Modal Ontological Argument

[SeekingCatholic]

Unlike the cosmological arguments, which I find cannot offer 100% proof of the existence of God, the modal ontological argument is rock-solid.

To avoid a certain confusion which sometimes comes in, I need to carefully define various meanings of the term “possibility”.
Epistemic possibility: something is epistemically possible if we can conceive of it. The set of epistemic possibilities may expand or contract with new knowledge.
Logical possibility: something is logically possible if its existence does not contravene the rules of logic. If something is logically possible, there will be at least one logically possible universe in which it exists. If something is logically impossible, it cannot exist in any logically possible universe.
Actual possibility: This only has relation to a given universe - it describes a logically possible entity actualized in that universe.

The epistemically and logically possible sets overlap, but are not identical. Before a beginning calculus student learns the rules for derivatives, it is epistemically possible for him that that d/dx (x^2) = x. But it isn’t logically possible. Once the calculus student learns derivatives, the above equation also becomes epistemically impossible. Likewise, the actually possible set is a subset of the logically possible set. It is logically possible that there exist three types of charged particles, but actually impossible in this universe.

So:

1. We define God as a necessary being who is omnipotent and first cause. The definition of “necessary being” = it must exist in all logically possible universes.
2. The set of epistemically possible universes includes, a priori, both those with God and those without Him. However, the set of logically possible universes must either consist only of those with God or those without Him, from the definition of God.
3. Therefore, either God exists (as a necessary being), if the true set of logically possible universes is those with Him; or His existence is logically impossible, if the true set of logically possible universes is those without Him.

Up to this point, the logic is absolutely iron-clad. It does not, as yet, prove the existence of God, but it does significantly shift the burden of proof for atheists: they must show God to be a logically impossible being.

Now the question comes: how to choose between the two epistemic possibilities. It is not enough, as some versions of the argument seem to have it, to merely state that one can conceive of the existence of God, proving His possibility and therefore existence. This is confusing epistemic with logical possibility. Otherwise the atheist could reply that one can conceive of a universe without God, proving His lack of necessity and therefore non-existence, and therefore we would have both proved God’s existence and His non-existence. Again epistemic possibility is confused with logical possibility. There could be something we as yet don’t know about God which in fact renders His existence logically impossible (just as the beginning calculus student). On the other hand, there could be something we as yet don’t know about the universe which renders His existence in fact necessary.

Moreover, arguing about the actual possibility of God in this universe misses the mark. Even if a first cause of this universe could be proved, that would only prove a first cause in this universe; e.g., a contingent first cause which might not exist in other logically possible universes. It wouldn’t prove the same being as necessary first cause for the other universes.

The right question to ask is: is it logically possible that God’s existence be a necessity? Is the presumed set of logically possible universes itself a logical possibility? In other words, assuming His existence, what is the reason rendering the existence of universes without Him a logical impossibility? A rational reason can easily be found for God’s necessity. God can simply, by His power, prevent such universes from coming into existence. It is logically impossible for Him to act otherwise; since otherwise He by definition would not be God, and logically possible for Him to so act, since He is omnipotent by definition.

Now, if it is logically possible that God’s existence be a necessity (e.g. necessary in all logically possible universes), it is logically impossible that God’s existence be logically impossible (e.g. impossible in all logically possible universes), since the sets of logically possible universes don’t overlap, as shown in step 2). Put another way, if the set of universes with God is logically possible, then the set of universes without God must be logically impossible. Thus, God exists by logical necessity. (Cont.)

 

[SeekingCatholic]

Here, discussing logical rather than epistemic possibilities, there is no flip-side argument for the atheist. The argument would need to go, is it logically possible that God’s existence be logically impossible? But we cannot answer this question directly, any more than we could answer whether God Himself is a logical impossibility. It requires more epistemic knowledge about God than we have.

 

[ateista]

The whole argument is based upon the concept of “necessary being”.

1. The set of all the epistemically possible worlds contains the “null-world” which is empty.
2. This world - being empty - cannot contain a logical contradiction, therefore it is logically possible.
3. The empty world does not contain anything, therefore it does not contain a “necessary being”.
4. Moreover, if there would be a “necessary being” in this world, it would not be empty - and that would be a logical contradiction.
5. Therefore there is no “necessary being”.

Conclusion: the argument fails to establish the existence of a god (Omnipotent or otherwise).

