Before I get started on this I need to make a caveat. Tillich was against the OA because he felt it contradicted the concept of the God as being itself, and instead sought to prove the existence of a greatest being which is contrary to the concept of God as being itself. He also imposed or at least said things taken by some to be imply a version of the OA that could be re-formulated. I have not had a chance to talk about this on my blog yet. I don't think I have time to present the ins and outs of it here. But it is important to understand that in some sense I agree with Miller and with opponents of the modal argument but in other ways I disagree with them.
This is the post Miller linked to that said his more sophisticated understanding of and refutation of the Modal argument.
Wednesday, March 24, 2010
Modal ontological argument, revisited
Let's revisit the modal ontological arguments for God. Though I have covered these arguments and variations at length, and have not changed my opinion about them, I didn't necessarily cover them in the clearest manner possible. It's a tough balance, because for most people, symbolic logic is like math. Math = scary! Other readers understand the symbolic logic, but clearly have difficulties translating between the symbols and their underlying meaning. My goal is to explain it so both groups understand what I'm saying.
I do understand modal logic, in a way, but I don't claim to be an expert. I don't like using the symbols, not because I think they are wrong for I have several problems with it, both intellectual and personal. The intellectual: I am a phenomenoloist so I don't like that sort hard cast logic, even though I do believe that it's right in matters that can be deduced. I don't like the perspective of trying to make that the major or only form of learning. Personal: I have dyslexia so the shift about of many symbols is hard for me becuase it tends to wind up in my little fevered brain switching the symbols on me. The same is true of letters in reading of course, but reading English is raiser and I'm more use to it.
Modal ontological argument, reviewedMeta:I think the premise is what you call "definition" and the second line is either a minor premise or corollary.No matter.
Definition: If God exists, then God necessarily exists.
Premise: It is possible that God exists.
[Insert mess of logical reasoning here]
Conclusion: God exists.
I omitted the mess of logical reasoning because I don't want to scare away my readers. Unfortunately, this makes it difficult to convey the amount of respect the logical arguments deserve. Richard Dawkins and other atheists often seem to think it's all a bunch of high-sounding gibberish. And perhaps it is. But that particular gibberish is absolutely solid, as solid as 2+2=4.
Meta: I appreciate that.
There are basically two reasonable objections to the argument. Either we must object to the premise, or object to the definition.
Objection to the premise
To explain the problem with the premise, I must distinguish between two kinds of possibility.
Epistemological possibility: For all we know, God exists.
Modal possibility: Among the set of "possible worlds", there exists a world in which God exists.
Meta:Problem: Plantinga's possible worlds argument (for God) asserts that God must exist in all worlds or none. You seem to imply here that the epistemological possibility is "God may exist in some world." While that is an epistemological possibility that possibility is demonstrated false by the argument Plantinga makes. Meanwhile the modal possibility is just as impossible. There cannot be a state of affairs such that God exists in one world only and not in all possible worlds. If it is possible that God exists in one possible world then God must exist in all possible worlds. That is a certainty if we define God as being itself.
The conclusion of the proof follows only from modal possibility, not from epistemological possibility. However, the epistemological statement is the one that is intuitively true, while the modal statement could be true or false. Modal possibility is intended to be a translation from epistemological possibility to logic, but the translation is not perfect.
Meta:I think the assumption here is false for reasons stated above.
In particular, the translation fails when we talk about the set of possible worlds itself.
Epistemological statement: For all we know, the universe is deterministic (ie there is only one possible world).
Modal translation: Among the set of "possible worlds", there exists a world in which it is true that there is only one possible world.
The epistemological statement is sensible, but if we naively copy it as a modal statement, it's a mess. The first statement only says that the universe may be deterministic, while the second statement can be used to prove that the universe must be deterministic. Clearly, we need to be careful with our translations when discussing determinism.
Meta:If I'm right about what you are trying to do then you are totally wrong. If I understand you correctly, that you are trying to supposes that the argument for God is based upon moving the possibility of God from epistemology to modality, that then you argue the impossibility of the move and that creates the impossible the "no such thing as God merely possible" clause can't be transformed from one to the other. If that's what you are doing you making several mistakes.
(1) Just because "for all we know God might exist" is an epistemolgoical statment that does not mean that the existence of God is only a epistemolgical possibility that is excluded in some way form the modal realm.
(2) the possibility of determinism is not a negation of God; God can create deterministic universes and thus God can exist in deterministic universes.
(3) There is also the possibility that determinism is impossible.
Similar to determinism, the existence of God also says something about the set of possible worlds. If God exists, then s/he exists in all possible worlds. If an object does not exist in all possible worlds, then we cannot call it God. So we need to be careful with our translations when discussing God too.Meta:That would seem to contradict my previous assumption, that I'm wrong about what you are trying to say. But I'm leaving it in anyway just in case.
