Sunday, April 17, 2011

Modal Argument

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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.

21 comments:

Mandy said...

That's informative and inspiring!

Happy moments, praise God.
Difficult moments, seek God.
Every moment, thank God.

Metacrock said...

those are not epithets one often hears of the modal argument, but thanks.

Kris Rhodes said...

Hi Metacrock,

You and I used to interact on CARM many many years ago. I was one of those Christian Universalist types the powers-that-be didn't like very much.

Anyway, the modal argument you give here doesn't work because it begins with the premise "If god exists then it is logically necessary that god exists." This is not true. It could be that God exists and yet doesn't exist logically necessarily. For what it means for it to be logically necessary is that there is no possible world in which God does not exist. Yet for there to be no possible world in which God does not exist, it would have to be that the proposition "God does not exist" either is or implies a contradiction. But it isn't and it doesn't. So there is a possible world in which God does not exist. So it's not logically necessary for God to exist--whether or not he actually does exist. Therefore its false to say that if God exists then it's logically necessary that he exist.

-Kris Rhodes

Metacrock said...

No Chris you are wrong. The atheist argument you support is fallacious. It is a contradiction to say there is no God, that is what the argument illustrates.

It starts with an either/or, however, not with just an assertion that God has to be necessary. The atheists only option is to demonstrate the impossibility of God.

Until they demonstrate that we have every reason to believe there has to be a God.

Anonymous said...

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."

This statement is false, and I can prove it.

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).

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.

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.

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.

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.

Continued in next post...

Anonymous said...

There's nothing special about "god exists" in this regard--as far as any propositional logic system can tell, "god exists" is just a proposition like any other. That's the nature of propositional (and modal propositional) logics. They're not equipped to prove that any particular proposition is [i]true[/i] (that is, unless it is tautological, which is a term with a particular technical meaning which does not admit "god exists" as included in the class), only that it validly follows or fails to validly follow from the hypothesized truth of other propositions.

That's the argument from the nature of propositional logic--propositional logic just isn't the right tool for the job, basically (nor is modal propositional logic).

Perhaps a modal predicate logic would do the trick but for whatever reason, I've never actually seen that attempted. This may be because modal predicate logics are (so I hear) necessarily incomplete, but I'm not sure.

If you think there is a contradiction to be derived from the statement "God does not exist," then it's up to you to show what that contradiction is and how it is to be derived. A contradiction, of course, is a statement of the form "A and not-A."

You may be thinking this is all beside the point because it's simply supposed to be part of the definition of God that he exists necessarily. If that's the definition of God, then if God exists, then God necessarily exists. But what I've shown, actually, is that there is no such thing as something which exists necessarily. The nonexistence of [i]anything[/i] is logically consistent. So God doesn't exist necessarily. So [i]if[/i] it's part of the definition of "God" that god exists necessarily, then God doesn't exist.

Of course I believe God exists. I just don't think it's part of the definition of "God" that god exists necessarily. He exists logically contingently just like every other object it is possible to talk about.

Metacrock said...

"There's nothing special about "god exists" in this regard--as far as any propositional logic system can tell, "god exists" is just a proposition like any other. That's the nature of propositional (and modal propositional) logics. They're not equipped to prove that any particular proposition is [i]true[/i] (that is, unless it is tautological, which is a term with a particular technical meaning which does not admit "god exists" as included in the class), only that it validly follows or fails to validly follow from the hypothesized truth of other propositions."

Right, it's not about proof. It's about rational warrant.

"That's the argument from the nature of propositional logic--propositional logic just isn't the right tool for the job, basically (nor is modal propositional logic).

Perhaps a modal predicate logic would do the trick but for whatever reason, I've never actually seen that attempted. This may be because modal predicate logics are (so I hear) necessarily incomplete, but I'm not sure.

If you think there is a contradiction to be derived from the statement "God does not exist," then it's up to you to show what that contradiction is and how it is to be derived. A contradiction, of course, is a statement of the form "A and not-A."


NO wrong:
(1) Hartshorne's argument is s5 modal.

