Answering an Argument that God Need Not Exist Necessarily

Charles Hartshorne: A Natural Theology
For Our Time


Remember the Modal Argument from a few days ago?

Hartshorne's version goes like this: (actually forest Baird's)
1) God can be analytically conceived without contradiction.
2) Therefore God is not impossible.
3) By definition God cannot be contingent.
4) Therefore God is either necessary or impossible.
5) God is not impossible (from 2) therefore, God is necessary.
6) Whatever is necessary by the force of Becker's modal theorum must necessarily exist.



Argument:my version

1) God can be analytically conceived, as eternal necessary being, without contradiction.

2) Therefore God is not impossible,(because no contradiction).

3) By definition God cannot be contingent (becasue God is eteral).

4) Therefore if God exists, God's existence is necessary, if God does not exist, it is because God is impossible.

5) God is not impossible (from 2) therefore, God is necessary.

6) Whatever is necessary by the force of Becker's modal theorum must necessarily exist.

An anonymous poster (who says he's not an atheist) calms to disprove the premises that God must exist necessarily. I don't see how anyone who is a Chrsitain can fail understand the essential aspect of this doctirne. That's basically denying who God is. The only alternatives to God existing necessarily are that God is impossible and can't exist at all, or that God is contingent, in which case he can't be the Christian God. A contingent God would be no better than superman. Superman could go nuts and deiced to be worshiped and force everyone to prya to him and call himself God he would be just as much God as a contingent God of the Bible would be. Of course the phase "contingent God of the Bible" is a contradiction in Terms becasue the Bible makes it clear God is not contingent, thus he has to be necessarily becuase those are the only choices.

There are four choices only, as streamlined as it can be: Two on the necessary side and two on the contingent side. Each two represent polar opposites:

(1) Necessary vs. (2) impossible

(3) exists contingently v. (4) fictional (contingent non existent)

It should be unthinkable to a Christian that God could be contingent. Yet this guy does some fancy foot work to manipulate the language of s5 modal logic to try and "demonstrate" just that. Before I ansser it want to challenge to find one single theologian other than a Derridian somewhere or a Postmodern, who asserts that the Christian God is contingent. I don't believe anyone ever has. Its' so obviously well known that the Christian God is always thought of as existing necessarily I don't think you can find a theologian form any time prior to the rise of Postmodernism who would say that. Of course I mean a believing theologian.

Here is the opening of this guy's gambit:

I'll try to rephrase my objection for clarity.

Hartshorne's statement of the argument begins with the line:

g --> N(g)

Which, interpreted, (remembering that the arrow stands for the _strict_ conditional,) means "Necessarily, if god exists, then necessarily god exists."

That is just a straightforward statement that if God exist he exists necessarily." No magic there.

This statement is false, and I can prove it.

O pshaw! I dare you! I dare you even.

To show that a statement of the form "Necessarily, X" is false, you must show that there is a possible world in which X is false. So my claim is that there is a possible world in which "g -> N(g)" is false (where this -> is not the strict conditional but the material conditional instead).

Not exactly mystical truth yet. Just a basic statement that to show false hood it must be the case that God exist in a possible world where he exits in a way that is not necessary. That doesn't tell us how he's going to prove there is such a possible world. It sounds like he really knows what he's doing but returned with the Holy Grail yet.

In order for a material conditional to be false, it must be that its antecedent is true and its consequent false. So my claim must be that there is a possible world in which god exist but does not exist necessarily.

What did I tell you? How will he demonstrate that there is such a possible world when it contradicts the concept of God in Christian thought? Reemmber now we are not talking about empircal knowledge, we are not talking about parallel worlds that exist, we are talking mere hypothetical possibilities.

Cashing out what "necessarily" and "possible" mean in standard interpretations of modal logic, (assuming S5 here) we have now a statement of my claim in detail:


There is a maximal set of propositions containing no contradiction which contains the proposition g, and there is a maximal set of propositions containing no contradictions which contains the proposition not-g.

Not so fast there man. This the lack of contradiction has not been demonstrated for -g nor can it be. It is not great trick to prove that the concept of the Christian God is that of necessarily being. Its' in all the theology going back to the beginning it's all over the Bible and it's all over the major doctrines. Aseity, reity, eternalness all of this implies necessary.

Since the concept of God is linked with necessary being then to raise the possibility of a possible world in which this is not the case is in and of itself a contradiction. It's a contradiction on the same grounds that the law of identity is not a contradiction.

Let A be "official definition of X is X."

If you say "i can think of a possible world in which A is not the case, then you are saying X is not X. How can X not be X? By definition X = X.

In terms of the modal argument this is not equivocate as defining God into existence. That's so beaus we are not talking God's actuality we are talking about the defintion of the concept. Sicne the concept to be true would require that there not be a possible world in which it was false you have to prove such a possible world on some other grounds tan the claim that your statment is without contradiction because it is. I suggest it woudl have to be proved on empirical grounds,which of course can't be done without travel to other dimensions.

