A Priori Proof for God's Existence

[Vera_Ljuba]

Maximum possible profit at zero cost.

You don’t know what I am talking about. You moved the cost from the objective function to the constraints of the problem. The point is that having several constraints with multiple objective functions is an unsolvable problem - in principle.

 

[inocente]

So what? I once had the misfortune to teach a kid who simply did not understand the concept of “per cent”. We, who understand this concept can have a conversation about it, even if some outsiders cannot follow our reasoning.

I’m just suggesting that if you want to convince others, you might want to use more familiar frameworks. You’ve already convinced me you’re wrong .

This is smoke and mirrors. "Could have been created" is not an argument. God is supposed to be the end result of a purely philosophical - therefore secular - line of reasoning. It is a fallacy to include God into the argument itself. During the presentation of the argument it is “forbidden” to try to “smuggle in” God.

And that’s one reason you’ve convinced me. Let G be the reason why world W exists. Therefore logically we need not expect G to be a member of W. But you declare by fiat that there’s no reason why W exists, so G doesn’t exist. And as soon as I object, you say I’m trying to smuggle G back in. Unsurprisingly, by defining G not to exist, you conclude G doesn’t exist.

*Nothing wrong with this. I already stipulated that the “null world” is not physically possible, but the concept of “possible world” does not demand that it should be physically possible, only that it does not contain a contradiction. In the original analysis I only considered the physically possible worlds (which are a subset of the ontologically existing worlds), and the final result (the one-electron vs. one neutron world) is clearly physically possible. *

I suspect a one-electron-world isn’t physically possible if you did the QM math. But I think it’s not relevant, no one knows what other physics are possible, and science is a posteriori, so what’s thought possible changes as knowledge advances, whereas the thread is about a priori.

But many people wish to extend the world to abstractions, which is erroneous, since abstractions do not exist ontologically - no matter what Plato asserted. So, I wished to accommodate these people, and allowed that the possible world could also composed of “non-ontological” aka. “abstract” entities. But this extension also includes the “null world” (a well known mathematical abstraction). So, no matter how one twists it, there is no entity which exists in all the possible worlds, therefore no necessary being.

Google couldn’t find ‘null world’, either as a well known mathematical abstraction or otherwise. I think the empty set isn’t a possible world, since it is a logical contradiction to claim nothing is something.

*Of course this has nothing to do with God’s existence of lack of it. It is just a refutation of the attempt that God’s existence can be established in an “a priori” manner. But that is not a disaster, after all the other attempts also failed. If I recall correctly, you also said that if a purely secular argument could be found, it would make “faith” unnecessary. (Maybe my memory is faulty. ) *

I don’t remember saying that, but yes, I don’t understand why so many think a proof of God is necessary or possible.An issue with a priori proofs is they can say nothing about God as a fact, only about the idea of God (and imho usually don’t even achieve that).

I have never seen this argument anywhere else. I suspect that the reason is that philosophers are not mathematicians and they simply did not think along these lines.

Alternatively, they knew it was wrong, but I like your sense of optimism.

 

[inocente]

Hi inocente,

Thanks for yer thots and the references.

It still appears to me that possible worlds analysis assumes that there are no necessary beings. Any entity in the actual world can be conceived of not existing in some possible world, by definition. The only criterion for conceiving a possible world is logical consistency. In this system of thought there is never anything inconsistent in conceiving that any X does not exist in a possible world.

So this whole attempt to determine the possibility of necessary existence within the framework of possible worlds is futile. We are asking a system of thought which assumes there cannot be an X which exists in all possible worlds whether there can be an X which exists in all possible worlds.

The logic is that if X exists in every possible world, then X is defined to be necessary. So yes, the starting assumption is that X is contingent until investigation shows it exists in every possible world.

I agree that the concept of possible worlds is very easily misunderstood. I’ve got no formal training, it just interested me so I did some reading, and there are plenty of pitfalls. I seem to remember some logicians question whether it even gives worthwhile results.

It’s not futile though, for instance Alvin Plantinga’s ontological argument is one of the better known ‘proofs’ of God based on possible worlds.

