Plantinga's ontological argument

Originally posted by twhitehead
Am I right that the argument is essentially nothing more than an unsupported assertion that every possible world contains a "maximally excellent" being and all the rest is just smoke and mirrors?

Yeah, pretty much. 🙂

Originally posted by SwissGambit
I'm going to skip the premise 1 stuff because we're both rejecting it now.

If there are a finite number of 'worlds' existing for a finite time then it is perfectly possible (in fact inevitable) that not all possible things will
happen.

I am thinking of the term 'possible worlds' in a philosophical sense, meaning something like 'possible ...[text shortened]... including all the branches. Whether that tree is infinite or not is another argument. 🙂

Then we are using different meanings of the term 'worlds' and it needs to be pinned down and defined so we
all know what we are talking about.

Originally posted by googlefudge
Then we are using different meanings of the term 'worlds' and it needs to be pinned down and defined so we
all know what we are talking about.

I provided the meaning I was using on page 1 and again on page 4.

Originally posted by SwissGambit
I provided the meaning I was using on page 1 and again on page 4.

Ok premise 2 states this...

2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

Now if you are going to define 'possible world' as being any possible description of reality, and you for the moment accept premise one...

Then it is true that as it's possible for an MEB to exist then it must be included in the set of 'all possible things that can happen '
and thus will 'exist' in one or more possible worlds...


However this is a trivial and meaningless tautology.

You are specifying that a possible thing exists in the set of all possible things.


However even in the event that we do live in a multiverse and there is more than just this one reality. It is an open question as
to whether all possible worlds/realities exist or just a finite subset (or even infinite subset) of those possible worlds/realities exist.


So even if you do allow that it is possible in some description of reality for an MEB to exist (which needs to be supported with evidence)
you can't just assume that all possible worlds/realities actually exist.

To claim as premise 2 does that an MEB exists in some possible world you must demonstrate that that possible world exists as well.


Something that exists only in an imaginary world does not in fact in any real way exist.


Otherwise premise 2 is guilty of the formal logical fallacy of 'begging the question'.
The argument is assuming the existence of the possible worlds when it states that "a maximally great being exists in some possible
world.". If the world doesn't exist then neither does anything in it or dependent on it.

Originally posted by SwissGambit
I provided the meaning I was using on page 1 and again on page 4.

You did. It would be good if the 5 step argument used "possible description of reality" instead of "possible world." This would require some rewording of the argument. It shows a flaw under this definition.

Here is just a rough pass at rewording to accommodate the definition you gave:

1. It is possible that a maximally great being exists. (This is not a statement that includes "possible world" so, no rewording is to be done.)

2. If it is possible that a maximally great being exists, then* a maximally great being exists in some possible world. (*This would be, "...then a description of reality possibly includes the statement that what is real has a MGB." )

3. If a maximally great being exists in some possible world, then it exists in every possible world. (This would require that every possible description of reality include a statement that it has an MGB, and not only that, that it has the same MGB as the one referenced in all descriptions of reality.)

Manifestly it is possible that a description of reality not include such a statement. For example a statement can be "In reality X, all B's are equal in greatness." Or they might be lacking in any greatness. This shows what happens when the definition you provide is used.

4. If a maximally great being exists in every possible world, then it exists in the actual world. (This says, if a possible description of reality includes the statement that it has an MGB, then all possible descriptions of reality necessarily include that statement. But as above, a contrary example can be given without the sky falling.)

5. If a maximally great being exists in the actual world, then a maximally great being exists. (This tautology is not about possible worlds as defined.)

Thus, the MGB cannot be defined into existence by enforcing the implications of one PW upon another PW.

Originally posted by SwissGambit
What threw me is that your first post started out with...'there is no fork in the road [with respect to god's existence] ... and thus no reason to divide reality into two worlds' (paraphrased) but then changed to 'the only valid application of the many worlds concept is if one world has god existing and the other does not' (paraphrased again), i.e., ther attempt to have them clarify that which they purposefully leave vague.

Thanks for working on my argument like this. Trouble is there are a lot of distinct points in your post for me to answer. Ah well. I'll take them out of order if you'll forgive me.

I see no problem with limiting the scope of God's power - for example, I don't think omnipotence includes the ability to do the logically impossible. Maybe there are certain laws of physics that are brute facts and cannot be changed, even by God.

