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

[TVAA]

I hate to gloss over all of the wonderful symbolic logic that has been brought to the argument, but it really isn’t that necessary. The basic concepts are fairly clear, after all.

Clearly, if anything exists (and presumably has at least one property), there must be an example of any existing property such that there is no better example. We take for granted that things exist, and that they have properties. There’s no problem.

The original Ontological Argument is not the same as the one presented in the OP, so its disproof isn’t relevant.

Forgive me if this has been brought up: what happens if there are two beings who are equally great, and all other beings are lesser? Considered as a category, the two beings are greater than all others, but there is no single being that is the greatest.

However, it would still be true that there would be no beings greater than the two.

[Liberal]

Vorlon

Forgive me if this has been brought up: what happens if there are two beings who are equally great, and all other beings are lesser? Considered as a category, the two beings are greater than all others, but there is no single being that is the greatest.

When (y = x), there aren’t two things, but one. Welcome to Straight Dope Great Debates.

[Liberal]

Ethic

God is then the set of all meta properties, which makes God more equivalent to a Platonic eternal state than a maximally compassionate and maximally loving being. We have in fact stripped the term God of its intuitive meaning.

Given the sublimely prejudicial nature of human intuition, that might be a good thing.

[Liberal]

Night

You still have not responded to the fact that this [it is self-contradictory] is not the reason he threw out <>~G. He threw it out, by his own admission, because it contradicted the definition. Because it is absurd to conclude that “the greatest POSSIBLE being” is not possible.

You misunderstood Tisthammer. He wrote:

“The greatest possible being cannot possibly exist,” which is absurd because of its self-contradictory nature given the coherent, meaningful definition of God.

Emphases mine.

And it is clear that the word possible is being used to mean possible in reality.

The word possible is being used strictly in its technical sense of truth in at least one possible world.

There is no way we can know that it is possible for any being to exist necessarily.

Please see above where I proved that assertion false. (I don’t take credit for it; it is a common knowledge proof that serves as the very basis for modal logic’s validity.)

[Liberal]

Dryga

Anyway, I can’t think of any other actual ways to define ‘perfect’. Of course you can list lots of attributes – the most knowledgeable, the one with the most physical strength, etc. – but shouldn’t it be possible to think of infinite attributes that are non-boolean and can be more or less perfect? Maybe even attributes that are self-contradictory?

There are technical reasons why the attributes that are assigned to God are Godlike in nature. Perfect goodness, for example, rather than perfect evil. And these have been covered in the discussion; e.g., all attributes assigned to Him must be negative since contingency is the primary positve ontological state. Necessary existence is derived from contingent existence as its negation. And so on. We can’t talk about how “big” or “little” He is because those attributes are contingent on comparisons to other things. We can say only that He is the “perfect size”.

But perhaps a more intuitive and less technical reason can be seen through a simple first-order syllogism via a thought experiment. Imagine a god who is perfectly evil, rather than perfectly good. Unless we change the definitions of good and evil, it can be assumed that the perfectly evil god will be perfectly destructive and will therefore already have destroyed himself and all necessary existence. But we can prove that necessary existence exists; therefore, God cannot be perfectly evil.

If God were self-contradictory, then self-contradiction would constitute perfect (necessary) existence. That would mean that our logic would be self-contradictory, and it isn’t. Contradiction implies contingency since no contradiction is evident without an implication.

[Dryga_Yes]

Sorry for going off on a tangent, Lib, but I’ve got another question: Is it possible that there exists a universe with no beings at all in it? If not, why?

[Liberal]

No, because a “being” is a thing that exists (derived from “to be”). A universe consisting of nothing has no context for existence.

[TVAA]

We can’t say how big or little something is, but we can talk about whether something is largest or smallest, since we can use the object itself to compare it. Thus, if there is only one object with the property of size, it is both the largest and smallest.

We can show that the greatest example of any property must exist if there is at least one thing existing that possesses that property, but we can’t show that there is necessarily something that is the greatest in all properties, or even more than one.

