Tuesday, November 27, 2012

Simplicity and multiple universes

In yesterday's post, I offered a criterion for when multiplicity of objects or kinds posited by a theory counts against the simplicity of a theory: namely, when it is a multiplicity of objects or kinds not explained by the theory.

Let's apply this to multiple universe theories, which people do tend to see as offending against simplicity.

Lewis's Modal Realism: Lewis's universes have no explanation of their existence. Their existence is simply a brute fact. Thus, the infinitude of Lewis's universes counts against the simplicity of a theory. Moreover, along with unexplained universes there will be unexplained kinds. Lewis's theory, for instance, implies that there exists a universe where an uncaused griffin exists from the beginning. Likewise, unicorns, Pegasuses, and so on. So Lewis's theory implies the existence of a great diversity of unexplained kinds of things. And that should count against the theory.

Theistic Multiverses: Theistic multiverse theories have an infinity of universes, but these universes are explained by God's goodness in creating all universes that it is worth creating. Thus there is only one unexplained entity in the theory--God--and there is no offense against simplicity.

Physicists' Multiverses: I don't know enough about string-theoretic multiverses to say anything about those here. But inflationary universes that bubble up out of other universes will be exempt from the worry if there is one root universe from which the others come, since then the cost in terms of unexplained entities is the same as that of single universe theories, and there is no offense against simplicity.


Lydia McGrew said...

I'm not convinced that this idea of simplicity does all the necessary work. Consider this example: I see a butterfly sunning himself on a rose. I go away and return five minutes later and see what looks visibly like the same butterfly. Suppose that out of the blue I hypothesize that the first butterfly was genetically duplicated by aliens, taken away to the mothership, and his visibly identical replacement left on the rose, and that it is the genetically identical replacement that I am now seeing.

This "explanation" does indeed tell why the butterfly I am now seeing looks just like the butterfly I saw five minutes ago and why it is in the same place on the rose. But it is obviously a _far_ more complex hypothesis than the hypothesis that I'm simply seeing the same butterfly.

Perhaps someone might respond that it's the introduction of the aliens that causes all the problems. But we can make up a theory without them. We could theorize that this is a special type of butterfly, never before discovered, that periodically splits into visibly identical butterflies, after which one of them decays instantaneously into invisible dust, and that this has happened during the five minutes while I was away. Again, even though the hypothesis includes a causal mechanism that purports to make it inevitable that I would see what I'm seeing now, that doesn't make its simplicity equivalent to that of the hypothesis that I'm just seeing the same butterfly.

I'm guessing that all of this means that I've misunderstood the proposed concept of simplicity, though.

Alexander R Pruss said...


I am just trying to capture one aspect of simplicity--the Ockhamist "entities should not be multiplied beyond necessity". I fully agree that there is more to simplicity than that.

Lydia McGrew said...

I think the Ockham criterion is pretty obviously meant in such a way that it won't do to get around it by postulating some kind of otherwise unmotivated law by which entity #1 spontaneously generates some number of other entities, and then to say, "Oh, I haven't multiplied entities without necessity, because they were 'necessitated' by this law that I attributed to the ancestor entity."

That is still, in my opinion, multiplying entities without necessity. There was no necessity (that is, epistemic justification) for postulating that butterfly #1 is of this special type that spontaneously generates a second butterfly! It's a pretty trivial shift to invent two entities where one would do the explanatory job for the evidence just fine and then to say that you "aren't multiplying them without necessity" because you attributed to the first one some sort of otherwise epistemically unjustified ability to generate the second one!

So it does seem to me that my butterfly example is multiplying entities without necessity even if I hypothesize some deterministic cause whereby the second butterfly comes from the first.

And the same, I would argue, applies to bubble universes. Simply to say that our universe is one in a long series without clear epistemic need for that hypothesis really is multiplying entities without necessity even if we build into our hypothesis that all of the universes are causally necessitated by the first. There was no necessity for a multiple universe generating mechanism any more than, in the butterfly scenario, there is a reason to hypothesize a "second butterfly generating" mechanism latent in the first butterfly.

Alexander R Pruss said...

We can think of the butterfly generating mechanism as an entity in an extended sense.

The inflationary multiverse theories I was interested in are ones where an inflationary theory we already have good reason to accept gives rise to bubble universes at least for some values of the the parameters in the theory.

Lydia McGrew said...

I think if that is the case we _are_ multiplying entities but can argue that we are doing it "with necessity" rather than "without necessity." It's not that the additional universes aren't additional entities. They clearly are. It's just that the mechanism by which they are generated is (allegedly) something we have independent reason to believe exists.

It's a bit like bacteria. It's not as though two bacteria are not more entities than one bacteria. If we hypothesize that bacteria reproduce by divid into two by some sort of natural law of their being, that _is_ multiplying entities. That's why if the only thing we'd ever seen was one bacterium, and if we'd never encountered other entities sufficiently similar to that bacterium who divide and reproduce spontaneously, it would be a violation of Ockham's razor to hypothesize more than one bacterium.

As things are, when we hypothesize that bacteria will begin to divide and make more, we are indeed "multiplying entities." However, we do it because we have evidence that bacteria do do this.

So I think the "work" in your discussion is being done not by the argument that the bubble universe hypothesis "does not multiply entities" but rather is being done entirely by the claim that we have independent evidence for this universe-multiplying tendency.

But in that case it doesn't really make much difference whether we are talking about evidence for the many universes separately or evidence for them as a result of this alleged bubbling-up tendency in the meta-universal set-up. Either way, there is a need for independent evidence for the multiple universes.

Crude said...


Pardon me if I'm massively misinterpreting things here, but I wanted to add this in.

I think the best way to consider what Alex is saying is in a comparing/contrasting way. Namely, you have 3 multiverse theories - which one of these three are the simplest in an Ockham sense? At least that's the way I took Alex. It's not that you aren't 'multiplying entities' in all three, it's an issue of comparison of whether one or another is less simple given what is or isn't explained.

That said, I do have a question for either of you. Let's look at those last two theories. Is there aything to be gained by pointing out that the 'unexplained entity' in the theistic multiverse is simple, has His properties necessarily, etc... versus one root universe that has all of its properties in a contingent sense?