Neither do I if you are content that the investigation of God may lead to discovering a God that bears no relation to the one promoted by a given religious belief. As remarked in a different thread, what happens to a Christian who dies and discovers that there is a God but it is the wrong one and after a lifetime of devout religious practice and devotion, he is damned for getting it wrong? However, I work from the reasonable suggestion that people arguing in favour of God's existence are usually trying to prove the truth of what they already believe. I do not hang my argument on this issue however and we can treat is as an aside.

I take exception to the idea that it is critical that scientists would not accept certain logical steps in a philosophical argument. This is borne of the fallacy that science is the ultimate authority on everything. [Indeed, I wish someone would remind Richard Dawkins of this when he is tempted to make some of his bad philosophical arguments.]

I understand your remark about Dawkins but I admire his writing. I do not agree or disagree with your comment about Science because I think you misunderstand my point. I do not make the crass assertion implied here.

Well, this debate is a philosophical one, not scientific.

Ah but is that exactly right? My contention is that there is something going on when Plantinga deploys his ontological argument in this form and I suggest that what he is doing is attempting to use a scientific tool in aid of a religious or philosophical argument. In other words, it seems to me, especially in the context of this forum, that people who support science were being challenged to say why a scientific sounding argument in support of God was defective. That is certainly what I set out in my first post. For this reason, I thought it was interesting to ask the question - how do scientists use the possible world concept in support of their arguments, and I gave the example earlier of its use in support for the theory of evolution in the face of its apparent improbability.

I am fully aware of course that philosophers quite like this tool and have taken to expressing propositions in the form "There is a possible world in which ....." But what gives this form of words any serious weight whatever, if it is not claiming to be or representing itself to be an application of the many worlds concept?

The concept of 'possible worlds' in philosophy can be thought of as 'possible descriptions of reality'. This provides some latitude in the way possible-reality is divided.

Yes, in this sense it is reasonable to talk in terms of possible worlds, providing you accept that this is no more than a language convention, an acceptable phrasing to which philosphers are accustomed. The only word that matters though is the word "possible" while the additional word "world" has no additional significance, except perhaps as a way to summon up a mental image. "There is a possible world in which I win a game of chess" is not different to saying "it is possible that I will win a game of chess" except that it conveys rather artistically the implication that that possible world is far away and long ago.

Maybe an example will help. I define a set of possible worlds, W consisting of the years 1962 to 1992, sliced into years - a set of 31 years. Now, the set obviously has properties that are true in all members of the set - The nation of the USA existed, televisions existed, television programs existed, The Tonight Show existed and its official host was Johnny Carson, etc. I don't need to consider other worlds in which, say, the nation of the USA never existed, because they're simply out of scope.

I have no difficulty at all with asserting whatever property you wish to regarding any set whatever that you wish to label "all possible worlds" nor with the idea that, with a carefully defined set, that assertion can be a true one or one that is capable of being tested for its truth (even though I have never experienced a show presented by Johnny Carson). It is no more than an assertion and it is one in which the reference to possible worlds plays no logical or functional role whatever, except as a descriptive term. In particular, the possible worlds notion does not help or hinder a decision regarding the validity or truth of the assertion. It is redundant.

I'm not a big fan of the multiverse theory. I think it is the result of succumbing to a devious ex-ante probability argument from the ID crowd. Niall Shanks deals with this in his book God, the Devil, and Darwin. The multiverse hypothesis might be dubbed Occam's hair-restorer [the embodiment of needless multiplication of entities], the creator-God hypothesis has one needless entity [God himself], while one-universe-by-chance emerges as the clean-shaven alternative.

The book title you reference looks rather dodgy to my taste. Sadly, an excellent book which I read a few months ago on this subject is in the possession of my daughter's partner, an absent minded mathematician, so I rely a on distant memory. Google seems to have an awful lot of problems activating the links I wished to pursue, reinforcing my paranoid fear that Google has been bought up by the American Right. (Don't answer that remark. It's a joke. Maybe.) However, Wikipedia comes to the rescue including a response to your comment about Occam's Razor which I have cut and pasted below.