What is the definition of evil? Why does evil have to be destructive? And what, exactly, does ‘perfect’ mean?

Lastly, if two things have exactly the same properties, they are the same thing. But, that doesn’t mean that two things which share a property that is the same are necessarily a single thing. Property X = Property Y does not indicate that X = Y.

[TVAA]

If the empty set is valid, why can’t an empty universe be valid as well?

[Liberal]

Vorlon

We can’t say how big or little something is, but we can talk about whether something is largest or smallest, since we can use the object itself to compare it. Thus, if there is only one object with the property of size, it is both the largest and smallest.

And as such, the terms are equivalent. You’ve just constructed a tautology.

We can show that the greatest example of any property must exist if there is at least one thing existing that possesses that property, but we can’t show that there is necessarily something that is the greatest in all properties, or even more than one.

The topic under discussion is ontology. We may speak only of properties of existence. Necessary existence is the greatest form of existence (unless you care to be the first to argue otherwise). And it can be proved that necessary existence exists.

What is the definition of evil?

Merriam-Webster gives “morally reprehensible” (1a), “causing harm” (3a), and “marked by misfortune” (3b).

Why does evil have to be destructive?

Because of its definition.

And what, exactly, does ‘perfect’ mean?

For this argument (and for ontology in general) it means the same as “necessary”.

Lastly, if two things have exactly the same properties, they are the same thing. But, that doesn’t mean that two things which share a property that is the same are necessarily a single thing. Property X = Property Y does not indicate that X = Y.

That’s correct. Are you asserting that necessary existence is somehow dichotomous?

If the empty set is valid, why can’t an empty universe be valid as well?

It’s the same as any oxymoron. An “empty universe” is like a “full hole”.

[TVAA]

All conclusions are tautologies given their premises.

I don’t see why necessary existence is the ‘greatest’ form of existence (except by using your definition of ‘greatest’, in which case it’s simply a restatement). Why not just use the word ‘necessary’ and avoid confusion?

And no, it is not clear that necessary existence must exist. I see no reason to assume it cannot, but none of the arguments presented so far shows that it cannot not exist.

You still haven’t specified how you would deal with two things that are equally ‘great’. While there would be no things that were greater than either of the two, neither of them would be the greatest.

Why isn’t a universe empty of all things considered valid? If containing at least one thing is part of your definition of a universe, what do you call something that is empty of everything? I’m not trying to be critical, just trying to establish terms…

I’m not implying that necessary existence is composed of two parts, although I see no reason to assume that necessary existence must be a singular and monolithic property.

Nowhere in the definition of evil is destructiveness implied. Anything which causes a property to change can be considered destructive (in the sense that it ends the previous state or condition of the property), but it is also creative (in the sense that it creates a new state or condition).

If we use the somewhat more intutive and everyday sense of ‘destructive’, then Webster’s definition of evil doesn’t imply destructiveness.

[Liberal]

All conclusions are tautologies given their premises.

That is factually incorrect. A tautology is a redundant propostion that cannot be negated, e.g., “a beagle is a dog”.

I don’t see why necessary existence is the ‘greatest’ form of existence (except by using your definition of ‘greatest’, in which case it’s simply a restatement). Why not just use the word ‘necessary’ and avoid confusion?

No one is confused.

And no, it is not clear that necessary existence must exist. I see no reason to assume it cannot, but none of the arguments presented so far shows that it cannot not exist.

Would you care to point out the flaw in the proof on the prior page that necessary existence exists? Did you read other posts before you jumped in?

You still haven’t specified how you would deal with two things that are equally ‘great’. While there would be no things that were greater than either of the two, neither of them would be the greatest.

We aren’t dealing with something that is merely “great”. I is the greatest. And that has been strictly defined.

Why isn’t a universe empty of all things considered valid? If containing at least one thing is part of your definition of a universe, what do you call something that is empty of everything? I’m not trying to be critical, just trying to establish terms…

I don’t mind criticism. Something that is empty of everything is nothing.

