A Priori Proof for God's Existence

[Perplexity]

Vera, you start rightly enough by assuming there’s a necessary being. But, then you eliminate everything except two contingent beings. What happened to the necessary being you were assuming? If you are in fact assuming there’s such a being, as you must for the indirect proof, then you have to say every possible world has at least it in common. If you are not assuming there’s such a being, then sure you could subtract things until you get two non-overlapping worlds. But, you would not in that case be conducting an indirect proof.

It’s a dilemma: you either assume a necessary being and the indirect proof fails, or you don’t assume a necessary being and there’s no indirect proof in the first place.

 

[Vera_Ljuba]

Vera, you start rightly enough by assuming there’s a necessary being.

I do not say it, I hypothesize it. Do you know what that means?

But, then you eliminate everything except two contingent beings.

Except two beings.

What happened to the necessary being you were assuming? If you are in fact assuming there’s such a being, as you must for the indirect proof, then you have to say every possible world has at least it in common.

The definition of a possible world is NOT that it contains a “necessary being”. It is simply a state of affairs without a logical inconsistency. The existence of a necessary being is simply a hypothesis, which turns out to be false.

If you are not assuming there’s such a being, then sure you could subtract things until you get two non-overlapping worlds. But, you would not in that case be conducting an indirect proof.

The elimination process is independent from the hypothesis.

It’s a dilemma: you either assume a necessary being and the indirect proof fails, or you don’t assume a necessary being and there’s no indirect proof in the first place.

I guess, I will have to start it again. The existence of a necessary being is a hypothesis, which may or may not prove to be true. Just like the “p” and “q” in the hypothesis of “p/q = sqrt(2)” where p and q are both integers and they have no common divisor. We hypothesize the existence of these two integers. And then perform a few simple steps (just like eliminating a few objects from the starting world) and at the end we realize that the hypothesis was false.

What you say is that at least one of the elimination steps was illegitimate, since it eliminated the “necessary being”. But that is not the case. Any and all eliminations are legitimate, because none of the “intermediate worlds” manifests a logical contradiction.

Just imagine. We start with the existing world.

• Then we eliminate all the galaxies, except the Milky Way.
• Then we eliminate all the solar systems, except ours (with the Sun in the middle).
• Then we eliminate all the planets, except Earth.
• Then we eliminate all the life-forms, and leave only the rocks.
• Then we eliminate all the atoms, except one deuterium.
• The deuterium has one electron, one proton and one neutron.
• Then we stop for a second, and eliminate the proton and the neutron.
• The result is a very simple system - just one electron.
• Alternately, we grab the deuterium and remove the proton and the electron.
• The result is another very simple system, just one neutron.
  Every step is legitimate.

You try to say that during this process I removed that hypothesized necessary being. What was it?

 

[inocente]

This seems to be Hume’s error, if I understand you right. The phrase is possible world, not logically consistent world, or imaginable world. If a world can’t be without God, it’s not a possible world.

In model logic, a possible world is this cosmos as it may have been, had history been different. The ‘possible’ in the term means it was logically able to turn out that way - it had the potential to be that way.

So the set of possible worlds doesn’t contain any logically inconsistent cosmos. These are in a separate set, known as ‘impossible worlds’. The first set is what our world could possibly have been like, the second what our world could not possibly have been like.

There’s no scientific requirement. Our knowledge of the laws of nature was gained by observation, a posteriori and there is no a priori reason why they couldn’t possibly be different.

I think the only axiom is logical consistency, so you would have to prove that there is a logical contradiction in the proposition ‘God does not have necessary existence in world W’. That seems difficult enough to prove, even before adding all possible conditions. For instance, suppose life in W is unremitting cruel, with no afterlife. W is still a logically possible world, but it might be a bit difficult to make a watertight logical proof that God is necessary, omniscient, omnipotent and omnibenevolent in W .

Of course, if you can’t prove it, then W could be our world. For Hume, a priori only speaks of ideas, of possibilities, not of facts. The proof of the pudding is in the eating, the fact is in the experience, like Romans 1:20, a posteriori.

 

[Perplexity]

Those who are familiar with deductive logic are going to be furling their brow at this point you do not deny the assumption in the premises, you deduce its denial as a conclusion and that’s what generates the contradiction. I think you know just enough logic to get in trouble, but this entire exchange would not have occurred had (as is customary) you stated the argument in premise-conclusion format and identified the rules of inference you used: in that case, you would have seen that the argument could not be validly constructed. It now seems you’re arguing that if there were a necessary being, it should be a contradiction to deny its existence. This exchange will spin in circles until the argument is given in premise-conclusion format: its invalidity will be recognizable in seconds.