Presumably you agree about the first part. My task then is to prove that there is a maximal set of propositions containing no contradictions which contains the proposition not-g.

I'm not sure what you are calling the "first part" if you mean the basic understanding of what modal logic is and the relation to possible worlds and contradictions in same, then yes.

But this is trivially proven, simply by reference to commonplaces about how logic (much less modal logic) works. For any proposition not-X whatsoever, we can build a maximally consistent set of propositions around it simply by running through every propositional variable a, b, c and so on, assigning it to either 'true' or 'false', and then constructing every possible propositional statement with connectives and determining its value from those of its constituent propositional variables.

Sorry, doesn't work that way. It's already beaten coming out of the shoot. That is so because it's a contradiction to the basic concept of God in Christianity. No way to maintain a possible world where it's contradiction because to contradict it is a contradiction to the concept we are working with. you are merely contradicting the concept of God. Running through variables isn't going to prove anything when the basic concept is being contradicted.

This is a standard lemma at the basis of every system of modal logic--take any propositional expression whatsoever, and you can build a maximally consistent set of propositions around it.

that sounds real impressive, but no magic. It's just the manipulations of terminologies to cover the fact that you didn't prove your argument. The fatal falw in your argument, if you are a Christian I suspetct in your faith is taht you don't know who or what God is.

here is the Answer Plantinga sent me in email

I think you friend is mistaken. He says:

But this is trivially proven, simply by reference to commonplaces about how logic (much less modal logic) works. For any proposition not-X whatsoever, we can build a maximally consistent set of propositions around it simply by running through every propositional variable a, b, c and so on, assigning it to either 'true' or 'false', and then constructing every possible propositional statement with connectives and determining its value from those of its constituent propositional variables.

This is a standard lemma at the basis of every system of modal logic--take any propositional expression whatsoever, and you can build a maximally consistent set of propositions around it.

He says: for any proposition not-x we can build a max cons set of props around it . . .; but this won't work for -(pv-p) for any p.

Maybe he means: for any proposition -X, where X is noncomplex. Here the answer is that we can build a set or props around it that doesn't formally entail a contradiction in first order logic. For example, we can do that with -(2+1=3). Still, -(2+1=3) is necessarily false, even tho you can't deduce a contradiction from it in first order logic. Those who, like me, think God is a necessary being, think the proposition -G is necessarily false in the same way that -(2+1=3) is. That's true, even if you can't deduce a contradiction from it in first order logic.

Modal Argument

Charles Hartshorne 1897-2000
Modern Champion of the modal argument

What follows is one of the most challenging subjects you will ever hear about. It is the best way to get a head ache, but I think it proves the existence of God. The problem is it requires a very specialized background to understand it. First you have to understand modal logic.

Modal Logic is so called because it turns upon the use of so called "modal operators." It's called "modal" because it is the logic of modes of being. "modes" as in what type of existnce something exits in, weather it is dependent upon other things, weather it can cease or fail to exist and so forth. The modal operators are "necessity," "contingency" "impossibly," "possibility."

Necessity and contingency lie at the base of our modern understanding of cause and effect. They come from scholastic notions of logic, but the distinction between the notion our modern notions of c/e and the shcoalstic ones in the middle ages is not that great. The scholastics had more levels of cause, efficient cause, final cause and several others. But one could everything we have done in modern science using the scholastic ideas of c/e.

Necessity doesn't mean has to exist. It doesn't mean God is necessary to the existence of the world (except in so far as if God exists then of closure God is necessary to the world as creator--without God there would be no world).The modal arguemnt does not begin with the assumption that God has to exist. It begins with the assumption that there is a valid distinction between necessity and contingency, which there must be.It proceeds along the lines of hypothetical consequence that obtain from different scenarios of God's existence. It concludes that is necessary. But by "necessary" it means not contingent, or not dependent upon something else for its' existence.

This is often misconstrued by atheists and taken to mean the argument proceeds from God's existence as an assumed first premise. This is not the case, the first premise is either/or. Either God's existence is necessary or it is impossible. This allows for the possibility that there is no God. So the argument does not begin by "defining God into existence."

Necessity means either non dependent or cannot cease or fail. By "fail" I mean there could not not be a God. That is the conclusion of the argument, not the premise.

Contingent means the opposite: that a thing is dependent upon a prior thing for existence, or that it could cease or fail to exist.

