Another modal cosmological argument

[punkforchrist]

R Daneel:

I don’t argue with that. There are two different states of affairs, each containing a different set of “existing” entities. I still don’t understand what is the point of bringing in the “uninstantiated == nonexistent” entities. We can describe a state of affairs by enumerating all the existing entities in it. I see no reason to bring in anything that does not exist, even if it “may” exist. What would be the point?

S is a state of affairs in which nothing contingent at all exists. I argue that S really is a possible state of affairs. The “non-instantiation” part isn’t very important.

 

[punkforchrist]

stenlis:

Are your ‘possible worlds’ really possible or are they theoretically possible? That would make a difference in you concluding a real god or a theoretical god.

If they are really possible, how would you demonstrate that?

I would say they are really possible, but that would take us into a discussion of the merits of “possible worlds theory,” which to be honest, I’m not interested in debating at the moment. The MCA has the advantage of persuading those who already accept that different worlds are really possible.

On top of that, I don’t think this is a disadvantage in any sense, either. The person who claims that reality must be the way it is is making a much stronger claim than the one who says that things could be different.

 

[R_Daneel]

S is a state of affairs in which nothing contingent at all exists. I argue that S really is a possible state of affairs. The “non-instantiation” part isn’t very important.

So, to clarify: “a state of affairs is the set of all existing concrete (not hypothetical) entities”. The word “contingent” does not mean that the entities are dependent on something else. It just means that a “contingent entity” possibly could not exist. The “non-contingent” entity means that it necessarily exists in all possible worlds. A possible world can be viewed two ways: “a state of affairs, which is without contradiction”, or “a state of affairs, which differs from our world in some respect”. And another thing to clarify: what is an “entity”?

The state of affairs “S” (as you presented) is one wihout contradictions. Therefore it is a possible world - in this sense of the word. In other words, it is the intersection of all the possible worlds. So far, so good.

If this intersection is not the null-world, then “S” is a possible world. This is the question: “is the intersection different from the null-world”? Are there any entities which appear in all the possible worlds? That is the next step.

 

[punkforchrist]

R Daneel:

So, to clarify: “a state of affairs is the set of all existing concrete (not hypothetical) entities”. The word “contingent” does not mean that the entities are dependent on something else. It just means that a “contingent entity” possibly could not exist. The “non-contingent” entity means that it necessarily exists in all possible worlds. A possible world can be viewed two ways: “a state of affairs, which is without contradiction”, or “a state of affairs, which differs from our world in some respect”.

I would agree with most of that, except that the actual world is a member of the set of possible worlds.

And another thing to clarify: what is an “entity”?

“Entity” is just synonymous with “thing.”

The state of affairs “S” (as you presented) is one wihout contradictions. Therefore it is a possible world - in this sense of the word. In other words, it is the intersection of all the possible worlds. So far, so good.

If this intersection is not the null-world, then “S” is a possible world. This is the question: “is the intersection different from the null-world”? Are there any entities which appear in all the possible worlds? That is the next step.

I don’t think S has to be the null world or the intersection of all possible worlds. Imagine that in some point in the past, nothing contingent existed (S obtains), yet something contingent existed both before and after S. This would be neither part of the null world nor the intersection of all possible worlds.

 

[R_Daneel]

I would agree with most of that, except that the actual world is a member of the set of possible worlds.

Yes, of course. The “difference” in this case is “nothing”.

“Entity” is just synonymous with “thing.”

I know… but how does one view a “thing”? You can view an apple as a “thing”, or as the collection of the atoms. The arrangement of the atoms is different, when the apple is cut into two halves. But they are still the same atoms. If one eats the apple, it will “disappear”, but the atoms do not. So just where do we draw the line?

I don’t think S has to be the null world or the intersection of all possible worlds.

It must be either one of those. We are talking about hypothetical worlds here. which may or may not have something in common. If there are “non-contingent” entities, they must be part of all the possible worlds, after all that is the definition of “non-contingent” entities - if there are any of these at all. And so the “S” you stipulated is the intersection of all possible worlds, and it is the largest possible intersection. If it exists, that is.

 

[punkforchrist]

R Daneel:

I know… but how does one view a “thing”? You can view an apple as a “thing”, or as the collection of the atoms. The arrangement of the atoms is different, when the apple is cut into two halves. But they are still the same atoms. If one eats the apple, it will “disappear”, but the atoms do not. So just where do we draw the line?

