Kenny

I’m not making the following claim: “Because God is maximally great, if there were another omnipotent being, it would be impossible for that being to frustrate God’s sovereign decrees.” I’m claiming, instead, that: “Because God is maximally great, it is logically impossible that God’s sovereign decrees could be frustrated.” This latter claim accords with the traditional Christian understanding of divine sovereignty as a worship-worthy-making property of God. It may, in turn, follow from this claim, in conjunction with God’s necessary existence, that it is logically impossible for certain other types of omnipotent beings, besides God, to exist. If the logical possibility of certain types of omnipotent beings other than God implies the logical possibility that God’s sovereign decrees could be frustrated, it follows, on theistic metaphysics, that it is not logically possible for such beings to exist.

Presumably there could only be one ground of all being in any particular possible world -- it doesn’t seem to make any sense to say otherwise. If possessing maximal greatness entails that one is the ground of all being in all possible worlds, and if it is impossible for anything other than the ground of all being, with respect to a particular possible world, to create ex nihilo (something which at the very least would seem a plausible candidate for a metaphysically necessary truth), it follows that in all possible worlds, any being which has the power to create ex nihilo possesses maximal greatness.

Perhaps that is where your intuitions lead you. I must point out, however, that since your argument is an internal critique of theism, it must assume theistic presuppositions at the outset, for the sake of argument, including theistic intuitions concerning what is and what is not a great-making property. That being said, within classical monotheism, the fact of God’s uniqueness is an aspect of His greatness; God is so great that He has no possible competitors; no other being could possible match Him in His greatness.

Within the boundaries of this discussion it is clear that there is at least one – namely, God. Again, since your argument is an internal critique of theism, it must take on theistic assumptions at the outset. You could argue, for instance, that it is impossible for God to be omniscient because it is impossible for God to exist and non-existent beings are incapable of knowing anything, but as a theist, I don’t see what I should find such an argument a compelling reason to believe that God does not exist.

Still, we can ask the question as to whether or not God has any compelling reason to believe that a maximally great being exists and that He is identical with this being, which, from what I gather from your discussion below, is the point you are driving at. I think the answer is “yes…”

It depends on which philosophers of religion you ask, I suppose. I don’t think that it is doubtful, especially if we are assuming theistic metaphysics for the sake of argument. Again, God, on classical theistic metaphysics, is understood to be a logically necessary being. Thus, it would seem that denial of God’s existence must entail a logical contradiction in some sort of non-trivial way. At least, it doesn’t seem plausible that a necessary truth is such that its negation could entail a logical contradiction solely by means of material implication.

On theistic metaphysics, it is impossible for a being to have all of God’s attributes and not be necessary. Being necessary is understood to be somehow fundamentally related to God’s attributes. As the Scriptures would put it, there is something about God’s nature such that God has “life in Himself.”

All that being said, I think it is beneficial to stop and reflect on where we are in this debate. I think we both agree that what I have proposed as a means by which God could verify that He is omniscient is an epistemic possibility, and therefore no rigorous contradiction has been demonstrated as following from the proposition that God knows Himself to be omniscient. The debate has thus shifted to a debate over whether or not it is plausible, given the other assumptions of theistic metaphysics, that God could know Himself to be omniscient. In order to make the case that it is plausible, all I have to do is effectively argue that the proposal I have set forth is also plausible on theistic metaphysics. I don’t, on the other hand, have to provide any sort of rigorous demonstration that my proposal is actually possible to make an effective plausibility defense. I think I have met my obligation in this respect, though part of the debate may, in the end, simply boil down to conflicting intuitions concerning the plausibility of certain scenarios. In that case, we would simply have to agree to disagree.

God Bless,
Kenny.

P.S. Thomas, I must say I am impressed with the quality of your posts, here and elsewhere. Though I do not have time at the moment to contribute, I have found your Does God pass the Maximal Power Test? thread to be most impressive. If you don’t mind me asking for the sake of my own curiosity, I noticed your profile lists you as a student. What are you studying, and at what academic level?

Kenny

With respect to the ontological argument, maximal greatness is to be understood in a qualitative moral/aesthetic sense. <a href="http://www.stats.uwaterloo.ca/~cgsmall/ontology.html" target="_blank">Kurt Godel</a> proposed that this might be understood in terms of possessing a maximization of all the positive aspects (those aspects associated with existence as opposed to non-existence) of being. Other related concepts may be “unlimitedness” (which might be interpreted in terms of a lack of being qualified by any negative aspects of being), or the maximization of all perfections. Within a Christian understanding, God’s maximal greatness is associated with God’s worship-worthiness. In other words, God’s great making properties and the manner in which God holds them are exactly those properties which make it not only fitting, but morally obligatory, to ascribe to God an honor above and qualitatively different than honor ascribed to any other being.