Side note: the concept of “first cause” is undefined and undefinable: causation cannot be defined for collections of objects (like the universe). It can only be defined for individual objects or events.

 

[Tim_Kirchoff]

Side note: the concept of “first cause” is undefined and undefinable: causation cannot be defined for collections of objects (like the universe). It can only be defined for individual objects or events.

Like the Big Bang, maybe?

 

[ateista]

Like the Big Bang, maybe?

The Big Bang simply means that the Universe in its current form originated as a singularity. It does not suggest that the Universe came from “nothing”. The concept of the conservation of matter / energy means that matter / energy cannot be created or destroyed.

That is not relevant, however, to the topic at hand. The modal ontological argument is supposed to establish the existence of a “necessary being”, and since the null-world is logically possible, there is no “necessary being”.

The side note was just that, a side note, which was directed at the second supposed attribute of God, namely “first cause”. And since the causation is only defined for individual objects and cannot be defined for collections of objects, it is meaningless to speak of the “cause” for the Universe.

 

[Mirdath]

The idea of defining God as a thing particular to a hypothetical universe, as if the universe possesses a deity, would seem to fly in the face of the definition of divinity. What’s with this ‘exists in’ stuff when we’re talking about something which is supposedly greater than and different from the entirety of creation?

As for the ‘no flip-side’ bit in post #2, that’s only true of strong atheists. ‘More knowledge is needed’ works just fine for the weak atheists (who are by far the majority) and for agnostics.

 

[SeekingCatholic]

The whole argument is based upon the concept of “necessary being”.

Well of course it does. And it proves a necessary being, in fact, necessary.

1. The set of all the epistemically possible worlds contains the “null-world” which is empty.

True.

1. This world - being empty - cannot contain a logical contradiction, therefore it is logically possible.

False. The world may have no ontological entities (beings) in it but we are still assuming the existence of logic. Therefore an empty universe may still contain a logical contradiction. Therefore it is possible an empty universe contains a logical contradiction and is therefore logically impossible.

Unless your empty universe is empty of even logic, in which case you can’t prove it empty, without the law of non-contradiction. Denying that logic has been successful in proving God by denying logic itself is really silly.

1. The empty world does not contain anything, therefore it does not contain a “necessary being”.

1. Moreover, if there would be a “necessary being” in this world, it would not be empty - and that would be a logical contradiction.

1. Therefore there is no “necessary being”.

As shown above, your argument is fallacious.

Conclusion: the argument fails to establish the existence of a god (Omnipotent or otherwise).

Conclusion: the argument still stands.

Side note: the concept of “first cause” is undefined and undefinable: causation cannot be defined for collections of objects (like the universe). It can only be defined for individual objects or events.

Since causation can be defined for individual objects or events, a first cause can be so defined for those objects and events as the first cause in the causal chain leading up to them. Therefore “first cause” has been defined in a manner which should be to your satisfaction.

 

[BlaineTog]

Now, if it is logically possible that God’s existence be a necessity (e.g. necessary in all logically possible universes), it is logically impossible that God’s existence be logically impossible (e.g. impossible in all logically possible universes), since the sets of logically possible universes don’t overlap, as shown in step 2). Put another way, if the set of universes with God is logically possible, then the set of universes without God must be logically impossible. Thus, God exists by logical necessity.

“If it is possible that God has to exist, then God’s existence can’t be impossible.” I’m pretty sure that that’s what you just said.

Imagine a space unicorn. This unicorn does not need to eat, sleep, or breathe, and it is immortal. It exists atemporally and before the universe. It has only one power: to prevent universes from appearing.

This is not logically impossible. This doesn’t make it true.

 

[BlaineTog]

False. The world may have no ontological entities (beings) in it but we are still assuming the existence of logic. Therefore an empty universe may still contain a logical contradiction. Therefore it is possible an empty universe contains a logical contradiction and is therefore logically impossible.

Logic does not exist, any more than math exists. Rather, “existence” is the wrong word to use with respect to them. Additionally, logical contradictions are something that words do. If there are no words, they cannot be put into logically incoherent sentences. So, an empty universe is still empty of logical faults.

Unless your empty universe is empty of even logic, in which case you can’t prove it empty, without the law of non-contradiction.

We don’t have to prove anything. We’re supposing.

Denying that logic has been successful in proving God by denying logic itself is really silly.

But, ironically enough, not logically incoherent.

 

[ateista]

False. The world may have no ontological entities (beings) in it but we are still assuming the existence of logic.