That’s an interesting question. If we are going to avoid existential nihilism, we have to concede that some things really do exist, and in a meaningful way. In your example, the apple’s atoms are all interrelated in a very specific way, so I think it makes sense to say that the apple itself is a thing, e.g. the apple is the interrelated whole of its atoms.

It must be either one of those. We are talking about hypothetical worlds here. which may or may not have something in common. If there are “non-contingent” entities, they must be part of all the possible worlds, after all that is the definition of “non-contingent” entities - if there are any of these at all. And so the “S” you stipulated is the intersection of all possible worlds, and it is the largest possible intersection. If it exists, that is.

Well, S is just the absence of any contingent entity. Maybe it would be helpful if we thought in more positive terms. Let’s say that C is the sum total of all existing contingent entities in a possible world, such that c1 is instantiated in w1, c2 is instantiated in w2, and so forth. If you find this agreeable, we may now ask: does any sum total of C possibly have an external cause?

 

[R_Daneel]

That’s an interesting question. If we are going to avoid existential nihilism, we have to concede that some things really do exist, and in a meaningful way. In your example, the apple’s atoms are all interrelated in a very specific way, so I think it makes sense to say that the apple itself is a thing, e.g. the apple is the interrelated whole of its atoms.

Yes, of course it does make sense. However, the atoms will exist, even if the apple does not (since we ate it). Matter / energy cannot be created or destroyed. This is why I would suggest to use the most basic level of existence, the elementary particles. There is no confusion there. No need to contemplate the complex entities, which are the composites of elementary particles.

Well, S is just the absence of any contingent entity. Maybe it would be helpful if we thought in more positive terms. Let’s say that C is the sum total of all existing contingent entities in a possible world, such that c1 is instantiated in w1, c2 is instantiated in w2, and so forth. If you find this agreeable, we may now ask: does any sum total of C possibly have an external cause?

Causation is not in the picture. That is why I am concerned about the phrase “contingent”, because it immediately suggest some causation. We agreed that there are two kinds of entities, let’s call them type-A and type-B. Type-A entities exist is all possible worlds, type-B exist in some but not all possibile worlds. No overtones are associated with this terminology.

The question is this: are there type-A entities? If there are, then “S” is the collection of all type-A entities. If there are none, then “S” is an empty set.

I think we are dancing around this question. I presented my mini-world examples, which deny the existence of type-A entities, by explicitly postulating two worlds without a common element. You said that you don’t think that these worlds are “possible”. Why not? They do not contain contradictions. They are very simple, but in the definition of “possible” words, there is no stipulation that a possible world must contain any specific number of entities. We did agree that a possible world cannot be totally empty, any possible world must contain at least one entity.

 

[punkforchrist]

R Daneel:

Yes, of course it does make sense. However, the atoms will exist, even if the apple does not (since we ate it). Matter / energy cannot be created or destroyed. This is why I would suggest to use the most basic level of existence, the elementary particles. There is no confusion there. No need to contemplate the complex entities, which are the composites of elementary particles.

The apple would just be an example of a thing that can cease to exist, even assuming that matter and energy cannot cease to exist. I’m willing to grant that matter and energy are temporally necessary, but that’s a long way from logical necessity.

Causation is not in the picture. That is why I am concerned about the phrase “contingent”, because it immediately suggest some causation. We agreed that there are two kinds of entities, let’s call them type-A and type-B. Type-A entities exist is all possible worlds, type-B exist in some but not all possibile worlds. No overtones are associated with this terminology.

When I say that something is “contingent,” I have already specified that I mean logical contingency. We don’t have to presuppose causality off the bat.

The question is this: are there type-A entities? If there are, then “S” is the collection of all type-A entities. If there are none, then “S” is an empty set.

I think we are dancing around this question. I presented my mini-world examples, which deny the existence of type-A entities, by explicitly postulating two worlds without a common element. You said that you don’t think that these worlds are “possible”. Why not? They do not contain contradictions. They are very simple, but in the definition of “possible” words, there is no stipulation that a possible world must contain any specific number of entities. We did agree that a possible world cannot be totally empty, any possible world must contain at least one entity.

I don’t want to jump ahead here. Let’s focus on whether it’s even possible for C to be externally caused, S5 notwithstanding. Is it possible for the sum total of contingent entities in w1 to be externally caused? I’m not asking whether this is necessarily the case, or whether S5 holds, but simply whether it is possible.