Impossible means logically impossible, something in the structure of the idea contradictions, such as square circles.

one of the sore spots that atheists get stuck on is the idea that God cannot be contingent. They will always leap to the conclusion that this is defining God into existence, because they don't understand the concept of God. God, by the nature of the concept, carriers certain parameters just as the existence of any human assumes humanity, or the existence of any tree assumes that the tree in question is a plant. To have to define that God is not contingent should not even come into it. The idea of God is that of eternal creator of all things. Thus God cannot cease to exits and cannot be dependent upon anything (or he wouldn't be the creator of all things). Atheists usually assume that all knowledge has to be empirical. they will argue this is defining God into existence. maybe God is contingent.

Maybe there is a begin like the one we talk about but he's not eternal or the creator of all things, but that means he's not the God we are talking about.



Hartshorne's version goes like this:

1) God can be analytically conceived without contradiction.
2) Therefore God is not impossible.
3) By definition God cannot be contingent.
4) Therefore God is either necessary or impossible.
5) God is not impossible (from 2) therefore, God is necessary.
6) Whatever is necessary by the force of Becker's modal theorum must necessarily exist.



Argument:my version

1) God can be analytically conceived, as eternal necessary being, without contradiction.

2) Therefore God is not impossible,(because no contradiction).

3) By definition God cannot be contingent (becasue God is eteral).

4) Therefore if God exists, God's existence is necessary, if God does not exist, it is because God is impossible.

5) God is not impossible (from 2) therefore, God is necessary.

6) Whatever is necessary by the force of Becker's modal theorum must necessarily exist.


A. The logic of the argument:

This argument is analytical, it proceeds from the basis in logic to argue that the concept of God is such that if we understood the meaning of the terms we would have to conclude that God must exist. Naturally that is a very controversial position. Many Christians and other theists reject the ontological argument on the grounds knowledge must be somewhat empirical. Nevertheless the argument has been used for a long time, and despite its many apparent deaths, it keeps returning in one form or another. Perhaps the best book on the subject is The Many Faced Argument by John Hick. Somehow the ontological argument just wont die. I feel that this is not so much because the argument itself is true as a proof, but because it gets at something deeper than proof, something to do with the way to think about God, and it strikes a deep cord in our consciousness, even though as a proof it may fail. For this reason alone it is important to know, if only to know the concept itself.

1) God can be analytically conceived without contradiction.
2) Therefore God is not impossible.
3) By definition God cannot be contingent.
4) Therefore God is either necessary or impossible.
5) God is not impossible (from 2) therefore, God is necessary.
6) Whatever is necessary by the force of Becker's modal theorum must necessarily exist.

(This is actually my re-statement of what Hartshorne is saying).

Hartshorne's actual modal logic looks like this:

The OA: an assessment:

by Ed Stoebenau

http://www.eskimo.net/~cwj2/atheism/onto.html Hartshorne's ontological argument is based on Anselm's second argument and claims that God's existence is logically necessary. Hartshorne's argument is given here, where "N(A)" means "it is logically necessary that A," "~A" means "it is not the case that A," "-->" is strict implication, "v" means "or," and "g" means "God exists":

g --> N(g)
N(g) v ~N(g)
~N(g) --> N(~N(g))
N(g) v N(~N(g))
N(~N(g)) --> N(~g)
N(g) v N(~g)
~N(~g)
N(g)
N(g) --> g
g



This argument is valid. Furthermore, given an Anselmian conception of God, premises one and five are sound. Premise two is just the law of the excluded middle, and premise three is a law of the modal logic S5. Premise nine is obviously sound, so this leaves premise seven as the only premise to question. Premise seven says that it is logically possible that God exists.



Yes, those funny lines, "g-->N(g)" are the argument, those are the formal symbols used in modal logic.

B. God's Possibility vs. Impossibility.

The argument turns on the distinction between necessity and contingency, and upon the distinction between mere possibility and the nature of necessary being as not mere possible. In other words, God is either necessary or impossible. If God exists than he is ontologically necessary, because he is logically necessary by definition. But if he does not exist than it is ontologically impossible that he exists, or could come to exist. This is because God cannot be contingent, by definition. A contingency is just not God. So if God is possible, he can't be "merely possible" and thus is not impossible, which means he must be necessary.

God is conceivable in analytic terms without contradiction:
The universe without God is not concievable in analytical terms; it is dependent upon principles which are themselves contingent. Nothing can come from a possibility of total nothingness; the existenceo of singularities and density of matter depend upon empiracal observations and extrapolation form it. By definition these things are not analytical and do depend upon causes higher up the chain than their being (note that the skeptic at this point probably denies the validity of analytic proofs but to reverse the arguement must accept such proof).

Since the concept is coherent nad not contradictory and is derived from analytic terms, to reverse the argument the atheist must show that God is impossible since the burden of proof is now on the one arguing that a contingent state of affirs could produce a universe in which being has to be.

D. Answering Objections:

1) The argument can be reversed

Atheists have tried to reverse the argument merely by saying:

1) either God exists or he doesn't
2) God is either necessary or impossilbe. Necessary if he eixists, impossible if he does not
3) God is impossible
4) Therefore God does not exist.

