God's Necessity

Discuss either theological doctrines, ideas about God, or Biblical criticism. I don't want any debates about creation vs evolution.

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Re: God's Necessity (Meta's response) part 1

Post by Metacrock » Fri May 06, 2011 1:46 pm

Speusippus wrote:Hello Metacrock, this is "anonymous" from your blog.

I used to be known as Dag Hammarskjold on CARM. (I no longer post there, though I do have an account under the name "Speusippus" over there as well.)
I remember you. I remember that you were a friend, you were someone I liked, My memory of specifics, when I knew you and what you said, very hazy. I did remember the name.
I am a Philosopher (as in, by profession*) and a Christian. But being a philosopher, I tend to focus more on arguments than on conclusions, so even though I do believe in God, I will typically argue against the soundness of any arguments for the existence of God that I see. (Similarly, if I'm participating in a conversation with Atheists and they are arguing against God's existence, I will typically try to argue against that as well--though I have to admit I find my own disposition to be more "prophetic" than "evangelical," by which I mean, I'm more likely to think it worthwhile and rewarding for all concerned to correct Christians when I think they're arguing badly than to correct Atheists when they are arguing badly. This is not to say I take that as a general rule everyone should follow--it's just the disposition I find myself saddled with.
I can see why you feeling confident to say that the greats are arguing badly but it come across well. I don't think anyone can say that Plantinga, Harsthorne and Malcom are not greats. They are authorizes and brilliant thinkers. Of cousre that doesn't' make them right. Pltinga is humble. He never says "O that guy is stupid." even when I tell him arguments that I consider to be stupid he answers them with no fan fare and no commentary on the arguers intelligence. Something I need to learn.
*That's not to say I'm a very good philosopher. Professionally speaking, I'm not--I have no publications and I almost never do research due to a complex of laziness, fear and despair. Let's just say I concentrate on my teaching.

that doesn't mean you are not good.

This post is a continuation of one thread of our conversation from your blog.
It is commonly taken as definitional concerning the term "God" that God be a necessary being. I won't dispute that. What I dispute is that this implies that God is logically necessary.
Ok but remember I said there are two kinds of necessity involved.
In fact, I won't even dispute that God is logically necessary. Rather, I will make the point that there is no such thing as logical necessity simpliciter. There are many systems of logic, and what is "logically necessary" will vary from system to system. If you're using a logical system which is inadequate to handle statements about God's existence, then even if God is actually necessary, nevertheless the statement "god exists", as interpreted in that logical system, may well turn out to be logically contingent.
even though I violate it on CARM, because it would confuses issues, I agree with Tillich that God does not "exist" pre se but that is not the same as saying "there is no God." Therefore, I don't say "God exists." I avoid saying it as much as possible.
On your blog, you presented an argument from Hartshorne which ends with the conclusion "God exists." You also said that this argument wasn't meant to be a proof but part of a larger project involving showing that there is rational warrant for belief in God's existence. That may well be, but what I have in front of me is an argument written in the language of propositional modal logic, which starts from premises and leads by valid steps (valid in propositional modal logic) to a conclusion. Seeing this, it is impossible for me not to understand this as a proof of the conclusion. It fits the definition of proof perfectly. The author's intention in writing it is almost irrelevant--what they've written, whether they like it or not, is definitely a proof. (And I doubt Hartshorne is unaware of this of course!) And since it's a proof, it's impossible for me not to evaluate it by assessing its validity (it's valid) and the truth of its premises.

He definitely presented it in the form of a proof. He did say he thought it didn't prove it, at least not by itself. It's part of a larger system. That is in a book by Hartshorne that I read several years ago. Plantinga said independently of that in email to me that he doesn't argue that it proves but that it's a good reaosn to believe. Even though it's pretended in the form of a proof both men were aware that there's more to it than that. My own presentations I always say up front I don't argue to prove the existence of God but offer rational warrant for belief.
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Response part 2

Post by Metacrock » Fri May 06, 2011 1:52 pm

And what I think is, it begins with a false premise. That premise is:

g-->[]g

where '-->' is the strict conditional (i.e., it means 'necessarily, if X then Y) and where 'g' is intended to stand for the statement 'god exists'.)

If we are very careful to understand exactly what that box means (the necessity symbol) then we can see that this statement is false.

