Possible worlds

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04 Jun 2010, 5:55 pm

http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
http://arxiv.org/abs/0709.4024

Tegmark's idea resonates with me quite strongly. When I first read Lewis' wonderful book On the Plurality of Worlds, it occured to me that there could be a kind of ersatzism that he didn't consider: something I would call 'mathematical ersatzism'. I was already a mathematical realist, so I thought that maybe mathematical objects could be the possible worlds. I'm not aware of any philosophers who've talked about 'mathematical ersatzism', so in the absense of any criticism of the view, I decided to adopt it.

But, I soon realized that there was a problem. I believe that some mathematical ersatz world represents this world completely, even down to the conscious beings inside it. I also believe that these mathematical objects really exist independant of the mind (that's part of why I considered mathematical ersatzism reasonable in the first place). So: why assume, as I did, that we're in the one concrete world, when there's a near infinity of purely mathematical worlds that I also believe in, and that from the insider's perspective would be indistinguishable from our own? Mathematical ersatzism seems to collapse into 'mathematical modal realism'.

I rejected mathematical modal realism as just as, if not more, ridiculous than Lewisian modal realism, but seeing somebody else (Tegmark) defend a very similar claim has started to push me towards it again. It occurs to me to now that mathematical modal realism doesn't result in the 'incredulous stare' that Lewisian modal realism animates (at least, it doesn't for me). Lewis elevated possible worlds to the same special status as our own. Mathematical modal realism, however, grounds modal realism in the claim that there's nothing metaphysically special about this world. If you're already a mathematical realist, then I'm not suggesting that you add any new entities to your ontology - rather, I'm deflating the status of this world. This world is just a mathematical structure, and so are all the other worlds.

Just a random thought I've been entertaining. Probably nonsense, but I might as well post it here.

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ruveyn
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04 Jun 2010, 6:01 pm

you_are_what_you_is wrote:

A Possible World is a world whose nature does not imply a logical contradiction. Any collection of non-contradictory statements is Possible although not necessarily True.

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04 Jun 2010, 6:06 pm

ruveyn wrote:

A Possible World is a world whose nature does not imply a logical contradiction. Any collection of non-contradictory statements is Possible although not necessarily True.

ruveyn

I'm not sure what point you're trying to make.

Lewis argued that possible worlds are as real as this world, a view he called modal realism. In his book, On the Plurality of Worlds, he outlines then criticises a few different ways of understanding possible worlds. These are all versions of ersatzism, which holds that possible worlds are abstract objects of some kind.

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Flair
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04 Jun 2010, 6:18 pm

From a dualist (I hold a dualist metaphysical perspective) perspective dreams allow multiple universes to interlap with each other. Other than that the concept of interacting with other universes is currently impossible thus the existence of a separate universe is unlikely.

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04 Jun 2010, 6:25 pm

you_are_what_you_is wrote:

ruveyn wrote:

A Possible World is a world whose nature does not imply a logical contradiction. Any collection of non-contradictory statements is Possible although not necessarily True.

ruveyn

I'm not sure what point you're trying to make.

The Possible need not be Actual.

A world which is just like the one we live in but in which I did not make this post, is Possible. But it is not the actual world we live in.

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04 Jun 2010, 6:25 pm

Flair wrote:

Other than that the concept of interacting with other universes is currently impossible thus the existence of a separate universe is unlikely.

Since Lewis argued that all worlds are spatiotemporally and casually isolated, then for him, interacting with those other worlds will always be impossible. He never claims that we should believe in them because we have empirical evidence of them. This does not mean there are no reasons to believe in those other worlds.

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04 Jun 2010, 6:31 pm

ruveyn wrote:

The Possible need not be Actual.

A world which is just like the one we live in but in which I did not make this post, is Possible. But it is not the actual world we live in.

ruveyn

There's no disagreement from me, or Lewis, on that point.

Lewis denies that the possible worlds are actual by claiming that actuality is indexical. On this view, just because a world isn't the actual world, that doesn't mean it doesn't exist. It's just not the world that we're part of.

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04 Jun 2010, 7:28 pm

you_are_what_you_is wrote:

Flair wrote:

Other than that the concept of interacting with other universes is currently impossible thus the existence of a separate universe is unlikely.

Since Lewis argued that all worlds are spatiotemporally and casually isolated, then for him, interacting with those other worlds will always be impossible. He never claims that we should believe in them because we have empirical evidence of them. This does not mean there are no reasons to believe in those other worlds.

