Specter of Reason

Monday, May 13, 2013

Possibility, Actuality and Necessity

In my last post, in response to Timothy Williamson's hesitations regarding naturalism, I rambled a bit about possible difficulties in sorting out a naturalistic understanding of mathematical truth.  I was reflecting on the problem of universality:  Logical and mathematical truths are not truths about the actual world, but extend to all possible worlds.  That would seem to be very hard to explain, if logical and mathematical truths are limited by local factors--factors which ground them in facts about our world.  Today I have worked out a possible solution.

The first step is to distinguish between two types of possibility:  logical possibility and physical possibility.  Another way of putting it is that possibility can be relative to a logical framework or a physical one.  When we say that something is physically possible, we mean it cannot be ruled out by the laws of physics (or, if you don't want to favor physics above other sciences, we can just say "laws of nature").  When we say that something is logically possible, on the other hand, we mean it is consistent with the rules of logic.

The next step is to consider that there is more than one possible set of physical laws.  (This can mean that there is more than one logically possible set of physical laws, or even that there is more than one possible set of laws which could adequately describe the known universe.)  I think of physical laws as predictive models or frameworks.  So, to say that something is physically possible is to say that it cannot be ruled out by our current predictive model for understanding the actual world.  Physical possibility, in so far as it is conceivable, is relative to a predictive model.

Similarly, there is more than one possible logical system.  To say that something is logically possible is to say that it cannot be ruled out by whatever logical system (or systems) we are using.  To put it more generally, we might say that logical possibility, in so far as it is conceivable, is relative to a logical system.

How then can we speak of all possible worlds, analytic truth--what is called "logical necessity?"  If something is true in all possible worlds ("logically necessary" or "analytically true"), it means that it is true according to the rules of a given language.  Analytic truth is truth by definition.  It is truth by language.  We can conceive of "all possible worlds" only so far as we have language.  Our linguistic capacities limit our understanding of all possible worlds.

Thus, we can distinguish between actuality and possibility, and speak of necessity, without postulating knowledge which is beyond the constraints of the actual world.  The actual world makes language possible.  The actual world places constraints on our language and thought.

A question arises:  Is it possible for there to be a world which is not constrained by any properties identical to any local (actual world) properties constraining our thinking?  If so, could we conceive of it?

Let X = such a world.  If X is conceivable, then we can conceive of something which is not constrained by anything local which constrains our thinking.  Therefore, either nothing local constrains our thinking or we arrive at a contradiction.  The contradiction may most easily be avoided by claiming that X is inconceivable, in which case we cannot say it is possible.  So either there is no possible world beyond the constraints of the actual world, or our thinking is not constrained by the actual world.

It is hard for me to comprehend the idea that our thinking could be unconstrained by the actual world.  So it seems more intuitive (to me) to say that there is no possible world beyond the constraints of the actual world.  However, this does not mean the actual world is the only possible world.  It rather means that we cannot conceive of a world that is completely unlike the world we inhabit.  Our powers of conception cannot completely transcend what we experience.

In my last post, I regarded science as testing claims about the actual world against claims about particular possible worlds (empirical hypotheses) and universals (all possible worlds:  the rules of language and logic).  I think it is more accurate to say that science tests empirical hypotheses (models of possible worlds) against the actual world (observation) via previously adopted models of possible worlds, the rules of logic and language.  What science gives us are possibilities, not actualities.  Philosophy, on the other hand, explores, deepens, illuminates and at times challenges the rules of logic and language.  What then of mathematics?  Does it provide models of possible worlds?  Does it explore the rules of logic and language?  Maybe it does something else entirely.  Maybe it gives us, not possibilities, but actualities.  Mathematical theorems are truths about the actual world.  However, they are truths which (at least partially) structure the rules of logic and language.  So they are also truths about all possible worlds.

