Analysis of Hartshorne's (1962) Proof of the Existence of God

[Owen Holden]

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 realize 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

 

[Evo]

I think it's a waste of time to even think about it. Do fairies exist? Do leprechauns or trolls or unicorns exist? God/fairies/leprechauns/trolls/unicorns are all the same. People believe what they want to believe, still doesn't make it real or true.

 

[Owen Holden]

I think it's a waste of time to even think about it. Do fairies exist? Do leprechauns or trolls or unicorns exist? God/fairies/leprechauns/trolls/unicorns are all the same. People believe what they want to believe, still doesn't make it real or true.

I don't agree. Surely it depends on how we define: faries, leprechauns, or unicorns.

I do agree that belief does not entail truth, but, you have not presented an argument for or against.

Why don't these things exist, is the question!

 

[Evo]

I do agree that belief does not entail truth, but, you have not presented an argument for or against.

That's because there's no point in arguing about it, IMHO.

Why don't these things exist, is the question!

Why? Why make something up and then ask why it doesn't exist? What is the point? You already know that the discussion is pointless since there is no proof for their existence (the burden of proof is on the person making the claim that something exists), why do people want to discuss pointless topics? Don't take me wrong, nothing against you or your topic. I am just really curious why people want to discuss such things, over and over and over. Hasn't this topic been beaten to death millions of times with no result?

 

[Owen Holden]

That's because there's no point in arguing about it, IMHO.

Why? Why make something up and then ask why it doesn't exist? What is the point? You already know that the discussion is pointless since there is no proof for their existence (the burden of proof is on the person making the claim that something exists), why do people want to discuss pointless topics? Don't take me wrong, nothing against you or your topic. I am just really curious why people want to discuss such things, over and over and over. Hasn't this topic been beaten to death millions of times with no result?

Your flippent understanding contributes no-thing.

"You already know that the discussion is pointless since there is no proof for their existence (the burden of proof is on the person making the claim that something exists), why do people want to discuss pointless topics?"

This is a very silly remark!

Why is the discussion pointless?
Why is there no proof of their existence?

Your unsupported claims suffer from your own criticisms, don't they?

If you know, then surely you can show why it is that you know.
You did no such thing.

 

[Evo]

Why is there no proof of their existence?

You don't actually expect anyone to take a question like that seriously do you?

 

[arildno]

Owen Holden:
Prove that you don't have an invisible and intangible hat floating above your head.

 

[Owen Holden]

Quote:
Originally Posted by Owen Holden
Why is there no proof of their existence?

You don't actually expect anyone to take a question like that seriously do you?

Of course I do. If you claim that you know what existence means, then why would you have difficulty saying that x exists or not?

For me: x exist means there is some property that x has, is confirmable.

I can prove that 'the present king of France does not exist' because there is no property of it that can be confirmed.

F(the present king of France) is false for all F.

There is no property of: fairies, etc., that can be confirmed either.

 

[Evo]

If you claim that you know what existence means,

Really? Show me the quote of where I said that. I said the discussion was pointless.

then why would you have difficulty saying that x exists or not?

I wouldn't, if we were to be addressing something that had a point, which we're not. You're jumping to the conclusion that you've posted something that has enough substance to be discussed.

I can prove that 'the present king of France does not exist' because there is no property of it that can be confirmed

F(the present king of France) is false for all F.

Uhm, was this supposed to make sense?

There is no property of: fairies, etc., that can be confirmed either.

Like I said...

Answer my first question. You said "Why don't these things exist (fairies, trolls, god, unicorns), is the question!" I asked "Why? Why make something up and then ask why it doesn't exist? What is the point?"

If you can't answer my first question, there is no point in continuing.

 

[arildno]

Owen: Just because you've learned yourself a few squiggly signs, doesn't mean you are able to prove or disprove any aspects of reality with them.
(One reason being, you haven't defined reality)
I'm sorry, but here it is: Grow up.

Understand this:
The so-called god proof was complete nonsense at the outset, no matter who presented it first.

 

[Owen Holden]

Really? Show me the quote of where I said that. I said the discussion was pointless.

I wouldn't, if we were to be addressing something that had a point, which we're not. You're jumping to the conclusion that you've posted something that has enough substance to be discussed.

Uhm, was this supposed to make sense?

Like I said...