Here is a much better translation to logic:Meta: you lost me on this. You seem to be creating a useless distinction between epistemology and logic where one need not be made. All logical truths are also epistemological problems, everything that exists epistemically also exists logcially.
Epistemological statement: For all I know, God exists
Logical translation: God exists, or God does not exist.
The conclusion of the ontological argument does not follow from this proper translation.
Even proponents of the modal ontological argument must accept that there are problems with translation. If we take the statement, "For all I know, God doesn't exist" and naively translate it to modal logic, then we would conclude that God doesn't exist.Meta: I think the translation bit is a useless gimmick. Belief in God is not confined to one type of thought and has to be "translated" into another. This is super metaphysics, I don't see any reason to make this sort of metaphysical assumption. Its' not as though some questions are intrinsically given to epistemology and barred from logic and vice verse. Its' totally a matter of the way you structure your sentences. Belief in God is as much at home in modal logic as anything. The statement "If God exists then God must exist necessarily" is a statement of modal logic. By calling it "definition" you have screened it off form the actual logic of the argument but it's as much a modal statement as anything.
In Baird's presentation of Hartshorne's argument he did not call it the definition.
Miller:Meta: Truth by stipulation. you can't stipulate the non existence of God.
Alternate premise: Logical consistency
Some ontological arguments have a cleverer premise to replace the old one.
Old Premise: It is possible that God exists.
New Premise: There is no contradiction in the existence of God. In other words, God is "consistent."
The old premise logically follows from the new one. If you're familiar with symbolic logic, I hope you already knew this. If not, here is a simple proof.
Suppose that the old premise is false; it is not possible that God exists. The statement "If P, then Q" is always true if P is false. Likewise, the statement "If God exists, then Q" is always true, because God doesn't exist. It's true even if Q is a contradictory statement (ie "God is blue and not blue"). Therefore, the new premise is false; the existence of God implies a contradiction.
The statement "If P, then Q" is always true if P is false.this I do not understand. If P is false (and the premise is "if P then Q") then the false nature of P means Q is also false because Q depends upon P. This is true in modus ponens.
If the old premise is false, then the new premise is false. Equivalently, if the new premise is true, then the old premise is true.
not what what said. you said if P is false than if P :. Q would mean Q is true.
But now we will run into another problem of translation. I will distinguish between two kinds of consistency.
Self-consistency: The object has no contradicting properties in its definition.
Logical consistency: The object implies no contradictions.
Proponents of the ontological argument often expect me to disprove the self-consistency of God. Perhaps they expect me to argue that God's omnipotence contradicts its omniscience, or something like that. But they fail to realize that I don't have to. The proof requires logical consistency, not self-consistency.
Self-consistency is not sufficient to establish logical consistency. For an object to be logically consistent, not only must its definition be properly formed, but the world must cooperate. (More precisely, the set of "possible worlds" must cooperate.) Suppose that the world does not cooperate, and the object does not exist. If the object does not exist, then the existence of the object implies a contradiction. Namely, it implies that the object both exists and does not exist. I didn't even have to look at the definition of the object.
Meta: There's a huge amount with this.
(1) you make an arbitrary distinction between "self constancy and logical consistency." that would assume there some disemboweled concept "logic" floating around out there that has nothing to do with objects per se. You are really assuming that things in the world have to fit with the rules of femoral logic and those rules are arbitrary. The only real contradiction that would matter is self consistency. I don't necessarily play that out in terms of omniscience vs omnipotence, it could be any number of ways.
(2) The world "cooperating" is begging the question. you can't argue the world is not reflecting the truth of God because three dozen God arguments show that it does. You can't start by asserting there is no God any more than I can start by asserting that there is.
(3) The OA in and of itself argues that the greatest thought is about the greatest truth. The argument is supposed to reflect the truth of God and is itself a matter of the reality cooperating to show the truth of God.
Of course, I don't know whether the world cooperates with the ontological proof or not. The proponents have no idea either, but think they do.
Meta we have a good hint in what I just said, the greatest idea is about the greatest truth.
Philosophers ought to teach themselves some mathematics. In geometry, there is a famous axiom called the Parallel postulate. It is famous because many mathematicians thought they could prove it. Modern mathematicians know that it is impossible to prove, because there is no contradiction in assuming it false. Likewise, it is impossible to disprove. The Parallel postulate is self-consistent. The negation of the Parallel postulate is also self-consistent. But in any given geometrical system, only one can be true. Thus, only one can be logically consistent.
Meta: But that's argument from analogy. That proves nothing about the modal argument.