I’m not implying that necessary existence is composed of two parts, although I see no reason to assume that necessary existence must be a singular and monolithic property.

I’m beginning to suspect that you and I have nothing to discuss…

Nowhere in the definition of evil is destructiveness implied.

And now I’m sure of it. I don’t intend to join in the exercize of redefining words and slinging them at each other — causing harm is not destructive, the biggest is the smallest, and nothing is something. You know, pigs can fly so long as we redefine fly to mean wallow in mud.

[Liberal]

I is the greatest.

And see that you don’t forget it!

[TVAA]

*Originally posted by Libertarian *
That is factually incorrect. A tautology is a redundant propostion that cannot be negated, e.g., “a beagle is a dog”.

If we’ve already defined a beagle as a dog, then that statement is a tautology, since it can be rewritten as “a dog is a dog”. All conclusions that proceed validly from premises can be rewritten as tautological statements: the ‘correctness’ of the conclusion is inherent in the assumptions made in the argument.

Did you read other posts before you jumped in?

Yes, I did. I don’t think that proof is correct.

And there is confusion, since I’m certainly confused.

Something that is empty of everything is nothing.

Would you say that the null set is nothing? If so, then we simply disagree, and I acknoledge your different of opinion. If you would say that the null set is something, then I must respectfully point out the contradiction in your statements.

[b[I don’t intend to join in the exercize of redefining words and slinging them at each other — causing harm is not destructive, the biggest is the smallest, and nothing is something.[/qb]

I’m not redefining the words, I’m simply being very careful about what their meanings actually are.

For example, intuition tells us that something can’t be both the largest thing and the smallest thing, but intuition is wrong. That’s normally the case: when we have things of different sizes, the largest thing is never the smallest thing. In the special case of when there is only one thing, there is nothing that is smaller than it (thus it is the smallest) and nothing that is larger than it (thus it is the largest). In the special case of when there are more than one thing that are the same size, there is no object that is the largest or the smallest (although there is a largest size and a smallest size that are the same).

Destruction and creation are very tricky concepts. Destroying condition A is equivalent to creating Not A. We don’t normally think of things this way, but it’s true. Saying that something is harmful implies that it’s destructive in the intuitive sense, but it’s both creative and destructive in the strict logical sense. So are things that are beneficial. It all depends on which state you decide to treat as being ‘real’: A or Not A.

You state that the more possible universes a being exists in, the greater it is. Fine and good. However, it could be possible that no being could be in more than n universes, where n is some number less than the total number of possible universes.

A ‘greatest’ being is logically necessary when we consider all possible universes (assuming of course that at least one being must exist in at least one possible universe, which is quite reasonable). However, it is not true that this being which necessarily exists exists in all possible universes. That being is logically necessary in possibility as a whole, but it is not necessarily present in all possible universes.

A being which existed in all possible universes would be the greatest being that could be imagined. The proof given earlier does not show that this being exists, or even that it’s possible.

In short, there must be some being that is the greatest, but the particular being that actually has the property of being the greatest being doesn’t necessarily exist.

I’m sorry if I’ve been stupid or dense. I’m just trying to understand your argument and be as correct as possible, and I’m not very good at either of those.

Would you be kind enough to point out wherever I’ve either misunderstood your points or made an error in my arguments? I’d appreciate it greatly.

[Liberal]

Sorry, but I don’t believe you.

[Nightime]

The word possible is being used strictly in its technical sense of truth in at least one possible world.

Yes, that is what I said.

Please see above where I proved that assertion false. (I don’t take credit for it; it is a common knowledge proof that serves as the very basis for modal logic’s validity.)

Again, I agree. It is possible that there is a being that exists necessarily.

1. G ⊃ G If God (on the definition above) exists, He exists necessarily.

The problem with this is that if the definition is using possible in its strictly technical sense of truth, it does not follow that god must exist necessarily. The greatest possible being, in other words the greatest being that does technically exist, does not have to be necessary. It should say that if god exists, then it is POSSIBLE he exists necessarily.