 

[ferdgoodfellow]

… This exchange will spin in circles until the argument is given in premise-conclusion format: its invalidity will be recognizable in seconds.

The definition of a necessary being is That Which Cannot Fail To Exist. So the question before us is whether there is a contradiction lurking somewhere in the definition.

It’s obviously not obvious, such as with round-squares or four-sided triangles.

Is there a premise-conclusion procedure which demonstrates a contradiction in our definition?

 

[Vera_Ljuba]

The definition of a necessary being is That Which Cannot Fail To Exist.

Yes. And it can be expressed in the form of: “which is present in every possible world”.

So the question before us is whether there is a contradiction lurking somewhere in the definition.

It’s obviously not obvious, such as with round-squares or four-sided triangles.

Is there a premise-conclusion procedure which demonstrates a contradiction in our definition?

The contradiction WAS demonstrated in my numerous posts on the subject.

 

[reggieM]

One neutron. Plus …

Space. Dimension. Identity. Difference. Distinction, Uniqueness, Order, Movement, Energy, Distance, Contingency, Causality, Time, Physicality, Observability

 

[inocente]

The definition of a necessary being is That Which Cannot Fail To Exist. So the question before us is whether there is a contradiction lurking somewhere in the definition.

It’s obviously not obvious, such as with round-squares or four-sided triangles.

Is there a premise-conclusion procedure which demonstrates a contradiction in our definition?

Philosophers have raised a number of issues, see plato.stanford.edu/entries/god-necessary-being

For instance, suppose God logically cannot fail to exist. Can God rule that ‘2 + 2 = 5.678’ or change any other abstract truth, such as the law of identity, the law of contradiction, the law of excluded middle?

If you say yes, then all the truths we take to necessarily exist would instead be contingent on God’s will, making the whole notion of necessary existence incoherent.

But if you say no, then there there are truths which necessarily exist without God.

Put another way, God seems determined to make sure we can neither prove nor disprove his existence.

 

[Vera_Ljuba]

One neutron. Plus …

Space. Dimension. Identity. Difference. Distinction, Uniqueness, Order, Movement, Energy, Distance, Contingency, Causality, Time, Physicality, Observability

None of these are ontological objects, they are abstractions. And abstractions only exist in the mind of sapient beings, who are able to conceptualize. Not to mention that they would be poor candidates to be “God”.

 

[reggieM]

None of these are ontological objects, they are abstractions. And abstractions only exist in the mind of sapient beings, who are able to conceptualize. Not to mention that they would be poor candidates to be “God”.

In Catholic theology, God designed and created the universe from an idea in His mind and through his Will. His idea for humanity is not an abstraction, but is rather, the foundation of what we know as reality.

An ontological object is: The real or existing object of an act of knowledge.

By definition, God is not an object or thing, but rather a spiritual being who is Knowledge, Truth, Goodness. A single neutron is contingent on many existent things which are not abstractions but are part of ontological reality. Calling something a “neutron” is an abstraction if you want to go down that path. Why do you make a distinction between “neutron” and “non-neutron”? That is all a mental construct.

 

[Vera_Ljuba]

In Catholic theology, God designed and created the universe from an idea in His mind and through his Will. His idea for humanity is not an abstraction, but is rather, the foundation of what we know as reality.

An ontological object is: The real or existing object of an act of knowledge.

By definition, God is not an object or thing, but rather a spiritual being who is Knowledge, Truth, Goodness. A single neutron is contingent on many existent things which are not abstractions but are part of ontological reality. Calling something a “neutron” is an abstraction if you want to go down that path. Why do you make a distinction between “neutron” and “non-neutron”? That is all a mental construct.

You are in the wrong room. Here we deal with “philosophy”, NOT “theology”.

 

[reggieM]

I addressed my comment in post #99 to ferdgoodfellow – could he respond to that when you get a chance?

A single neutron is contingent on many existent things which are not abstractions but are part of ontological reality. These things are all necessarily shared in every possible world.

 

[Vera_Ljuba]

A single neutron is contingent on many existent things which are not abstractions but are part of ontological reality. These things are all necessarily shared in every possible world.

So far you only quoted some abstractions.