(2) ask Plantinga; (where do you teach logic, notre Dame I doubt doubt it, he does).

(3) Wrong to think it's my burden of proof to show that "God does not exist" is a contradiction. It's not my argument, thus it's not my burden. It's the atheist argument so their burden.


"You may be thinking this is all beside the point because it's simply supposed to be part of the definition of God that he exists necessarily. If that's the definition of God, then if God exists, then God necessarily exists. But what I've shown, actually, is that there is no such thing as something which exists necessarily. The nonexistence of [i]anything[/i] is logically consistent."

Bull shit you have not shown anything. Where's the argument? all you've done is assert your opinion.



"So God doesn't exist necessarily. So [i]if[/i] it's part of the definition of "God" that god exists necessarily, then God doesn't exist."

you are making from a charge that to the assertion that contra of the chruch must be true. that's a fallacy in itself.



"Of course I believe God exists. I just don't think it's part of the definition of "God" that god exists necessarily. He exists logically contingently just like every other object it is possible to talk about."

It's pathetic how little you know and how arrogant you are. I've talked many times to the top expert in the world on this argument I don't think you have.

yes obviously it is part of the defiton of God that if he exist s(the IF PART IS A BIG YOUR MAJESTY) then he must do so necessarly. otherwise you are worshiping a ontignernt god. how the hell can a continent God be the king of the universe? he's not better than Zeus he can be dpossed.

shape up and learn some theology. No Christian philosopher in the heifer of the faith has ever said God was contingent no one!

yes sweet heart the choice is either necessary or contingent those are the only choices, impossible, necessary and contingent.

Metacrock said...

I'm going to deal with the alleged "proof" on Monday.

this is total brainlessness. It wouldn't be if you just admit you are atheist then you can claim ignorance.n o Chrsitian would ever says God is not necessarily that's totally stupid.

a contingent God is not worthy of worship. If God is eternally contingent then worship the thing he's contingent upon.

you must be a gnostic.

Anonymous said...

Hi Metacrock,

I look forward to seeing your post dealing with the proof.

To clarify my view on God's existence, it's that God's existence is not _logically_ necessary (nothing's existence is, it's the nature of (propositional) logic) but it's fair to say God'e existence is _metaphysically_ necessary. There are many things that are metaphysically necessary which are not logically necessary. For example, it is metaphysically necessary that anything that is blue all over is not green anywhere--but it's not logically necessary! There is no contradiction contained within the statement "this thing is both green and blue all over." Yet the statement can't be true, because of the metaphysics of color. The impossibility is metaphysical, not logical.

Similarly, the impossibility of God's existence would be metaphysical, not logical.

You can't use propositional logic to prove God's existence, because propositional logic can't look inside the proposition "g" to see what it's talking about. It must treat "g" just like any other proposition (that's what propositional logic does by definition) and since any [i]other[/i] simple proposition can be shown to be contingent in propositional logic, it follows that the simple proposition "g" must be contingent in propositional logic, no matter what it means.

Kris Rhodes said...

Also, I invite you (in a wholly friendly fashion) to show my posts to your logician friend whom you said you've been discussing this with, and see what they have to say. One mistake I certainly made was to claim that you can take _any_ propositional expression and build a maximally consistent set of propositions around it. That was strictly wrong--it only works if the propositional expression is not itself a contradiction.

Also, it is standard in logic and in philosophy in general, when someone claims that a statement implies a contradiction, that other logicians and philosophers think that person has a responsibility to show what that contradiction is and how it's derived. If he doesn't do that, no one else has any basis upon which to evaluate his claim.

If someone says "'God does not exist' implies a contradiction," no one is equipped to give a relevant reply until that person has explained how the contradiction is supposed to arise.

Metacrock said...

on that latest post I include the email Plantinga sent me in response to your argument.

Metacrock said...

Hi Metacrock,

I look forward to seeing your post dealing with the proof.

To clarify my view on God's existence, it's that God's existence is not _logically_ necessary (nothing's existence is, it's the nature of (propositional) logic) but it's fair to say God'e existence is _metaphysically_ necessary.

that's an old argument made by John Hick. It's true that God's existence has to be ontologically necessary it is also logically necessary. you are misconception what the argument proves.