What the proof is saying, is that since necessary existence is possible, then god exists necessarily in at least one possible world. And therefore he exists necessarily in all possible worlds. No matter how many times you say this is logical, it just isn’t. Treating each possible world as if it actually exists is useful in proving things, but it is not technically true. It is useful for logic, but it is not part of logic.

For example, say I have a ball hidden under one of three cups. It is possible that the ball is under the middle cup. This is useful in trying to logically find the ball. But it is not technically true that there is a world in which the ball is under the middle cup.

The reason why the proof fails is that when it comes to actual truth, just because something is possible does not mean that there is a world where it is true. The proof is treating possible worlds as if they really exist. If something is possible that means it conceivably could exist, not that it does exist somewhere. For instance, saying black holes are possible means that they could conceivably exist and therefore it is logical to believe in them if they adequately explain things. It does not mean that there is a world where black holes definitely exist. You are confusing a useful logical device as being an actual fact.

[TVAA]

I think you’re completely right, Nighttime.

The being we’re talking about must exist in the multiverse (the set of all possible universes), but it doesn’t necessarily exist in all of the possible universes.

It must exist somewhere, but it doesn’t have to exist everywhere.

[TVAA]

Libertarian, could you please make a logical argument instead of just saying that you don’t agree? I’d like to know why you don’t agree with the point.

[Nightime]

For instance, saying black holes are possible means that they could conceivably exist and therefore it is logical to believe in them if they adequately explain things. It does not mean that there is a world where black holes definitely exist. You are confusing a useful logical device as being an actual fact.

On the other hand, it could be argued that the concept of god DOES explain things about our world, its existence for example. In that case, the proof would show that it is logical to believe in god, because god is necessary in some conceptual world, and because that concept explains things in our world.

[Newton_meter]

Originally posted by ethnicallynot *
Furthermore, as for all our discussions of various logical systems and semantics, IMHO we need to reign in our horses a bit. Personally, I’m only interested in such systems that intuitively form a complete epistemic system. If a system fails to incorporate a priori knowledge that I have, it’s too weak for any discussion about God being a necessary conclusion of human reasoning. Therefore, modal systems like K which have no means of reducing modal operators are weak and epistemically incomplete. Also transitivity and symmetry to me seem so basic that I would claim that systems without them are like houses without walls. I say this because one of Newton’s objections to an argument of mine was it didn’t apply to systems without transitivity and symmetry.

You have a priori knowledge that whatever is possible is necessarily possible? Or that if something is required, then that fact itself is required? Cool, can I get one?

I can think of two “kinds” of modalities that I think we use quite frequently in our discourse, and they both have asymmetric accessibility relations. First, when we speak of something being “possible”, we often mean that the fact will hold at some future time (in our own world); and when something is “necessary”, we mean it will never fail to hold at a future time. Accessible possible worlds are possible future states of affairs. In that case, whatever is necessary is necessarily necessary, but whatever is possible is not necessarily possible.

Secondly, when we say that something is “necessary”, we sometimes intend the word to carry moral force (It is necessary for you to finish your homework before the weekend, i.e. you ought to or must do it). Accessible possible worlds are worlds that are “at least as good (morally)” as this world–everything that ought to be the case in our world either also ought to be in every accessible world, or is in every accessible world. In this case, accessibility is also not symmetric.

I personally don’t feel that every notion of “possibility” we have requires symmetry. At least, it’s not obvious to me that it does. And I wouldn’t be harping on it but would just take Tisthammer’s and Lib’s word for it, if the combination of axiom 1 and axiom 2 (of the original proof) suggests that accessibility cannot be symmetric.

*** K doesn’t include the axioms A -> A and <>A -> <>A. Not having such axioms means you can’t simplify redundant iterations of modal operators. And no I don’t know how to get the dagger in a post!**

But I don’t want to simplify those operators if they’re not redundant. That (they are actually redundant) hasn’t been shown to my satisfaction. I don’t know how to put in a dagger† either, but I have an idea.

---

[sub]† I think that one can just clone erl’s original dagger all one wants.[/sub]