In other words, what I am saying is that the following statement is true: -(g-->[]g).

-(g-->[]g) means the same as -[](g->[]g) (where -> is the material conditional*).
-[](g->[]g) means the same as <>-(g->[]g) (where <> is the possibility operator as opposed to the [] necessity operator)

*the material conditional means "Either x is false or y is true," or in other words, "if x is true then y is true (but no necessity necessarily attaches to either)"

Before I continue, let's be clear about <> and [].

We're using the system S5 (as stipulated by Metacrock on the blog) which means they are to be interpreted as follows:

[] =def "in every possible world"
<> =def "in some possible world"

But what's a possible world?

Modal logics have been created to capture many different senses of possibility (and also of tense and of other concepts as well). But absent stipulation otherwise, the convention is to interpret the box and diamond, in s5, as having to do with what is logically possible.

For a world to be logically possible is for it to contain no contradictions.

But what's a world? Again, when we start using S5 in an argument, the convention is to understand a "world" to be a "maximal set of propositions." Meanwhile, a logically possible world is a "maximally consistent set of propositions." What's a maximally consistent set of propositions? It's what you get when you do the following:

1. List every simple proposition (i.e. 'A', 'B', 'C' and so on--propositions which contain no logical connective like And, Not, Or etc)
2. Assign a value of true or false to each, arbitrarily as you like
3. Create every possible complex proposition (i.e. 'A&B', 'XvY', (A&C)v(Y->Z), etc
4. Assign a value of True or False to each complex proposition according to the truth or falsity of its constituent simple propositions and the rules governing the connectives joining them.

There's a lemma which I forget the name of which proves that once you've done this, you've created a set of propositions that is internally consistent--that contains no contradictions. And a "logically possible world" in propositional modal logic just is a set of propositions built using the above method.

To return to the statement formulated in propositional modal logic above, what I've claimed is that the following statement is true:

<>-(g->[]g) ('it is possible for it not to be true that if god exists then god necessarily exists')

In propositional modal logic, -(X->Y) can be replaced with (X + -Y) (where '+' here means 'and')so another restatement of my claim is:

<>(g+-[]g)

-[]g can always be changed to <>-g so once again, my claim is:

<>(g+<>-g)

Having clarified what the box and diamond mean, we are now prepared to interpret this statement more exactly:

"There is a maximally consistent set of propositions within which 'g' is true and '<>-g' is true."

Since we're using S5, what's possible in one world is possible in all worlds. So finally we have this restatement of my claim:

"There is a maximally consistent set of propositions within which 'g' is true, and there is a maximally consistent set of propositions within which '-g' is true."

Of course, someone arguing that god exists agrees with the first part--there is a maximally consistent set of propositions within which 'g' is true, if 'g' is to be interpreted as 'god exists'.

So my task is to argue for the second part--there is a maximally consistent set of propositions within which '-g' is true, even if '-g' is to be interpreted as 'god does not exist'.

But this claim can be shown simply by reference to the explanation of "maximally consistent set of propositions" given above. I have already shown you how to build a maximally consistent set of propositions in which '-g' is true. Simply build a maximally consistent set of propositions in which 'g' is false. Follow the four steps listed above, making sure 'g' is assigned 'false' in step two, and you'll end up with a maximally consistent set of propositions in which '-g' is true.

So I've shown that there is, in propositional modal logic, a possible world in which -g is true. If '-g' means "god does not exist" then I've shown that there is (in propositional modal logic) a possible world in which God does not exist. And that renders the first line of Hartshorne's argument (g-->[]g) false. A valid argument with a false premise is not sound, so his argument is not sound.

I've tried to emphasize that I'm only able to say this because we're using propositional modal logic. God's existence may be necessary, but it is not logically necessary in a way that can be captured using the language of propositional modal logic. God's existence may be necessary, but if that is to be a truth of logic (rather than just a truth in English) then we're not going to be able to express God's necessity using propositional modal logic. Some other logic will have to be used.

Predicate logic is built to deal with concepts like existence, so you might hope a modal prepositional logic might work. But using reasoning similar to that I've already given, we can show that the following statement is true:

<>-ExGx (where "Ex" is meant to refer to the existence operator and "Gx" is to be interpreted as "x has the property of being God."

Modal prepositional logic is also inadequate to the task.