But of course this is merely stipulation. They assume that what the argument is doing is just stipulating everything that has been said about God, but on the "Modes of Being" page I show that each of these modalities of existence are logical deductions.Either a thing exists or it does not. One can equivocate about the meaning the term "existence," but here I clearly mean concete actual existence in the "real" world. If a thing does not exist it is either that it could, but just doesn't happen to exist, or that it cannot exist because it is a conceptual contradiction, such as square circles, or round triangles and so on. Therefore, if it does exist, it is either that it exists contingently or that it is not contingent but exists necessaryily (that is it could not fail to exist without contradiction). These are the four most basic modes of being and cannot be denied. They could be subdivded, for example fictional contingency, such as Sueprman or Dick Tracy, that which would be contingent if it had real concete actuality, but is merely a fictional concept. But the four modes are the basic logical deductions about the nature of existence.

The idea that the argument can be reversed just by switching the lines and declairing God impossible merely begs the question. Is God really impossible just because we can utter those words? Is God logically necessary just because we can utter those words?. No, but that's not what is being said. God is logically necessary as a concept. That is the nature of the God-concept, that's the idea of God. To deny that would be like saying "how do you know that tables are things to put things on?" Or "how do you know that triagles have three sides?"The question is one of actuality, so if it is possible that God exists than God is ontologically necessary and thus has real concete existence because since God is not contingent it cannot be that God is "merely possible." If it is at all possible that God exists, than it's not impossible. To show that the argument can truely be reversed the atheist must show why God is impossible, and to do that he/she must show that God cannot be understood analytically without contradiction.


Another attempt at reversing the argument, which is always used on message boards when I make this argument: just to put not in front of each line. "It is possible that god does not exist." The premise is they don't have to prove God is ipossible, but just that the possiblity of God's not existing reverses the argment.

The problem is, the premise is false. If god is not analytically impossible (contradictory) then God must exist. Thus it is not ture that it is possible that God does not exist. The logic works like this:


(1) If God is indeep possible, the God cannot be impossible.

(2) to say God is not possible is the same as saying god is impossible.

(3) if something is possible, it can't be impossible.

(4) you must show why God is impossible.

(5) I have showen why God is possible, becasue God is concievable without contradiction.

(6) anticipating answer on eneity and consciousness, consciousness is not a primary quality of God. Other things are conscoiuss, that is not something quiquely estabishes God as God, logical necessity is such a thing.

(7) If God is possible, and can't be impossible, and can't be contingent, then to be possible for God is to be logically necessary. Thus it does not work to say God is not possible because it isn't true, thus it's a false premise.



To make good on any reversal they must show a contraidction in the concept of God. To this they always retort "well you can't prove that God is not contradictory." But I don't have to prove that. One can assume that if there is no contraiction it is not contradictory. They are the one's seeking to make the reversal, so it's their burden of proof. But to prove that God is possible all one need do is concive god analytically without contradiction. what else could one do to prove a possiblity?


2) The assumption that we are merely loading the concept with terms that make it necessary, or that the deftion of God as necessary is arbitrary.

This is really the same arguement one must make to reverse the argument of necessary being. This is what atheists always argue. The first thing they say bout it is that we are just arbitrarily sticking on the term "necessary" and playing word games. Some go so far as to try and demonstrate this by sticking the term necessary on other things, such as "purple cow" or anything they think of, and that's suppossed to show what we are doing. I regard this move as nothing more than a demonstration that they do not understand the concepts The necessity of necessity and why it must be applied to God is demonstrated on the "modes of being" page. Moreover, this move is nothing more than the perfect Island argument. It can't wrok becaus it merely enthrones contingencies. Our reason for saying that God is necessary is much more logical and organic and is much more than a mere word game.

While it is true that God as being itself is a pre-given postulate and is idependent of proof because it is part of the defintion of God, the realization that being has t be means that this must be the case.

3) The assumption that we are lending existence to a fictional being.

This is merely an assumption. The necessary existence of God is implied in the possibility of God's existence and the realization that the the only alternative is impossibility. God is possible and thus necessary. Some have tried to argue that they are breaking up the four categories with a 5th not seen, that of "fictional" but that applies to the category 4 that of non-existing contingency.

4) Equivocating between types of necessity.

The argument says that to say God is necessary as a postulate of defintion is speaking of ontological necessity, than to assert the actuality of it is moving from logical to ontolgocial necessiy.

To say that a thing is logically possible is to say that it might have existed in the past or may exist in the future. But for God to exist he must always have existed; in the past, in the future, or all time. Given logical necessity the logical possibility of God 's non existance is impossible. Therefore, ontoloigcal necessity implies logical necessity. One implies the other and it is a rational move from one to the other.



