Modal Ontological Argument

[FrankSchnabel]

Seeking Catholic,

Where does your mode of arguing the modal OA come from? I read that Plantinga has a version. Is this it?

Ateista and Blaine Tog, does it make sense to speak of a Greatest Conceivable Being or Unsurpassible Reality?

Frank

 

[FrankSchnabel]

Also, along with Bogeydog, I wonder about positing a “null-world.” Isn’t that the same as absolute nothingness?

cordially,

Frank

 

[ateista]

So you admit 2) is wrong then. What you really mean is that if a world is logically possible, there is a subset of the world which is also logically possible, not that each subset of the world is logically possible, by definition. You need to provide a formal proof of this then.

On further consideration, I am not sure that even a random removal of anything from a logically consistent world could be considered impossible. If it were so, then we could subdivide the logically consistent world “A” into two parts: “B” and “C”, where either “B” or “C” (or both) would be logically impossible. Therefore “A” would contain a logically impossible subset, and as such “A” would contain a logical contradiction and as such it would be logically impossible.

Reflecting on your example of removing each second generation from our world, it would simply mean that the existing generations would be differently “conceived”, that they would have different parents.

Or we could postulate that the removal of any part of a causal chain would also automatically remove all its “children”. Just like in a properly set up database, where the removal of a record automatically triggers the removal of all records contingent upon the existence of the removed record.

No, what I meant was, in a universe where “A” causes “B” by necessity, e.g. if you have an “A” you (definitely, not just maybe) get a “B”, and that is the only way to get a “B”. If you by nature and not by choice are forced to procreate, and it is impossible that a procreation attempt could be unsuccessful, then a world in which you don’t have a child is logically impossible.

That would be reverse causation. I don’t think that is logically coherent.

In the first place, the burden of proof is on you to prove the assertion “for each logically possible world there exists a subset which is also logically possible”. There may be another objection besides that of causation which holds in these cases.

“May” be does not count.

And what you say is not true no matter how you slice it anyway. There either has to be an infinite regress or a first cause.

In the case of an infinite regress, every subset of the infinite regress, obtained via reverse causative removal of a finite number of causes, is logically possible. I’ll grant you this, because it was at one point in the past the actually existent universe, which means it must be logically possible.

But you still have an infinite regress when you’re done, no matter how many causes you remove. You don’t get to the null-world this way. As I pointed out ad nauseam to those who didn’t get the point in the thread on infinite regress, t = -infinity never “actually existed” and therefore the null-universe cannot be proven logically possible in this manner. Every point that actually existed existed at a finite time in the past, even assuming an infinite regress. Note here that I am not denying the possibility of an infinite regress. But the logical possibility of an infinite regress does not imply the logical possibility of a null-world.

In the case of a first cause, you can get to the first cause by removal but not beyond, for this is no longer removal from a causal chain. Whether the first cause itself can be removed is a separate question. We cannot ask what was “before” this point, causally speaking.

Good argument. You showed that the physical successive removal may have problems with infinite regress. But the hypothetical removal of all entities in “one fell swoop” does not present such problems.

If this first cause is the necessary being, his removal is logically impossible, because he must exist. Why must he exist? Because it’s his nature to exist necessarily. IOW, if God exists, His non-existence is logically impossible by definition.

And if the “first” cause is not necessary, then there is no problem with removing it and thus the existence of an empty world is logically possible. Remember, you must prove that a necessary being exists, before you can argue about it.

 

[ateista]

But actually, modern physics shows that the laws of nature indicate “something” is more stable than “nothing”.

Well, first of all this is a new hypothesis, which may of may not be correct. Second, we do not argue about the physical possibility of any world. Just because something is logically possible it does not follow that is must physically exist.

If these physical laws apply universally to all universes (and I think have provided a very good argument why this is the case), and these physical laws show that “something” is more stable than “nothing”, that “nothing” will turn into “something”, I think I have shown that it is at least possible that laws of logic could mandate the existence of something.

Again, physical laws are not relevant. We conduct a though experiment, and everything that is not logically impossible can be postulated. Besides, it is the physical laws that might mandate the changing of a null world into something else, not the laws of logic.

But here is where we differ. There could be laws of existence, applicable to all universes, which mandate that a null universe change.