Critics argue that to postulate a practically infinite number of unobservable universes just to explain our own seems contrary to Occam's razor.[19]

Max Tegmark answers:

"A skeptic worries about all the information necessary to specify all those unseen worlds. But an entire ensemble is often much simpler than one of its members. This principle can be stated more formally using the notion of algorithmic information content. The algorithmic information content in a number is, roughly speaking, the length of the shortest computer program that will produce that number as output. For example, consider the set of all integers. Which is simpler, the whole set or just one number? Naively, you might think that a single number is simpler, but the entire set can be generated by quite a trivial computer program, whereas a single number can be hugely long. Therefore, the whole set is actually simpler. Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution. The former is described by a few equations, whereas the latter requires the specification of vast amounts of initial data on some hypersurface. The lesson is that complexity increases when we restrict our attention to one particular element in an ensemble, thereby losing the symmetry and simplicity that were inherent in the totality of all the elements taken together. In this sense, the higher-level multiverses are simpler. Going from our universe to the Level I multiverse eliminates the need to specify initial conditions, upgrading to Level II eliminates the need to specify physical constants, and the Level IV multiverse eliminates the need to specify anything at all."

He continues:

"A common feature of all four multiverse levels is that the simplest and arguably most elegant theory involves parallel universes by default. To deny the existence of those universes, one needs to complicate the theory by adding experimentally unsupported processes and ad hoc postulates: finite space, wave function collapse and ontological asymmetry. Our judgment therefore comes down to which we find more wasteful and inelegant: many worlds or many words. Perhaps we will gradually get used to the weird ways of our cosmos and find its strangeness to be part of its charm."[4]

As you will see from the list of multiverse theories in Wikipedia, the many worlds theory is just one from the list and has very specific application to discussing events with more than one possible outcome. Of course, I have used the term"possible worlds" instead of "many worlds" and in that respect I need to correct myself now. In my view, when Plantinga attempts to argue that there is a possible world in which ... in order to make an assertion about what is, rather than a remark about what is possible, then it is this concept that he is invoking since otherwise he would have no ground for making such a move. From this the rest of my argument follows.

'the only valid application of the many worlds concept is if one world has god existing and the other does not' (paraphrased again), i.e., there must be at least a fork (if not a branch) in the road with respect to god's existence. This strikes me as contradictory and I should have asked for a clarification before proceeding.

I need you to tell my why my claim is contradictory. I consider that I am just referring back to the many worlds theory and saying that, if this is to be used in a way that is explanatory or significant, rather than just as a descriptive turn of phrase, then it cannot avoid splitting reality into two alternative worlds, in one of which there is a God and the other of which there is not a God. Here also is the reason why I refer to a fork in the road.

Originally posted by googlefudge
Ok premise 2 states this...

2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

Now if you are going to define 'possible world' as being any possible description of reality, and you for the moment accept premise one...

Then it is true that as it's possible for an ME ...[text shortened]... If the world doesn't exist then neither does anything in it or dependent on it.[/i]

Then [Premise 2] is true that as it's possible for an MEB to exist then it must be included in the set of 'all possible things that can happen '
and thus will 'exist' in one or more possible worlds...

So far, so good...

However this is a trivial and meaningless tautology.

No - a tautology is an expression that evaluates as true no matter what combination of inputs it has. "If A then B" evaluates to false if A is true and B is false, so it's not a tautology.

...you can't just assume that all possible worlds/realities actually exist.

No one is.

To claim as premise 2 does that an MEB exists in some possible world you must demonstrate that that possible world exists as well.

Not so - if I roll a die, I have 6 possible worlds but only one real outcome. [I think 'exists' is the wrong word here - feel free to clarify if needed.]

Something that exists only in an imaginary world does not in fact in any real way exist. Otherwise premise 2 is guilty of the formal logical fallacy of 'begging the question'.

The formal logical fallacy is "A is true because A is true". Premise 2 is of the form "If A then B". As I understand it, even "If A, then A" is NOT Begging the Question [but it is a tautology] because A is not actually asserted to be true. LJ can correct me if I'm wrong. 🙂

Originally posted by JS357
You did. It would be good if the 5 step argument used "possible description of reality" instead of "possible world." This would require some rewording of the argument. It shows a flaw under this definition.

Here is just a rough pass at rewording to accommodate the definition you gave:

1. It is possible that a maximally great being exists. (This is not a ot be defined into existence by enforcing the implications of one PW upon another PW.

3. If a maximally great being exists in some possible world, then it exists in every possible world. (This would require that every possible description of reality include a statement that it has an MGB, and not only that, that it has the same MGB as the one referenced in all descriptions of reality.)

The word 'it' is confusing. My guess is that Plantinga is referring to the concept of MGB and not specifically the same one.

It's true that you can come up with a description of reality that involves no maximal greatness. But, as explained earlier, I can go from "possibly MG" to "possibly necessarily ME" to "necessarily ME" to ME = true under the axioms of S5. ME is now instantiated in every possible description of reality, and thus, so is MG. Yes, I know. I had the same initial reaction to Premise 3. But it's valid under S5. Them's the rules.