This argument may seem like merely a trick of words, and modal logic may be conroverial, but it turns on very basic logic, such as modus tolens or modus ponens which is accepted by all logicians. On Argument 1 I document Antony Flew saying that the logoical categories of "Necessary" and "contingent" truth are accepted by all logicians.

TrentDougherty
Concise intero to the Modal Ontological Arugument for The Existence of God.

http://www.abarnett.demon.co.uk/atheism/ontol.html

TERMS

‘Modal’ – Pertaining to the modes of existence (de re) or of propositions (de dicto) as necessary or possible. ‘Necessity’ is a mode of being for a thing or proposition as is ‘Possibility’.
‘Ontological’ – from Greek ontoV for being.
‘Argument’ – designed to logically support a proposition (not to be confused with persuasion which is a psycho-social phenomenon, not a philosophical one).
Throughout this description I shall use standard notation and notation used when the font is restricted to a single typeset as in a text only document for HTTP purposes on the Internet.

The modalities are symbolized as follows:
A square or in typeset [] preceding an expression means “It is necessary that…” or “It is necessarily the case that…” or simply “Necessarily…” e.g. as applied to a propositional function.

Ps/[]Ps – “It is necessarily the case that s is P” where s is a constant referring to some individual and P is a predicate.
A Diamond à or in typeset <> preceding an expression means “It is possibly the case that…” or “It is possible that…” or simply “Possibly…”

SEMANTICS

Possibility is defined as consistency. àPs/<>Ps reads as “Possibly, s is P” and means that there is no contradiction in attributing P to s. Necessity is defined as “not possibly not the case”. If something cannot not be, then it must be.

Psº~à~Ps or []Ps=~<>~Ps
THE CALCULUS

There are many different ways to axiomatize a logic, just as there are different ways to axiomatize geometry. Axioms in some systems will be theorems in others, but since axioms and theorems have the same validity it is only a matter of formal difference. One of the most used systems of modal logic is called S5. There is an interesting theorem in S5 called Brouer’s Theorem.
(PàP)à(àPàP) or (P-->[]P)-->(<>P-->P)
This theorem is derivable in weaker systems as well.
The modal ontological argument for the existence of God is just a substitution instance for this theorem. There are only two propositions needed.
THE PROPOSITIONS

First comes the definition of God as a being who, IF he exists, does so necessarily, i.e. a Necessary Being. This is only the definition of what God would be like IF he existed. The proposition is formalized as
GàG or G-->[]G
“If God exists, then he necessarily exists.”
The other proposition is the assertion that it is possible that God exists.
àG or <>G
“Possibly, God exists.”
RULES OF INFERENCE

The only rule of inference needed is Modus Ponens.
PàQ “If P, then Q”
P
Therefore Q
Now we are ready to put the argument together.

THE ARGUMENT
1. (GàG)à(àGàG)
2. GàG
3. àG
4. àGàG
5. G
(Theorem, sub G for P)
(Def of God)
(premise)
(1, 2 MP)
(4, 3 MP)

or
1. (G-->[]G)-->(<>G-->G) (Theorem, sub G for P)
2. G-->[]G (Def of God)
3. <>G (premise)
4. <>G-->G (1, 2 MP)
5. G (4, 3 MP)

COMMENTARY

It is quite a simple argument which makes it hard to understand its fullness. The simple is packed with meaning. As you can see, there is one and only one premise, that it is possible that God exists. If this be granted, then his necessary existence follows. Since all efforts to show that the concept of God is contradictory have failed heretofore I conclude, somewhat reluctantly, that God exists. Kai Neilson tried to argue this in his debate with J.P. Moreland, but didn’t make much progress.

Now I realize that to the average person, this seems like a trick, but the average person is not particularly accustomed to following logical arguments at all, much less highly specialized forms of logical calculi developed by professional philosophers. Most professors at the University level don’t even know modal logic and many have never studied it and some have never heard of it. What do those who know it, but don’t believe in God say? They say that the concept of God is incoherent. I have not yet seen an even slightly plausible argument to that effect. Until I do, the OA will be cogent to me. I might add that I am a convert on this argument. I argued for years that the ontological argument was flawed until someone showed me the modal version. I have always followed Reason wherever it lead and, as usual, it lead to God.

SELECTED BIBLIOGRAPHY

Adams, Robert M., _The Virtue of Faith_, esp. “The Logical Structure of Anselm’s Arguments,” Oxford University Press: 1987.
Moris, Thomas V, _Anselmian Explorations_, esp. “Necessary Beings,” University of Notre Dame Press: 1987.
Plantinga, Alvin, _The Nature of Necessity_, esp. “God and Necessity,” Oxford University Press: 1974, 1992.
Plantinga, Alvin, _The Ontological Argument_, Anchor Books, 1965.
Swinburne, Richard, _The Coherence of Theism_, Oxford University Press: 1977, 1993.



