A Modal proof of God's existence

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Reply Sat 20 Mar, 2010 06:21 am
Hartshorne's (1962) proof of the existence of god:

(~) = not, (v) = or, (&) = and, (->) = implies (<->) = equivalence,
[] = necessarily, <> = possibly, (=>) = strict implication,

(p => q) =df [](p -> q)

<>p =df ~[]~p.

g = god exists.


The argument is thus:

1. g => []g (premise)
2. []g v ~[]g
3. ~[]g => []~[]g
4. []g v []~[]g
5. []~[]g => []~g
6. []g v []~g
7. <>g (premise)
8. []g
9. []g => g
10. g


This argument is valid but not sound.
It proves that: ((g => []g) & <>g) -> g, is necessarily true, ..nothing else.

The argument is true for any proposition p.

1. g => []g
7. <>g
:.
10. g


A. (g => []g) <-> [](g -> []g)
B. (g => []g) <-> (<>g => g)
C. (g => []g) <-> (<>g -> []g)

Note: A, B, C, are theorems of modal logic (S5).

Because of C, the argument becomes:

1. <>g -> []g
7. <>g
:.8. []g

8. []g
9. []g -> g
:.10. g


If we substitute ~g for g, we get the atheists' side of it.

1a. <>~g -> []~g
7a. <>~g
:. 8a. []~g

8a. []~g
9a. []~g -> ~g
:.
10a. ~g.


This argument has two other equivalent variations.

1. [](g -> []g) & <>g .-> g
2. [](<>g -> g) & <>g .-> g
3. (<>g -> []g) & <>g .-> g

Once we realise that: [](p -> []p) <-> (<>p -> []p),
and [](<>p -> p) <-> (<>p -> []p), we can see that each argument is equivalent to 3.

Hartshorne was wrong to assert that this argument proves that g (god exists) is true.

It seems that Theists need only show that 'God does exists' is possible
in order to prove that it is necessary or that it is true.
And, that Atheists need only to show that 'God does not exists' is possible
in order to prove that it is necessary or that it is true.

Note: <>(god exists) & <>(god does not exist), is contradictory.

What do you think?

Owen
 
kennethamy
 
Reply Sat 20 Mar, 2010 08:41 am
@Owen phil,
Owen;141495 wrote:
delete eeeeeeeeeee


I thought that the modal proof was, the Ontological Argument. But I dimly recall that Godel was supposed to have offered one too. Leibniz argued that it was "the privilege of the Deity, alone" that He needs only to be possible to be actual. But that is clearly a mistake.
 
Owen phil
 
Reply Sat 20 Mar, 2010 10:23 am
@kennethamy,
kennethamy;141522 wrote:
I thought that the modal proof was, the Ontological Argument. But I dimly recall that Godel was supposed to have offered one too. Leibniz argued that it was "the privilege of the Deity, alone" that He needs only to be possible to be actual. But that is clearly a mistake.


Hi Ken,
I was browsing Hartshorne's Modal proof which assumed (God exists => [](God exists)), which was taken from Leibniz's claim, but, it became fouled up and I wanted to delete the post.
Perhaps I should re-post it, given there is some interest in 'Modal ontological proofs'.
 
Owen phil
 
Reply Sun 21 Mar, 2010 12:08 pm
@kennethamy,
kennethamy;141522 wrote:
I thought that the modal proof was, the Ontological Argument. But I dimly recall that Godel was supposed to have offered one too. Leibniz argued that it was "the privilege of the Deity, alone" that He needs only to be possible to be actual. But that is clearly a mistake.


I don't agree. If [](p -> []p) then (<>p -> p), is true.

I think it was Leibniz who included 'that whose possibility ensures its necessity' in a definition/description of god.

"God, the creator of the physical universe, exists" is analytic not contingent. It is either tautologous or contradictory.
That is; It is true that God exists, is equivalent to, It is necessary that God exists, is equivalent to, It is possible that God exists.
 
kennethamy
 
Reply Sun 21 Mar, 2010 12:21 pm
@Owen phil,
Owen;141930 wrote:
I don't agree. If [](p -> []p) then (<>p -> p), is true.

I think it was Leibniz who included 'that whose possibility ensures its necessity' in a definition/description of god.