The argument proves God can't fail to exist. It's not logical necessity in the sense of a tautology because that is merely linguistic and doesn't require an argument. It's logically necessary in the sense that it can't fail to exist.




There are many things that are metaphysically necessary which are not logically necessary. For example, it is metaphysically necessary that anything that is blue all over is not green anywhere--but it's not logically necessary!


you are equivocating bewteen aspects of logical necessity. Here you are using some made up category called "metaphysically necessary" to mean actual.



There is no contradiction contained within the statement "this thing is both green and blue all over." Yet the statement can't be true, because of the metaphysics of color. The impossibility is metaphysical, not logical.

Similarly, the impossibility of God's existence would be metaphysical, not logical.

that's total bull shit. God cannot fail to exist, ti's not a matter of empiricism there's no such thing as Metaphysical necessity. Metaphysics is not a form of proof.


You can't use propositional logic to prove God's existence, because propositional logic can't look inside the proposition "g" to see what it's talking about. It must treat "g" just like any other proposition (that's what propositional logic does by definition) and since any [i]other[/i] simple proposition can be shown to be contingent in propositional logic, it follows that the simple proposition "g" must be contingent in propositional logic, no matter what it means.

sorry you are totally out of it. You need to study this stuff much better. the modal argument is not positionally that's why ti's called model, it deal modal oporaters..

no kind of logic an prove the existence of God because it's beyond our understanding.That's not even if the goal the argument. Please try to come up to speed.Read a bunch of posts form this blog going back over the last couple of years.

goodle "rational warrant." and "realizing God."

Anonymous said...

It is clear from this conversation who has "studied this stuff" and who has not.

Of course in that last paragraph when I said "propositional logic," I was referring to propositional modal logic.

Your claim that Hartshorne's argument isn't trying to prove that God exists seems clearly false--the conclusion of the argument is 'g', which, interpreted, means "God exists."

You may not think there is any such thing as metaphysical necessity, but it's not a "made up concept" if by that you mean I made it up. It's a philosophical concept that is used quite often.

Hartshorne's proof attempts to show that God exists, using just the tools of modal propositional logic. I have explained why that can't be done, and Plantinga, as quoted by you, agrees with me. (By the way, you should have simply asked me for a copy of his email to me, as I invited you to do--the one he sent you turns out to be almost identical in wording to the one he sent me.) He agrees that you can not derive a contradiction from "God does not exist" using just the tools of propositional logic. This, in turn, means that Hartshorne's proof fails if it is meant to be a proof that God exists--and I don't see how it can be interpreted otherwise.

Using Hartshorne's argument, by the way, one could just as easily prove "-g" in exactly the same way.

One could also prove both that the Goldbach conjecture is true and that it is false.

(BTW I'm bothered by this--it looks like we can prove a contradiction from true premises using propositional modal logic. That's odd!)

The argument form simply doesn't work if we try to interpret "g" as involving concepts like existence and truth. Some other logical system needs to be used, if any will work.

Again, main points:

God's necessity isn't provable using propositional modal logic.

But Hartshorne's proof is an attempt to prove God's necessity using propositional modal logic.

Therefore, Hartshorne's proof doesn't work.

And God's necessity must be cashed out in some sense other than "necessary according to propositional modal logic."

I suggest no logic will get you God's necessity. You'll have to look at something like "metaphysical" or "absolute" necessity. Plantinga suggests you could prove god's necessity in second-order logic, but I don't know how that's supposed to work.

Metacrock said...

I stated studying the modal argument in about 1985.

Joshua Rasmussen said...

Interesting post and discussion. I'm with Metacrock that if God exists, then it is necessary that God exists (and I'm a recent phd graduate from ND :)). But I have a different objection to offer and then a way to reply.

Metacrock supports the possibility premise (that God's existence is possible) on the grounds that we can conceive god analytically without contradiction. But why couldn't one find it just as easy to conceive ~god analytically without contradiction? It seems just as easy for me to conceive the one as the other. So, without a further reason to think that the ~god conception is contradictory, it seems to me that we are at a stalemate. (Perhaps this actually gets at the heart of Kris' objection.)