4. If a maximally great being exists in every possible world, then it exists in the actual world. (This says, if a possible description of reality includes the statement that it has an MGB, then all possible descriptions of reality necessarily include that statement. But as above, a contrary example can be given without the sky falling.)

No - it says that, if every possible description of reality includes the statement that it has an MGB, then MG exists. Premise 4 is trivially true.

The hard thing [at least for me] to realize is that the damage has already been done in Premise 1. This is because the S5 trick I showed has already happened in P1. But, as you say, clearly it is possible that no maximally great being exists. Conclusion: We should not accept P1.

Originally posted by SwissGambit

3. If a maximally great being exists in some possible world, then it exists in every possible world. (This would require that every possible description of reality include a statement that it has an MGB, and not only that, that it has the same MGB as the one referenced in all descriptions of reality.)

The word 'it' is confusing. My guess is s possible that no maximally great being exists. Conclusion: We should not accept P1.

It's true that you can come up with a description of reality that involves no maximal greatness. But, as explained earlier, I can go from "possibly MG" to "possibly necessarily ME" to "necessarily ME" to ME = true under the axioms of S5. ME is now instantiated in every possible description of reality, and thus, so is MG. Yes, I know. I had the same initial reaction to Premise 3. But it's valid under S5. Them's the rules.

I wonder if there is, then, under S5, anything more expressed in "ME=true" than is expressed in "possibly MG" and where that alteration in content/meaning comes from. Is the "possibility of MG implies actuality of MG" entirely due to the putative attributes of the possible MG? Can other putative entities benefit from this bootstrap process?

The hard thing [at least for me] to realize is that the damage has already been done in Premise 1. This is because the S5 trick I showed has already happened in P1. But, as you say, clearly it is possible that no maximally great being exists. Conclusion: We should not accept P1.

I'm not so sure P1 is the culprit, although it introduces a notion that is equivocated in P2.

1. It is possible that a maximally great being exists.

This is not a PW statement, so it does not fall to the definitional problem of PW.

2. If it is possible that a maximally great being exists, then* a maximally great being exists in some possible world. (I commented: *This would be, "...then a description of reality possibly includes the statement that what is real has a MGB." )

The definitional problem of P2 is that saying a being exists in a PW is, by the definition you provided, saying that there is a description of reality that includes the statement that there is a MGB. Of course there can be a statement like that. But it is not valid to equivocate between "There is a statement that there is a MGB in a PW" (which is the same as 'A MGB is possible"😉 and "there is a MGB in a PW." The latter IS the statement. No progress is made by acknowledging that there is this statement.

If stating that there is a MGB in a PW is enough under S5 to imply that "MGB=true" then I'd say S5 is not the analytical system to use, or it is misunderstood.

Originally posted by twhitehead
So, can we say that the me of today is in any way identical to the five year old you? (since we are both human beings). If not, then the connection surely has more to do with continuity with this universe (possible world). So how can I be said to be connected to a being in another possible world that is very similar but not identical? Based on what proper ...[text shortened]... from the 'God' of another possible world in all respects except the key defined properties?

So, can we say that the me of today is in any way identical to the five year old you? (since we are both human beings).

No, I would not think so. Those two beings may be similar in many respects (such as both being human), but they are neither numerically nor qualitatively identical.

So how can I be said to be connected to a being in another possible world that is very similar but not identical? Based on what properties? If, in another possible world there are two beings that each differ from me by 1%. Are they both me? Is neither of them me? Would there be a connection between the five year old me in this world and the five year old me in another world even if they are very dissimilar although at 40 we are now near identical?

These are good questions, but I am not sure I am in a position to answer them. I think this discussion would touch on the ontological status of possible worlds, which I find to be a very complicated subject. To tell the truth, I am not exactly sure what Plantinga's stance would be on that. By the way, are you familiar with modal realism? Are you a modal realist? I ask because some of your discussion on possible worlds strikes me as hyper realist, but I could be mis-interpreting you.

At any rate, mostly what I was trying to point out with the numerical/qualitative distinction is that I think your earlier argument was confused. The way I interpreted your claim (top of page 3) was that, basically, two beings cannot be identical with each other if they are not exactly similar in virtually all respects. But that is false, since failing to be exactly similar rules out being qualitatively identical, but not numerically identical. And It seems to me that numerical identity is actually the relevant one here, since it is definitionally concerned with multiple things being actually one and same. If, for example, Plantinga is committed to multiple beings in different possible worlds being identical with each other, as in one and the same being, (and I am not saying that he is, but if he is&hellip😉 then presumably what he needs is some account of their numerical, not qualitative, identity. I guess that was basically my point.