 

[R_Daneel]

The apple would just be an example of a thing that can cease to exist, even assuming that matter and energy cannot cease to exist. I’m willing to grant that matter and energy are temporally necessary, but that’s a long way from logical necessity.

How do you define “logically necessary”? We might need to stop and define these concepts. Especially “logically possible and or necessary”, “metaphysically possible and or necessary” and “physically possible and or necessary”. We might have a different meaning associated with these concepts.

When I say that something is “contingent,” I have already specified that I mean logical contingency. We don’t have to presuppose causality off the bat.

And by “logical contingency” we mean a type-B existence, don’t we? By the way, I am going to stick to the terms, type-A and type-B. I am concerned about the use of “necessary” and “contingent”, and will not use them again.

I don’t want to jump ahead here. Let’s focus on whether it’s even possible for C to be externally caused, S5 notwithstanding. Is it possible for the sum total of contingent entities in w1 to be externally caused? I’m not asking whether this is necessarily the case, or whether S5 holds, but simply whether it is possible.

I wish I would know why do you consider this relevant.

Now, let me clarify. We talk about “worlds” and “entites”. Formally speaking a “world” W is the collection of entities, where the entity is a bit vague, but we “pretty much” know what we are talking about. So W = {e1, e2, e3,…}. Among those entities there are some which are type-B, that is they only exist is some of the worlds. Now you say, let’s collect all the type-B entities and make a superset (you called it “C”), which contains all the type-B entities. And your question seems to be: “is it possible that C has an external cause for its existence?”. This is how I understand your question.

If this is what you asked, I am afraid I am unable to answer. Not because I don’t want to answer, rather because I don’t understand how do you define “causation” for a “set”? And what do you mean by “external” causation?

As I said, I have no idea where do you want to go with this. I presented my argument. Why is there a need to postpone the discussion?

 

[punkforchrist]

R Daneel:

How do you define “logically necessary”? We might need to stop and define these concepts. Especially “logically possible and or necessary”, “metaphysically possible and or necessary” and “physically possible and or necessary”. We might have a different meaning associated with these concepts.

Logically necessary = existence in all possible worlds
Logically contingent = existence in at least one, but not all possible worlds

Metaphysically necessary = if X exists in W, then X exists at all times in W
Metaphysically contingent = if X exists in W, then X exists for at least one time in W, but can fail to exist in W

Physical necessity/contingency would fall under the category of metaphysical necessity/contingency.

And by “logical contingency” we mean a type-B existence, don’t we? By the way, I am going to stick to the terms, type-A and type-B. I am concerned about the use of “necessary” and “contingent”, and will not use them again.

If all you mean by “type-B” is how I’ve defined logical contingency above, then yes.

I wish I would know why do you consider this relevant. . . . As I said, I have no idea where do you want to go with this. I presented my argument. Why is there a need to postpone the discussion?

My entire argument begins with the possibility premise, so it’s not a matter of postponing anything. It’s absolutely vital to establish whether or not it’s possible.

Now, let me clarify. We talk about “worlds” and “entites”. Formally speaking a “world” W is the collection of entities, where the entity is a bit vague, but we “pretty much” know what we are talking about. So W = {e1, e2, e3,…}. Among those entities there are some which are type-B, that is they only exist is some of the worlds. Now you say, let’s collect all the type-B entities and make a superset (you called it “C”), which contains all the type-B entities. And your question seems to be: “is it possible that C has an external cause for its existence?”. This is how I understand your question.

If this is what you asked, I am afraid I am unable to answer. Not because I don’t want to answer, rather because I don’t understand how do you define “causation” for a “set”? And what do you mean by “external” causation?

The term I used wasn’t actually “set,” but “sum total.” Think of a house, which is just the sum total of its parts. Surely the house as a whole has an external cause of its existence, right? Think of a construction company, for example. The external cause is simply an entity not included in the sum total, but which is nevertheless causally related to the sum total.

 

[R_Daneel]

Logically necessary = existence in all possible worlds
Logically contingent = existence in at least one, but not all possible worlds

Ok. And a logically possible world is a set (or collection) of elements (entities) where there is no logical contradiction.

