Monday, May 31, 2010

Necessary Existence and the Ontological Argument

An atheist (here) says that the ontological argument fails because, "what it hinges on is the definition of God as being "maximally great" and of maximally great as including the idea of necessary existence. Necessary existence simply isn't logically possible." When asked for a reason to think this, he said, "Something cannot be logically necessary if it's contrary is logically possible. It certainly appears that a world with no God is logically possible." But this is demonstrably false.

When considering the ontological argument, you have to differentiate between metaphysical possibility (actualizability) and epistemic possibility (imaginability)1. The statement that it appears that it is logically possible for there to be a world with no God only has epistemic merit, in that we could think of God not existing. To say, however, that it is possible for a necessary being to not exist is truly square circle territory metaphyiscally. How could a being that is necessary not exist? While it may be possible to imagine it, it is impossible to actualize a world where a being that must exist doesn't. That is why the ontological argument works. It shows that God is either necessary, or impossible. So, David must show that it is impossible that a maximally great being exists. But it certainly seems possible...

Furthermore, the statement, "it is possible that God does not exist," is not the negation of, "it is possible that God exists." Rather, the negation of "it is possible that God exists" would be "it is not possible that God exists." So his contention fails at that point as well.

1 William Lane Craig and J.P. Moreland, Philosophical Foundations for a Christian Worldview (Downers Grove, IL: IVP Academic, 2003), P. 497

24 comments:

Steven said...

Why shouldn't a theist just deny his claim that it is possible that God doesn't exist?

Of course, then it becomes a shouting match over whether or not God necessarily exists or is impossible. But it is much more obvious to me that God is not impossible than it is that his nonexistence is logically impossible.

bossmanham said...

Well I would, but as it pertains to the ontological argument, it is pretty irrelevant either way to say "it's possible God could exist or it's possible God may not exist."

For the OA, the metaphysical reality of the modal axioms make it clear that either He does exist, or it is impossible that He exists.

I agree that it's fairly clear that God's existence is possible, and therefore real. The atheist assumes a huge burden of proof in claiming His existence is impossible.

This guy's fundamental mistake is thinking "it's possible for God to not exist" is the negation of "it's possible that God does exist." He doesn't understand what a negation is.

Tyler DiPietro said...

Actually, I wouldn't quibble with the OA itself given its premises. My objection is that the modal axiom (which I understand to be the necessity of A implies A) to be a convenient fiction. "Necessity" is too ill-defined, and all attempts to define it that I've seen end up being circular ("something is necessary when it's necessary").

Skeptical Rationalist said...

I'm curious as to how you can know that God is necessarily existent. I've never seen any variation of the Ontological Argument that wasn't begging the question in some way, shape or form.

Steven said...

"I'm curious as to how you can know that God is necessarily existent. I've never seen any variation of the Ontological Argument that wasn't begging the question in some way, shape or form."

How does the modal argument beg the question?

Tyler DiPietro said...

I would like to amend my previous comment to note that there is one definition of "necessary" that I'm familiar with that isn't circular, and that is "follows from certain premises". Of course, in the OA and modal arguments in general, necessity is itself a premise, so that definition isn't applicable as far as I can tell.

bossmanham said...

I'm curious as to how you can know that God is necessarily existent.

It follows after reasoning throught the ontological argument.

"Necessity" is too ill-defined, and all attempts to define it that I've seen end up being circular ("something is necessary when it's necessary").

The modal ontological argument shows that God is necessary as a result of being a maximally great being. The conclusion that, if it's possible God exists, He exists necessarily is the conclusion, not the premise of the modal argument.

Of course, in the OA and modal arguments in general, necessity is itself a premise

It's actually the conclusion.

bossmanham said...

Tyler, one definition that Webster gives for "necessary" is "cannot be denied without contradiction." That doesn't seem to beg its own definition. However, necessary may simply be a tautology.

Tyler DiPietro said...

"The modal ontological argument shows that God is necessary as a result of being a maximally great being."

Not quite, it assumes that a "maximally great" being either necessarily exists or is impossible and uses the excluded middle law to establish the existence. "Necessity" is a premise.

"Tyler, one definition that Webster gives for "necessary" is "cannot be denied without contradiction.""

I think that's more or less logically equivalent to my definition, in that the negation is not satisfiable.

bossmanham said...

I think we're talking past each other here a little bit. If you're saying because the OA states something in the premises that then is stated in the conlcusion, it is begging the question. But if that were the case, any deductive argument would also be begging the question (ie if you're a human you are mortal, you're a human, therefore you are mortal). But that is not begging the question, rather it's giving the conditional premises that lead to the conclusion, as does the OA. If it's possible that God exists, then He exists.

Not quite, it assumes that a "maximally great" being either necessarily exists or is impossible and uses the excluded middle law to establish the existence. "Necessity" is a premise.

