A modern symbological assessment of the ontological argument for the existence of God

Great Debates
41

—Egad, it occurs to me that you don’t know what we mean by positive and negative descriptions. Positive definitions are descriptions of immediate observations. Negative definitions are descriptions of mediate observations. Tisthammer et al are not saying what God is not.—

Aren’t they? Then where do they say what it is? And none of these definitions can come from any theoretical observation without at least one theoretical immediate observation. How would you know WHAT you are looking at to determine that it was not part of a particular set?

—They’re describing what God is in terms that they cannot know directly, but can only conceive.—

By concieving only of what it is not!

—That is what is meant by positive and negative descriptions.—

Every description used so far has been a case of describing what this entity god lacks. But an entire host of lacks does not add up to an entity (unless this is a “process of elimination” out of a finite number of known possible entities). A negative description is certainly useful for distinguishing elements of a set from everything else, but it alone CANNOT define a specific entity.

I’m simply making the point that it is trivially easy to prove anything you wish when you do away with the need to ever specify what it is that you are proving.

—Infinity is no different. You have never observed a set that remains the same size when an element is removed. It is something that you must conceptualize.—

But I can’t conceptualize it, can you? I can only mouth the words that make up its definition, and then try to analyze whatever logical content I can unpack from that definition. But that exercise alone is simply not enough guarantee that we are discussing anything at all.

—And some of this childish ridicule at the God definition sounds like someone making fun of the idea that both the set of integers and the set of even integers are the same size.—

You can address my arguments if you please, or not if they are beneath you, but no editorializing or accusations please. I apologize for the over the top oogly comment, but the gist of it is that “define negatively as the intrinsic maximum of existence” does not seem to have any meaningful content that I can analyze, especially containing, as it does, this strange term “maximum of existence.” How can “existence” have a “maximum”? What does this claim mean?

—But it[infinity] does exist in a context of topological space, where you can use it to describe what certain sequences of numbers converge to.—

As I noted, it exists because a particular definition is given, and portions of that definition are unpackable so as to draw workable logical points. But that simply does not guarantee that we are having a meaningful discussion. One can pack anything they wish into a definition for use later on, even the stipulation that none of its elements contradict.

—No serious treatment of the ontological argument, even by its most famous detractors, wastes time and intellectual resources by quibling over whether the definition is adequate.—

I suppose you are an arbiter of what a “serious” treatment is? To even give the argument a serious treatment one would first have to agree that it is a meaningful argument. But many do not: they can’t give it any sort of treatment at all. So obviously if you go looking for serious treatments of it, you aren’t going to find dectrators of my sort.

—Nor can you use descriptors that are ontologically dualistic. You may not, for example, assign to Him both the maximum power and the maximum impotence, nor the maximum goodness and the maximum evil.—

Why not? Isn’t that a great feature of “f”?

42

Let’s put aside my second observation for the moment and let me concentrate on the first.

**
Of course you can. I can use this proof to prove that there exists a being that has any one of the attributes of God as easily as I can use it to prove that there exists a being that has all the attributes of God. Your comment regarding “The being different from both of them that is both omnipotent and omniscient.” suggests you agree that these beings need not be the same being. In other words, there exists a being that is omnipotent “as possible” but not necessarily omniscient “as possible.” This being isn’t “God” under the definition but can still be shown to exist using the proof.

You could, I suppose, impose a condition in the definition that only “God” can have any of the attributes of God. This again, however, raises the “orthogonality” problem. Nor do I see how this can be a valid proposition. By the same token, you could simply refuse to define what you mean be "greatest possible being. However, this gets you right back to the “greatest possible chicken” problem.

**
Why not? I can use any descriptor that is a) an objective criteria and b) has an intrinsic maximum. Define “God” (maximal perfection) anyway you like, “God” is as omnipotent “as possible,” and as omniscient “as possible,” etc., etc. I can then use your definition and this proof to show that there is another being that meets all of the criteria of your definition and yet has some non-essential, yet unique, property.