Originally posted by JS357
"So, being identically specified in all respects should not be considered necessary for saying that twhitehead is the same person he was a day ago. Why should it be considered necessary for saying B1 and B2 are the same being?" (In W1 and W2.)

Because PW theory is a conceptual construct or system, it is up to its users to decide this. There can be differing ...[text shortened]... g non-identity across worlds is that two worlds sharing an object may collapse to one world.😉

Yes, I pretty much agree with you here.

Originally posted by googlefudge
In physics there is a distinction between things that might be possible, "possibly possible" as you put it.
And things that are known to be possible.

Let me put it this way...

There things that are known to be impossible, as they violate known and verified laws of physics.

There are things that are known to be possible, That have been observed th there being a difference, and an important one, between possible, and possibly possible.

There things that are known to be impossible, as they violate known and verified laws of physics.

There are things that are known to be possible, That have been observed and are allowed by the laws of physics.

And there are things that may or may not be possible and we just don't know yet.


(&hellip😉

So I will stick with there being a difference, and an important one, between possible, and possibly possible.

As far as I can tell, your argument does not show that there is any difference (let alone an important one) between possible and possibly possible because your argument seems to rest on a mistake. The mistake is to assume that "X may or may not be possible and we just don't know yet" translates to "X is possibly possible". But I see no reason to think it so translates. Unknown modal status should translate more to "either possibly X or necessarily not-X", which is rather trivial.

Let p(X) signify possibly X and let n(X) signify necessarily X, and let ~X signify not-X.

You first state that there are some things known to be impossible. Okay, this means there are A such that ~p(A), or equivalently, n(~A). Then you state that some things are known to be possible. Okay, this means there are B such that p(B), or ~n(~B). Then you say there are some things for which you do not know the modal status. If anything, that should translate to ?(C), or as I said maybe it translates to {either p(C) or n(~C)}. Do you mind explaining how you infer from this to p(p(C))?!? If you cannot do it, then instead of p(p(C)) not collapsing to p(C), what you are actually saying is that {either p(C) or n(~C)} does not collapse to p(C). But that is somewhat trivial and does not give us any reason to reject S5.

If you are intent on dismissing S5 (S4 too, for that matter), I think you'll need a different argument because this shows nothing in my opinion. Also, how far exactly do you intend to go with the non-collapsable repetition of modal operators? In your opinion, does p(p(p(p(p(p(p(p(p(p(p(p(p(X))))))))))))) collapse to anything, or do you simply have to trudge through every iteration?

Originally posted by googlefudge
Right now S5 Modal logic is striking me as a big pile of useless nonsense that bares no resemblance to reality.


There is a difference between 'possibly possible' and 'possible' and failing to recognise that difference is in
my view inane.


The point of this argument is supposed to be to demonstrate that an actual god [MEB] actually exists in t ...[text shortened]... argument.


Thus S5 Modal logic absolutely can't be used in debating this argument.

See my previous post. Your rejection of S5 seems to rest on an argument that is flawed.

Anyway, what kind of axiom would you propose to govern the iteration of modal operators, if any?

Originally posted by JS357
[quote]It's true that you can come up with a description of reality that involves no maximal greatness. But, as explained earlier, I can go from "possibly MG" to "possibly necessarily ME" to "necessarily ME" to ME = true under the axioms of S5. ME is now instantiated in every possible description of reality, and thus, so is MG. Yes, I know. I had the same init d say S5 is not the analytical system to use, or it is misunderstood.

I wonder if there is, then, under S5, anything more expressed in "ME=true" than is expressed in "possibly MG" and where that alteration in content/meaning comes from. Is the "possibility of MG implies actuality of MG" entirely due to the putative attributes of the possible MG? Can other putative entities benefit from this bootstrap process?

I think if there is any trickery or whatnot going on here, it does not have to do with S5 itself. I think it has to do with MG being not just any property, but a world-indexed property; or it has to do with the conjoining of world-indexed properties and S5. It is rather nifty though: just let MG be equivalent with n(ME), and you get

p(MG) -> p(n(ME)) -> n(ME) -> MG. Ta-da!

If stating that there is a MGB in a PW is enough under S5 to imply that "MGB=true" then I'd say S5 is not the analytical system to use, or it is misunderstood.