Even if a physical null-world would change into a physical non-null world, it would take time to happen, and before that happens, it is a null-world.

No, there is a metaphysical area between mere “concepts” and “objectively existing ontological objects”. There is such a thing as “hypothetically existing ontological objects” and relationships can exist between them. These objects do not exist in our universe, but they exist in other universes and might exist in ours. It is possible universally valid relationships exist between them.

That is true, but what is the relevance?

The null-world cannot be fully known. All that is known is what exists actually. What exists potentially is unspecified.

I don’t agree. The null-world is a thought-experiment. It does not have to physically exist. It is the exact equivalent of the mathematical null-set, or the number zero.

Now let’s consider: what is an actual logical contradiction (as opposed to a sentence)? It would necessitate the existence of **at least one **actual object with at least two attributes, where these attributes are mutually exclusive, or at least two actual objects, the existence of which contradict each other.

In a hypothetical world, with one or less actual objects with one or less attributes there can be logical contradiction, since there is nothing else to contradict to. Even if you are correct that we cannot know everything about the null-world (or the “one”-worlds) that does not not mean that we know nothing about them. We do know that there can be no contradiction in them.

The consequence of this is that there can be no “necessary” being.

 

[SeekingCatholic]

Seeking Catholic,

Where does your mode of arguing the modal OA come from? I read that Plantinga has a version. Is this it?

My version is original. IMHO some other versions confuse at the end the idea of epistemic vs. logical possibility.

Ateista and Blaine Tog, does it make sense to speak of a Greatest Conceivable Being or Unsurpassible Reality?

Frank

My version doesn’t use the concept of a “Greatest Conceivable Being”.

 

[SeekingCatholic]

On further consideration, I am not sure that even a random removal of anything from a logically consistent world could be considered impossible.

Right. But that’s the point. You aren’t sure. Neither am I. I am arguing from the point of view of lack of knowledge about the logical possibility of any world besides our own.

If it were so, then we could subdivide the logically consistent world “A” into two parts: “B” and “C”, where either “B” or “C” (or both) would be logically impossible. Therefore “A” would contain a logically impossible subset, and as such “A” would contain a logical contradiction and as such it would be logically impossible.

Yes, but “B” could be logically impossible without “C”, and “C” could be logically impossible without “B”. Yet both “B” and “C” together could be logically possible. For instance, a universe with only electrons (no positrons) or with only positrons (no electrons) could be logically impossible. Yet a universe with both electrons and positrons is possible.

Reflecting on your example of removing each second generation from our world, it would simply mean that the existing generations would be differently “conceived”, that they would have different parents.

Which begs the question about whether such “conception” is in fact logically possible.

Or we could postulate that the removal of any part of a causal chain would also automatically remove all its “children”. Just like in a properly set up database, where the removal of a record automatically triggers the removal of all records contingent upon the existence of the removed record.

But you might also have to remove the parents, if A is a necessary and sufficient cause of B, if A’s existence necessarily implies B’s existence you can’t get rid of B without also getting rid of A. If the causal chain is an infinite regress then there is the problem stated above.

“May” be does not count.

Yes it does. The burden of proof is still on you to formally prove statement 2), and still unmet. That you think 2) is true is not enough.

Good argument. You showed that the physical successive removal may have problems with infinite regress. But the hypothetical removal of all entities in “one fell swoop” does not present such problems.

This is merely saying that there is a well-defined removal operation from our universe, resulting in the empty set.
Again as I pointed out on the other thread, the “intersection” or “removal” operations are possible on transfinite sets, but it is necessary to define exactly the manner in which those are performed so as to not end up with an undefined result. Your “one fell swoop” has to be defined to be in the reverse-causative order, starting with what is now.

But it does not show that the empty universe must be itself logically possible. Just because you can define the operation doesn’t make the result logically possible. Just like I can define the operation t → -infinity doesn’t mean t = -infinity actually existed. I can prove each finite point existed (in the case of an infinite regress). Thus you can prove each universe after a finite number of reductions is logically possible. You can’t prove the logical possibility of the empty universe this way.

And if the “first” cause is not necessary, then there is no problem with removing it and thus the existence of an empty world is logically possible. Remember, you must prove that a necessary being exists, before you can argue about it.