To illustrate, consider the “maximally perfect” circle. We can easily, and precisely, define what this means. A “maximally perfect” circle has a radius. However, the radius is a non-essential property of “maximally perfect circularity.” A circle with “radius 5” can be just as “maximally perfect” as a circle with “radius 1/2” there are, therefore, an infinite number of “maximally perfect” circles.

43

That makes no sense. If you go around it 10 times, the distance will be 10 * (pi)d. If you go one less time, the distance is 9 * (pi)d. The latter is smaller than the former.

Newton,

Your non-modal objection sounds an awful lot like Alston. But as both Oppy and Plantinga have said, existence may be analytic. In such cases, comprehension about the essence of God is not an essential part of an ontological argument. The question is whether this is one of those cases.

It is very important to make the assumption that G->G because if we don’t, then we aren’t even talking about God. Being merely possible is not the same as being necessary. And God has been defined as the maximum possible perfection. If existence exists, then the greatest possible form of existence is necessary existence. Thus, it is axiomatic that if God exists, then He exists necessarily.

It’s not a4; it’s e4.

I think what you’re wrangling with most is the second axiom. But you simply cannot put together <>~G with G->G unless you are equally willing to assume that existence might not exist. ~G would not hold true in any possible world. You end up with a contradiction of the definition.

Your modal objection seems mainly centered around applying Becker’s Postulate to ~G because the postulate does not apply to the modal category of actuality. If it did, we could, as you say, simply say that God exists, therefore God exists. However, actualities are inclusive of possibilities (everything that is actual is possible). So, if we step from an actual world to a possible word and then back, it is no dirty trick. To reject the application of Becker’s Postulate to this step would be tanamount to talking about things that are “possibly impossible” (in S[sub]4[/sub] modality) or “categorically impossible” (in S[sub]5[/sub] modality).

Despite what Kant said, there are existential propositions that are analytically true (e.g. “there is a prime number between 7 and 12”). Existence is predicative (as you pointed out). And remember that denial can be substantive. If you want to posit that there is no perfect chess player, then you must first posit that the perfect chess player is possible (a substantive claim).

That’s another reason you can’t posit that there is no God without at least positing the possibility of His existence. And doing that, of course, forces you to posit that if He exists, then His existence is necessary for the reasons stated above.

Apos,

I apologize for my high-handedness with you. That was a reflection on my own weak character, rather than your academic ability. I really can deal with only one of your questions:

It means existence where perfection converges (i.e., necessary existence).

44

No, you can’t. What would your first axiom be?

Because that would make the universe a shoe (gravity — the shoe would “eat” the universe).

45

But that’s a priori synthetic. Why does it need an ontological argument?

46

Fine. It is also very important to make the assumption that G, that God necessarily exists. If you allow the assumption that it is possible that he doesn’t exist, then I construct the proof:


1. G -> []G, assumption: if God exists he necessarily exists
2. ~[]G, assumption: it's possible God doesn't exist
3. ~G, modus tollens: God doesn't exist

If you adopt the axiom G->G with the intention of proving God exists, you are compelled to insist on the axiom G, that God has to exist.

Well, then. Since we have the modal axiom A->A (known as M, used in the other proof, valid whenever our accessibility relation is reflexive), why not just exhibit this proof:


1. []G, assumption: God has to exist, consequence of adopting G->[]G
2. G, modal axiom M: God exists

It’s shorter, simpler, and avoids all my concerns about which accessibility relation you’re using (or that you might surreptitiously vary it). God has to exist, therefore he does. The assumptions are the same as before, the line of inference is obvious, it’s perfectly valid.

I suspect that this is the type of proof that you will find convincing if you believe that God exists, but not very illuminating at all if you haven’t decided or if you don’t believe that. My objection is, though it’s hidden under a thick layer of modal baggage, the proof rests on the direct assumption that God has to exist.

47

**

You need merely “re-define” God[sub]omnipotent[/sub] to be that being with the greatest possible omnipotence.

**
You are unintentionally misquoting me. The key point here is the “as possible.” While I cannot speak of a shoe that is larger than the universe, I can speak of a shoe that is as large “as possible.”