 

[Vera_Ljuba]

And that’s one reason you’ve convinced me. Let G be the reason why world W exists.

Let’s don’t and say we did . There is not one word about a “reason” here. We start with the existing physical reality, which is possible, since it exists. Then we keep “downsizing” it. There is nothing problematic about the process. You may not “add” something to a possible world, since the addition process can lead to a logically inconsistent state of affairs. But you can always take something away. Removing a subset from a possible world will always lead to another possible world.

I suspect a one-electron-world isn’t physically possible if you did the QM math.

Why not? But, of course that was just a convenient way to demonstrate one possible process to get to a “super-simple” existence. It could be one world containing a bunch of protons, and another one containing a bunch of anti-protons. The actual entities are irrelevant, all we need is two of them which have no overlap. One could contain “Jack” and the other one could contain “Jill”.

I think the empty set isn’t a possible world, since it is a logical contradiction to claim nothing is something.

No, it does not. Using another way to express it, it is an empty container, or an empty set. That does not mean that there is “a nothing” in it. Of course I readily accepted it that an “empty” world cannot exist physically. But it does exist conceptually, and it does not have a contradiction built into it. Therefore - it IS a possible world.

 

[inocente]

I’m not following this, I don’t think.
An idea has to come from somewhere. It references something.
If the proposition of God is that He is “the power that sustains all being” - then wherever there is being, there is God.
Yes, if the idea we were talking about was Harry Potter, that would be different - although Harry Potter references a human being.
The idea of a human being exists wherever there are human beings.
The idea of existence being different from non-existence is present wherever there is some kind of being.

Your proposition has a few issues. Let G be the power that sustains all being. But G could be null if everything is self-sustaining, and I don’t see how you could prove a priori that G isn’t null, and therefore just a wrong idea.

It’s always seemed a wrong idea to me for another reason. I think the original logic was based on Aristotle’s incorrect ideas about motion/change. I debated it on CAF with a Thomist some time back, and was being asked to believe G has to keep everything going in billions of stars in billions of galaxies, which sounded like a demented plate juggling act on steroids. But also, isn’t Aquinas’ argument a posteriori, not a priori?

(I’m saying G because I think G is a philosopher’s God, not the God of the bible or who most people believe in).

Beyond that, when talking about a neutron, there are many things needed to support the existence of a neutron.

There is a song by a Christian (Baptist I think) which offers the view that everything is everything, because everything depends on everything else, and without that, nothing would be as it is. Lauryn Hill - Everything Is Everything - youtube.com/watch?v=i3_dOWYHS7I

 

[reggieM]

But also, isn’t Aquinas’ argument a posteriori, not a priori?

Good point and yes. With what I said you’d have to start with a premise from an a posteriori argument. Although I think the idea of “power that sustains being” is better than “mover”. But we might improve that to “power that defines being” to get away from your concern about juggling. In this case, being is defined by boundaries. So, in “possible worlds” a thing is “in a world” which would require some defining boundaries.

As you point out, G could be null, but this leaves a lot of self-sustaining or self-bounding things.

I wonder if the Plantinga argument also relies on an a posteriori argument for the premise:

If God exists then he has necessary existence.

Not sure on that.

There is a song by a Christian (Baptist I think) which offers the view that everything is everything, because everything depends on everything else, and without that, nothing would be as it is. Lauryn Hill - Everything Is Everything - youtube.com/watch?v=i3_dOWYHS7I

I like that and it makes a lot of sense.
There is a long chain of dependencies that enable us to observe or define things - comparing and contrasting them with other things and understanding relationships.
The fact that things fit together and have pattern and order is another aspect.
Chaos is the absence of order, which we wouldn’t recognize without the existence of order.

 

[ferdgoodfellow]

The logic is that if X exists in every possible world, then X is defined to be necessary. So yes, the starting assumption is that X is contingent until investigation shows it exists in every possible world…

Hi inocente,

This still doesn’t make any sense.

An entity exists necessarily if it cannot fail to exist. Where is the contradiction in this definition? It is not apparent as in the cases round squares, four-sided triangles and such.