Oddly enough that quotation is linked to a site by an atheist named Adrian Barnett who is attacking my older version of this argument, but he was gracious enough to put this quotation, which I think works against his argument, by a philospher in the UK.


About Hartshorne


Hartshorne Lived to be 103, at the time of his death in the Fall of 2000, he was known as "the greatest living Metaphysician." Hartshorne was one of the major forces in the "back to God" movment in Philosophy (a term coined by Christianity Today in a 1979 article. His first and greatest calim to fame is as the second most influential voice in process philosophy, along with Alfred North Whtiehead, but he is also credited as the man who brought the Ontologcial argument back from ignorminious defeat by Kant almost two centuries earlier. Hartshorne was also a recognized authority on birdsong, and an authority on bycicles, having never driven a car a single time in his centogenerian lifespan. Hartshorne devoted the last years of life to waging a letter's to the editor campgaign to advocate social issues such as medical care.

Plantinga Answers Miller

 Just for grins I sent part of Miller's argument against the modal argument to Plantinga to see what he would say. Here's the bit I sent:

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.

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.

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.

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.

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.

 I thought just for grins I'd put up Plantinga's answer. This he sent to me in private email and he sent permission for me to post it.

I'd say that a proposition is *logically consisstent* if it's not possible to deduce a contradiction from it in ordinary *first order) logic.  Obviously the existence of God is logically consistent.  But note everything that is logically consistent is possibles in the broadly logical sense: false arithmetical propositions for example, are logically consistent but impossible in the broadly logical sense.  The question of the ontological argument is whether the existence of God is possible in the broadly logical sense.  If it is, then it is also actual and also necessary.

As for the parallel postulate, it might very well be necessary in the broadly logical sense--which is all you can say for the other axioms on geometry.  When people say it isn't provable, they mean that it isn't deducible from the other axioms--but that (I think) is also true of each of the other axioms.

Answering Miller's "Right post" on Modal Argument

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.

Miller:

Modal ontological argument, reviewed

Definition: If God exists, then God necessarily exists.
Premise: It is possible that God exists.
[Insert mess of logical reasoning here]
Conclusion: God exists.

Meta:I think the premise is what you call "definition" and the second line is either a minor premise or corollary.No matter.

Miller:

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.

Miller:

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.

Miller:

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.

Miller:

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.

Miller:

Here is a much better translation to logic:

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.

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.

Miller

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:
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.

Meta: Truth by stipulation. you can't stipulate the non existence of God.

Miller:

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.

Miller:

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.

Miller:

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.


Miller:

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

Miller

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.


Miller:

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.


Miller:

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.


Miller:

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."

Miller:

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.


Miller:

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.


Miller:

Alternate definition: The greatest being

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."

Meta: 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."

Miller:

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.

Miller:

I think that this new definition hurts the ontological argument. 

Meta: So did Paul Tillich, and of course what Tillich thinks I think. ;-)

Miller:

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."

Miller:
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.

Answering Ojbections to Model Argument.

I'm not going to spend the rest of my life answering these arguments. But Hermit (regular poster and extreme critic of this blog--well, he's Canadian--) produced a link that is a skeptic attacking modal arguments. I am going to make some comments on one of his attacks. From Skeptic's Play, "a modal ontological argument."  

scroll down to second article on the page.

This guy writes in symbolic logic which would lead one to believe that he knows modal logic. Yet I think many of his uses are misleading and he doesn't really unpack everything that's in the argument.  If he understands it he's being a bit shady in his dealings with it.

To briefly review the simpler ontological argument: The argument says that we can define God as a necessarily existing being. Therefore, by definition, God exists. However, this takes the power of definition too far. The most we can say is that if there exists an object which we can properly call God, then that object, by definition, exists. If God exists, then God exists.

Right away he begin with a dishonesty (let's skip over the bad understanding of the Supra essential Godhead in the use of "a necessarily existing being" since most of the users of model arguments don't read Tillich, and Tillich criticizes them for that very thing) but this is a false version of the argument up front. Why do these guys have such an conversation to quoting actual theistic arguments up front? Is it becuase they know if they do that they can't beat them? None of the major users of modal ontological argument say "we can define God as X therefore God must exist." The conclusion  of God's existence is not predicated upon the definition but upon the consequences of demonstrating that the definition by corroborate to something real. Atheists believe that this is what theists are doing so their criticism always follows that line even though it's made plain that it's not the case!


The first line of the argument I use says:

(1) If God exists, he must exist necessarily, if God does not exist his existence is impossible.
See the difference? I don't' say "Since if define God as existing then he must exist." It begins conditionally, "If God exists."
 His confused ramblings about the nature of definition are designed to destroy the belief system so that one is no longer defending one's belief but the straw man the atheist wishes him to defend:

The most we can say is that if there exists an object which we can properly call God, then that object, by definition, exists. If God exists, then God exists.