I think you are also missing the explanation of my thinking which would be that bit after “Why not?”

48

Well put, Newton! You truly cut through to the chase, although I hope you don’t mind if I rephrase this:

It rests on the direct assumption that if God does exist, He must exist necessarily.

I believe that you and I have now found common ground thanks to your excellent expository skills.

But I was asking about your first axiom after you’ve redefined God that way. How will you say that the existence of a being who is not the most knowledgeable, for example, is necessary? You can’t begin with the axiom G -> G.

Yes, but we can synthesize how large that is.

You mean this?

But I thought my circle answer dealt with the whole general notion of existential arguments about synthetic propositions. What’s the point of it? You can make much more effective and direct arguments without concerning yourself about the nature of existence. Remember that, by definition, all of God’s attributes are essential (or necessary). He has no nonessential attributes.

49

Libetarian:
[qutoe]. If you want to posit that there is no perfect chess player, then you must first posit that the perfect chess player is possible (a substantive claim).
[/quote]

Why?

Newton Meter:
I don’t think your charge of question begging is fair. The term “question begging” refers to a conclusion made before it is proved. By insisting that a verdict be rendered on <>~G before the proof begins, you are, for lack of better term engaging in “entrapment”.

50

Because the denial of any positive existential statement would be self-contradictory. (See “The Ontological Argument Revisited”, by William Alston, Philosophy Review vol 69, 1960, pp 452-474)

51

Newton,

This just occured to me as I was responding to Ryan. Would you agree at this point that so-called “hard atheism” is the least tenable philosophical position toward God inasmuch as it will not even allow the possibility of His existence, thereby constituting a substantive denial of a positive ontological proposition; i.e., how can that which is not possible be possibly impossible?

52

**
Sure you can. Let me lay it out using the same framework.

You say, “God is the greatest possible being. The greatest possible being has the greatest form of existence which is necessary existence.”

I say, “God[sub]-omnipotence[/sub] is the greatest possible being that is not omnipotent. The greatest possible being who is not omnipotent still has the greatest form of existence which is necessary existence.”

You can repeat this as needed to unbundle each of “God’s” attributes.

Let me return to your other points later.

53

Why, that’s silly, Truth. :slight_smile: If power exists, then necessary power is the greatest power, and God, as the necessary being, must have it as an attribute. I think you’re the one being orthogonal. You’re chipping God up as though you’re cutting a diamond. He must have every necessary attribute and none that are unnecessary. That is the only way that the axiom “if God exists, then God’s existence is necessary” makes any sense.

54

Why? And just what are the definitions that you are using for all those big words?

And what do you make of the phrase “the most perfect denial of a positive existential statement”?

55

A positive statement is a statement that is synthetic a priori. An existential statement is an ontological proposition. A denial is the negation of a positive statement. And a self-contradiction is a statement that has no truth value in any possible world.

My guess would be that “the most perfect denial of a positive existential statement” would be ~e (existence does not exist).

56

Yes, I am treating the attributes of “God” as independent. Which I believe they must be, otherwise, the definition of “God” as the greatest possible being has a subjective component. (It’s that “as possible” thing again.)

Remember, I’m not, for the moment, talking about “God,” I’m talking about whether this argument we are discussing can be used to prove the existence of a being who is just like God except that it is not omnipotent, or whatever. My definition of God[sub]-omnipotent[/sub] is not "God.’ However, it seems to me that if this argument proves that “God” exists under your definition, then it also proves that God[sub]-omnipotent[/sub] exists under mine.

As for whether “if God exists, then God’s existence is necessary” makes any sense or not, well, that’s one of the things we are trying to determine. As you know, one cannot dismiss a reductio ad absurdum argument by claiming the result is silly. On the contrary, that’s the hallmark of validity!

57

I don’t have a problem with your reduction per se. The problem that I have is with your reduction attempting to retain the same axiom that g -> g. I don’t think you can say that unless you’re dealing with the whole g. If Newton is concerned about Tisthammer jumping between worlds, he ought to recoil in utter horror when it is done with the very first assertion that is expected to be taken as true on its face.

