Multiverses and Modal Space

[Playfishpaste]

I am curious what peeps here think about modal realism (the thesis that all possibilities are real, concrete worlds with stuff going on in them which are causally sealed off from other worlds).

It seems to me a multiverse would have to be identical with all of the possible worlds, because otherwise you'd get an actual infinite.

For instance, suppose that W_a is a possible world that is actual, and W_p is a possible world. Suppose that there are four possible worlds:

{W_a,W_p1,W_p2,W_p3}

Now suppose the multiverse is going on in W_a. It is quite plausible that there are an infinite number of possible universes, so there are gonna be an infinite number in W_a. But that means there's an actual infinite! So that's assuradly impossible.

Lemma 1. if the actual world includes the multiverse, then the set of all possible worlds has uncountably infinite states of affairs, and hence has a cardinality equal to ℵ₁.

Proof. Consider the gravitational constant G. Assuming multiple universes, there is always a universe in which the gravitational constant is half what it is in another universe. E.g. there are ℵ₁ universes with distinct gravitational constants. Let x be the number of constants in the actual universe. Now x∈S where S⊂ℕ, given there are finitely many constants. However, there are infinitely many possible worlds for each state of affairs in the actual world, and so for every constant in this universe and every consequent of that constant, there is a possible universe in which that constant holds and at least one thing is different. Hence there are infinitely many worlds for every constant. All of the sets specified here are countable except the one specifying the number of universes with different gravitational constants, so the set of them is uncountable. Eg. the cardinality of the set of possible worlds is equal to ℵ₁.

But the cardinality of the set of possible worlds isn't uncountably infinite if the multiverse is a part of the actual world. It's not even four, which we generously granted earlier. In fact, the set only would have one member, the actual world, since all possibilities are supposed to be realized in the multiverse.

Hence, I contend the multiverse has got to just be the same thing as the set of all possible worlds, or modal space. However, I think that means that the multiverse really doesn't exist, or at least it's not a concrete object. Why? Well:

Axiom 1. A concrete object must stand in causal relations with other objects.

Lemma 2. If the multiverse is concrete, its members are concrete.

Proof: Immediate.

Lemma 3. If the multiverse is the set of possible worlds, its members are not concrete.

Proof. A possible world cannot interact with its members or other possible worlds. Since these are the only objects available to interact with, it is not itself concrete.

Ergo:

Theorem 1. The multiverse is not concrete.

Proof. Immediate.

What if that's just not convincing? Well there are other reasons for thinking modal space doesn't really exist or is just abstract. But they themselves are rather abstract. For instance, what is modal space? Is it a state of affairs? If so shouldn't it be a member of some possible world? If it is, then by definition, the set of all possible worlds is a member of itself.

That doesn't seem to work. Thoughts?

[Veliky Kaiser Theos]

I don't agree with the first lemma, as there is an infinite amount of variations in the way you do that thing. E.g. If you are talking, the specific wavelength or frequency at a moment has an infinite amount of possibilities.

[Playfishpaste]

I don't understand. Are you saying it's uncountably infinite? The only way that could be the case is if it contained a set which was uncountably infinite, but the proof seems to show it does not.

[Veliky Kaiser Theos]

I'm saying that you can endlessly divide certain variables into smaller amounts, giving an infinite amount of possibilities.

[Playfishpaste]

I'm saying that you can endlessly divide certain variables into smaller amounts, giving an infinite amount of possibilities.

Well if I understand what you mean correctly (in the sense of multiplying the number of pencils or the size of the universe), I pretty much agree, but I don't see how this affects things (lemma 1 is saying there are an infinite amount of possible worlds).

[visser300]

Does anybody here even speak English?

[Jack04]

I've never been particularly keen on the concept of multiverses in this form, but I do wonder about the concept (on occasion). The problem with your argument, as I see it, is that there need not be an actual infinite in the case of (for example) you holding the pencil. All that is required is a number of universes in which every possible event can occur. Which might be a pretty enormous number, but need not be infinite.

So, in:

It is quite plausible that there are an infinite number of possible universes, so there are gonna be an infinite number in Wa.

I'm not sure if it is plausible for an infinite number of universes. An impossible to comprehend quantity perhaps, but not infinite. Every universe only has so many particle combinations it can make.

Although I believe (its been a while since I've read about this) that the guy who proposed this (Lewis, Google tells me) actually mentioned a similar issue in the critique of his own creation?

As I say, I'm not overly bothered about the idea (and its been a while since I read about it), so I'm afraid I can't (and wouldn't) make much of a counterargument to your point. When it comes to this kind of thing, I much prefer the many-worlds quantum example, at least then you get quantum immortality...

[Playfishpaste]

Indeed, the pencil example is bad because it doesn't illustrate the plausibility of an infinite amount.

I've switched the proof to one dealing with different real values of G (the gravitational constant).

As to MWI, I don't think that gets you a distinct result. Namely that for every event, there exists a universe in which an outcome of that event obtains which has a probability greater than 0.

[Imperial Glory]

Why can't there be an infinity?

[Gordon Freynman]

Why can't there be an infinity?

Because hit hurts most people's brains to think about so they just try to hand wave it away.

[Legourou]

Everyone seems to look over the most wild and exciting of the implications of the Multiverse.

If there really are unlimited amounts of universes each with unlimited amount of possible properties, no one ever thinks that somewhere out there, there's an infinite amount of World of Warcraft universes. Or of Lord of the Rings Universes.

In fact, there is a universe out there right now where I am the emperor of the largest, oldest, richest, most technologically savvy, intergalactic empire.

Fascinating. Now, how do I get there? That's another mystery. :S

[Armatus]

I think, but am not sure that the answer might lay with 'time'

If there are multiple quantities of possibilities for every waking moment in time then the universe not only exists in parallel to other possible and similar like universes, but they proceed and succeed each other in time.

As in sci-fi stories where time travelers never know what type of future they will end up in or who travel back and alter the course of the future (present time).

Reality for us could be a collage of snapshots interconnecting everything in time forward and backwards. It really only maters to whoever is looking at them and following the story.

So if it's possible to go into the future or into the past then I think we can prove that the multiverse exists. For example, in the past could they have proven that some day we would exist in the present? No yet here we are just one more link in the chain of events and we exist separately from that which came before.

I really don't know anything about the topic, just find it an interesting subject.