Of course, this all presupposes that there are such things as objective moral/aesthetic truths, something which many atheists (but definitely not all!) would be inclined to challenge. However, since I am not using the OA in this thread to argue for the truth of theism, but to defend theism from an internal critique, and since theism typically presupposes that there are objective moral/aesthetic truths in some sense, I don’t feel any particular burden to defend the existence of such truths on this thread.

God Bless,
Kenny

Apikorus

I'm not quite sure what a "positive aspect" means. For example, is "tastiness" positive? Is "compassion" positive? What makes an attribute a positive one? If the answer is God, then the process becomes circular. If the answer lies outside God, then goodness (or positivity) exists independent of God, which might be problematic for theists.

The scale of greatness is also an issue. Is it a discrete or continuous variable? If there is a continuous measure of greatness, then it might be that the greatness scale is homeomorphic to the unit interval, with God's greatness equal to 1.00. There are still an infinite number of things arbitrarily close to God in greatness.

A related question has to do with the topology of the "greatness space", assuming it isn't something as trivial as a one-dimensional line segment. In that case, it may not be possible to maximize all greatness coordinates independently. For example, on the circle one can maximize x or y but not both simultaneously. There is an "easternmost" point and a "northernmost" point, and they are not the same point. It hardly seems clear a priori that one should be permitted to naively assume it possible to maximize all "positive qualities".

[ November 12, 2002: Message edited by: Apikorus ]</p>

Kenny

A “positive aspect of being,” as Godel defined it, is not being defined in a moral/aesthetic sense, but in an ontological sense. The idea is that contingent things are defined not only by those things which they are (the positive aspects of being), but those things which they are not (negative aspects of being). As a human being, for example, there are properties of being which I possess and properties of being which I lack. God, on the other hand, is not lacking in any positive properties of being, and thus God is not to be described in terms of any negative properties – that is, there are no aspects of non-existence associated with God’s essence. This accords with the classical theistic notion that, with respect to God’s being, existence and essence are identical. There is also a moral/aesthetic connection which intuitively follows from this. Philosophers and Theologians through the ages have associated the beautiful and the good with that which deepens our appreciation of being.

So, the answer to the question, “What makes an attribute a positive one?” is that a positive attribute attributes a quality existence to something whereas a negative attribute denies a quality of existence to something. Asking whether or not something’s being a positive aspect of being is a function of God’s nature or is independent of God’s nature, I think, may be meaningless if this version of the OA works; since, all the positive aspects of being are simply identical to God’s nature.

I’m not an expert in set theory so I might be going out on a limb here, but I think a better analogy might be the absolute infinite of set theory with something like the reflective principle being in operation. The reflective principle states that no matter how one tries to characterize the absolute infinite, there is always some other ordinal which falls short of the absolute infinite that meets said characterization. This analogy would accord nicely with Anselm’s definition of God in his original version of the OA: “God is that which none greater than can be conceived.” This definition could be taken to imply that no matter how great we might conceive something as being, God is still greater. This would also accord with the typical theistic intuition of God’s infinitude and that there is a sense in which God is ineffable (not that nothing positive can be said about God, but that it is impossible for a finite mind to fully grasp God’s nature conceptually).

Perhaps it isn’t possible to maximize all positive properties of being in conjunction with one another. It may be that, on certain intervals, certain positive aspects of being increase in degree while others diminish. That doesn’t necessarily mean that greatness, as a function of those aspects, doesn’t have a maximum. For instance, one might argue that a conceivable being (not necessarily a logically possible being) which can do all that God can do and also do evil is conceivably more powerful than God who can only do good (I’m not sure that this would actually be the case, but it is arguable). Consequently, one might argue that God’s goodness limits God’s power. However, one might still consistently hold that a being which cannot do evil is greater in a moral/aesthetic sense than a being that can do evil while still maintaining, all else being equal, that power is a great-making property.

Now, all that being said, I should point out that since we are assuming theistic metaphysics for the sake of argument here, we are assuming that there is something such that it is that which none greater than can be conceived (namely, God). If we were debating the OA within the context of an attempt to argue for the existence of God, then considerations such as you give above might be considered plausible reasons for objecting to the possibility premise of the OA. But, within the context of this discussion, we are already assuming, for the sake of argument, that the possibility premise holds (since if God exists, then it must be possible for God to exist).