Now for my reply. We can argue for the possibility premise as follows:

(1) necessarily, every beginning POSSIBLY has an explanation.

support: for each beginning, we can coherently conceive it having a beginning, and there's no "reverse" argument that defeats this.

(2) possibly, there is a beginning to the exemplification of being contingent.

support: we can coherently conceive this, and there's no "reverse" argument that defeats this.

(3) Therefore, possibly a beginning to the exemplification of being contingent has an explanation.

(4). no contingent thing could possibly explain the beginning of the exemplification of being contingent (as that would entail that a contingent thing exists prior to all contingent things, which is plainly impossible).

(5) therefore, it's possible for there to be a necessary thing capable of explaining the existence of all contingent things.

(6) necessarily, a necessary thing capable of explaining the existence of all contingent things would be maximally excellent.

support: if it weren't maximal, then it's degree of excellence would be on a continuum of more and less and so would be contingent and so would be explicable (because we can conceive of an explanation; and no reverse argument defeats this). But nothing could explain its degree of excellence without circularity--see my paper, "From a Necessary Being to God" for details.

(7) therefore, it's possible that a maximally excellent, necessarily existing being exists.

(8) therefore, it's possible that god exists.

There you go. :)

Metacrock said...

thanks for your excellent post Rasmussen. I have heard of you but have not seen stuff yet. I appreciate your reponse. I would love to see you take on Space money on CARM, that's where they attacked your argument in a thread.

one question. if I accept that god can be continued with contradiction doesn't that blow the argument that they must com eup with the contradiction? My argument to the impossibility side of the dilemma is that there is no concept of contradiction ni god. If I a stipulate that there could be doesn't' that give away the store?

my understanding of the whole Ontological principle is that it's true by definition and if we just know the terms we can understand how it's true. If it's possible to conceive God with contradiction doesn't blow this principle?

Metacrock said...

also Joshua are you related to the Rassmussen who did the major study on Nuclear power plant safety i the 70s?

Joshua Rasmussen said...

thanks. I'm not sure if I'm completely tracking your question--and if not, I apologize.

I think it's useful to distinguish between one's seeing that something is possible and one's failing seeing that something is impossible. E.g., I might fail to see that the denial of Goldbach's conjecture is impossible (because I perceive no contradiction in its denial), but if it's true (and it plausibly is true), then it's necessarily true. Now one's failure to see a contradiction in something might provide prima facie evidence that it's possible. So, one's failure to see a contradiction in the proposition that god exists might provide prima facie evidence that that proposition is possibly true. But we should be cautious: something "could" still be impossible even if we don't perceive a contradiction in it (the "could" is epistemic, not logical).

Moreover, one might reason this way. I perceive no internal contradiction in the concept of ~god. Therefore, ~god is possible. Therefore, god is impossible. Therefore, the concept of god has an unforeseen external contradiction. This is a bad argument, of course. But it's no different in form from this one: I perceive no internal contradiction in the concept of god. Therefore, god is possible. Therefore, ~god is impossible. Therefore, the concept of ~god has an external contradiction.

So, I don't think it suffices to point out that there's no internal contradiction in the concept of god. If the claim is that there's no external contradiction, then it may be harder to see that that's true without an additional argument... At least, that's how I'm seeing things.

...I wasn't alive in the 70s. :)

Metacrock said...

Thanks for answering. I would like to have further discourse on God arguments. I need people advise me on the books I'm witing (and when it's reading to review it). If would be willing to help please let me know.

I thought you might be that Rassmusen's son. o well.

Also please either go over to carm and spank them for their treatment of your argument, or give me your arguments here and I'll post them on my blog.

It's not exactly about your argument it's about an argument by weaver they call "Rassmussen like"

here

Joshua Rasmussen said...

<> I'm address it now under an alias.

Metacrock said...

I saw that, I figured it was you.that's great. would you mind talking by email? Metacrock@aol.com.

thanks.