But, we are told, we can translate our definition of necessary existence into: An entity exists necessarily if it exists in every possible world. What is a possible world? It is any conceivable way the actual world could have been. In conceiving a possible world, the only rule is that when we change any element of the actual world we don’t create nonsense. If it false that unicorns exist in the actual world, there is nothing illogical if we suppose it is true. And so it is with each and every element of the actual world. the T/F or exists/doesn’t exist switches can be flipped as to any element.

Now given these simple rules we can tell right away that it is impossible for anything to exist in every possible world, because I can always conceive of a given entity as not existing. No need to engage in Vera’s possible world reduction thought experiment. Take any X and flip the switch to “doesn’t exist” and I’ve done it.

But wait a minute, why is it true that we can always conceive of any given entity as not existing? Just because.

 

[ferdgoodfellow]

The argument dies right here. “Greatness” is a composite attribute. Your concept of greatness can and does differ from someone’s concept of greatness. There is no reason to continue, because the basic premise “greatness” is undefined. In other words, greatness is subjective. …

It does seem that greatness, when applied to any concrete object, is hopelessly subjective. E.g. greatest conceivable island. We will never get agreement on what makes an island unsurpassably great. But what if we think abstractly with the highest degree of generality? For example, couldn’t we all agree that we can’t think of anything greater than All That Exists or the Whole of Reality? Whatever it is that contributes to greatness is certainly contained therein.

 

[Vera_Ljuba]

It does seem that greatness, when applied to any concrete object, is hopelessly subjective. E.g. greatest conceivable island. We will never get agreement on what makes an island unsurpassably great. But what if we think abstractly with the highest degree of generality? For example, couldn’t we all agree that we can’t think of anything greater than All That Exists or the Whole of Reality? Whatever it is that contributes to greatness is certainly contained therein.

Yes, you can start it from here: “The whole caboodle that exists”. But not all “things” that exist contribute to some “positive” feature of existence. And we can “imagine” another (pesky ) possible world where there are fewer “negative” features, or none at all. In other words, we are back to the problem: “is this the best possible world”?

Obviously not. In our bodies there are bacteria, and we live in a symbiosis with them. About 95% of these bacteria are useful or neutral for our existence. Without them we would be unable to digest food - for example. However, there is the other 5% of them, one ones which can cause illnesses, problems. If these microbes would not be there, we would not miss them. So this “whole reality” is not the “greatest or best possible reality”.

 

[inocente]

Let’s don’t and say we did . There is not one word about a “reason” here. We start with the existing physical reality, which is possible, since it exists. Then we keep “downsizing” it. There is nothing problematic about the process. You may not “add” something to a possible world, since the addition process can lead to a logically inconsistent state of affairs. But you can always take something away. Removing a subset from a possible world will always lead to another possible world.

Why not? But, of course that was just a convenient way to demonstrate one possible process to get to a “super-simple” existence. It could be one world containing a bunch of protons, and another one containing a bunch of anti-protons. The actual entities are irrelevant, all we need is two of them which have no overlap. One could contain “Jack” and the other one could contain “Jill”.

You’re still pre-defining God out of existence by limiting existence to physical things.

No, it does not. Using another way to express it, it is an empty container, or an empty set. That does not mean that there is “a nothing” in it. Of course I readily accepted it that an “empty” world cannot exist physically. But it does exist conceptually, and it does not have a contradiction built into it. Therefore - it IS a possible world.

Perhaps the easiest way for you to see your error is read the Semantics section here - en.wikipedia.org/wiki/Modal_logic#Semantics

You’ll see that the model specifies “the truth-values of all propositions at each of the worlds in G”. An empty set doesn’t contain any propositions or anything else, and so cannot be a member of G.

 

[inocente]

Hi inocente,

This still doesn’t make any sense.

An entity exists necessarily if it cannot fail to exist. Where is the contradiction in this definition? It is not apparent as in the cases round squares, four-sided triangles and such.

But, we are told, we can translate our definition of necessary existence into: An entity exists necessarily if it exists in every possible world. What is a possible world? It is any conceivable way the actual world could have been. In conceiving a possible world, the only rule is that when we change any element of the actual world we don’t create nonsense. If it false that unicorns exist in the actual world, there is nothing illogical if we suppose it is true. And so it is with each and every element of the actual world. the T/F or exists/doesn’t exist switches can be flipped as to any element.