Metaphysically necessary = if X exists in W, then X exists at all times in W
Metaphysically contingent = if X exists in W, then X exists for at least one time in W, but can fail to exist in W

Very well. We don’t have to be concerned about this, since we already chose the model where there is no need to contemplate time and change. We can simply view the “changed” state of affairs as a different possible world. Each possible world can be considered static.

Physical necessity/contingency would fall under the category of metaphysical necessity/contingency.

That is not very clear. You view “physical existence” as a subset of “metaphysical existence”. Since it is a subset, there might be some things which are “metaphysically possible”, but not “physically possible”. I suspect a problem here, but let’s accept your terminology and continue. One thing is certain: if something is physically possible, then it is also metaphysically possible, and also logically possible. I am sure we can agree on that.

If all you mean by “type-B” is how I’ve defined logical contingency above, then yes.

Yes, we are clear on this.

My entire argument begins with the possibility premise, so it’s not a matter of postponing anything. It’s absolutely vital to establish whether or not it’s possible.

Ok. I will wait for the “meat”, so to speak. In my understanding if something is possible, that means that there is a possible world, where that entity exists. I agree with this.

The term I used wasn’t actually “set,” but “sum total.”

The two terms are interchangable. You speak of complex entites, which may or may not have an external cause for their existence.

Think of a house, which is just the sum total of its parts. Surely the house as a whole has an external cause of its existence, right? Think of a construction company, for example. The external cause is simply an entity not included in the sum total, but which is nevertheless causally related to the sum total.

Not “surely”. Using your example, it is possible that the “house” is not the result of a conscious activity, rather it is the result of some natural process. Think of a neutron, which is the “combination” of a proton and an electron. There is absolutely no need to assume a causative factor for the neutron’s existence. In the house example, there can be a possible world, where the elements of the house just happen to form that structure. Indeed such a state of affairs is extremely unlikely, but we have infinitely many possible worlds, and so this arrangement is possible. I would like to recommend a wonderful piece by Stanislaw Lem. Here is the link: psychadelicbus.tripod.com/mymosh.txt a very deep line of thought.

Besides, I am not happy with dragging “causation” into the picture. All the possible worlds are static, there are is no time, no change, no causation in them. What we would call the result of a causative element is simply a different state of affairs, a different possible world.

 

[punkforchrist]

R Daneel:

The two terms are interchangable. You speak of complex entites, which may or may not have an external cause for their existence.

Often when people use the word “set,” they mean some mathematical collections. My use of “sum total” just emphasizes some concrete collection of interrelated parts. That’s why I gave the example of a house, which is a concrete entity. However, if you’re using “set” in the same way, then that’s fine.

Not “surely”. Using your example, it is possible that the “house” is not the result of a conscious activity, rather it is the result of some natural process. Think of a neutron, which is the “combination” of a proton and an electron. There is absolutely no need to assume a causative factor for the neutron’s existence.

I’m not reading “intelligent design” into its causation. All I’m saying is that these complex entities have a cause of some sort, intelligent or otherwise. The combination that forms a neutron would count as a type of cause.

In the house example, there can be a possible world, where the elements of the house just happen to form that structure. Indeed such a state of affairs is extremely unlikely, but we have infinitely many possible worlds, and so this arrangement is possible. I would like to recommend a wonderful piece by Stanislaw Lem. Here is the link: psychadelicbus.tripod.com/mymosh.txt a very deep line of thought.

Thanks. I’ll take a look at the link. Even if it’s possible for the house to exist by chance alone, the point is that it’s also possible (and highly likely) that it has an external cause. That’s all I’m saying.

Besides, I am not happy with dragging “causation” into the picture. All the possible worlds are static, there are is no time, no change, no causation in them. What we would call the result of a causative element is simply a different state of affairs, a different possible world.

I’m not sure why you want to focus on a static state of affairs. Besides, the whole premise of the MCA is that there is possibly a necessary cause. So, it doesn’t make sense to overlook the issue of causation.

 

[R_Daneel]

Often when people use the word “set,” they mean some mathematical collections. My use of “sum total” just emphasizes some concrete collection of interrelated parts. That’s why I gave the example of a house, which is a concrete entity. However, if you’re using “set” in the same way, then that’s fine.

Agreed. But the “set” is more generic, it may contain either “related” or “unrelated” entities. You said: “Think of a house, which is just the sum total of its parts. Surely the house as a whole has an external cause of its existence, right?”, which indicates that you view the “house” as a set of parts, and you said that such a complex entity must have an external cause for its “structured” existence. I agree, that it “can”, but want to point out that it also can happen that it just exists.