The initial question was, How is it that we can have necessary truths in mathematics if we are constrained by the actual world?  The answer is:  Because mathematical truths are both truths about the actual world and truths which structure our thinking about logical and linguistic possibility itself.  And since necessary truths are truths by virtue of logic and language alone, then mathematical truths are by definition necessary truths.  They are no less empirically grounded for all that.

Sunday, May 12, 2013

A challenge to naturalism?

In a 2011 Stone column, Timothy Williamson writes:

"One challenge to naturalism is to find a place for mathematics. Natural sciences rely on it, but should we count it a science in its own right? If we do, then the description of scientific method just given is wrong, for it does not fit the science of mathematics, which proves its results by pure reasoning, rather than the hypothetico-deductive method. Although a few naturalists, such as W.V. Quine, argued that the real evidence in favor of mathematics comes from its applications in the natural sciences, so indirectly from observation and experiment, that view does not fit the way the subject actually develops. When mathematicians assess a proposed new axiom, they look at its consequences within mathematics, not outside. On the other hand, if we do not count pure mathematics a science, we thereby exclude mathematical proof by itself from the scientific method, and so discredit naturalism. For naturalism privileges the scientific method over all others, and mathematics is one of the most spectacular success stories in the history of human knowledge."

Quine's naturalistic position is that we judge mathematical validity by relation to empirical observation.  In contrast, Williamson says that mathematical validity is determined by looking only at mathematics itself, and not the world.  Williamson's reasoning seems obviously flawed.  If Quine is correct, then whenever we look at internal consistency or coherence in mathematics, we are looking at consistency/coherence within an empirically-grounded framework.  So, when mathematicians determine whether or not a proof is mathematically valid, they are determining whether or not it fits with empirical givens.  They might not always be doing so directly, but then, physicists and chemists don't always deal directly with observable givens, either.


If there is a problem with Quine's naturalistic position, it will have to be found elsewhere.

Edited to add the following clarifying remarks (which, unfortunately, are a bit on the rambling side):  I have strongly naturalistic tendencies.  I might not say that science is the only way to knowledge, though.  I would rather say that science is the most reliable way to shared knowledge of the world.  (Actually, I would define "science" as the pursuit of shared methods for discovering new knowledge about the world.)  And I would say that all facts about the world can, in theory, be discovered scientifically--even if nobody will ever be in a position to discover them.  That makes me a naturalist, I think, but it leaves open two possibilities:  one is that we can have private knowledge of the world; the other is that we can have knowledge which is not worldly.

Philosophical knowledge--knowledge of logical relationships (and we might include mathematics here)--is not necessarily worldly.  I think philosophical knowledge must have a worldly foundation, but it might not be reducible to facts about the world.  It might better be thought of as facts about all possible worlds, even if our knowledge of all possible worlds must, in some way, be limited by the facts about the world we live in.

For example, consider mathematics:  Our mathematical knowledge might be empirically grounded, as Quine claims, but, at the same time, it is knowledge of all possible worlds.  Our knowledge of logical relationships--like the analytic truth of "all bachelors are unmarried"--is similarly grounded in empirical knowledge.  (We know through experience what "bachelor" and "unmarried" are, as well as the verb "to be" and the qualifier "all.")  Yet, the extension of that knowledge is beyond the actual world.  All bachelors are unmarried in all possible worlds.

The issue here is between claims about particulars (facts about the actual world, or individual possible worlds) and universals (facts about all possible worlds).  Science and philosophy deal in both, but in different ways.  Science comes down to developing methods for testing claims about the actual world against claims about possible worlds.  A scientific experiment uses facts about individual possible worlds (empirical hypotheses) and all possible worlds (mathematical and logical relationships) to test claims about the actual world. In contrast, philosophy explores the consistency and coherence of facts about possible worlds.  These are two different ways of pursuing knowledge, and they are not mutually exclusive.  So it seems to be that science (as the pursuit of methods for discovering shared knowledge of the world) is not the only path to gaining knowledge. We also have philosophy, which can work with science for their mutual benefit.  But philosophical knowledge as such is not knowledge of the actual world (even if it has an empirical foundation).  (This is leaving aside the possibility of an intrinsically private knowledge.)