"God, the creator of the physical universe, exists" is analytic not contingent. It is either tautologous or contradictory.
That is; It is true that God exists, is equivalent to, It is necessary that God exists, is equivalent to, It is possible that God exists.


Oh, I agree that if God is a necessary being then, if He is a possible being, then He he exists. What I meant is just that it is a mistake to think that God is a necessary being.
 
Owen phil
 
Reply Sun 21 Mar, 2010 12:32 pm
@kennethamy,
kennethamy;141932 wrote:
Oh, I agree that if God is a necessary being then, if He is a possible being, then He he exists. What I meant is just that it is a mistake to think that God is a necessary being.


Agreed.

I have re-posted the original post, did you see it?
 
HexHammer
 
Reply Sun 21 Mar, 2010 12:35 pm
@Owen phil,
I find it amazing how people can know so much about a mysterious being, when they know almost next to nothing abou themselfs, and their next door neighbour.
 
kennethamy
 
Reply Sun 21 Mar, 2010 12:45 pm
@HexHammer,
HexHammer;141936 wrote:
I find it amazing how people can know so much about a mysterious being, when they know almost next to nothing abou themselfs, and their next door neighbour.


We are not claiming to know anything much about God. Only about modal logic. Did you notice the word "if" all around? All we were saying was that if God had these and these properties, then he would have to have, these and those properties. Of course, whether he has the first set of properties is unknowable. When I say that if some animal it a dog, then that animal is a mammal, I am not asserting that the animal is a dog. I am just asserting that if the animal is a dog, the animal is a mammal.
 
HexHammer
 
Reply Sun 21 Mar, 2010 12:56 pm
@kennethamy,
kennethamy;141938 wrote:
We are not claiming to know anything much about God. Only about modal logic. Did you notice the word "if" all around? All we were saying was that if God had these and these properties, then he would have to have, these and those properties. Of course, whether he has the first set of properties is unknowable. When I say that if some animal it a dog, then that animal is a mammal, I am not asserting that the animal is a dog. I am just asserting that if the animal is a dog, the animal is a mammal.
Why don't I think see any "if's" on making a simple accurate weather forecast? ..because it's next to impossible?

Let me add, it's not to stop you in your tracks, I just felt like commenting it.
 
kennethamy
 
Reply Sun 21 Mar, 2010 01:03 pm
@HexHammer,
HexHammer;141941 wrote:
Why don't I think see any "if's" on making a simple accurate weather forecast? ..because it's next to impossible?


A weather forecaster is supposed to not only know what will happen if a cold front is coming, but also know whether the cold front is, in fact, coming. There is a big difference between saying, "If a cold front passes, there will be rain", on the one hand, and saying, "Since a cold front will pass, it will rain". The first is hypothetical. The second is not. Logicians say what is hypothetical.

You haven't stopped me in my tracks at all.
 
HexHammer
 
Reply Sun 21 Mar, 2010 01:15 pm
@kennethamy,
kennethamy;141942 wrote:
A weather forecaster is supposed to not only know what will happen if a cold front is coming, but also know whether the cold front is, in fact, coming. There is a big difference between saying, "If a cold front passes, there will be rain", on the one hand, and saying, "Since a cold front will pass, it will rain". The first is hypothetical. The second is not. Logicians say what is hypothetical.

You haven't stopped me in my tracks at all.
I see that as a poor interpetation of weather forecasts. They can only resort to such rough forecasts since doing anything else would have flawed results.
 
kennethamy
 
Reply Sun 21 Mar, 2010 01:19 pm
@HexHammer,
HexHammer;141946 wrote:
I see that as a poor interpetation of weather forecasts. They can only resort to such rough forecasts since doing anything else would have flawed results.


I said nothing about the roughness of the forecasts. Only that the forecasters were not saying anything hypothetical. Whether or not they felt certain about their forecasts is not the issue (as you seem to think it is).
 
HexHammer
 
Reply Sun 21 Mar, 2010 01:33 pm
@kennethamy,
kennethamy;141948 wrote:
I said nothing about the roughness of the forecasts. Only that the forecasters were not saying anything hypothetical. Whether or not they felt certain about their forecasts is not the issue (as you seem to think it is).
Excelent wordplay, however such professional people would never resort to assumptions and spekulation, therefore it's irrelevant.

I'm sure you would be an excelent lawyer in some way.
 
 

 
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