You assume, I don’t. Logic is not an ontological entity, it is the rules of thinking. In the absence of thinking beings it is nonsensical to speak of “thinking”. I wonder if you allude to the concept of “abstract objects”, which I find an incoherent concept.

Therefore an empty universe may still contain a logical contradiction.

“May” is not enough. In order to prove that an epistemically possible world is logically impossible, you have to show that it “does” contain a logical contradiction, not just “may”.

Therefore it is possible an empty universe contains a logical contradiction and is therefore logically impossible.

As I said, “possible” is not enough.

Unless your empty universe is empty of even logic, in which case you can’t prove it empty, without the law of non-contradiction. Denying that logic has been successful in proving God by denying logic itself is really silly.

I don’t have to prove anything. The empty world is by definition empty. I do not deny logic. I deny that logic has an ontological existence.

You can attempt to prove that the empty world (which is by definition empty) nevertheless actually contains a logical contradiction (which would render it not empty) and therefore it is logically impossible. Good luck.

 

[ateista]

Since causation can be defined for individual objects or events, a first cause can be so defined for those objects and events as the first cause in the causal chain leading up to them. Therefore “first cause” has been defined in a manner which should be to your satisfaction.

No it cannot. It is simply incoherent to speak of a “cause” for a collection of objects. Just because a concept can be coherently defined for some entities, it does not mean that it can be defined for all entities, or collections of entities.

Just an example: On the surface of the Earth the concept of direction can be defined. On all points on the surface (except one) the direction of “north” can be defined. But at the North Pole the direction of “north” cannot be defined.

There are many syntactically legitimate questions, which are nevertheless semantically incoherent. An example would be: “What is to the north at the North Pole?”. Or another: “When did you stop beating your wife?”. Questions like these adhere to the rules of grammar yet they cannot be answered, because they are incoherent, meaningless composition of words.

The questions “What was before the Universe came into existence?” or “What exists outside the Universe?” and specifically “What caused the Universe?” all belong to this category. Syntactically correct, yet semantically nonsensical questions.

 

[SeekingCatholic]

“If it is possible that God has to exist, then God’s existence can’t be impossible.” I’m pretty sure that that’s what you just said.

That’s the modal ontological argument in a nutshell.

Imagine a space unicorn. This unicorn does not need to eat, sleep, or breathe, and it is immortal. It exists atemporally and before the universe. It has only one power: to prevent universes from appearing.

This is not logically impossible. This doesn’t make it true.

All you’ve done is rename God a “space unicorn”. The rest of the proof goes through same as before. The proof says nothing about the nature of God.

Except that a necessary God must exist outside of “space”, and cannot therefore have the properties of a “unicorn”. A “space uniform” God is therefore logically impossible.

 

[SeekingCatholic]

Logic does not exist, any more than math exists. Rather, “existence” is the wrong word to use with respect to them…

Hold it right there. If logic does not exist, then the law of non-contradiction does not exist, and therefore logic could exist and not exist at the same time. If you’re going to deny basic axioms of logic, we can go no further. Your response to a logical proof of the existence of God is to deny the existence of logic. That doesn’t at all rebut the proof as a logical proof, which assumes logic as a starting point.

Additionally, logical contradictions are something that words do.

Ridiculous. Words state the contradictions but don’t make them. Again, if you’re going deny the self-evident axioms of logic we can go no further. Without the law of non-contradiction you can’t even state this; logical contradictions could both be and not be something that words do.

 

[SeekingCatholic]

You assume, I don’t. Logic is not an ontological entity, it is the rules of thinking. In the absence of thinking beings it is nonsensical to speak of “thinking”. I wonder if you allude to the concept of “abstract objects”, which I find an incoherent concept.

Both you and BlaineTog are using the fallacy of the “stolen concept”. Without accepting the law of non-contradiction as axiomatic (present in all universes) then it can be both nonsensical and sensical to speak of thinking in the absence of thinking beings. I’m not saying logic is an ontological entity, but I am saying the basic axioms are present in all universes.

“May” is not enough. In order to prove that an epistemically possible world is logically impossible, you have to show that it “does” contain a logical contradiction, not just “may”.

As I said, “possible” is not enough.

Yes, possible is enough. I don’t need to prove that any given epistemically possible world is logically impossible. The argument, as I have stated it above, assumes a lack of knowledge as to whether the world is logically possible or not.

I don’t have to prove anything. The empty world is by definition empty. I do not deny logic. I deny that logic has an ontological existence.