This is by No means "the most" we can say. Since Christians believe that God is the basis of all reality, being itself, the ground of all being, then we have to define God in that way, period. We choice but to do so because anything less would not be that in which we believe. In fact Anselm does this when he says "the greatest thought should be about the greatest reality." That's basically what Anslem's original ontological argument was saying. This is not defining into existence because it takes up form a bleieve system that is already in place and merely asserts the ontologically necessary nature of that thing. Of course the atheist can't understand this because bound up in thing hood. He can't reason from from the basis of realization of God's reality due to the depth of being so he has to reason backwards from things and because that's all he can do he imagines the believer must be doing so as well. This is why atheist wind up making the mistake of thinking that "the reason" to believe is because we need to explain how things came to be. Actually this is really far removed from the core reasons for belief.

The problem with the argument is that it's rather useless to define God as a being which exists. But hold on! I never defined God as a being which exists. I defined God as a being which necessarily exists. This definition is not quite as useless. We can say that if there exists an object which we can properly call God, then that object, by definition, necessarily exists. If God exists, then God necessarily exists.

By definition of God: g g

Now here he is right in that the model aspect, which is taking account of the particular kind of existence under discussion add something to the nature of the case and is more than just saying "I define God as existing." It's a conditional statement however, as my statement above "If god exists he must exist necessarily" and this guy is not reflecting this fact. He acknowledges the model aspect he's not recognizing the conditional nature of it.

The letter "g" represents the specific statement "God exists". Note, however, we did not completely define God. In fact, we could replace God with all kinds of absurd objects, and the proof would still hold. This is actually quite a problem for the ontological argument (as well as many other proofs of God). The proof is valid for any statement p as long as pp is necessarily true. For instance, we could replace the object God with "the invisible pink unicorn which necessarily exists" or "a left shoe which necessarily exists".

 What's he's saying here is total bull shit. It's quite strange that this guy knows symbols for modal logic (which I don't) but he still doesn't know the argument now does he know the literature. He could really do with reading John Hick's book The Many faced Argument. This approach (that we could define God in any number of ways) is nothing more than one of the oldest arguments again Anselm, and one of the most fallacious, the Perfect Island argument by Gaunilo (1033-1109) (see On Behalf of the Fool). It just says we should say God is a prefect island and by the same logic the argument would prove that a perfect island exists, therefore, something must be wrong with this logic since it would prove such a ridiculous thing. But the answer is that it would not be possible to assert God is a perfect island (perfect tomato, purple, cow, pink unicorn, swizzle stick,  or what have you) unless that thing was eternal, necessary, and the ground of being. Why assert that the necessary ground of being is some contingent thing like an island or a tomato? At that point, since it has to have the attributes of God it is God then there's no point in linking it with things that are clearly not God, that contingent, temporal, man made and so on. What it really boils down to is that we cannot define God in any old way we wish. There is a very strict definition of God, that dis guided by the basic belief systems that embrace the notion of God. In all major world religions these same basic attributes are always there for the major God, the father God, those are: the creator God: eternal, necessary, ground of all being. It matters how one defines it and you can't do so in just any old way.

Nonetheless, let's continue onward. I'm going to go through the proof, step by step.

• Theorem 1: ¬g ¬g (The contrapositive of the definition of g)
  
• Theorem 2: ¬g ¬g (Using the definition of to substitute into Theorem 1)
  
• Theorem 3: (¬g ¬g) (Application of Axiom N to Theorem 2)
  
• Theorem 4: ¬g ¬g (Application of Axiom K to Theorem 3)
  
• Theorem 5: ¬g¬g (Axiom 5 applied to ¬g)
  
• Theorem 6: ¬g ¬g (Combining Theorems 4 and 5)
  
• Theorem 7: ¬¬g ¬¬g (The contrapositive of theorem 6)
  
• Theorem 8: gg (Using the definition of to substitute into Theorem 7 twice)
  
• Theorem 9: g g (Combining Theorem 8 with Axiom T)

You may have noticed that I did not prove what I set out to prove. I only proved g g, which says that if g is possible, then it is true. That's not quite the same as saying that g is true, but it's still something. Now, all we have to do is prove that g is at least possibly true.

And here is where the problems begin. All the previous work was purely logical manipulation, and is necessarily true if you accept the axioms of modal logic. I thought the axioms were pretty reasonable, and rejecting them would be too high a price to pay. However, it seems we need another premise, g. To support this premise, lots of arguments have been offered by various people, but I don't think they're nearly as fun or rigorous as the modal logic section.