Yes, IF the first cause is not necessary, the empty world is logically possible. IF the first cause is necessary, the empty world is not logically possible. Again I’m not assuming a priori knowledge about either the existence of a necessary being or about the logical possibility of an empty world, or any other.

We’re left with two possibilities: either a necessary being exists (in which there is no logically possible universe without him) or a universe without a necessary being is logically possible (in which case a necessary being does not exist in any logically possible universe, and is therefore logically impossible).

 

[SeekingCatholic]

Well, first of all this is a new hypothesis, which may of may not be correct.

Exactly. We don’t know everything about the nature of being itself. However, I find the hypothesis more than credible.

Second, we do not argue about the physical possibility of any world. Just because something is logically possible it does not follow that is must physically exist.

We do argue about this, if physical laws are not contingent, but logically necessary. In that case physical possibility is the exact same thing as logical possibility.

Again, physical laws are not relevant. We conduct a though experiment, and everything that is not logically impossible can be postulated.

Everything? How do you know everything that is not logically impossible? Are you omniscient?

Besides, it is the physical laws that might mandate the changing of a null world into something else, not the laws of logic.

Not if the physical laws themselves are products of the laws of logic. Then the laws of logic dictate the “changing” of the null world.

Even if a physical null-world would change into a physical non-null world, it would take time to happen, and before that happens, it is a null-world.

There is no “before”, whether the non-null world exists temporally or eternally. The null-universe, the quantum vacuum if you will, doesn’t exist in time.

That is true, but what is the relevance?

I will show relevance.

I don’t agree. The null-world is a thought-experiment. It does not have to physically exist. It is the exact equivalent of the mathematical null-set, or the number zero.

You’re committing the fallacy of conflating empty sets.

The null world is a particular empty set. The empty set is a mathematical device. It is defined as the intersection of two sets which don’t contain a common object, in our superset of “epistemically possible universes”.

All empty sets are not “equal” and cannot be conflated. The empty set in the superset of “boxes containing fruit” is an empty box. The empty set in the superset of cars is lack of a car. But each empty set has a certain potential, meaning, what it can contain. The union of the empty box with oranges is a box with oranges. The union of the empty box with a Corvette is undefined, a truly null result, and not an empty set. Moreover, the intersection of a Corvette with a box of oranges is also a null result and not an empty set.

Now let’s consider a specific subset of boxes containing fruit - the subset of boxes containing at least oranges. In this subset the “empty set” is a box with oranges. Taking the intersection of any two members in the subset, the box will always contain oranges. Trying to go outside the subset and take an intersection with a box containing cherries yields a null result, not an empty set.

Failing to make these types of distinctions is what leads to logical paradoxes. It’s just like asking, is this true or false - “The following sentence is true. The preceding sentence is false” - it’s neither true nor false - it’s “null”.

The point here is that the empty set in the superset of “epistemically possible universes” is not necessarily the same empty set as exists in the subset of “logically possible universes”. And this is what is meant by the empty set being “logically impossible”. If you do not obtain the same empty set from any intersection operation among logically possible universes as you do from epistemically possible universes, then the empty set in the superset of epistemically possible universes is “logically impossible” - it’s outside the subset.

Therefore, it’s not sufficient to merely say “empty set”, you have to describe what the empty set has the potential to contain, under penalty of likely ending up in a logical paradox. And this is why all “null-worlds” are not created equal. This is why it is absolutely necessary to specify, not only what actually exists, but what can hypothetically exist, to have a complete description of a null-world. Therefore, it is necessary to know which superset the null-world is a member of, and therefore, to know all about the null-world, it is necessary to know all about the superset. (Cont…)

 

[SeekingCatholic]

Now let’s consider: what is an actual logical contradiction (as opposed to a sentence)? It would necessitate the existence of **at least one **actual object with at least two attributes, where these attributes are mutually exclusive, or at least two actual objects, the existence of which contradict each other.

That would be a sufficient condition for a logical contradiction. It is not a necessary one. A world is logically impossible if contradictions exist, not only in what actually exists, but in what might exist. A null world is logically impossible if an actual object could hypothetically exist with two mutually exclusive attributes. We can see this from the set theory. This null world is not the “empty set” from the superset of logically possible universes. There would need to be an intersection operation between two universes, one of which contains that object - but such a universe does not exist in the subset of logically possible universes.