I’m not reading “intelligent design” into its causation. All I’m saying is that these complex entities have a cause of some sort, intelligent or otherwise. The combination that forms a neutron would count as a type of cause.

I understand, but cannot agree that it is meaningful to posit that any and all complex entities must have an external causative factor for their existence. The so-called “elementary” particles are “composed” of quarks, and thus they are complex, but that does not point to any causative factor for their existence.

Thanks. I’ll take a look at the link.

Your time will be well spent. It is a short story, merely a few pages long, but very deep indeed.

Even if it’s possible for the house to exist by chance alone, the point is that it’s also possible (and highly likely) that it has an external cause. That’s all I’m saying.

No doubt. It is extremely likely. But when we talk about possible worlds, we have an infinite amount of possibilities, so not even the most “farfetched” can be excluded - as long as it is logically possible. (Kolmogorov probability space).

I’m not sure why you want to focus on a static state of affairs.

Simply because the concept of “possible worlds” is based on it. The whole idea is to evaluate the all the possible worlds (states of affairs) and find the common element in them, if there is such an element. This is the crux of the whole question.

Now, we could use two models. One is that each state of affairs is static, there is no time and change. In this case the “change or causation” of the affairs is simply represented by another possible world. The other is to examine one possible world, and include the concept of change and get another possible world. The two models are identical, but the static one is much easier to contemplate.

Besides, the whole premise of the MCA is that there is possibly a necessary cause. So, it doesn’t make sense to overlook the issue of causation.

Yes, that is supposed to be the final outcome. Causation is not really overlooked. The comparision of two static possible worlds is the same as contemplating one, changing world.

 

[punkforchrist]

I finally have some free time, so I want to focus on a couple of points:
R Daneel:

Agreed. But the “set” is more generic, it may contain either “related” or “unrelated” entities. You said: “Think of a house, which is just the sum total of its parts. Surely the house as a whole has an external cause of its existence, right?”, which indicates that you view the “house” as a set of parts, and you said that such a complex entity must have an external cause for its “structured” existence. I agree, that it “can”, but want to point out that it also can happen that it just exists.

The “must” is related to the actual world. One may postulate that there is a possible world in which a house just exists inexplicably, but that wouldn’t be the best inference to make in the actual world where we know that construction companies, etc., build houses.

I understand, but cannot agree that it is meaningful to posit that any and all complex entities must have an external causative factor for their existence. The so-called “elementary” particles are “composed” of quarks, and thus they are complex, but that does not point to any causative factor for their existence.

I guess you’re focusing on efficient causality to the exclusion of material causality. Nevertheless, is there anything problematic about postulating a possible world in which an efficient (and external) cause of these quarks exists?

Simply because the concept of “possible worlds” is based on it. The whole idea is to evaluate the all the possible worlds (states of affairs) and find the common element in them, if there is such an element. This is the crux of the whole question.

Now, we could use two models. One is that each state of affairs is static, there is no time and change. In this case the “change or causation” of the affairs is simply represented by another possible world. The other is to examine one possible world, and include the concept of change and get another possible world. The two models are identical, but the static one is much easier to contemplate.

Why do you say that the concept of possible worlds is based on a static set of relationships? The sheer postulation of a construction company having built a house necessitates change and causality. I don’t know why anyone would think an analysis of a static world would make things easier. A world W in which something changes doesn’t result in W becoming ~W. The compossible set of propositions includes tensed facts.

 

[R_Daneel]

I finally have some free time, so I want to focus on a couple of points:

That is fine. No hurry.

The “must” is related to the actual world. One may postulate that there is a possible world in which a house just exists inexplicably, but that wouldn’t be the best inference to make in the actual world where we know that construction companies, etc., build houses.

No doubt. But it has no relevance to the point. We are talking about all possible worlds. This is we must focus upon. The concept of “necessary” or “type-A” existence simply means that an entity exists in all the possible worlds. The “contingent” or “type-B” existence means that the entity exists in some, but not all possible worlds. We are not making “best” inferences.

I guess you’re focusing on efficient causality to the exclusion of material causality. Nevertheless, is there anything problematic about postulating a possible world in which an efficient (and external) cause of these quarks exists?