Answer my first question. You said "Why don't these things exist (fairies, trolls, god, unicorns), is the question!" I asked "Why? Why make something up and then ask why it doesn't exist? What is the point?"

If you can't answer my first question, there is no point in continuing.

I agree, that this thread has resulted in "flames" shows my failure in communicating with you.

Perhaps we can talk in the context of a different topic. Perhaps not!

 

[Owen Holden]

Owen: Just because you've learned yourself a few squiggly signs, doesn't mean you are able to prove or disprove any aspects of reality with them.
(One reason being, you haven't defined reality)
I'm sorry, but here it is: Grow up.

Understand this:
The so-called god proof was complete nonsense at the outset, no matter who presented it first.

A very bold and unsupported assumtion on your part.

Why is 'God exists' nonsense??

Can you support any of your claims?


PS: at 70 I don't have time to "grow up".

 

[cronxeh]

Mathematics is pointless if its not constrained. For all I care I can say from -inf to +inf the sum of all numbers is basically zero and therefore numbers don't exist.

This is just what your 'logic' proof is - taking numbers, and manipulating them in a manner which will suite to _your_ desired answer.


Physics on the other hand is based on experimental evidence, which defines the limits for the mathematics that are performed. Those 'limits' come from the experimental data which comes from the Universe in which we live in.

If you are a theists and claim there is god, the burden of proof is upon you. First of all you are to prove that Universe has a purpose then you will say god created it, then you will say "therefore god exists". Second of all I will tell you that you weren't around 16.5 billion years ago, and relativety back then was different than today - for all intensive purposes it could have been a vacuum, and the expansion occurred from singularity. Where was god? What is an omnipotent all powerful thing that doesn't obey laws of physics?

To me you are simply saying that god is the number 0 - wherever god goes he screws up the laws and nothing applies to god and that he created everything. Well to me, then, god doesn't exist

Have a nice day

 

[Owen Holden]

Mathematics is pointless if its not constrained. For all I care I can say from -inf to +inf the sum of all numbers is basically zero and therefore numbers don't exist.

Garblygook. Numbers clearly exist.

Are you not (1), that is: obviously you are unique.
How can it be otherwise??

If you deny your own uniqueness, then we cannot talk at all !

If there are no things then, you are not!

 

[Gokul43201]

What do you think?

Owen

You said it yourself. The proof is independent of the choice of the assertion g, and hence should also hold for ~g, in addition to any other p.

So, assuming the reasoning is not flawed, this calls into question the stated premise. How does one justify this premise in the particular case of the existence of "god" (which of course, I imagine you will define more rigorously) ?

 

[Thor]

God is the icon for an original 'creator'. If all which exists was created, then God was created by a predecessor. I THINK I WILL WORSHIP HER...(she is beautiful and sexy)

 

[cronxeh]

Garblygook. Numbers clearly exist.

Are you not (1), that is: obviously you are unique.
How can it be otherwise??

If you deny your own uniqueness, then we cannot talk at all !

If there are no things then, you are not!

I am defined - right now I have the (x,y,z,t) coordinates assigned to my center of gravity, I have mass, I have a past and all the laws of physics apply to me. Simply put I belong to the 'matrix' of the universe - I am part of the grid.

Your 'god' however doesn't have anything.

 

[reasonmclucus]

What is God?

From a physics standpoint, the question is what would be the physical characteristics of a godlike being, which depends in part on the nature of physical reality. The description of the God of Abraham implies a hyperdimensional being which would require the existence of higher physical dimensions.

From traditional n-dimensional geometry we know that any projection from a higher dimension into lower dimensional space would possesses the characteristics of the lower dimensional space. That is the projection can only possesses the dimensions of the lower space. Thus detecting a hyperdimensional being would be difficult. The chaotic nature of physical reality would allow such a being to use very minor actions to affect changes. Effects created by such a being could appear to occur naturally, particularly if the being didn't want to be too showy.

 

[saltydog]

My goodness people. It's just not there. God I mean. How fragile we all are, really. We invent all sorts to buttress survival in a harsh world still ruled by jungle law candy-coated by civilized rules of law and order.

If religion and God aid in the survival of the gene pool, which I believe they do, then I shall find favor with them even if I know fully well, they pay homage to an empty hope.

 

[DaveC426913]

People believe what they want to believe, still doesn't make it real or true.