Therefore, things such as a null world in which 2 + 2 = 3 is logically impossible. And, a null world in which the laws of physics, necessitated by the laws of logic, mandate that something exist is logically impossible.

In a hypothetical world, with one or less actual objects with one or less attributes there can be logical contradiction, since there is nothing else to contradict to. Even if you are correct that we cannot know everything about the null-world (or the “one”-worlds) that does not not mean that we know nothing about them. We do know that there can be no contradiction in them.

The consequence of this is that there can be no “necessary” being.

As shown, this is false.

 

[IvanKaramozov]

You assume, I don’t. Logic is not an ontological entity, it is the rules of thinking.

I think you will be hard pressed to find a modern logician who supports that latter statement, the former is a matter of dispute.

 

[ateista]

Right. But that’s the point. You aren’t sure. Neither am I. I am arguing from the point of view of lack of knowledge about the logical possibility of **any world **besides our own.

Well, if that were true, then the whole discussion would be quite moot, wouldn’t you say? Your OP argued about the existence of logically possible worlds (in plural) and continued from that point of view. Now you say that we can not know if other logically possible worlds can exist? What is the point of the discussion then?

Whether they physically can exist or not is irrelevant. The question is if they are logically possible.

But your current assertion is false. We can know that other logically possible worlds exist. I will give you two examples:

1. An epistemically possible world with is identical to ours in every respect, but one, namely that all the protons are replaced by anti-protons and all the electrons are replaced by positrons. It is usually called anti-matter. All the relationships would be same, and since our “positive” world is without contradiction, so is the “negative” world.
2. Another epistemically possible world where the spin of each elementary particle is reversed. Logically it would be identical to ours.

So we can know if some other hypothetical worlds are logically consistent, There is no inherent need to assume that the logical consistency of any hypothetical world (to wit: the null-world or the “one-worlds”) is unknowable to us.

You must prove that the null-world or the “one”-worlds contain an actual contradiction in order to invalidate their logical coherence.

Yes, but “B” could be logically impossible without “C”, and “C” could be logically impossible without “B”. Yet both “B” and “C” together could be logically possible. For instance, a universe with only electrons (no positrons) or with only positrons (no electrons) could be logically impossible. Yet a universe with both electrons and positrons is possible.

I am sure you wanted to say electrons and protons (not positrons). And no, that world might be logically possible, but physically impossible.

But more to the point, let me give you a crude analogy. Imagine a world of a pool table where the ontological entities are billiard balls and a cue-stick. Suppose that this world is logically possible. When you hit one ball, it will create a succession of movements, and let’s call this the causative chain of events.

Now, let’s reset the table, and remove some of the balls. This would be a subset of the original world. Hitting the same ball with the cue-stick would merely create a different causative chain of the events.

Going back to original analysis. If a world “A” is without contradiction and its two subsets “B” and “C” would contain a contradiction, then by transitivity “A” would contain contradictions and as such it would not be logically possible.

In your OP you defined that a logically possible world cannot contain an actual contradiction. Therefore it is clear that “B” and “C” cannot have contradictions in them. Therefore it is proven that the null-world (which is a subset of all possible worlds) is without contradiction - and thus it is logically possible.

 

[ateista]

Not if the physical laws themselves are products of the laws of logic. Then the laws of logic dictate the “changing” of the null world.

But I gave you two different examples of worlds which are logically equivalent to ours, and where the physical foundation of the worlds is different. Therefore the laws of nature are not contingent on the laws of logic.

One more example: we could postulate another possible world where oppositely charged magnetic particles repel and similarly charged particles attract and replace all the electrons with positrons - all else being equal to our existing world. This would be a world with totally different physical laws, also governed by the same laws of logic.

You’re committing the fallacy of conflating empty sets.

The empty set is an abstraction. It does not exist as an ontological object.

The null world is a particular empty set. The empty set is a mathematical device. It is defined as the intersection of two sets which don’t contain a common object, in our superset of “epistemically possible universes”.

Not “superset”, subset.

