that x exists and is F, or just that if x exists, then x is F (by a priori/conceptual necessity)? If the former, I’d deny premise 1.2. If the latter, I’d deny 1.0. Either way, I suspect there’s some sort of equivocation going on.

    February 2, 2010 — 21:07
  • A Posteriori Necessity

    “Again, almost no theist maintains that we know the essential properties of God aposteriori. The reason this is rejected is because it entails that we might have discovered that God was less than essentially perfectly good, etc.”
    Almost no chemist maintains that we know the essential properties of gold a posteriori. The reason this is rejected is because it entails that we might have discovered that gold had an atomic number less than 79, etc.

    February 3, 2010 — 1:35
  • Shouldn’t the logical form of 1.2 be the necessitation of a conditional? It’s an a priori conceptual truth that (If God exists, then God instantiates essential property M). Like Jeremy, I presume that properties are instantiated only by (or in) existing things. Unicorns, being nonexistent, don’t instantiate any properties. So your argument would show only that the same conditional is metaphysically necessary: If God exists, then God instantiates essential property M. It wouldn’t establish the existence of God.
    Analogy: Let “C” abbreviate “the smallest counterexample to Goldbach’s Conjecture.” To use your phrasing, it’s a priori that C is essentially an even number, essentially greater than two, essentially not the sum of two primes, and necessarily existent [if existent at all]. But none of that shows that C exists; disproving Goldbach’s Conjecture isn’t that easy.

    February 3, 2010 — 6:20
  • Mike Almeida

    I think there is a more serious problem, though. Doesn’t instantiation assume the thing you’re instantiating exists? You can’t instantiate unless you already know that there is such a thing that you’re naming.
    Jeremy, I’ve instantiated a conditional, so there’s no problem. You might not think that there are sets, but I know apriori that the empty set is essentially empty only if it is essentially empty as a matter of metapysical necessity.
    Addendum:
    Jeremy, you might be worried about 1.2 rather than 1.1. Steve has the same worry below. See if my response to him helps at all.

    February 3, 2010 — 6:55
  • Mike Almeida

    Shouldn’t the logical form of 1.2 be the necessitation of a conditional? It’s an a priori conceptual truth that (If God exists, then God instantiates essential property M).
    Hi Steve,
    No, not for traditional Anselmians who accept the argument from Proslogion 3 (Malcolm, for instance, and I think most theists). On this view, it is a conceptual impossibility that God should lack the essential property of necessarily existing. That is, it is apriori impossible that God should fail to (necessarily) exist. That is the concept of God we are talking about in (A). On the other hand, I do not know apriori that there is the C you are talking about.
    I think the concept in (A) is the common concept of God among theists (or maybe theists who are philosophers). I think it hasn’t been noticed how quickly it entails that God exists. I also think you’d be right to wonder whether we do know apriori that God has the essential property of necessarily existing. I happen to think we know that aposteriori, and the same goes for the remaining essential properties, but I’m in the minority (maybe a minority of one).

    February 3, 2010 — 7:11
  • Mike:
    I can’t parse (A). Did some word drop out?

    February 3, 2010 — 7:54
  • Mike Almeida

    Right, thanks Alex! It’s corrected now.

    February 3, 2010 — 8:27
  • A couple of issues, some very minor:
    i. I think a lot of theists think we know God’s essential properties a posteriori–specifically, think we know God’s essential properties by divine revelation.
    ii. I am having a hard time following the argument, because I don’t know how the word “God” is functioning in it.
    Option 1. “God” is a definite description. In that case, as it stands, (A) trivially commits one to the existence of God, at least on Russell’s analysis of definite descriptions. To get out of the commitment, we need to say something like: For all x, x is divine only if …. But then we don’t get to use “G” in 1.1.
    Option 2. “God” is a proper name. In this case, (A) begs the question, unless we are working in a free logic. Is free logic the trick here?
    iii. In 1.0, you are assuming, I think, that entities can instantiate non-logical properties in worlds where the entities don’t exist. (Suppose Descartes is right that it’s a priori that I’m essentially a thinking thing. Then, by 1.0, in all worlds I am a thinking thing. But I don’t exist in all worlds.)
    iv. What about parodies? Isn’t it a priori that the necessarily existent non-divine person essentially has the properties of (a) necessary existence and (b) possible non-divine personhood? But then we conclude that there necessarily exists someone who is possibly a non-divine person. But the only being that is both possibly a person and necessarily exist is God, and God is not possibly non-divine.