Objection to the Definition of God
Definition: If God exists, then God necessarily exists.
If we define a fork to be an object with a handle and prongs, then we can give the following statement: "If a fork exists, then it has prongs". If a fork does not exist, we can't even talk about "it", much less ascribe it properties. If an object does not have prongs, then it is not a fork. That is the rationale behind the definition.
Meta: I think I already dealt with this stuff before. First of all you are making a mistake by calling it a defintion.The statement is conditional, definitions are not conditional statements so it can't really be one. It's more like a first premise. But it's based upon the definition of God as necessary and not contingent. That definition is not open to debate. It is not defining God into existence and the assertion that it is is merely clutching at straws. It's a failure to understand this is a given, it's what we believe. It can no more be disputed or disproved as a valid premise than the statement that I love my mother or that my name is Joe.It's a basic given, the fundamental of a belief system and the assumed construct of the God concept that we talk about. you have to deal with it what we believe on it's own terms of not seek to discuss it. You can't dictate or alter our belief system just becuase you don't like it's fundamental premise.
Now proving that God can't exist necessity would come under the heading of showing a contradiction in the concept of God. That would be valid if you could do it, so good luck with that. You can't just make the premise go away just because you don't like.
How can you disagree with a definition? Can't we define any object we like? If the definition makes no sense, can't we just say that the object doesn't exist?Meta: no because your objective is not founded upon it not making sense or you would be able to prove a contrdication in God. You passed on that before, you can't show me one. This concept makes sense. Its not a contradition and it's not something something makes no sense I understand it perfectly, it makes sense to me, it makes sense to the believer.
Ah but here's a major major MAJOR sign post: big read sign here saying "THIS IS IMPORTANT>"
Atheist and theist live in two different worlds. The world I live in is totally different from the world tha Miller lives in. It doesn't make sense to him because his ideology has led him to embrace only constructs that eject this notion from reality. But because I have come to see the universe in terms of this construct, and I find it true becuase works and my understanding of the world works perfectly with it, the two fit hand in glove, but they do so only because I can see it. The ground shifted for me and it has not so shifted for Mr. Miller. That is no poor reflection on him, it's just the way it is..
What this means is the way he looks at the world the world doesn't cooperate with the argument and the concept of necessary God does not make sense. I suspect this is in large part because he thinks of God as a big man in the sky and when I say "eternal necessary being" he thinks "a being" rather than being itself. Of course that's problematic because he's not going to see it unless he wants to. IF I try to explain it he will probably say (he has already no doubt) "what the hell is being itself?" We will be back at square one because he doesn't see the world that way either.
So that's what's really stand between us, this view of things that will not allow one to understand the concept and will not allow the other to let go of it.
I don't know about philosophy, but in mathematics, you can't just define any object you like. Consider the set of all sets that do not include themselves (like the male barber who shaves all men who do not shave themselves). Call this Russell's Set. In "naive" set theory, you are allowed to define any set you like, including Russell's set. But Russell's set leads to a paradox. Therefore, "naive" set theory is inconsistent.Meta: Part of the problem here is you are thinking of it as an object. That what I mean when I say atheist are "thing bound." You are wrapped up in the surface level of things and it's a matter of empirical objects vs objects of thought in your head and that's just putting everything on the level of thing hood. Along comes God who is not a "who" and not "he" and not an "it" but something beyond understanding and you go "wait, If I can't understanding I can't control it, so I can't accept somethign I can't control."
That's really what it's all about. belief vs skepticism is about being willing to let go of control and be controlled by the ultimate, vs trying to control the ultimate and reduce the unconditioned to an "it." This is what I'm talking about above where I sate the caveat.
Naturally, mathematicians want a set theory that doesn't have paradoxes. So they formulated Zermelo-Fraenkel set theory, which has specific rules dictating what sets you are allowed to define. These rules do not allow us to define Russell's Set, and thus avoid its paradoxes.
Meta: So much the worse for mathematicians. Jesus said "unless you become as an undergraduate, you can't enter the graduate school of heaven."
Is modal logic more like "naive" set theory, or like Zermelo-Fraenkel set theory? Can you define anything you like, or do you have to follow specific rules? I suspect it depends on your choice of axioms. It's a difficult question that I don't feel qualified to answer, which is why I prefer objections to the premise.Meta: Remember I said the problem goes back to thinking of it as an object (God). If you think of God as an object that can be proved, (then of course that also means it can be controlled) you are reducing God from the ground of being to an object in being. Then you are trying to ask if we can define objects anyway but you already doing that. You are doing exactly what you castigate the MA for doing, reducing reality to an object that you can control and then trying to define it yourself.