All empty sets are not “equal” and cannot be conflated. The empty set in the superset of “boxes containing fruit” is an empty box. The empty set in the superset of cars is lack of a car. But each empty set has a certain potential, meaning, what it can contain. The union of the empty box with oranges is a box with oranges. The union of the empty box with a Corvette is undefined, a truly null result, and not an empty set. Moreover, the intersection of a Corvette with a box of oranges is also a null result and not an empty set.

These are just visual approximations of the abstract empty set. An abstract empty set is simply a set without any elements.

Failing to make these types of distinctions is what leads to logical paradoxes. It’s just like asking, is this true or false - “The following sentence is true. The preceding sentence is false” - it’s neither true nor false - it’s “null”.

Very true. The true-false value is undefined for these logical constructs.

 

[ateista]

That would be a sufficient condition for a logical contradiction. It is not a necessary one. A world is logically impossible if contradictions exist, not only in what actually exists, but in what might exist.

No, it is not necessary, and I tell you why in the next paragraph.

A null world is logically impossible if an actual object could hypothetically exist with two mutually exclusive attributes.

At that point it would cease to be a null-world, it would become one of the “one”-worlds. That is not a contradiction, it is merely a redefinition. If the null-world would change into a “one”-world with one actual object with one attribute to it, it would still be logically possible.

(Side note: the hypothetical change in a null-world would be contingent upon the laws of physics in that particular world. But since the world is void of ontological objects, there can be no “interrelationships” between “them”, and so there are no laws of physics.)

And precisely that is why I emphasised before that we postulate all the epistemically / logically possible universes (let’s call them E/LPU) as our “experimenting” ground. (In strict accordance to your OP, I might add.) If all the E/LPU are postulated, then there is no need to assume or contemplate a change in any one of them, since any difference is already considered as one of the “other” E/LPU. This way we can focus on the “static” properties of each E/LPU and find out if any one of them has an actual (not hypothetical) logical contradiction in it.

Therefore, in the static null-world or some of the specific one-worlds (not all, but some) the grounds for a logical contradiction are missing (no objects, or one object with one only property) and thus we know that they are without contradiction and as such - logically possible.

And, a null world in which the laws of physics, necessitated by the laws of logic, mandate that something exist is logically impossible.

As said before, supported with several examples, the laws of physics cannot be reduced to or derived from the laws of logic - though, of course, they cannot contradict them.

 

[ateista]

Well, first of all this is a new hypothesis, which may of may not be correct.

An observation: let’s suppose it is a correct hypothesis. If a null-world would be an actual entity (and not just an abstraction) and it would spontaneously change into a non-null-world (and that is what the hypothesis suggests), then there is no need to postulate a necessary being, which would “cause” this change. A pretty strong argument against God, wouldn’t you say?

 

[FrankSchnabel]

Hi Seeking,

Let’s look at epistemic, logical and actual possibility.

What is epistemically possible is always viewed subjectively. When someone makes a statement about what is epistemically possible, he implicitly prefaces his statement with, “For all I know” or “Based on my current state of knowledge.”

Now supposing I knew what roundness is but not squareness, I might conceive of a round square and posit its existence. But when informed what a square is and reminded of the rules of logic, I would then learn my statement is contradictory nonsense. It is logically impossible. And what is logically impossible is also actually impossible.

But suppose I posit the existence of unicorns. There is nothing logically impossible about unicorns. It’s an empirical question. It is actually possible that unicorns exist. As I gain knowledge about animals in the world I then can gain or lose confidence as to the probable existence of such creatures.

So what is epistemically possible for me, assuming I am rigorous, consistent and honest in my seeking knowledge, will change as I absorb the rules of logic, think my statements through for consistency and coherence, and investigate the empirical world.

So weit, so gut

 

[ateista]

Sorry, I missed this post:

Ateista and Blaine Tog, does it make sense to speak of a Greatest Conceivable Being or Unsurpassible Reality?

No, not to me. “Greatest” is a subjective assessment. Something that is “great” to you, may not be “great” for me.

An actual example: it has been said many times before that one of God’s attributes is that “God is unable to lie” or “God is unable to commit evil”, or generally “God cannot act against his nature”. (Of course all this can be summarized as “God has no free will”, but that is just a side observation.)

For me someone who is able to lie, or commit evil, or go against his own nature - but chooses not to - is “greater” than the one who is unable to do so. The one who is unable to do so is simply a robot. Nothing “great” about it.

So, “my” great is not necessarily “your” great.