    February 3, 2010 — 9:20
  • Mike: I interpret Malcolm (1960) differently. He rejects the Proslogion 2 argument as “fallacious” (44) because it relies on the “false” (44) and “remarkably queer” (43) doctrine that existence is a perfection. He defends the Proslogion 3 argument because it relies on the more plausible doctrine that necessary existence is a perfection. But in order for his different attitudes toward those two arguments to make sense, Malcolm must mean that
    (N) Necessary existence is a perfection in anything that already exists: among those things that exist, those that exist necessarily are (in that respect, and all else equal) greater than those that exist only contingently.
    But N implies only the conditional “If God exists, then God exists necessarily”; N doesn’t discharge the antecedent of that conditional. Malcolm later says (58), “Can anything be clearer than that the conjunction ‘God necessarily exists but it is possible that He does not exist’ is self-contradictory?” There I’ve always read him as simply confusing epistemic and logical possibility: critics of the second ontological argument agree that God necessarily exists if God exists at all, but they say it’s epistemically possible that God doesn’t exist (just as in the case of C in my example). There’s nothing self-contradictory in that criticism.
    You, by contrast, interpret Malcolm as saying that the Anselmian concept of God is such that, a priori, the concept must be fulfilled, i.e., such that, a priori, something must answer to the concept. In that case, however, I can’t make sense of Malcolm’s rejecting the Proslogion 2 argument and spending pages defending N as distinct from the doctrine that existence is a perfection. I don’t know which of our readings is less charitable. In any case, if you’re not relying on the doctrine that existence is a perfection, why should anyone accept that the Anselmian concept of God is such that, a priori, the concept must be fulfilled?

    February 3, 2010 — 9:48
  • Mike Almeida

    (N) Necessary existence is a perfection in anything that already exists: among those things that exist, those that exist necessarily are (in that respect, and all else equal) greater than those that exist only contingently.
    Steve,
    I’m pretty sure that is not the right reading. Malcolm writes,
    . . . when the concept of God is correctly understood one sees that one cannot “reject the subject.” “There is no God” is seen to be a necessarily false statement. Anselm’s demonstration proves that the proposition “God exists” has the same a priori footing as the proposition “God is omnipotent.” (51)
    His view is that denying that God exists is the expression of an apriori impossibility. It is tantamount to denying that triangles are three-sided.

    February 3, 2010 — 10:07
  • Mike Almeida

    i. I think a lot of theists think we know God’s essential properties a posteriori–specifically, think we know God’s essential properties by divine revelation.
    I htink that’s right. All I need is that God’s essential properties (most anyway, excepting the world-indexed properties) can be known apriori.
    Option 2. “God” is a proper name. In this case, (A) begs the question, unless we are working in a free logic. Is free logic the trick here?
    No, I don’t assume a free logic. (A) expresses an apriori necessary, conceptual truth. So, the analogy goes as follows,
    1. It is apriori necessary that the empty set has the essential property of being non-membered.
    2. It is apriori necessary that God has the essential property of necessarily existing.
    I know (2) in the same way that I know (1).

    February 3, 2010 — 10:15
  • Mathis

    “Almost no chemist maintains that we know the essential properties of gold a posteriori. The reason this is rejected is because it entails that we might have discovered that gold had an atomic number less than 79, etc.”
    I was thinking the same thing.

    February 4, 2010 — 8:10
  • Mike Almeida

    “Almost no chemist maintains that we know the essential properties of gold a posteriori. The reason this is rejected is because it entails that we might have discovered that gold had an atomic number less than 79, etc.”
    I was thinking the same thing

    I’m not sure I take the point, or know what the point is supposed to be. I don’t know any chemists that could offer a decent definition of ‘essential property’ or ‘aposteriori necessity’, let alone have beliefs about them. But obviously every chemist believes that all we know about gold is known only aposteriori. The reason theists do not believe that we can know God’s essential properties only aposteriori is in fact because they do not believe that it’s discoverable that God is less than omnipotent, etc.

    February 4, 2010 — 8:46
  • Mathis

    Mike
    The reason theists do not believe that we can know God’s essential properties only aposteriori is in fact because they do not believe that it’s discoverable that God is less than omnipotent, etc.
    This seems to rely on something like “A truth that can’t be known a priori is contingent” and “Gold’s atomic number is 79” seems like a counterexample.

    February 4, 2010 — 10:41
  • Mike Almeida

    This seems to rely on something like “A truth that can’t be known a priori is contingent” and “Gold’s atomic number is 79” seems like a counterexample.
    Oh, I see now. Let me clarify. Statements of aposteriori necessity–say, it is aposteriori necessary that gold’s atomic number is 96–are compatible with the discoverability that gold does not have atomic number 96. The claim that it is discoverable that gold does not have atomic number 96 is a claim about epistemic possiblity, not a claim about metaphysical possiblity. So while I of course agree that it is metaphysically necessary that gold has atomic number 96, it is nonetheless epistemically possible that it doesn’t.
    Theists won’t concede that it is even epistemically possible that God fails to have the traditional essential properties. They deny it because it entails that we can conceive of God as a less than omnipotent, omniscient, etc. being. But we cannot so much as conceive of God that way.

    February 4, 2010 — 13:29
  • Mathis

    Now I know what you are talking about! Makes sense now, but now I’m more worried about parody-arguments. I will have to re-think this.

    February 4, 2010 — 14:03
  • Mike Almeida

    . . . but now I’m more worried about parody-arguments. I will have to re-think this.
    One way to handle parodic arguments is to deny, for instance, that we know apriori that perfect islands necessarily exist. It’s obvious that we do not know that, since for any island I in any world W, it is possible that I does not exist. Take a perfect island on planet earth, for instance. Since it is possible the planet does not exist–it might have been blown to bits by any number of meteorites–it is possible that the island doesn’t.
    But as I said in the post, I’m not so interested in the soundness of the argument. I happen to think it is unsound. I’m interested in showing how implausibly strong traditional concept of God is. It’s so strong that it makes neat apriori demonstrations easy to generate.

    February 4, 2010 — 14:39