Just to isolate this one thing, if you want to deal with it further: the problem with your definition of God is that you must develop some other first axiom than G -> G. Clearly, a being that is not as perfect as possible is not as perfect as possible.

And it isn’t a matter of objectivity versus subjectivity, but of direct observation versus indirect. All observations are subjectively processed, and those matters would address the nature of reality rather than existence, and as such, would belong to a more general metaphysical treatment. For an ontological argument, you need not concern yourself with what a maximum is, but merely with whether it is.

58

You have a valid criticism. One man’s petitio principii is another’s convincing deductive argument. In my defense, I was not merely tossing accusations of question-begging around hoping they would stick. The essence of begging the question is not that it’s an invalid argument (it is valid), but that the argument lacks explanatory or (especially) persuasive power due to assuming (possibly indirectly) that which is to be proven. I feel that Tisthammer’s argument suffers this.

Wow, that really puts me on the spot. If I understand the question (I think I do), then my answer has to be “yes”. I think hard atheism is necessarily unsound and incomplete. It is proves too much. Soft atheism can be made to avoid this criticism.

Well, I recoiled, but maybe not in utter horror. I have a different criticism of the argument than you do, Truth Seeker. My criticism is that Tisthammer is forced to adopt a modal semantics such that we can no longer claim to think that his set of “possible worlds” necessarily includes the actual world. The same problem is present for any modal interpretation of his axioms and proof. An attempt to give a different value for G or assign a different meaning to G->G, and then use the same proof to arrive at an absurdity will be vulnerable to my criticism.

It may be that the arugment is vulnerable to reductio ad absurdum as well, but that’s not clear to me. In either case, I think my objection trumps yours. I’m not sure that absurdities that are incapable of entering the actual world are damning :slight_smile:

kg m²/s²

59

**
With respect to the attribute of existence, why is my God[sub]-omnipotent[/sub] any “less perfect” than “God?”

I think you risk slipping from logic to religion here. The original premise of this particular argument, to quote Tisthammer was, “One argument for the first premise is that the greatest possible being would by definition have the greatest possible form of existence: necessary existence. If this is true, it logically follows that If God exists, he does so necessarily.”

You may, if you like, postulate that omnipotence is a prerequisite to necessary existence. This strikes me a being more a matter of religious faith, however, as I do not understand why this would be logically required.

Within the structure of this proof, my “being who is just like God except not omnipotent” has every characteristic of “God” except omnipotence. If God exists, one of God’s characteristics is necessary existence. Therefore, God[sub]-omnipotent** exists if God exists.

This is closely related to the “greatest possible island” problem except that it removes the objections regarding subjectivity, etc.

I think this illustrates a problem with a lot of ontological proofs. They’re fine until you do concern yourself with the definition. When you do, you find that these arguments may “prove” all kind of things that their proponents may be uncomfortable with.

Newton Meter
Perhaps I can be a back-up argument. :wink:

60

It isn’t. But that isn’t what it’s saying. It’s not saying that omnipotence is a prerequisite to necessary existence. It’s merely saying that if power exists, then the greatest possible power must exist necessarily. God is the convergence of all greatest possible attributes.

You’re making a mistake. There is no lack of definitions. Maximum is defined. But that does not mean that you know (or even can know) what the manifestation of that maximum might be. It is a positive attribute.

Regarding your general disdain for ontological arguments, I’m afraid that if you eliminate ontology, you wipe out science with one fell swoop. Another term for “ontological observation” is “common sense”. See Formal Ontology, Common Sense and Cognitive Science, by Barry Smith, from the International Journal of Human-Computer Studies, 1995.

Finally, regarding definitions, you may pick at them all you like, so long as you allow the gander to enjoy what the goose enjoys. For example, how would you like it if I began to hone in on your objection, and ask you to define “definition”. Believe me, if you allow this process to begin, we will be here until one of us dies.