God Bless,
Kenny

Apikorus

Kenny, the discussion still seems rather vague to me. Some concrete examples of "positive aspects of being" would be helpful. Could you explain, for example, whether "tastiness" is such a positive aspect?

I think your invocation of ordinals does not address my point on the topological properties of "greatness". On the unit interval, for example, the number 1.00 is "something such that none greater might be conceived". However, there exists an infinity of other numbers arbitrarily close to it. This doesn't seem to be quite what Anselm had in mind, but there doesn't seem to be anything inconsistent with this view.

What you say could be true if greatness itself were a scalar function of the (uncountably many?) positive aspects of being, i.e. a mapping from the space of positive aspects to the real numbers, say. But what if the target space itself is of higher dimension? What makes you think that greatness must be a scalar?

Even if we suppose that greatness is a scalar, that does not necessarily imply that it can be uniquely maximized. For example, on the unit disk with boundary, the radius is maximized anywhere along the boundary. There is an infinite continuum of (x,y) pairs which have the same value. One can even remove the boundary from this analysis and work with lim sup (taken along various radial directions).

The problem here seems to be that the fundamental working concept of "greatness" is ill-defined. I'm somewhat less concerned about the definition of a "positive attribute", but I think that is also susceptible to unraveling.

The problem here, it seems, lies in the origin of this moral/aesthetic sense. If it is determined by God, then again one has problems with circularity. If it exists independent of God, then that may contradict the notion that God possesses all positive attributes of being, since the moral/aesthetic sense itself seems to be a good candidate for such an attribute.

[ November 13, 2002: Message edited by: Apikorus ]</p>

Kenny

With respect to theistic metaphysics, power (since potential to act requires existence), goodness (since evil is merely the distortion or perversion of the good, goodness and not evil is fundamental to being), and consciousness (since, in theism, consciousness is something fundamental to the nature of reality as opposed to something derivative) are things that would be considered positive aspects of being.

“Tastiness,” in itself, would seem to be something which is by definition subjective, and therefore would not seem to be something, in itself, which is a positive aspect of being.

There may not be any immediately perceivable inconsistencies with such a view, but, if we are talking about a space consisting of other possible beings, it conflicts with the typical theistic intuition that there is an infinite qualitative distinction, in terms of greatness and worthiness of honor, between God and any other possible being. Since, within the context of this discussion, we are assuming theistic metaphysics for the sake of argument, I think we can dismiss this possibility. I suppose if we were talking about a space consisting of other conceivable beings (as a broader category than just logically possible beings) there might be some sense in which there are conceivable beings which are arbitrarily close to God in greatness, but, if so, this would seem to be a trivial matter. If I define God as the greatest conceivable being, then I can conceive of a definition of some other being, say Zoe, which is defined as being arbitrarily close to God in greatness, but not as great as God. Just because I can conceive of such a definition for Zoe, however, that does not render Zoe logically possible (there are many things that I can conceive of, such as a unit circle with a circumference exactly equal to 3, for example, which are not logical possibilities).

I don’t see how greatness, understood in this sense, could be anything else but scalar. With respect to positive aspects of being, we are talking about qualities with varying degrees. I don’t see how it could even make sense to talk about any sort of vector space in this context.

Again, if the OA were being used here as an attempt to prove the existence of God, then a consideration such as this might be a plausible reason to cast doubt on the possibility premise of the OA. However, since the OA is not being used here to prove the existence of God and we are assuming the existence of God for the sake of argument, this has no relevance to the current discussion. Within theistic metaphysics it is understood that in God’s being, greatness is uniquely maximized. Therefore, on theistic metaphysics, the topology of the greatness space is such that greatness does have a unique maximum.

If there is an objective and fundamental relationship between moral/aesthetic considerations and positive attributes of being, then I think it may be meaningless to ask whether this sense is determined by God or independent of Him. If God uniquely maximizes beauty and goodness by holding within Himself all the positive attributes of being, then God’s essence is simply identical with ultimate beauty and goodness, with beauty and goodness being neither independent of God (because something cannot be independent from itself) nor arbitrarily determined by God (since God’s essence is what defines God, not something arbitrarily determined by God).

That all being said, I’m not exactly sure what relevance this all has to the current discussion. As I have already argued, if classical theistic metaphysics are true, then it would seem that there must be a successful ontological argument. Since we are assuming such metaphysics for the sake of argument, and if I am correct in my arguments on this account, then it would seem we would also have to assume the existence of a sound ontological argument for the sake of argument (even if we are incapable of producing it). Objections to the possibility premise of the OA might be considered independent reasons for doubting the existence of a necessary being and therefore doubting theistic metaphysics, but that would be a different line of argumentation than what was presented in the OP. Consequently, I have no desire to get involved in a lengthy discussion of the possibility premise of the OA here, except in-so-far as that discussion relates to the OP and the plausibility, on theistic metaphysics, of the scenario which I have presented.

