The 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 existence 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 scholastic ones in the middle ages is not that great. The  scholastic 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 argument 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.



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 eternal).

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 theorem 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 conceivable in analytical terms; it is dependent upon principles which are themselves contingent. Nothing can come from a possibility of total nothingness; the existence of singularities and density of matter depend upon empirical 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 argument must accept such proof).

Since the concept is coherent and 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 affairs 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 impossible. Necessary if he exists, 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 concrete 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 necessarily (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 subdivided, for example fictional contingency, such as Sueprman or Dick Tracy, that which would be contingent if it had real concrete 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 declaring 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 concede 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 truly 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 impossible, but just that the possibility of God's not existing reverses the argument.

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 indeed 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 shown why God is possible, becasue God is conceivable without contradiction.

(6) anticipating answer on entity and consciousness, consciousness is not a primary quality of God. Other things are consciousness, that is not something uniquely establishes 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 contradiction 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 contraction 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 conceive god analytically without contradiction. what else could one do to prove a possibility?


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

This is really the same argument 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 supposed 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 work because 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 independent of proof because it is part of the definition 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 definition is speaking of ontological necessity, than to assert the actuality of it is moving from logical to ontological necessity.

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 existence is impossible. Therefore, ontological 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 controversial, 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 logical 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 philosopher 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" movement 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 Ontological argument back from ignominious 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 campaign to advocate social issues such as medical care.