An interesting statement. Note that it works both ways.

Evo (for example) believes what he/she wants to believe. That doesn't make the existence of God any less real or untrue.

Thus, the only thing we all are left with (atheists included) is that:
- it is a personal choice, and that each choice is equally valid.
- the only wrong choice is to conclude that someone elses choice is wrong.

 

[MrMorden]

well, for one thing, most atheists automatically assume that since they don't believe in God that the idea of God was made up by someone who did. which cannot be proven true. I've often made the argument that likewise, the existence of God cannot be proven either. the farther you attempt to explain God scientifically or mathematically, the farther away you become. the very definition of God states that he cannot be "proven" because he would then be nothing more than the sum of his parts, which implies that he could be broken down (theoretically of course) into subsequent mathematical equations. you cannot build God or break God down because he then would not be infinite. infinite in this context meaning he exists outside of the space-time continuum, therefore the normal three dimensional space and the time dimension have no jurisdiction over his existence.

so, in one sense, it is useless to debate God's existence since a clear answer cannot be determined, but its not useless to debate his existence if you're doing so for some other purpose than attempting to prove him or disprove him. imo, debates like this are healthy as they force one to think about these philosophical problems which cannot be resolved mathematically

 

[cronxeh]

The burden of proof is on theists, not the atheists

Prove to me, beyond a shadow of a doubt and any possible scientific explanation, that there exists an all powerful entity that 'created' this Universe, that answers your prayers, that exists in some hyperdimension and transcends through all the time and space.

You'll choke yourself silly trying to get past the 'created the Universe' point - why do you even bother arguing it? People assume that they have a personal buttler they call 'god' - who will answer their prayers and in time of crisis bail them out.

 

[DaveC426913]

The burden of proof is on theists, not the atheists.

Why?

Prove to me, beyond a shadow of a doubt and any possible scientific explanation, that there exists an all powerful entity...

Nope, only need to come up with a working theory that does a good job at explaining a set of phenomena. The phrase ''beyond a shadow of a doubt" simply does not exist in the Scientific Method. You know better than that!

...that answers your prayers...a personal buttler they call 'god' - who will answer their prayers and in time of crisis bail them out.

This is a quaint and highly unjustified preconception of God on your part. Don't put words in other people's mouths.

You'll choke yourself silly trying to get past the 'created the Universe' point

Actually, it is physicists that choke on this. They have no explanation. Theism does have the virtue of at least postulating an explanation for the beginning of the Universe.


BTW, in case it looks like I'm beating the God horse, I am actually an atheist/agnostic. I just can't stand arguments that are dismissive or generalistic or otherwise poorly founded. That degrades me too, since in such an environment, my own beliefs will not be taken seriously. And I want them to be.

 

[cronxeh]

Why?

Because I was born without knowing of god and then I was told, notice- TOLD, by humans that there is god

I didnt discover that on my own like most other things - walking, talking, etc, but was TOLD so by other humans. The fact is that there is absolutely no materialistic proof that something like god exists(ed), and I don't want to get into whole Jesus debunking here, but it was done before

 

[DaveC426913]

Because I was born without knowing of god and then I was told, notice- TOLD, by humans that there is god

I didnt discover that on my own like most other things - walking, talking, etc, but was TOLD so by other humans. The fact is that there is absolutely no materialistic proof that something like god exists(ed), and I don't want to get into whole Jesus debunking here, but it was done before

You have to recognize how weak that argument is.
1] We were taught how to talk - by humans. About 99% of what we "know" was told to us by humans.
2] There has been no materialistic proof (until the last couple of years) that atoms existed, only very good theories. Did you not believe in atoms until you saw them with your own eyes?
3] Note that the scientific method (at least philosophically) does have something to say about standing on the shoulders of those who have gone before. Without it, we have no progress.
4] You cannot have learned everything from first principles, or you'd still be banging rocks together and grunting.

So, I put it to you that the existence of God is actually a quite well-established theory. I submit that the burden is as much on aetheists to disprove the theory.

 

[cronxeh]

Your argument on the contrary misses my point entirely:

Everything we taught is correlated, and belongs to a set, let's call it "B"
B = { reality }

Scientific method is when your postulates are based on data and have mathematical meaning.

god, devil, hell, heaven, etcetera - Let's say they all belong to set A - aka "life after death" - according to religion. I think you got definition of word 'god' completely wrong - you assigning everything that is unknown to that word, I am saying god is that specific thing religion refers to that claims that god created set B.