 

[ateista]

Here is another argument for the logical consistency of the null-world.

1. If we have a logically consistent world “A”, and add something “X” that is also logically consistent to it, the resulting world “A-prime” is also logically consistent.
2. If we have a logically consistent world “A”, and add something “X” that is not logically consistent to it, the resulting world “A-prime” will not be logically consistent - since it contains a logically inconsistent part, namely “X”.
3. If we have a logically inconsistent world “B”, and add something “X” that is logically consistent to it, the resulting world “B-prime” will also be logically inconsistent - since it contains “B”.
4. 1. If we have a logically inconsistent world “B”, and add something “X” that is also logically inconsistent to it, the resulting world “B-prime” will also be logically inconsistent - since it now contains two logical contradictions, both “B” and “X”.

Summary: from a logically consistent world we can create a logically inconsistent one - by violating the laws of logic, of course, but from a logically inconsistent one we can never create a logically consistent one.

I hope we can agree on this, to me it is obvious, almost axiomatic.

Now, going back to the null-world. From the null-world we can use successive additions to arrive at any arbitrary non-null-world. Observe, that addition does not involve the same problems as removal. There is no problem of infinite descent.

If the null-world would be logically impossible, then by 3) and 4) no matter what we would add to it, it would never result in a logically consistent world. And since with successive additions we can navigate from the null-world to any world (logically possible or not) we can navigate to our existing one, and as such the null-world cannot be logically inconsistent - because that would imply that our world is logically impossible.

 

[SeekingCatholic]

Well, if that were true, then the whole discussion would be quite moot, wouldn’t you say? Your OP argued about the existence of logically possible worlds (in plural) and continued from that point of view. Now you say that we can not know if other logically possible worlds can exist? What is the point of the discussion then?

We can assume that there are other logically possible worlds. What I said was, to know whether any hypothetical world is in fact logically possible we need to know all about it. Otherwise, it could in fact contain a logical contradiction we are unaware of.

But your current assertion is false. We can know that other logically possible worlds exist. I will give you two examples…

I don’t disagree, although it can be argued whether this is really a different world, since the labeling of electrons vs. positrons is merely a matter of convention.

So we can know if some other hypothetical worlds are logically consistent, There is no inherent need to assume that the logical consistency of any hypothetical world (to wit: the null-world or the “one-worlds”) is unknowable to us.

No, but we do not know that there are any logically consistent “rules for existence”, so to speak, other than what we see in our own. In our own world, “anything that can happen, does”, so to speak, in particle physics. It is one of the most astonishing findings (to me, anyway), that the existence of a particular type of particle could be predicted solely on the basis of the math, and for that prediction to be verified later when sufficiently powerful particle accelerators could be built.

You must prove that the null-world or the “one”-worlds contain an actual contradiction in order to invalidate their logical coherence.

And I have done that.

Assumption about the nature of being: if something does not come into existence, that is either because it is prevented from coming into existence by some other entity, or because its existence is logically impossible.

Therefore,
The null-world is therefore a contradiction by definition. There is nothing preventing anything else from coming into existence.
The one-world is a contradiction unless the existent entity has the power to prevent anything else from coming into existence; if so, he is the necessary being.

My conclusions are correct if the above assumption is true. If you want to refute the assumption, you are going to have argue with a Nobel laureate physicist who says the same thing - e.g. the universe would exist unless God prevented it. If you cannot refute the assumption, then the null-world is possibly logically impossible. This is why I have constantly referred to the necessity of knowing what I have termed the “nature of being”.

I am sure you wanted to say electrons and protons (not positrons). And no, that world might be logically possible, but physically impossible.

I disagree. I meant to say positrons. The Dirac equation follows necessarily from the postulate that physics should be point-of-view invariant. I claim a point-of-view variant physics is a logical contradiction and violates the law of identity. The Dirac equation predicts the existence of both electrons and positrons. It is logically as well as physically impossible that there could be a universe with electrons but without positrons.

Going back to original analysis. If a world “A” is without contradiction and its two subsets “B” and “C” would contain a contradiction, then by transitivity “A” would contain contradictions and as such it would not be logically possible.

Repeating the same refuted argument doesn’t make it any better. It’s simply not possible to gloss over the relationships between the objects.