 

[ferdgoodfellow]

I addressed my comment in post #99 to ferdgoodfellow – could he respond to that when you get a chance?

A single neutron is contingent on many existent things which are not abstractions but are part of ontological reality. These things are all necessarily shared in every possible world.

Hi Reggie,

I agree with you that a single proton world and a single neutron world do not have nothing in common, even though the proton world has no neutrons and the neutron world has no protons. As I’ve said before, there must always be some abstract residuum in common between the two worlds, and you have suggested many things implicit in entities such as protons and neutrons which both worlds must have in common.

But we have to agree that a proton is not a neutron and vice versa. They are different entities. For me it is easier to think in terms of X’s and Y’s, which we stipulate are different entities. Vera’s possible world reduction thought experiment was designed to show one can construct one possible world (A) with only an X and another (B) with only a Y. Looking at the two of them we can then observe that B has no X’s in common with A. If our hypothesis is that there can be an X in all possible worlds, we have just disproved that because we have shown that we can conceive of world B with only a Y and no X in it. This works, taking for granted the assumptions of Vera’s thought experiment.

However, whether A and B have anything in common or not is not the problem with Vera’s analysis.

 

[ferdgoodfellow]

So we began by asking whether there can be an entity which cannot fail to exist. Vera translated that to: Can there be an X which is present in all possible worlds? To get to the proton only and the neutron only worlds he assumed that each and every element of the actual world can be eliminated.

If we imagine my Possible World Truth Table which completely describes the actual world, pick any existential proposition you want and flip the switch from T to F. If you want to eliminate all galaxies except the Milky Way, flip all those other galaxies to F and only the Milky Way is left. And so on.

The assumption that one can flip any switch is itself a denial of the possibility that
X can exist in all possible worlds. No matter what possible world we want to imagine, the “X exists” proposition can be switched to F. So we end up testing our hypothesis with a system of thought which denies the hypothesis.

 

[inocente]

The assumption that one can flip any switch is itself a denial of the possibility that X can exist in all possible worlds. No matter what possible world we want to imagine, the “X exists” proposition can be switched to F. So we end up testing our hypothesis with a system of thought which denies the hypothesis.

Not so fast .

The idea of possible worlds was invented by philosophers to explore logic. There’s no requirement that a possible world contains anything in particular or that it has any given laws of nature. The only requirement is that it doesn’t involve any logical contradictions (after all, we’re exploring logic). Therefore, as it were, the laws of logic must necessarily exist in all possible worlds.

The question then is, is there anything else that must necessarily exist in all possible words? The answer is yes, but only if it can be proved as a theorem from the laws of logic alone. It’s then as necessary as the laws of logic. Otherwise, like X, it’s contingent and need only exist in some worlds or in one world.

If you’ve not seen them, there’s a round-up of philosophical works on possible worlds and God here - oxfordbibliographies.com/view/document/obo-9780195396577/obo-9780195396577-0249.xml

An influential paper is Alvin Plantinga 1976 andrewmbailey.com/ap/Actualism_Possible_Worlds.pdf

 

[Vera_Ljuba]

The idea of possible worlds was invented by philosophers to explore logic. There’s no requirement that a possible world contains anything in particular or that it has any given laws of nature. The only requirement is that it doesn’t involve any logical contradictions (after all, we’re exploring logic). Therefore, as it were, the laws of logic must necessarily exist in all possible worlds.

I always heard that “possible world” concept was supposed to be a tool to prove God’s existence. And that is how it is being used in the thought experiments.

The “laws” of logic are NOT ontological entities, they are abstractions. If we postulate that the “possible world” is not restricted to ontological objects, but it allows concepts as well, then the mathematical concept of “null world” (or “empty world”) also becomes a possible world. However, this world contains NO entities at all, neither ontological, nor abstract. Obviously, this world contains no logical contradiction, being totally empty of any elements. So we can conclude that there cannot be any element, ontological or abstract, which is present in ALL the possible worlds.

Of course the null-world is just an abstraction, it cannot have “physical” existence. (Though it is very useful in mathematics.)

So we have two choices. If we consider only ontological entities (of which God would be one), then the “super-simple worlds” of one electron / one neutron are possible, and therefore there is no necessarily existing ontological entity. If we “allow” the abstractions to be part of the “possible world”, then the “null world” will disprove the existence of a “necessarily existing entity”.