What could possibly be the “cause” for elementary particles to exist? We can hypothesize almost anything, as long as it does not lead to a logical absurdity. Maybe you wish to hypothesize a world, where the conservation laws do not exist, and matter/energy can be created or destroyed. Or maybe a world where the magnetism works so that like charges attract, and different charges repel each other. None of these are logically impossible, though they are physically absurd. Now the definition of a possible world is a world, which is different from our existing world in some respect. These worlds are not just “different”, they have nothing in common with our existing one. Yet, I do not object. I am wondering however, why did you say that my mini-worlds “might” not be possible? Those mini-worlds are much closer to our existing one, then the far-out ones I brought up.

Why do you say that the concept of possible worlds is based on a static set of relationships? The sheer postulation of a construction company having built a house necessitates change and causality. I don’t know why anyone would think an analysis of a static world would make things easier. A world W in which something changes doesn’t result in W becoming ~W. The compossible set of propositions includes tensed facts.

I don’t suggest that our world is static. Obviously it is not. But that again does not matter for the purposes of this discussion. Take a “snapshot” of our world, and you see a possible world. Take another snapshot a “Planck’s time later” and you see another possible world. These worlds are obviously connected by a causative relationship, but that is neither here nor there. They are two possible worlds - and that is all that matters.

Let’s take a simple example. A world “W” is the collection of three entities, W = {A, B, C}. Some causative factor combines A and B, and you get W’ = {AB, C}. Now these are simply two possible worlds. What the causative factor might have been (external or “built-in”) is irrelevant.

The whole modal cosmological argument hinges on the concept of “type-A” (necessary) existence. The crux of the matter is to establish if such existence is possible. This examination can be done much easier if we concentrate on the “snapshots”.

 

[punkforchrist]

R Daneel:

No doubt. But it has no relevance to the point. We are talking about all possible worlds. This is we must focus upon. The concept of “necessary” or “type-A” existence simply means that an entity exists in all the possible worlds. The “contingent” or “type-B” existence means that the entity exists in some, but not all possible worlds. We are not making “best” inferences.

Right, and I originally gave the example of a construction company just to illustrate how there could be an external cause of something.

What could possibly be the “cause” for elementary particles to exist? We can hypothesize almost anything, as long as it does not lead to a logical absurdity. Maybe you wish to hypothesize a world, where the conservation laws do not exist, and matter/energy can be created or destroyed. Or maybe a world where the magnetism works so that like charges attract, and different charges repel each other. None of these are logically impossible, though they are physically absurd. Now the definition of a possible world is a world, which is different from our existing world in some respect. These worlds are not just “different”, they have nothing in common with our existing one. Yet, I do not object. I am wondering however, why did you say that my mini-worlds “might” not be possible? Those mini-worlds are much closer to our existing one, then the far-out ones I brought up.

The law of conservation of energy holds in the actual world, but only in a closed system. We can overlook this, however, and postulate all kinds of possible worlds. I will get back to explaining why I don’t think your mini-worlds are possible later. First, I just want to establish whether C (where “C” is the sum total of contingent entities in a possible world) possibly has an external cause.

The cause of elementary particles would have to be some kind of transcendent entity. Right now, I’m just focusing on whether C possibly has an external cause of its existence.

I don’t suggest that our world is static. Obviously it is not. But that again does not matter for the purposes of this discussion. Take a “snapshot” of our world, and you see a possible world. Take another snapshot a “Planck’s time later” and you see another possible world. These worlds are obviously connected by a causative relationship, but that is neither here nor there. They are two possible worlds - and that is all that matters.

I’ve never heard this description before. Do you have a source that uses possible worlds in this way?

The way the world is at the present and the way it is a Planck’s time later are both part of the same world. That’s what I mean when I say that tensed facts are part of a possible world.

. . . The whole modal cosmological argument hinges on the concept of “type-A” (necessary) existence. The crux of the matter is to establish if such existence is possible. This examination can be done much easier if we concentrate on the “snapshots”.

The snapshots you allude to exclude causality, so it doesn’t make it easier, in my estimation.

To put the question again: is it possible that C has an external cause?

 

[R_Daneel]

Right, and I originally gave the example of a construction company just to illustrate how there could be an external cause of something.

That is fine. In some cases there can be. In other cases this assumption is not necessary. We have examples of both cases.