No, this is what the ontological argument eventually shows. It all hinges on the first premise; it is possible that a maximally great being exists. Following that, using the modal axioms, it shows that God exists. If it is impossible for a maximally great being to exist, then it shows that He doesn't.

1. It is possible that a maximally great being exists.

2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

3. If a maximally great being exists in some possible world, then it exists in every possible world.

4. If a maximally great being exists in every possible world, then it exists in the actual world.

5. If a maximally great being exists in the actual world, then a maximally great being exists.

6. Therefore, a maximally great being exists.

All of these are uncontrovercial premises other than the first one, but that is what Plantinga showed to be the case. Either God exists, or His existence is impossible.

Tyler DiPietro said...

"No, this is what the ontological argument eventually shows. It all hinges on the first premise; it is possible that a maximally great being exists. Following that, using the modal axioms, it shows that God exists."

Which is my problem, the modal axioms are convenient fictions. The OA is valid given its premises, but I consider the conclusion to be unsound. For instance, we see this:

"1. It is possible that a maximally great being exists.

2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

3. If a maximally great being exists in some possible world, then it exists in every possible world."

Premise number three is equivalent to the iteration axiom in modal logic (possibly A implies necessarily possibly A). If you assume this axiom, then your conclusion is valid. But why should be adopt this axiom? Why doesn't possibly A imply contingently possibly A? We need a definition of "necessary" in this case that isn't circular, and modal logic doesn't produce one.

bossmanham said...

Which is my problem, the modal axioms are convenient fictions.

Well that's a nice assertion, but I haven't seen any reason to think that. As I said, most philosophers are fairly willing to accept that the rest of the argument follows if the first premise is true. It's easy to say you don't think something is correct, but the rules of logic aren't debatable.

Premise number three is equivalent to the iteration axiom in modal logic (possibly A implies necessarily possibly A). If you assume this axiom, then your conclusion is valid. But why should be adopt this axiom?

P3 is based on the definition of a maximally great being. So yes, you'd have to accept the definition here. But I'm not willing to say that the definition is as ambiguous as you want to make it. "Necessary" or "maximally great" seems fairly straightforward to me. Perhaps there's an issue with your understanding?

Skeptical Rationalist said...

Bad example. I can *demonstrate* that humans are mortal. We have no evidence that any immortal human exists, and it would be arguable that they might not be a member of the set of beings called "humans."

The problem with using the term "maximally great" is that you have an unstated major premise that renders the argument fallacious. Maximally great being defined as all things great, grand and wonderful, universe-creating, omniscient, omnipotent, et cetera, et cetera, and at the end of the very long list of superlatives is the attribute "and whose existence is necessary."

I could define a unicorn as "an animal with white skin, an ivory horn, cloven hooves, a flowing mane and tail and which exists" but that doesn't mean I get to declare victory.

As if that weren't enough, you also running into a similar definition problem that believers like to throw at nonbelievers whenever morality comes up: by what objective standard are you judging maximal greatness? If I say all-forgiving and you say all-just are maximally great, why should either of us listen to the other? It comes down to "necessarily exists" is the only relevant element of greatness, and we're back to the naked question-begging.

bossmanham said...

Further, I think you are confusing necessity de re with necessity de dicto. If we say "Necessarily, I am human," that does not mean that I exist in every possible world. Rather, it means that I am essentially human. Any world that I do exist in I would be human.

I think the axiom used in P3 is obviously true. If it is possible that something exists, then that is equivalent to saying that it is necessarily possible that something exists. You're confusing definitions if you're saying that saying possibly P can equal maybe or maybe not possibly P. That's not really saying anything. No, if it's possible, then it's possible.

So the iteration axiom is obviously true.

Tyler DiPietro said...

"It's easy to say you don't think something is correct, but the rules of logic aren't debatable."

So you're saying that the correctness of the modal axioms is not debatable? You're on some pretty shaky ground there, especially when it comes to iteration.

"P3 is based on the definition of a maximally great being."

You didn't make that clear. Part of the difficulty in discussing "the" ontological argument is that there are many variants. However, I've never seen one that didn't hinge on some variant of Anslem's postulate that perfection cannot exist contingently. You just replaced "perfection" with "maximally great". In other words, your argument relies entirely on the traits you ascribe to the unproven statement.

""Necessary" or "maximally great" seems fairly straightforward to me."

Perhaps, then, you could clarify.

Tyler DiPietro said...

"If we say "Necessarily, I am human," that does not mean that I exist in every possible world. Rather, it means that I am essentially human. Any world that I do exist in I would be human."

Let's reduce it further. You could say, "necessarily, I have dark brown hair", which means that in every world you exist you have dark brown hair. But that you have dark brown hair is a contingency of gene expression. If you don't necessarily have dark brown, why do you necessarily have higher level traits?