That is all. (By the way, the laws of logic would be a poor substitute for God )

 

[reggieM]

Hi Reggie,

I agree with you that a single proton world and a single neutron world do not have nothing in common, even though the proton world has no neutrons and the neutron world has no protons. As I’ve said before, there must always be some abstract residuum in common between the two worlds, and you have suggested many things implicit in entities such as protons and neutrons which both worlds must have in common.

Where I would disagree here is in making a distinction between a neutron and all of the necessary entities that allow a neutron to exist. I don’t think those are “abstract” but are actually existing. In the same way, one could call the concept of a neutron as an abstraction. Why distinguish between neutron and non-neutron? That we make distinctions is invisible and epistemological.

But we have to agree that a proton is not a neutron and vice versa. They are different entities.

I don’t know about that really. Is “non-proton” an entity? The only way to distinguish that a single proton exists is to have some category for non-proton. Additionally, if we had only two protons, we would distinguish them by real entities (distance, space, difference, movement, composition, dimension) that necessarily exist.

For me it is easier to think in terms of X’s and Y’s, which we stipulate are different entities.

They share something in common though since they both come from the same alphabet of characters. So, I do not think we can create two possible worlds that have nothing in common. Or I will say, thus far we haven’t shown that.

If we say that God is “the power that sustains all Being” then any world that exists must necessarily have God in it.

Vera’s possible world reduction thought experiment was designed to show one can construct one possible world (A) with only an X and another (B) with only a Y. Looking at the two of them we can then observe that B has no X’s in common with A. If our hypothesis is that there can be an X in all possible worlds, we have just disproved that because we have shown that we can conceive of world B with only a Y and no X in it. This works, taking for granted the assumptions of Vera’s thought experiment.

As above, this is where I disagree. You cannot remove all shared entities required for the existence of X or Y.

However, whether A and B have anything in common or not is not the problem with Vera’s analysis.

I’m not following this. I believe you are saying that A and B do not have anything in common, right?

 

[reggieM]

Therefore, as it were, the laws of logic must necessarily exist in all possible worlds.

Yes, but more precisely, the laws of logic are reducible to first principles and one of these is there is a distinction between existence and non-existence. That distinction necessarily exists in every possible world.

 

[inocente]

I always heard that “possible world” concept was supposed to be a tool to prove God’s existence. And that is how it is being used in the thought experiments.

I think the concept started with Leibiz, as in ‘the best of all possible worlds’ (his possible worlds are those which God could have willed instead of this one). The idea then got resurrected to explore modal logic. I’m not sure it’s a very helpful concept as it gets misunderstood big-time.

The “laws” of logic are NOT ontological entities, they are abstractions. If we postulate that the “possible world” is not restricted to ontological objects, but it allows concepts as well, then the mathematical concept of “null world” (or “empty world”) also becomes a possible world. However, this world contains NO entities at all, neither ontological, nor abstract. Obviously, this world contains no logical contradiction, being totally empty of any elements. So we can conclude that there cannot be any element, ontological or abstract, which is present in ALL the possible worlds.

Of course the null-world is just an abstraction, it cannot have “physical” existence. (Though it is very useful in mathematics.)

So we have two choices. If we consider only ontological entities (of which God would be one), then the “super-simple worlds” of one electron / one neutron are possible, and therefore there is no necessarily existing ontological entity. If we “allow” the abstractions to be part of the “possible world”, then the “null world” will disprove the existence of a “necessarily existing entity”.

That is all. (By the way, the laws of logic would be a poor substitute for God )

Trouble with what you say here is God isn’t a member or property of this world. He created it so he can’t be. Likewise for all possible worlds.

What you have to do instead is start with something which can exist in all possible worlds. You could start with a proposition such as ‘God is all powerful’’. That proposition can be made in any possible world, but could be true or false. If you can prove there is at least one possible world where it is false, then you’ve proved (at the least) that God is not omnipotent.

You’re right about abstractions. One of the many problems with trying to prove God’s existence a priori is it makes God into an abstraction which circles back on itself - see sections 2 and 3 in plato.stanford.edu/entries/god-necessary-being/

Yes, but more precisely, the laws of logic are reducible to first principles and one of these is there is a distinction between existence and non-existence. That distinction necessarily exists in every possible world.

Please see above. One issue is that God could exist as an abstract concept in all possible worlds, but then an invisible pink unicorn could exist as a concept too. So there needs to be a proposition in which God is substantial rather than just an idea.