The law of conservation of energy holds in the actual world, but only in a closed system. We can overlook this, however, and postulate all kinds of possible worlds. I will get back to explaining why I don’t think your mini-worlds are possible later.

Very well. I can hardly wait.

First, I just want to establish whether C (where “C” is the sum total of contingent entities in a possible world) possibly has an external cause.

Yes, it may be possible, if and only if it can be established that it is even sensible to postulate such a cause. The point is that we must avoid the fallacy of composition. First, let’s define C rigorously. C is a set (or collection) of type-B entities, formally: C = {e1, e2, e3…}. Each of these entitites exist in some possibkle world (but not in all of them). Some of these may be “caused”, some may not be. Second, even if all entities would require an external cause for their existence (which is not true) it still would not establish that causation for the sum of those entities (C) can even be defined. (To postulate that such a causative factor must exist would be the fallacy of composition.) All I can say, that depending upon those entities it may be the case that the causative factor can be defined (or may not be) and if such a causative factor can be defined, then it may be the case that such causative factor exists (or may not be). I am not trying play “hard to catch”. At the level of generality we investigate, there simply cannot be a more definitive answer.

The cause of elementary particles would have to be some kind of transcendent entity.

The trouble is that the assumption of some transcendant entity cannot be assumed at this point. This is supposed to be the final result of the MOA. It would be a fallacy to include the expected final result into one of the premises. So, for the time being we cannot say that the elementary particles can be “caused”. It is not a sensible assumption.

I’ve never heard this description before. Do you have a source that uses possible worlds in this way?

No, I don’t. I am merely presenting my analysis.

The way the world is at the present and the way it is a Planck’s time later are both part of the same world. That’s what I mean when I say that tensed facts are part of a possible world.

It can be viewed as such, certainly. Or it can be viewed as I suggested. Both models stand on their own right.

The snapshots you allude to exclude causality, so it doesn’t make it easier, in my estimation.

No, they do not exclude causality, they just do not concentrate on it, because the possible existence of a possible world can be investigated in and by itself.

One can create all sorts of different models for the same phenomenon. Some models might be easier to investigate than others. Just an example. Suppose we want to investigate die-tosses and the distribution of the results. We can “imagine” one person to toss one die repeatedly, many times (say a thousand times). Or we can “imagine” one person to toss a whole lot of dice (also one thousand) one time. Or we can “imagine” one thousand people all tossing one die. Or ten people tossing one die a hundred times. And so on… the possible models are almost endless. The distrubution pattern is, however, invariant to the model we choose. So we can safely choose the model which is the simplest. And that is what I am doing with the snapshot scenario.

To put the question again: is it possible that C has an external cause?

I gave my answer above.

 

[R_Daneel]

To put the question again: is it possible that C has an external cause?

I will have to amend my previous answer. Building on the definition of “C” above, where “C” is the collection of all type-B entities, I can give a definitive answer now, and tye answer is “not possible”. And this is because an external “cause” cannot be defined.

I explain. When we speak of a subset of “C”, such an external cause can be sometimes defined, and the cause p(name removed by moderator)ointed. Your example of a “house” was a good example for that. The house can viewed two ways, either as a simple entity on its own right, or as a composite entity of its parts (bricks, mortar, etc). Yet, we can easily point to the builder as an exetrnal causative agent.

However, for another composite entity, consider a plant. It can be viewed as one entity, or it can be viewed as a composite of its parts, like stems, leaves, flowers and such. For the plant we cannot say that it has an external causative agent for its existence. There is an internal causative factor, the seed from which it developed. The seed transformed itself into the plant, so it cannot be considered an “external” factor.

So, for a smaller set, a subset of “C”, it may or may not be the case that we can both define, and find an “external” causative agent.

Furthermore, a set can be totally arbitrary, where the individual entities have nothing in common. Example could be a set made up of two entities, an apple, and a sonata. For the members, the apple can said to be “caused” by the apple tree, while the sonata can said to have been caused by the musician. Yet, there is no sensible way even to define a causative factor for the set itself.

Now, going back to your “super set”, C, the set contains all the different entities, and all the different sets of type-B. Since some of the entities and the sets cannot be assigned a “causative” factor, therefore the whole set cannot be assigned to have one, either. So to even speak of a causative factor for C (be it either internal or external) is impossible. As such, the answer is “no”, for the set or collection of all type-B entities, we cannot define (much less find) an external or internal causative factor.