But is your conclusion sound, here

"That's not really saying anything. No, if it's possible, then it's possible."

I understood the axiom as saying that A possibly being necessary is the same as saying that A is necessary. What you're describing is really just the identity law in ordinary Boolean logic.

Tyler DiPietro said...

Or, it could be that something being possible means it's possible in all possible worlds. Such a statement is certainly not obvious.

bossmanham said...

SR,

We have no evidence that any immortal human exists, and it would be arguable that they might not be a member of the set of beings called "humans."

Empirical testability doesn't have any bearing on the ontological argument. That example was to show how a deductive argument works. The OA is deductive, in that if the premises are true (mainly the first one, since the others follow by definition). You can argue deductively without having actually seen something.

The problem with using the term "maximally great" is that you have an unstated major premise that renders the argument fallacious. Maximally great being defined as all things great, grand and wonderful, universe-creating, omniscient, omnipotent, et cetera, et cetera, and at the end of the very long list of superlatives is the attribute "and whose existence is necessary."

How is the premise unstated if it's included in the definition of a word? And what fallacy invalidates the argument?

I could define a unicorn as "an animal with white skin, an ivory horn, cloven hooves, a flowing mane and tail and which exists" but that doesn't mean I get to declare victory.

Well a unicorn wouldn't work in the OA because it isn't a maximally great being. If it were, then it wouldn't be "an animal with white skin, an ivory horn, cloven hooves, a flowing mane and tail and which exists." And you've also given no reason to think this unicorn exists. The OA gives a deductive reason to think that, if it's possible that God exists, then He exists.

Words have to have definitions. I'm sorry that that's the way language works.

by what objective standard are you judging maximal greatness If I say all-forgiving and you say all-just are maximally great, why should either of us listen to the other?

The maximally great being would have both of those. The maximally great being would have excellent making properties such that the being would be the locus and standard by which we compare all those who lack maximal greatness to. That is why this being is maximally great.

Tyler DiPietro said...

I don't see why a maximally great being would have to exist necessarily. There are classes of objects that possess no maximally great element (that would include every countably infinite number system).

Tyler DiPietro said...

Excuse me, every uncountably infinite AND countably infinite number system.

I'll stop posting for a while now, I'm clogging up your comment thread.

bossmanham said...

But that you have dark brown hair is a contingency of gene expression. If you don't necessarily have dark brown, why do you necessarily have higher level traits?

This doesn't make any sense. If I necessarily have brown hair, then any world in which I exist, I will have the genes that express brown hair. It says nothing about the necessity of other traits.

I understood the axiom as saying that A possibly being necessary is the same as saying that A is necessary. What you're describing is really just the identity law in ordinary Boolean logic.

The (S5) axiom is: ◊A -> □◊A or ◊□A -> □A.

When we're speaking of the logical possibility of a maximally great being existing in one possible world, then I think it is obvious that would extend to any possible world, since that is the definition of maximal greatness. There has to be some logical impossibility of this, or else the contention doesn't hold.

bossmanham said...

I don't see why a maximally great being would have to exist necessarily. There are classes of objects that possess no maximally great element (that would include every countably infinite number system).

Well, likewise, an island could never reach a peak in excellence either. Rather, the properties that make up maximal excellence have "intrinsic maxima." There could always be one more number, or there could always be one more palm tree on an island, but there could be nothing greater than omnipotent or omniscient.

I'll stop posting for a while now, I'm clogging up your comment thread.

Don't worry about it. I learn these arguments the best when I discuss them. Admittedly, I haven't studied modal logic a whole lot, so this helps me come to grips with the argument in my own mind. But I'll be busy for a while myself.

Skeptical Rationalist said...

Empirical testability doesn't have any bearing on the ontological argument.

No, but the validity of premises has to be agreed upon. I can say "All plants are green, eggplants are plants, therefore eggplants are green," and my syllogism is not unsound. But since P1 is false, it's not valid. Similarly, asserting that "necessary existence" is not a fictitious concept is not something I am prepared to grant.

If the definition of "maximally great" includes "necessary existence," then your argument basically boils down to:

"Because god is maximally great, he must necessarily exist. Therefore he exists." All else is mere obfuscation, with a side order of Shifting the Burden of Proof onto your opponent to prove that something is impossible, which is ludicrous.

Tyler DiPietro said...

This gets back to what I mean when I say that the axioms of modal logic are convenient fictions. Some proposition being possibly necessarily true has an obvious corollary that said proposition is possibly necessarily false. If we adopt the logical justification for S(5) then we also have to accept the logical justification for ~S(5). Adopting the iteration axiom results in two completely contradictory conclusions.

This leads me to believe that possible world semantics is inherently incoherent. Thus it can't prove the existence of god(s).