Now given these simple rules we can tell right away that it is impossible for anything to exist in every possible world, because I can always conceive of a given entity as not existing. No need to engage in Vera’s possible world reduction thought experiment. Take any X and flip the switch to “doesn’t exist” and I’ve done it.

But wait a minute, why is it true that we can always conceive of any given entity as not existing? Just because.

You’re doing the same as Vera - by flipping the switch you’ve defined X not to exist. But that scheme is just what’s called a truth table, the purpose of which is to lay out every combination of possibilities, including X=true and X=false. So of course it includes at least one line where X doesn’t exist, and includes at least one line where it does.

Unfortunately that not how modal logic and possible worlds frameworks work. Here’s Plantinga’s modal logic ontological argument, as he wrote it:

(25) It is possible that there be a being that has maximal greatness.

(26) So there is a possible being that in some world W has maximal greatness.

(27) A being has maximal greatness in a given world only if it has maximal excellence in every world.

(28) A being has maximal excellence in a given world only if it has omniscience, omnipotence, and moral perfection in that world.

,] it follows that there actually exists a being that is omnipotent, omniscient, and morally perfect; this being, furthermore, exists and has these qualities in every other world as well. For (26), which follows from (25), tells us that there is a possible world W’, let’s say, in which there exists a being with maximal greatness. That is, had W’ been actual, there would have been a being with maximal greatness. But then according to (27) this being has maximal excellence in every world. What this means, according to (28), is that in W’ this being has omniscience, omnipotence, and moral perfection in every world.

Note Plantinga defines what he means by greatness.

 

[inocente]

Good point and yes. With what I said you’d have to start with a premise from an a posteriori argument. Although I think the idea of “power that sustains being” is better than “mover”. But we might improve that to “power that defines being” to get away from your concern about juggling. In this case, being is defined by boundaries. So, in “possible worlds” a thing is “in a world” which would require some defining boundaries.

As you point out, G could be null, but this leaves a lot of self-sustaining or self-bounding things.

Yes, and I think it gets even more complicated if we try to ask what exactly is it that’s being sustained. The “chair-ness” of an armchair and “horsy nature” of a horse seem to be more about how we conceive them. And if we wait long enough, both turn to dust, and dust is made of atoms, and atoms of particles, but “particle-ness” also seems more about how we conceive them so it doesn’t get us very far.

I wonder if the Plantinga argument also relies on an a posteriori argument for the premise:

I don’t think so but his paper is very long, Here’s the link (pdf): static1.1.sqspcdn.com/static/f/38692/304006/1262176924360/Plantinga±+The+Ontological+Argument.pdf?token=u11ZuE0Kci0lMegQFpZ8WCf8qvo%253D&usg=AFQjCNF-Xrx4Gp7Uj74kseA4rfacY2C-QQ

Before wading through it, note his summary is a bit underwhelming:

Still, it is evident, I think, that there is nothing contrary to reason or irrational in accepting this premise [that the existence of a maximally great being is possible]. What I claim for this argument, therefore, is that it establishes, not the truth of theism, but its rational acceptability. And hence it accomplishes at least one of the aims of the tradition of natural theology.

I like that and it makes a lot of sense.
There is a long chain of dependencies that enable us to observe or define things - comparing and contrasting them with other things and understanding relationships.
The fact that things fit together and have pattern and order is another aspect.
Chaos is the absence of order, which we wouldn’t recognize without the existence of order.

Yes, maybe what’s sustained are the patterns (in the physical law and so on).

 

[Vera_Ljuba]

You’re still pre-defining God out of existence by limiting existence to physical things.

I am sorry, but you keep on misrepresenting what I said. Not one word has been said of “God”. The concept of “maximally great being” is discussed. And that concept is simply undefined and undefinable - in other words - vacuous.

Here’s Plantinga’s modal logic ontological argument, as he wrote it:

(25) It is possible that there be a being that has maximal greatness.

(26) So there is a possible being that in some world W has maximal greatness.