The fact is that there is no such (f: B -> A) so card(B) = card(A)

 

[Jameson]

I ask this: If religion requires faith, that is believing in parts of it without physical proof, then why are people trying to justify it logically?

If it was completely provable, that would be using knowledge, not faith. So to those of us who are religious/spiritual/anything else that falls on faith, do you try to rationalize it to explain your view to others or to tell yourself you're right?

I am very aware, that we all take many things on faith, like we don't know if we really exist in this reality; we could all be a some kind of "Matrix" world. Even so, many things in this world are "provable" to the highest extent we can prove them. Physics, math, and other rational subjects do not call on faith as a proof.

I have nothing against faith, I just wonder why people try to mix the categories of faith and logical/rational justification. To put these things together seems quite like a paradox.

-----------------

I also agree with cronxeh. We are technically all born as atheists. I don't see how you could argue we are born with a belief in God.

 

[DaveC426913]

Your argument on the contrary misses my point entirely:

Everything we taught is correlated, and belongs to a set, let's call it "B"
B = { reality }

And what I'm saying is that most of what one "knows" is taken on faith, at someone else's word, because we don't have an infinite amount of time to do first-hand experiments ourselves. We have no problem taking a vast amount of our world on faith.

The fact is that there is no such (f: B -> A) so card(B) = card(A)

Sorry, I am not familiar with formal logical notation, so you've lost me here.

god, devil, hell, heaven, etcetera - Let's say they all belong to set A - aka "life after death" - according to religion.)

Why take such an antiquated view of God? Why not merely take a more general view of the creator that create the universe? Heaven, hell, and the Devil are antiquated notions; you won't find leaders of the church talking about them literally.

If, for the purpose of this discussion, you are calling forth a view of God that includes Heaven, Hell and the Devil, then I - as well as most educated religious followers - will agree with you that it has slipped into legend.


Point of order:
The temptation to use "you" as opposed to "one" is getting stronger as the syntax becomes more awkard! (i.e. "You take a lot on faith")

But I wish us to remain in advocate positions - meaning that I target the arguments and never target you as a person. IOW, this is not personal, and I don't intend to let it become so.

I just don't know how long I can keep saying 'one'!

 

[AKG]

In all fairness, a lot of the discussion that goes in the general discussion forum, or elsewhere in "casual" parts of this website are pointless crap as far as I'm concerned, but if the discussion interests you, then go ahead and discuss it. However, if it doesn't interest you, or it seems pointless to you, what in the world is the point of going into a thread and saying it? I wouldn't bother going into those threads in GD and complaining, "Oh god! This topic is so pointless, why are you guys posting here?!" Evo, I couldn't care less how cute your dog is, but that's the reason why I haven't looked at your thread and not gone into it and posted how pointless the topic was.

On topic, indeed the argument is valid for any P, but the premise G -> []G (or some variant) is not true for all G. God, being defined as the greatest conceivable/possible being, is said to thus have the greatest possible existence, namely necessary existence. Because God is said to have necessary existence, then if he exists, he exists necessarily, hence G -> []G. Invisible hats aren't greatest possible beings, nor do they have necessary existence for other reasons, so the premise is not true for invisible hats. Although the argument is valid for any G, it is not sound for all G, one reason being that G -> []G is not true for all G. For that reason, the MOA has more credibility as a proof for god than it does for an invisible hat.

But if G is so defined such that G -> []G is true, then the remaining premise, <>G, is the only possible point of contention. I see no justification for <>G, so although the MOA does have some credibility as a proof for God, it doesn't have enough to be convincing.

 

[Evo]

In all fairness, a lot of the discussion that goes in the general discussion forum, or elsewhere in "casual" parts of this website are pointless crap as far as I'm concerned, but if the discussion interests you, then go ahead and discuss it.

GD is just for fun, the philosophy forum isn't.

However, if it doesn't interest you, or it seems pointless to you, what in the world is the point of going into a thread and saying it?

Because Owen Holden asked what people think about the example he posted about trying to justify the existence of "god". I told him I think it's pointless, and it is. No one is going to prove or disprove it.