If interacting with them is always impossible, how is that different from multiple universes simply not existing?

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04 Jun 2010, 8:45 pm

Flair wrote:

If interacting with them is always impossible, how is that different from multiple universes simply not existing?

I'm sorry? I think I may be misunderstanding you. Are you saying that the existence of other possible worlds is contingent upon whether or not humans interact with those worlds?

Anyway, just because we can't interact we them, doesn't mean they aren't useful.

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04 Jun 2010, 8:54 pm

I tend to value these kinds of theories by what it is that they explain. For example, I always thought of (actualist) theories of possible worlds as explaining the status we intuitively give to the ways things could have been - possible worlds exist in the sense that other possibilities exist, as I speak of and understand them. So: what would this sort of mathematical modal realism explain?

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04 Jun 2010, 9:15 pm

Hector wrote:

For example, I always thought of (actualist) theories of possible worlds as explaining the status we intuitively give to the ways things could have been - possible worlds exist in the sense that other possibilities exist, as I speak of and understand them.

They can be used to explain a lot more than that, too.

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So: what would this sort of mathematical modal realism explain?

Not much more than what's already out there. 'Mathematical modal realism', as I'm thinking of it, isn't a whole lot different from Lewisian modal realism. But Lewis was aware that the ontological cost of his modal realism is very high, and - if you're already a mathematical realist, as I am - mathematical modal realism vastly reduces that cost. It also seems to be more compatible with the discoveries of quantum physics, at which level, as far as I'm aware, matter simply stops behaving in any way we could intuitively understand it and can only be described by mathematics.

As I said, though, this is probably just nonsense. I don't take it too seriously myself - at the moment, anyway.

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04 Jun 2010, 9:21 pm

you_are_what_you_is wrote:

Flair wrote:

If interacting with them is always impossible, how is that different from multiple universes simply not existing?

Yes

How is something useful if you cannot effectively prove its existence?

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04 Jun 2010, 9:30 pm

Flair wrote:

Yes

So, for you, at the moment the other worlds do not exist, but if we interacted with them (how we could interact with something that doesn't exist, I have no idea), they would just pop into existence?

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How is something useful if you cannot effectively prove its existence?

The theory in question may be able to explain a variety of things, and the arguments in its favour may outweight the arguments against it. That, to me, is a good reason to believe the theory is true. Regarding this topic, I want to have an account of possibility and necessity. It may be that empirical study cannot provide such an account. We shall have to arrive at it by other means.

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04 Jun 2010, 9:36 pm

Flair wrote:

you_are_what_you_is wrote:

Flair wrote:

If interacting with them is always impossible, how is that different from multiple universes simply not existing?

Yes

How is something useful if you cannot effectively prove its existence?

Possible worlds semantics come in handy as an explanatory tool in the analysis of statements like "it is possible that..." or "it is necessary that..." (to give just two examples) in natural language. Possible worlds are, at least, theoretical constructs. The debate over whether the possible worlds exist or not may not be as relevant to a typical logician.

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05 Jun 2010, 12:55 am

you_are_what_you_is wrote:

Flair wrote:

Yes

So, for you, at the moment the other worlds do not exist, but if we interacted with them (how we could interact with something that doesn't exist, I have no idea), they would just pop into existence?

Quote:

How is something useful if you cannot effectively prove its existence?

what benefits does having multiple universes provide? I do not assume that multiple universes are an impossibility, but declaring them real while having no way to experience them through our senses seems silly. I do not assume that multiple universes would make themselves known through random occurrences. I would expect the entrance would be entered through a "door" within our universe the problem is such possible doorways (a black hole as one possibility) is that we do not exactly have a safe way to enter or know if any universe aside from our own exists beyond a wormhole or black hole. With regards to having a dualist perspective dreams are another possibility but dreams have a tendancy to follow the laws of this universe as well.

I really want to play kingdom hearts now after all this talk about other worlds and doors XD

Last edited by Flair on 05 Jun 2010, 1:02 am, edited 1 time in total.

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05 Jun 2010, 1:01 am

Hector wrote:

Flair wrote:

you_are_what_you_is wrote:

Flair wrote:

If interacting with them is always impossible, how is that different from multiple universes simply not existing?

Yes

How is something useful if you cannot effectively prove its existence?

The same can be said about religion. It is generally better to rely on theories that can be demonstrated to our senses as oppose to relying on a faith concept. Again I am not saying Multiple Universe Theory is false but it seems to be better to rely on more solid theories as oppose to the ones that cannot currently be proven..

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