That's all basically true. But of course the argument does turn on not the idea that g is possible the idea that g is not merely possible. If g is not impossible then since g can't be merely possible (might or not might not be) then g must exist. In other words, g must be impossible or else g must be. Thus since g is not impossible  g must be. He's wrong here again where I put it in red, he changes the meaning of the argument. This is why I don't like this guy because he tries get away with subtle changes that have profound implications and yet he carefully avoids the real answers that theists have given. The subtle difference is that g can be merely possible so it's not a matter of if g is possible then g must be true but rather that g is not impossible.

One common argument for g is that g is self-consistent. I can conceive of a God without having any contradictions. Based on my current knowledge, it is entirely possible that God exists. It's possible that God exists, therefore God exists.

Again he does not present this properly.He should really be saying that the basis for asserting that God is not impossible is that there are contradictions to belief in God. The atheist has the burden to assert what criteria would prove the impossibility of God. Its' not fair to expect the theist to mount an endless litany covering every possibility when the argument is rightfully the atheists burden to prove. That is if the theist has done his job properly and not argued 'this proves the existence of God' but set it up the right way and argued rational warrant.


The problem is that this same argument seems to apply to the statement ¬g. ¬g is a self-consistent statement. I can conceive of a world in which God does not exist without having any contradictions. Indeed, I can conceive of a world where nothing at all exists, where there could not possibly be any contradictions since there is nothing around to contradict. Based on my current knowledge, it is entirely possible that God does not exist. Therefore we can take the premise ¬g. By Theorem 2, we conclude ¬g: God does not exist.

Obviously, the premises g and ¬g cannot both be true. Either God exists in all possible worlds, or God exists in none of them. Since we used the same argument for both both g and ¬g, that argument must be fallacious. But where exactly did it go wrong?

The error, I think, is in the concept of . g does not quite mean "g is possibly true." In fact, it means "Among all possible worlds, there exists at least one in which g is true." The concept of "All possible worlds" was never exactly defined. In fact, the definition is arbitrary. I could have declared "all possible worlds" to be our world and our world alone, and you never would have been able to prove me wrong from the axioms.

Possible words don't change the argument. It's just a  means of introducing modes of being, possible worlds are contingencies, every contingent thing represents a possibility of its own negation. It' garbage to thin that "possible world" is not defined. That's a major main stay of reformed apologetic everyone from Plantinga to Hartshorne has defined it well.  that is not problem anyway because all it means is in the likelihood of each contingency negated. what he says declaring all possible worlds to be our world is dead wrong. He doesn't set it up right, but the modal argument be made without the possible word's even being mentioned. That's another argument, it's a good argument and he's treating it wrongly, but that's not germane to this one.

I also could have declared "all possible worlds" to be the set of worlds which are metaphysically possible (a rather complex philosophical concept). Under this definition, we would not be able to prove g or ¬g.

He's made a red herring. He can't answer the actual argument that he started with so he's shifted to something that's not even part of Hartshorne's modal argument so the can harp on it. The reader is diverted from the fact that he never answered the argument to begin with.

However, if I had declared "all possible worlds" to mean the set of all worlds which are self-consistent, then we would run into problems. Because under this definition, both g and ¬g appear to be true (unless the concept of God is inconsistent). And they contradict each other.

But no one did. another red herring.

Similarly, if I had declared "all possible worlds" to mean the set of all worlds which are epistemologically possible (meaning, it may be true, for all we know), then we would have the same contradiction.

And what happens if we construct a pathological definition of "all possible worlds" such that g is true and ¬g is not true? Then I might question Axiom T, since it is no longer obvious that our world is included among this so-called set of "all possible worlds."

The possible world's thing is easily defended. But I am not going to do so here because it's not part of the argument I made. take that out because its not part of my argument and look at my argument and that he did not answer it. Hermit thrust this link because he doesn't understand what it says. He thinks any sort of criticism of any ontological argument beats all of hem and such is not the case.

And it goes on and on. Well, wasn't it clever, at least at first? I think so. It seemed for a moment that we arrived at a paradox, a sort of 1=2 moment. Ontological arguments tend to be that way. Most people immediately recognize that it is a little too clever, that it proves a statement which is a little too strong to be true. Similarly, most philosophers think that ontological arguments fail, though they may disagree on exactly why they fail.

Now he's trying to beat the argument by quilting it for being beyond his understanding. It's too clever for him, he seems to think that's a liability if it was an argument for atheism is we would be bragging about how clever it is and how stupid stupid theists don't get it. But the "too-clever" bit is not even part of the original argument which he has still not answered. None of his mocks against possible words beat the argument that says "If God is not impossible then he must be necessary." To that one he tells us nothing about it's apparent fallacious nature.

In my opinion, ontological arguments are merely interesting philosophical curiosities. It's rather silly when an apologist actually tries to use one as a serious argument.

Yes that 's what Gaunilo said, on behalf of the fool.