Ontological arguments

Great Debates
201

You are correct, the Lambda 5 system does not require all code to be mobile (A -> A), and the type system makes a distinction between mobile and non-mobile code.

However, there is a new problem. Lambda 5 is an intuitionistic version of S5, so you can’t use double negation elimination. That doesn’t necessarily mean that you can’t prove <>(P -> P), but you’ll need a different proof.

To see why double negation elimination doesn’t work, consider the interpretation of ~A as A -> False. From a function of type (A -> 0) -> 0 we don’t have any way to obtain a value of type A.

202

OK. What does it mean for a being to be “greater” than another? “More ontologically perfect”?

And crucially, what ensures that the being that is “more perfect” (whatever that means) than any other being is actually “perfect”? We already know that you assume it, but why should anyone else?

Why is “God exists” a more reasonable assumption than “nobody’s perfect”?

203

My first thought on reading Lib’s proof. But I’m not well-versed in modal logic, so I didn’t butt in.

204

Maybe G=Gravity? It seems to fit (G -> G).

205

The problem is, ontological greatness and what we usually consider greatness are mutually exclusive.
If anything has “ontological perfection”, then it has to exist in world 81203, which is made up of nothing but an endless empty vacuum. And in world 1045, which is filled with nothing but the excrutiating torment of the innocent.
Remember, the proof says greatest POSSIBLE existence. Because of worlds with no beings, the greatest possible existence cannot be a being.

Similarly, if we use greatness in the usual, non-ontological sense, it becomes immediately clear that existence in all possible worlds is not a property of the greatest possible being.

The greatest possible being would only exist in the greatest possible world. That’s just common sense.

To exist in hell-worlds can hardly be considered a quality that makes a being greater (again, in the non-ontological sense). Clearly the greatest possible being only exists in the greatest possible world. And since we do not live in the greatest possible world, the greatest possible being does not exist in our world.

So what do we have?

The greatest (ontological sense) possible existence exists. But because of possible worlds with no beings, and possible hell-worlds, we know that the greatest (ontological sense) POSSIBLE existence cannot be a being. The greatest (ontological sense) possible existence is no more sentient than the law of non-contradiction.
The greatest (normal sense) possible being exists in the greatest possible world. Unless we live in the greatest (normal sense) possible world, the greatest (normal sense) possible being is not here. This does not preclude the possibility that we have a pretty darn good being somewhere around here.

The real problem with the proof comes after it is finished, and the determined interpreter decides to conflate ontological greatness with what we usually call greatness, when a little logical thought tells us they are mutually exclusive.

206

I don’t know. You’d have to ask the person who used the phrase “more ontologically perfect”. Barring that, you could just assign it to me and proceed as though I said it. Oh, wait…

207

The reason why no one (of note) criticizes the proof that way is because they don’t confuse existence with perception. The being exists in every world but is not everything that exists. In a world without eyes, it is not the being Who is blind.

208

After you are done with the proof, and you are at the point of hopefully trying to connect ontological greatness with what is normally considered greatness, that is where the problem develops.
Existing in a possible “world without eyes” does not make a being greater.
I can’t believe you are arguing that existing in infinite hell-worlds makes a being greater in the normal sense of the word

In the ontological sense, yes. But that just illustrates the point: ontological greatness is at odds with regular greatness.

In the normal sense of the word, the greatest possible being exists in the greatest possible world. There is nothing to be gained from any other world, because by definition if there was it would already exist in the greatest possible world.

Try as you might to convince people that existing in possible hell-worlds would make a being greater in anything other than an ontological sense, I suspect you will fail, due in no small part to your claim being completely illogical.

209

Ontological greatness is not at odds with anything. As Hartshorne has said, this is not a competition. A being can have both existence and essence.

210

Lib, do you have an argument against G=Gravity? It may sound stupid, but I don’t immediately see a contradiction with any premises put forth so far (other than my opinion that <>G is something less than G, but I’ll sideline that for the moment).

211

For =gravity, I would discard G -> G since gravity is contingent on mass.

212

Not good enough, Lib.

You see, the proof doesn’t say anything about a being.
You can only begin trying to think of it as a being afterwards, when you have come up with a coherent idea of a being with necessary existence. This is done (by those who use this proof) by arguing that the greatest (normal sense) possible being has ontological perfection.

In other words, it is up to you to prove that ontological greatness and normal greatness are one and the same, or at least that each implies the other.
And that is where you (and others who give this proof meaning) fail.

Normal greatness does not imply ontological greatness.
Existing in infinite possible hell-worlds does not make a being greater in anything but an ontological sense.
The greatest (normal sense) possible being exists in the greatest (normal sense) possible world.