At this point we exhaust my knowledge of logic. I wouldn't know how to build a language adequate to the expression of the statement "God exists necessarily" which allows that statement to be a logical truth. I was thinking about it yesterday, and it seemed to me you'd need a language which can express something about God's attributes in a significant way. For example, you might express his omnipotence by saying something like "If it is logically possible for God to do something, then it is within God's power to do that thing." This statement seems naturally to lend itself to a language which includes two sets of modal operators--one ranging over logical possibility, and one ranging over the kind of possibility that involves things being "within the power" of this or that entity to do. And perhaps you could prove, in some useful logical language, that there necessarily exists an entity fitting the description just given, or an entity fitting some even more elaborate description of God. But I'm above my paygrade now.

So again to summarize:

I am not saying God's existence is contingent.
I am saying that Hartshorne's proof, read as it naturally presents itself (i.e. as a proof following the conventions of propositional modal logic) fails at line one because line one is false.
The falsity of line one does not mean God's existence is contingent, only that it is logically contingent when expressed using the tools of propositional modal logic. The logical consistency of a statement is relative to the language one uses to express the statement.

I guess it is really stupid of me to argue the modal argument when I'm so bothered by symbols of logic. Because of my dyslexia the profusion of symbols just plays havoc with my mental processing of terms and meanings. I need to discuss such things in plain english. I can understand the principles I can comprehend the symbols in their meaning. I can get the concept but with a profusion in logicese I just flood mentally in ny neural net. It's a great way to give a dyslexic a break down.

I think the ideas have to make sense in regular English or they aren't really about anything.

all the things you say above I already knew and understand. I'm not clear exactly what you think is the crux of your opposition to God being necessary. can you say it plain English?
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Re: God's Necessity

Post by URBILD » Fri May 06, 2011 2:01 pm

How ya doing, Kris? Remember me? :ugeek:

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Re: God's Necessity

Post by Metacrock » Fri May 06, 2011 2:14 pm

I've tried to emphasize that I'm only able to say this because we're using propositional modal logic. God's existence may be necessary, but it is not logically necessary in a way that can be captured using the language of propositional modal logic. God's existence may be necessary, but if that is to be a truth of logic (rather than just a truth in English) then we're not going to be able to express God's necessity using propositional modal logic. Some other logic will have to be used.
seems simple to me.

He has to be either necessary or impossible because he can't be contingent. What kind of necessity? something that's neither contingent nor impossible.

the argument comes in terms of the place that laves when you consider he can't be one or the other he has to be necessary. Something neither impossible nor contingent.

People tend to read that as though it's an a prori tautological statement, all husbands are married men. I think there's more to the type of necessity garnered in this argument than that.
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Re: God's Necessity

Post by sgttomas » Wed Feb 01, 2012 4:39 pm

Hm....any chance he comes back to talk about this?

I know exactly where he's coming from and wanted to run something by him.

-sgttomas?
Prophet Muhammad (God send peace and blessings upon him) is reported to have said, "God says 'I am as My servant thinks I am' " ~ Sahih Al-Bukhari, Vol 9 #502 (Chapter 93, "Oneness of God")

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Re: God's Necessity

Post by Metacrock » Wed Feb 01, 2012 10:35 pm

sgttomas wrote:Hm....any chance he comes back to talk about this?

I know exactly where he's coming from and wanted to run something by him.

-sgttomas?
send him an Instant message he might respond.
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Re: God's Necessity

Post by Metacrock » Wed Feb 01, 2012 10:37 pm

Unfortuantley he was deleted in the purge of spammers becuase he only made that one post.
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Re: God's Necessity

Post by sgttomas » Thu Feb 02, 2012 1:28 am

Oh...oops.

Well, if he posts again on your blog or something...or maybe if he sees this post, I hope he feels welcome to come back!
Prophet Muhammad (God send peace and blessings upon him) is reported to have said, "God says 'I am as My servant thinks I am' " ~ Sahih Al-Bukhari, Vol 9 #502 (Chapter 93, "Oneness of God")

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Re: God's Necessity

Post by Metacrock » Sat Feb 04, 2012 3:41 pm

sgttomas wrote:Oh...oops.

Well, if he posts again on your blog or something...or maybe if he sees this post, I hope he feels welcome to come back!
maybe we can track him down on Google.
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