If the existence of “B” is a necessary and sufficient cause for the existence of “C”, then a world with “C” but without “B” is logically impossible. Likewise if the nature of causation is “inevitable” (e.g. whenever you have a “B” you get a “C”) then a world with “B” but without “C” is logically impossible.

Likewise, if the world doesn’t contain “C”, but “C” would have come into existence but for the existence of “B”, then a world with neither “B” nor “C” is logically possible.

In your OP you defined that a logically possible world cannot contain an actual contradiction. Therefore it is clear that “B” and “C” cannot have contradictions in them. Therefore it is proven that the null-world (which is a subset of all possible worlds) is without contradiction - and thus it is logically possible.

Your “proof” is trivially falsified above.

 

[SeekingCatholic]

Here is another argument for the logical consistency of the null-world.

It still doesn’t work.

1. If we have a logically consistent world “A”, and add something “X” that is also logically consistent to it, the resulting world “A-prime” is also logically consistent.

Not necessarily. If we add “X”, and the nature of “X” is such that “X → Y”, we also need to add “Y” to maintain consistency.

1. If we have a logically consistent world “A”, and add something “X” that is not logically consistent to it, the resulting world “A-prime” will not be logically consistent - since it contains a logically inconsistent part, namely “X”.

This is true.

1. If we have a logically inconsistent world “B”, and add something “X” that is logically consistent to it, the resulting world “B-prime” will also be logically inconsistent - since it contains “B”.

It could resolve the previous inconsistency - adding “Y” to the world “B + X”.

1. 1. If we have a logically inconsistent world “B”, and add something “X” that is also logically inconsistent to it, the resulting world “B-prime” will also be logically inconsistent - since it now contains two logical contradictions, both “B” and “X”.

This is true.

Summary: from a logically consistent world we can create a logically inconsistent one - by violating the laws of logic, of course, but from a logically inconsistent one we can never create a logically consistent one.

I hope we can agree on this, to me it is obvious, almost axiomatic.

I can’t agree. It depends on why the world was logically inconsistent. I add the component “parents” to a world. The world is logically inconsistent until I add “children”.

Now, going back to the null-world. From the null-world we can use successive additions to arrive at any arbitrary non-null-world. Observe, that addition does not involve the same problems as removal. There is no problem of infinite descent.

This still doesn’t work in the case of infinite regress. You can use finite additions to arrive at a non-null-world from another non-null-world. It is still possible here for a null-world to be logically impossible while an infinite regress is possible. The null-world never “actually existed” and hence in that case you would not have an actual transition from a logically impossible universe to a possible one.

If the null-world would be logically impossible, then by 3) and 4) no matter what we would add to it, it would never result in a logically consistent world. And since with successive additions we can navigate from the null-world to any world (logically possible or not) we can navigate to our existing one, and as such the null-world cannot be logically inconsistent - because that would imply that our world is logically impossible.

The infinite regress is sufficient to refute your position.

As is the argument that adding something to a universe could resolve a previous inconsistency.

Adding a necessary being to a null universe resolves the inconsistency about why nothing would exist, without any entity preventing it.

 

[ateista]

We can assume that there are other logically possible worlds. What I said was, to know whether any hypothetical world is in fact logically possible we need to know all about it. Otherwise, it could in fact contain a logical contradiction we are unaware of.

That is not true. We certainly do not know “everything” about the existing world, and still we know that it is without logical contradictions, since it physically exists…

In the case of a hypothetical world we can rely on the definition of the world. In the case of a “one”-world with one object in it, which object has only one attribute, we know everything about that world - because we define it in a certain manner. Exactly the same way as we speak of the null-world. Since there are no ontological objects in it, there can be no contradiction.

I don’t disagree, although it can be argued whether this is really a different world, since the labeling of electrons vs. positrons is merely a matter of convention.

In a sense, yes, but don’t try to collide the two worlds… unless you want a serious kaboom. And this objection does not apply to the other hypothetical world, where the spin of the particles is reversed. Interestingly the left-right spin is significant.

Assumption about the nature of being: if something does not come into existence, that is either because it is prevented from coming into existence by some other entity, or because its existence is logically impossible.

As I said, that is just an assumption. Nothing more.