Just use common sense for a second - is a being which is consistent with infinite unjust hell-worlds better than a being which is only consistent with the greatest possible world, in any sense but ontological greatness?
Most people would say that the being which is only consistent with the greatest possible world is greater (normal sense) than the being which is consistent with possible hell-worlds.
Once again, I wonder how existence in a possible hell-world makes a being greater than if it only existed in the greatest possible world.

But what you have to remember is, you only got to the point where you could speak of a being at all after you decided that the greatest (normal sense) possible being must have ontological perfection. Since that was incorrect, your entire line of reasoning falls apart.

213

“be·ing n. 1. The state or quality of having existence. See Synonyms at existence.” — American Heritage

214

Gravitational force is contingent on mass, but the existence of gravity is not.

Similarly, God’s influence would be contingent on something to influence, but his existence would not.

215

And it has been my impression, frankly, that this world is pretty much a hell-world. :frowning:

216

It is. If there’s no mass, there’s nothing to set up a gravitational field.

217

Interesting, that’s right, I forgot that. I’ll have to think about this.

218

Those are good examples, because all three of those assumptions are veiwed with suspicion. In my field, a massive amount of progress was made by rejecting the law of the excluded middle, for instance.

AC is a good example. It was an open question before Godel proved that ZDC + AC has a model, and Cohen (I think?) proved that ZDC + ~AC has a model.

But if I didn’t know that, what would I expect a proof of the axiom of choice to look like? It would be a proof within ZDC that AC were true. If I were presented with that sort of proof, then I would claim that I had a reason to believe that AC were true, namely, ZDC.

But we don’t have that sort of proof here. We have a proof that, in ZDC plus one of the propositions that are equivalent to the axiom of choice, like Zorn’s lemma or the wellordering theorem, then you can prove the axiom of choice.

Under the assumption (G -> G), you can prove <>G -> G using Libertarian’s proof. You can also prove G -> <>G. Thus, we have

(G -> G) |- G <-> <>G

If we agree that (G -> G) is not controversial, and is true of G = “the greatest imaginable being”, then what Libertarian is doing is assuming a proposition equivalent to his conclusion, and claiming that is a “proof of God’s existence”.

This is not a “proof of God’s existence”. This is a demonstration that if you define “God” in a certain stylized way, and then assume that he exists, then he will exist.

Just as the proof that Zorn’s lemma is equivalent to the axiom of choice is not usually viewed as a proof of the axiom of choice.

219

I did not assign the phrase to you. I offered it as a suggestion of how I was interpreting you.

  1. G is not a being, G is a proposition. I invited you to be explicit about the proposition G, and you said:
  1. ultrafilter reminded you that G is not a being, G is a proposition. He then invited you to be explicit about what you meant by “greatest”. You replied:
  1. I notice that you have not actually answered the question. ultrafilter asked about “greatest” and you responded with “greatness”. Now, I don’t think I’m just being picky if I wonder: when comparing two beings, is the “greater being” one that has “more perfection”? Is the “greatest” of several beings the one that has the “most perfection”?

You say you are talking about the greatest “possible being”, the greatest being X of which <>“X exists” is true. Now that sounds to me that the set of all beings (I hope that sets themselves aren’t “beings”) that exist in some possible world (by definition: all beings of which <>“X exists” is true) has a greatest element. Now, I’m not assuming that the set is denumerable, or that there is a computable procedure for finding the greatest element.

You are defining “greatest” as “ontological perfection” and assuming you will find it in this set. You are assuming at the outset that one of the beings in the set of “possible beings” has “ontological perfection”. Assuming the conclusion, not convincing.

On the other hand, if you hold off and define “ontological perfection” in terms of the greatest being in this set, then you have no guarantee that that being exists in all possible worlds (unless you assume that it does).

220

We’ve been over this. And over it. And over it.

G absolutely positively IS a being. The proposition is “G”. (Note the quotation marks). It is like the difference between a number and a numeral. The numeral “2” represents the number 2. You can’t add numerals, but you can add numbers. In programming, it is like the difference between a memory location and the value it contains. For convenience, you might call it A. But what is happening is that when you reference A, the computer is retrieving a value from a memory location where the value of A is stored.

Nothing is being assumed at the outset. If it were, one premise would be G. It isn’t. You do the modus tollens.

For whatever reason, you’re abandoning your civility and resorting to crap like calling me evasive. If I respond in these threads, I’m beating a dead horse. If I leave them, I’m being a coward and dodging the “tough” questions. The fact of the matter is that people can hold honest differences and not be dodgers or beaters. If you think you’ve found something significant, then publish it in a peer reviewed journal like all the rest of them have done for the past 50 years.