I also have quite a bit of skepticism that S5 is appropriate when dealing with world-indexed properties, such as in this argument. However, I am quite confident that even if we stick to S5 here, Plantinga's argument fails, for reasons already described.

Originally posted by finnegan
Thanks for working on my argument like this. Trouble is there are a lot of distinct points in your post for me to answer. Ah well. I'll take them out of order if you'll forgive me.

[quote] I see no problem with limiting the scope of God's power - for example, I don't think omnipotence includes the ability to do the logically impossible. Maybe there are also is the reason why I refer to a fork in the road.

You're welcome. Thanks for working with me on this argument.

However, I work from the reasonable suggestion that people arguing in favour of God's existence are usually trying to prove the truth of what they already believe.

That's probably true in a lot of cases, but according to the Stanford website, Plantinga himself does not believe this argument is conclusive proof of God's existence. He is content with the idea that it shows belief in God to be rational.

My contention is that there is something going on when Plantinga deploys his ontological argument in this form and I suggest that what he is doing is attempting to use a scientific tool in aid of a religious or philosophical argument.

I don't see it that way at all...but I'll elaborate more later.

I am fully aware of course that philosophers quite like this tool and have taken to expressing propositions in the form "There is a possible world in which ....." But what gives this form of words any serious weight whatever, if it is not claiming to be or representing itself to be an application of the many worlds concept?

Before I compare weightings, I'd like to know which many-worlds hypothesis is in play...is it the Multi-World interpretation from QM? The Multiverse theory from Cosmology?

"There is a possible world in which I win a game of chess" is not different to saying "it is possible that I will win a game of chess" except that it conveys rather artistically the implication that that possible world is far away and long ago.

I don't see why 'possible world' should convey the idea that something happened long ago...but it does sound sort of far-away. If I heard the former statement, I'd be tempted to think that the speaker had not yet won a game of chess in his life and was desperately trying to convince himself not to give up the game - to keep seeking that elusive first victory. 🙂

The goal of my Tonight Show example was very modest - I was just making sure you agreed that a set of possible worlds is not invalidated because some entity exists in every member of the set. Mission accomplished...

I found Shanks' book to be a very interesting read, even if I did not agree with everything in it. He's a biologist and not a cosmologist, so the cosmology stuff should be treated more skeptically [it did lead me to other writing on the subject, which was immensely helpful in clearing up some of the mistakes and misconceptions].

For example, consider the set of all integers. Which is simpler, the whole set or just one number? Naively, you might think that a single number is simpler, but the entire set can be generated by quite a trivial computer program, whereas a single number can be hugely long.

I have programmed for a living, so I get the idea that sequences with recognizable patterns are easier to generate than purely random ones. See http://www.scholarpedia.org/article/Algorithmic_information_theory
The information content or complexity of an object can be measured by the length of its shortest description. For instance the string

"0101010101010101010101010101010101010101010101010101010101010101"

has the short description "32 repetitions of '01'", while

"1100100001100001110111101110110011111010010000100101011110010110"

presumably has no simple description other than writing down the string itself.

However, I'm afraid I'm going to have to remain 'naive' for now. The simplest C program to output the number 1 is

printf("1" );

...while the simplest C program to output an infinite set of integers is:

for(int x=0, int y=-1; ; x++, y--) {
printf("%d %d ", x, y);
}

...so I can't see how generating a single number requires a longer computer program than one that generates the whole set of integers. Presumably, I must be 'breaking the rules' by giving the first program the number 1 as an input, but if I'm not allowed to give any such arbitrary input to the first program, then I also cannot tell the integer set generator where to begin. 🙂

I get where he is going with the idea of algorithmic complexity, but I need some proof that these various levels of Multiverses are actually less computationally complex, as well as some explanation as to how so many worlds could all exist (at the same time?!)

In my view, when Plantinga attempts to argue that there is a possible world in which ... in order to make an assertion about what is, rather than a remark about what is possible, then it is this concept that he is invoking since otherwise he would have no ground for making such a move.

I don't think so. I see nothing in P's argument that requires a Multiverse hypothesis of any kind. The argument would remain unchanged even if there is only one actual universe and one actual description of reality. Philosophically speaking, there is nothing in the idea of possible worlds/descriptions of reality that says that all the 'worlds' must actually exist.

I need you to tell my why my claim is contradictory. I consider that I am just referring back to the many worlds theory...

I don't think Plantinga is using or is committed to the many-worlds theory, so I'll stop here.