(27) A being has maximal greatness in a given world only if it has maximal excellence in every world.

(28) A being has maximal excellence in a given world only if it has omniscience, omnipotence, and moral perfection in that world.

,] it follows that there actually exists a being that is omnipotent, omniscient, and morally perfect; this being, furthermore, exists and has these qualities in every other world as well. For (26), which follows from (25), tells us that there is a possible world W’, let’s say, in which there exists a being with maximal greatness. That is, had W’ been actual, there would have been a being with maximal greatness. But then according to (27) this being has maximal excellence in every world. What this means, according to (28), is that in W’ this being has omniscience, omnipotence, and moral perfection in every world.

Note Plantinga defines what he means by greatness.

Plantinga’s verbal trickery does not work.
(25) Maximal greatness is subjective.

(26) Since (25) is undefined there is no reason to even contemplate it.

(27) is sheer nonsense.

(28) is Plantinga’s subjective definition.

No more needs to be said.

 

[reggieM]

Regarding greatness:

In order to reason about anything, one must necessarily accept that what is true has a greater value than what is false.

That cannot be left to a subjective judgement.

From that starting point, you arrive at a maximally great being.

 

[Vera_Ljuba]

Regarding greatness:

In order to reason about anything, one must necessarily accept that what is true has a greater value than what is false.

That cannot be left to a subjective judgement.

From that starting point, you arrive at a maximally great being.

No, you cannot. Is “evil” greater than “no evil”? To be in a “big hole” is not better than being in a “small one”. It is not always true that “bigger is better”.

 

[reggieM]

Is “evil” greater than “no evil”?

“No evil” is what we call “good”. So as I said, when you start by stating that true is greater than false, you’ve already established that good is greater than evil.

To be in a “big hole” is not better than being in a “small one”. It is not always true that “bigger is better”.

If that’s your argument then for you, the biggest possible hole (absolute nothingness) would be greater than any smaller one.

But that’s obviously absurd.

 

[ferdgoodfellow]

You’re doing the same as Vera - by flipping the switch you’ve defined X not to exist. But that scheme is just what’s called a truth table, the purpose of which is to lay out every combination of possibilities, including X=true and X=false. So of course it includes at least one line where X doesn’t exist, and includes at least one line where it does…

All I am saying is that Vera’s way of doing possible worlds assumes that all existential propositions can be true or false. It should come as no surprise, then, that Vera’s analysis concludes that no entity can exist in all possible worlds. According to his definition of possible worlds, they can’t.

 

[Vera_Ljuba]

All I am saying is that Vera’s way of doing possible worlds assumes that all existential propositions can be true or false.

No, not ALL. Only those ones which do not contain a logically inconsistent state of affairs. The existential proposition: “in the possible world X, married bachelors can exist.” cannot be “true” But a somewhat similar proposition “in the possible world X, violin-playing elephants can exist.” can evaluate to true, based upon the size of the elephant and the violin, and the dexterity of the animal.

 

[ferdgoodfellow]

No, not ALL. Only those ones which do not contain a logically inconsistent state of affairs. The existential proposition: “in the possible world X, married bachelors can exist.” cannot be “true” But a somewhat similar proposition “in the possible world X, violin-playing elephants can exist.” can evaluate to true, based upon the size of the elephant and the violin, and the dexterity of the animal.

Hi Vera,

So the only possibilities for any proposed entity are necessarily non-existent (married bachelor) or contingently existent. We supposedly have eliminated necessarily existent. And how was that done? We posited that there is an X which exists in all possible worlds. But that was demonstrated to be impossible. How? By showing that we can conceive of two possible worlds with no existents in common. How? By assuming that anything conceivable exists contingently.

 

[Vera_Ljuba]

Hi Vera,

So the only possibilities for any proposed entity are necessarily non-existent (married bachelor) or contingently existent. We supposedly have eliminated necessarily existent. And how was that done? We posited that there is an X which exists in all possible worlds. But that was demonstrated to be impossible. How? By showing that we can conceive of two possible worlds with no existents in common. How? By assuming that anything conceivable exists contingently.

Almost. The last sentence should read: “By showing that anything conceivable exists contingently.” So what now?