God Bless,
Kenny

Thomas Metcalf

Kenny:

Sorry about the late reply, first of all. I've had plenty of schoolwork and work-work (albeit in the philosophy department's writing center) but I think I'm ready to get back into this discussion.

"Still, we can ask the question as to whether or not God has any compelling reason to believe that a maximally great being exists and that He is identical with this being, which, from what I gather from your discussion below, is the point you are driving at."

Yes; I should have been clearer about this.

"Again, God, on classical theistic metaphysics, is understood to be a logically necessary being. Thus, it would seem that denial of God’s existence must entail a logical contradiction in some sort of non-trivial way."

But my criticism is that ontological arguments seem to make some very fundamental mistake about reasoning itself. I trust that no one can see how the denial of God's existence entails a contradiction without already knowing that God exists, and that no one would even know where to begin to look. I must say again that until I have reason to believe some ontological argument might be sound, even to God, I will not find it likely that such an argument is available. The continued failure of ontological arguments simply raises too much doubt in my mind, and leads me to a suspicion that all the salient ones make a similar mistake somewhere. I think there's a reason that no ontological argument seems to appear intuitively sound to anyone when she first hears it, and most philosophers seem to end up rejecting them even after careful study. In short, I'm prepared to assert that no ontological argument is sound in the right way, and such a broad generalization should be very vulnerable to what look like counterexamples.

"On theistic metaphysics, it is impossible for a being to have all of God’s attributes and not be necessary. Being necessary is understood to be somehow fundamentally related to God’s attributes."

Then this again is just highly dubious. In my experience, no one can think of a reason why God's other attributes suggest necessary existence, why any attribute could even be connected to necessary existence save other alethic modal predicates or contradictory attributes, or even that alethic modal status is a determining predicate in the first place. In my experience, there are no necessarily existing entities; furthermore, there are no entities whose alethic modal status is at all tied up to their attributes except if they have contradictory attributes. These are all some reason to doubt that necessary existence can be inferred from God's other attributes, so I would hope for positive reasons in the other direction.


As for God's omnipotence and his being the Ground of all Being.

"Because God is maximally great, it is logically impossible that God’s sovereign decrees could be frustrated."

As I see it, either God's omnipotence is tied up with His maximal greatness or it isn't. If it is, then God can't confirm His own omnipotence because He still doesn't know whether He is maximally great (because He doesn't know whether He is omniscient yet). If it isn't, then there could be omnipotent, yet non-maximally-great beings. God could very well know He is omnipotent, but not yet know that He is maximally great and therefore that there is a being Whose sovereign decrees are never frustrated. God could know He is omnipotent but not yet know that theistic metaphysics are true. I guess I'd need more argumentation to show that God can tell His sovereign decrees could never be frustrated, not just that they never are frustrated.

"...and if it is impossible for anything other than the ground of all being, with respect to a particular possible world, to create ex nihilo..."

I'm afraid this doesn't seem to follow for me at all. Presumably, God is finding Himself to be able to create ex nihilo, but this just means to create without using physical stuff antecedently. It certainly seems possible for God to give other beings the ability to create ex nihilo if He chose, and some dualists about the mind would probably say that humans create ex nihilo all the time.

"If you don’t mind me asking for the sake of my own curiosity, I noticed your profile lists you as a student. What are you studying, and at what academic level?"

I'm a junior in philosophy at the University of Washington, in Seattle. Right now the two philosophy classes I'm taking are Intermediate Logic and Modern Philosophy, and next quarter I will be in Philosophy of Law, Bradley's Idealism, and a graduate seminar on personal identity. My principal interests are philosophy of religion, ethics, and social/political philosophy, although I'm having a hard time narrowing down to a few foci.

In response, you have provided by far the best consistent apologist response on this thread, and are one of two theist posters that make things (happily) far from easy for me on this board. Strong debate helps me to refine my arguments, and yours is some of the strongest, so I must thank you in return. What are you studying?

[ November 21, 2002: Message edited by: Thomas Metcalf ]</p>

Apikorus

Why is "tastiness" any more or less subjective than "goodness"?

That there might be different dimensions to greatness is hardly bothersome to me. Perhaps the assumption that greatness is a scalar is unwarranted.