Of course that's the necessary first step in the battle for control of the object. If you are doing to seek to ban God from his own reality then you have to first take control of the concept of of God as an object, control is what all reductionists seek. Reduction = control.
At this rate the MA might be wrong-headed so the argument has been beaten by its own need to be proven. Not beaten by being false but beaten by being something that requires proof, the mere fact that it can be proved makes it worse. That's such an absurdity.
It's far more logical to think about it in its proper terms, not as an object but as a belief, as a apprehension, something religious belief lights upon and grasps as a perception. It's not a definition at all. It shares with definitions that both are merely illumination, not controls. We have to understand God as the unconditioned then we know we can't jack around definitions at all.
The argument is saved and put back together by the realization that it's proving a ratinoal warrant not a proof that can't be disputed. It 'not proving an object but a concept. What's proved about the concept is the prima facie nature of it as a reason for belief. That's the very aspect that definition argument was designed by atheists to mask.
For what it's worth, Immanuel Kant's original objection to the ontological argument might fit in this category. Kant argued that existence is not a property that you can include in the definition of an object.
Meta: that argument is by the modal nature of the nature of the argument. The difference in modality and propositional understanding per se is the addition of the type of being that is discussed (weather contingent or necessary). That status (modal) adds new information and that means in that case existence is a property because the type of existence discussed changes the situation. If necessary I can find a half dozen experts who say this. I don't have the quotes anymore but I have documented this with a huge number of logicians in the past. If you want to take my word for it save us both a lot of time.
Alternate definition: The greatest beingMeta: The greatest begin is not an option. I mean by that not according to a huge portion of Christian thought. Sure the unaware, the uneducated, those not in the know, those who don't read theology, those "not with it" (aka people who disagree with me--I speak tongue in cheek) will say that God is the greatest being; but the Tillichian background from which I am working argues that God is not "a being" at all. God is the ground of being, being itself, not a being. God is the basis upon which all things cohere, not another thing in creation alongside "things." The idea of a supreme being is what I mean when I say atheist are bound up in "thing hood."
Many proponents of ontological arguments like to have it both ways. On the one hand, we are allowed to define God. On the other hand, we are not allowed to define "the unicorn which necessarily exists."
But to be fair, they're not exactly parallel. In most ontological arguments, God is not defined as "the deity which necessarily exists". Rather, God has a much more specific definition.
Definition: If God exists, then s/he is the greatest being conceivable.
Additional premise: We can conceive of a being as greater by conceiving it as necessarily existing.
Meta: Anselm said "God is that which noting greater than can be conceived." He did not say "the greatest being," although he may have said it somewhere but the famous formation doesn't refer to a being. Tillich's criticism of the OA is that it is aimed at production of proof of "a supreme being." The problem with that is God cannot be "a being" since God is the basis of all being, the ground, being itself. Of course atheists harp upon the "greatest" idea, but that's becuase they don't understand the being itself thing becasue they are too bound up in thing hood to understand the concept. I am not saying atheists are not smart enough to get it or that no atheists do understand it, but by and large they tend not to because it's alien to the way they think.
I think that this new definition hurts the ontological argument.
Meta: So did Paul Tillich, and of course what Tillich thinks I think. ;-)
For one thing, we have a whole new premise. I don't have any particular problem with the premise, but it just seems so extraneous and unnecessary. I refuse to argue with the additional premise, because it seems like a tactic to draw attention away from the real flaws of the ontological argument. In my naive optimism, I expected this tactic from conspiracy theorists, not philosophers.Meta: If I was of a mind to defend the premise of greatest conceivable being you could not get away with just saying that. But since its' antithetical to my theological outlook I am actually in agreement with you to some extent. This this is a good time to point out the importance of reading theology. The Dawkins "theology is stupid I don't have to know about it" is so self defeating. If you know theology you could beat anyone trying to argue this version of the OA but just showing that it's contradicted by some of the major theologians throughout history; in that those who agree that God is being itself disagree that God is "a being" so God can't be "the supreme being" because the "supreme being" is still "a being."
And the new definition does not help in the slightest.
Let's say that Russell is the name of "the male barber who shaves all men who do not shave themselves. As I said before, in Zermelo-Fraenkel set theory, there are rules against defining Russell. If we are not allowed to define Russell, then obviously, we are also not allowed to define Russell's wife! Russell's wife may not have any self-referential paradoxes, but she requires the existence of Russell, who does have self-referential paradoxes.
Let's say we have a rule against defining necessarily existing beings. Obviously, we are also not allowed to define the wives of any of those beings. We are not allowed to make any definition which implies necessary existence. If we accept the additional premise, then the definition of God implies necessary existence. Therefore we are not allowed to construct the definition of God.
Meta: by the same token not arguing the supreme being thing means this argument doesn't apply to my view.