Without logic, your empty world could be both empty and non-empty at the same time.

You can attempt to prove that the empty world (which is by definition empty) nevertheless actually contains a logical contradiction (which would render it not empty) and therefore it is logically impossible. Good luck.

An empty world is a world in which the existence of anything is actually impossible.
If nothing prevents anything from coming into existence, the existence of anything is not in fact actually impossible.
If something prevents anything from coming into existence, the something exists and the world is not empty. QED.

Look, if your response to a logical proof of God’s existence is going to be to deny the universal applicability of logic, then just say so. There’s no sense arguing logic with someone who has made up his mind not to be logical.

 

[SeekingCatholic]

BTW, you also contradicted yourself in your last attempt. If as you say logic is not an ontological entity (e.g. not a “something”) than an empty universe (with “nothing” in it) can certainly contain a logical contradiction as logic is not a “something”.

No it cannot. It is simply incoherent to speak of a “cause” for a collection of objects.

Which is why this is not how I am speaking of “cause”.

Just because a concept can be coherently defined for some entities, it does not mean that it can be defined for all entities, or collections of entities.

A cause can be coherently defined for each individual object. A cause of the cause can also be coherently defined, and a first cause can be coherently defined as the terminus of the chain for each object. This is what “first cause” means in the modal ontological proof.

The questions “What was before the Universe came into existence?” or “What exists outside the Universe?” and specifically “What caused the Universe?” all belong to this category. Syntactically correct, yet semantically nonsensical questions.

Your point is? These questions don’t even enter into the modal ontological proof.

This is why the modal ontological proof succeeds where the cosmological proofs fail.

 

[ateista]

Both you and BlaineTog are using the fallacy of the “stolen concept”. Without accepting the law of non-contradiction as axiomatic (present in all universes) then it can be both nonsensical and sensical to speak of thinking in the absence of thinking beings.

We speak from this world about those possible worlds. In an empty world, which is the equivalent of a mathematical null-set, there is no one to “speak” or “think”. Therefore it is nonsensical to speak of the laws of logic there.

I’m not saying logic is an ontological entity, but I am saying the basic axioms are present in all universes.

The laws of logic are axiomatic. They exist as concepts. Concepts exist where sufficiently developed physical entites exist who are able to make abstractions of the physical world, who are able to conceptualize. In a physical, non-empty world without thinking beings there are no concepts. It is nonsensical to speak of concepts without beings who are able to conceptualize.

Yes, possible is enough. I don’t need to prove that any given epistemically possible world is logically impossible. The argument, as I have stated it above, assumes a lack of knowledge as to whether the world is logically possible or not.

I am not speaking of “any” epistemically possible world, only about the null-world. If you wish to prove the concept of necessary being, you must prove that the null-world is logically impossible.

Without logic, your empty world could be both empty and non-empty at the same time.

It cannot, because we define it as emtpy.

An empty world is a world in which the existence of anything is actually impossible.

No it is not. It is merely one where nothing exists - by definition.

If nothing prevents anything from coming into existence, the existence of anything is not in fact actually impossible.

Irrelevant. There is nothing in a null-world, so there is no need to “prevent” it.

If something prevents anything from coming into existence, the something exists and the world is not empty.

Nothing prevents it, because there in nothing there.

Look, if your response to a logical proof of God’s existence is going to be to deny the universal applicability of logic, then just say so.

Logic is univerally applicable whereever there are beings who are able to recognize them.

There’s no sense arguing logic with someone who has made up his mind not to be logical.

And what is that supposed to mean?

 

[ateista]

BTW, you also contradicted yourself in your last attempt. If as you say logic is not an ontological entity (e.g. not a “something”) than an empty universe (with “nothing” in it) can certainly contain a logical contradiction as logic is not a “something”.

Hehe, are we going to play word-games now?

Logic is not a physical entity, it is a concept. Concepts are not “nothing”, though they are not ontological entities. So there is no contradiction.

And I have to stress, just because something is not logically impossible it does not mean that it can be actualized, that it can be a physically existing object. A temperature below zero Kelvin is not a logical impossibility, it is a physical one. We can imagine temperature below zero Kelvin and it does not lead to logical contradiction, but it cannot be actualized.

 

[ateista]

All you’ve done is rename God a “space unicorn”. The rest of the proof goes through same as before. The proof says nothing about the nature of God.