And further, just because something possible does not exist in any particular world, it does not follow that it was “prevented” (what an anthropomorphic view!) or that it is impossible. In this world we do not have “unicorns” and that does not mean that “unicorns” are logically impossible or that some deity “prevented” them from coming into existence.

Therefore,
The null-world is therefore a contradiction by definition. There is nothing preventing anything else from coming into existence.The one-world is a contradiction unless the existent entity has the power to prevent anything else from coming into existence; if so, he is the necessary being.

Except that there are infinitely many possible “one”-worlds and that makes your “necessary” being rather incoherent. Also there is no need to speak of “preventing” something else.

My conclusions are correct if the above assumption is true. If you want to refute the assumption, you are going to have argue with a Nobel laureate physicist who says the same thing - e.g. the universe would exist unless God prevented it. If you cannot refute the assumption, then the null-world is possibly logically impossible. This is why I have constantly referred to the necessity of knowing what I have termed the “nature of being”.

Please do not try to appeal to authority. An assumption is just that… and it does not even speak of a logical null-world, only about a physical one. And many times we agreed that a logical world does not have to be actualized.

I disagree. I meant to say positrons. The Dirac equation follows necessarily from the postulate that physics should be point-of-view invariant. I claim a point-of-view variant physics is a logical contradiction and violates the law of identity. The Dirac equation predicts the existence of both electrons and positrons. It is logically as well as physically impossible that there could be a universe with electrons but without positrons.

If something is physically impossible, it is also logically impossible.

Repeating the same refuted argument doesn’t make it any better.

In what way does this further the discussion?

It’s simply not possible to gloss over the relationships between the objects.<snip to prevent the 5000 char limit>

The whole point is this: If there is a “B” and a “C” which are logically contingent (in some way) in this world, and we remove either one of them, we are talking about a brand new world. If that new world is logically coherent, there is no problem. If it is not logically coherent, adding the missing component will not “fix” it. The definition of logically possible world is that it cannot contain a logical contradiction. This was your definition, too. Why do you deviate from it?

 

[ateista]

Not necessarily. If we add “X”, and the nature of “X” is such that “X → Y”, we also need to add “Y” to maintain consistency.

The “nature”? What does that mean? Adding a logically consistent object to an already logically consistent world cannot create a contradiction. Relationships are not objects.

This is true.

Good.

It could resolve the previous inconsistency - adding “Y” to the world “B + X”.

Not possible. The “B-prime” world already contains a contradiction - namely “B” and that cannot be “fixed”. It is part of the world “B-prime”.

This is true.

Now that is a huge surprise. The exact opposite is what you adamantly stated all along: that a “logically inconsistent world can be fixed by adding another logically inconsistent entity to it”.

I wonder what kind of a truth table do you apply? Mine is simple, let “T” be a logically consistent set of entities, and “F” denoting a logically inconsistent set. Here is the truth table:

T + T = T
T + F = F
F + T = F
F + F = F

I can’t agree. It depends on why the world was logically inconsistent. I add the component “parents” to a world. The world is logically inconsistent until I add “children”.

The “parent” is not an entity, it is a concept! Likewise “child” is a concept. Sure they are relationships between two entities. But if all the children would die, the parents would not disappear, they would simply cease to be “parents”. The world would still be logically consistent (or possible) but one specific relationship would be absent. That is not a logical contradiction.

This still doesn’t work in the case of infinite regress.

With additions there can be no infinite regress.

You can use finite additions to arrive at a non-null-world from another non-null-world.

At least we can agree on this.

It is still possible here for a null-world to be logically impossible while an infinite regress is possible. The null-world never “actually existed” and hence in that case you would not have an actual transition from a logically impossible universe to a possible one.

What is the “actual existence” you speak of? Logical or physical? You agreed right above that adding one entity to a “one”-world will create a “two”-world. Why do you deny that adding one entity to the “zero-world” will create a “one”-world?

The infinite regress is sufficient to refute your position.

There is no infinite regress when the only operation is “addition”.

As is the argument that adding something to a universe could resolve a previous inconsistency.

Not “something”: an object! Relationships are not ontological objects.

Adding a necessary being to a null universe resolves the inconsistency about why nothing would exist, without any entity preventing it.

Except that it would not be a null-universe, would it? How come you are comfortable with that logical contradiction?