Except that there can infinitely many “space unicorns”, each of whom are responsible for different aspects of existence. None of them leads to logical cotradcitions, so, by your reasoning, all must exist.

Even if the ontological argument would succeed (and it does not), it would only establish a hodge-podge of different gods.

 

[SeekingCatholic]

In an empty world, which is the equivalent of a mathematical null-set, there is no one to “speak” or “think”. Therefore it is nonsensical to speak of the laws of logic there.

No, it isn’t. Even in a possible world without a rational being, it is impossible that an entity exist and not exist at the same time. Do you really deny this? Do you really claim in that world, it is really possible for such entity to exist and not exist, merely because there is no one around to speak or think the law of non-contradiction?

In a physical, non-empty world without thinking beings there are no concepts. It is nonsensical to speak of concepts without beings who are able to conceptualize.

So in a world without thinking beings, it is therefore possible for an entity to be and not-be at the same time, merely because there are no sufficiently developed physical entities available to conceptualize?

According to this logic, assuming atheism is true, in this universe, and before humans arrived on the scene, a violation of the law of non-contradiction would really be possible. Care to take this position?

I am not speaking of “any” epistemically possible world, only about the null-world. If you wish to prove the concept of necessary being, you must prove that the null-world is logically impossible.

Not so. Read the proof again. The proof makes no direct assumptions about the logical possibility or impossibility of any world, including the null-world. The proof in fact assumes that we lack sufficient knowledge to prove logical possibility or impossibility of any world. To do that, we would need to know everything about it. Without such knowledge, our “possibilities” are only epistemic possibilities. We don’t know whether or not the next bit of knowledge gained about the world will be logically incompatible with previous knowledge.

And the “concept” of necessary being is already proven insofar as we have already conceived of it (epistemic possibility). It is proving the existence of such a being which is what the modal ontological argument is about.

And I could turn the tables and ask for your proof that God, or a universe with God, is logically impossible. As the proof shows, if God is logically possible, then He exists.

It cannot, because we define it as emtpy.

So? Without the law of non-contradiction, it can be both empty and non-empty at the same time.

And, does the proposition “this universe is empty” exist in this universe? If so, then logical propositions and hence logical contradictions can exist in an “empty” universe.

No it is not. It is merely one where nothing exists - by definition.

You can’t make a logically impossible universe possible by merely “defining” it as such. I can “define” a shape which is a circle with four sides but that doesn’t make a squared circle logically possible. And you can “define” a universe where nothing exists but that doesn’t make it logically possible either.

Why doesn’t something just pop into existence in this null universe? Saying “because it is a null universe” says nothing. It doesn’t prove a null universe possible. It is possible that in every supposed logically possible null universe, that something will in fact pop into existence.

Irrelevant. There is nothing in a null-world, so there is no need to “prevent” it.

Again begging the question. You’re assuming the null universe is logically possible merely because you’ve defined it. You don’t know that in all of your supposed null worlds, something won’t in fact pop into existence.

Nothing prevents it, because there in nothing there.

The only way you can know this is if there is something preventing it, but that leads to a contradiction.

Put another way: if there is nothing preventing something from popping into existence, that something’s existence is an actual possibility. Then you don’t have knowledge that that something won’t, in fact, pop into existence. Merely because you can “conceive” of it not happening doesn’t mean that it in fact won’t.

You’re making the same mistake that some proponents of the modal ontological argument make: confusing epistemic possibility with logical possibility.

Logic is univerally applicable whereever there are beings who are able to recognize them.

So, therefore before humans arrived on the scene logic is not applicable, and therefore it is possible the earth is both 4.5e9 years old and 6,000 years old. It is possible evolution of whales is both true and false. It is possible the Big Bang occurred, and that it did not, at the same time.

 

[SeekingCatholic]

Except that there can infinitely many “space unicorns”, each of whom are responsible for different aspects of existence. None of them leads to logical cotradcitions, so, by your reasoning, all must exist.

No, for two reasons:

1. because remember the necessary being was defined as first cause, of which there can be only one by definition and
2. Those “different aspects of existence” don’t exist in all logically possible universes. Hence such a “space unicorn”, if he existed, would only be a contingent being.

Even if the ontological argument would succeed (and it does not), it would only establish a hodge-podge of different gods.

The ontological argument succeeds. You haven’t pointed out a single flaw in the reasoning. Because there are none to point out. It’s 100% pure logical reasoning. So far you’ve resorted to desperate hand-waving.