We have to wonder, though.  If mathematics is true of all possible worlds, then how can it be arrived at by empirical means?  How can we determine universal truths if we are limited by the particulars of the actual world?  It's tempting to dismiss this as a language game.  Mathematical truths are true of all possible worlds only because we define them that way.  Mathematics is a universalized construction based on certain empirical features of our world--specifically, features which allow for the analysis of patterns.  To say that mathematics (or logical relationships) are true in all possible worlds is only to say that the features which make pattern analysis possible are universalizable. But that universalizability is a feature of the actual world.  It is a feature of all possible worlds.  To put it another way, you cannot have a world with features that make pattern analysis possible without those features being universalizable.  This is part of the identity of those features.  At this point, I have to pause and reflect on what it means for such features to be universalizable, and also on how it can be that we can know that they are universalizable.

Update:  See follow up:  Possibility, Actuality and Necessity

Iron Man 3 Review (with mega spoilers)

I may be the only person I know who thinks Iron Man 2 is the best of the three Iron Man movies. I'm not much of a fan of any of them. I probably enjoyed the second the most because I went into it with very low expectations. I had been disappointed by the first Iron Man, which strained credulity beyond the breaking point, and even thematically seemed utterly confused. So I went into Iron Man 3 with very low expectations, too. Given that, I was surprised at how disappointing it still was.  To put it bluntly, I see no reason to recommend this movie unless you're devoted to the franchise or just can't live without a superhero fix, no matter how unfulfilling. It's passable as blockbuster entertainment, but that's about it, and that's not saying much.  The biggest problem I had was that the charisma and charm that carried the first two movies is almost nowhere to be found in this installment. That made the rest of the film's weaknesses that much graver.

That's it for the spoiler-free portion of this post.  What I have written below spoils some of the movie's biggest plot points. You've been warned. What follows is NOT a review for people who are deciding whether or not to see the movie. It's a review for people who have already seen it and who are looking to dwell on its faults.

Here are some of them:

There is no reason to give Tony Stark anxiety attacks. They never get worked into the plot. Strangely, he never has an attack that makes any difference at all to the story. He never has any problems engaging his enemies, or getting from point A to point B. Furthermore, he never actively tries to deal with his anxiety. His anxiety attacks have no function in the movie whatsoever, except as a gimmick. But for what? To make him more sympathetic? We don't need any gimmicks to make Tony Stark sympathetic. We're already invested in the character by now. The anxiety attacks are a distraction, plausibly an attempt to make the movie seem more character-driven than it really is.

The attempt to make Stark into a sort of father figure was not convincing or compelling.

There is no explanation for the villains' powers (apart from the power to regenerate). Why do their eyes turn red? Why are they able to burn things? Why are they super strong?

How is Pepper able to kill Killian by shooting a curiously shaped grenade she kicks at him, but Stark can't kill him by exploding him inside of one of his robotic suits? (And did the serum give her sensational martial arts skills, too?)

We are led to believe that Stark perfects the science behind Killian's project, leading to its reasonably safe application as well as a viable process for reversing its effects. (He reverses the effects on Pepper, and he uses the process on himself to get rid of his chest problem.) And then what? Stark destroys a technology that would cure the human race of all disease and ailment? What does he do with it? Nothing, apparently.

Why, with an army of JARVIS-controlled robots waiting to be deployed, does Stark spend half the movie more or less out of service (or out of robotic suit, at least)?

How did Favreau's character survive that blast? How did he survive it without major burns covering his entire body?

How is Stark able to save 13 people from falling to their deaths when JARVIS says he can only carry four? Is it supposed to be because they're all "carrying" each other? That doesn't make sense, physically speaking. Stark is the only one able to resist the force of gravity. The fact that they're all holding hands doesn't make one whit of difference. He tried to carry 13 when he could in fact only carry four. They all should've died.

Those are some of the more ridiculous plot holes that annoyed me as I watched the movie. Plot holes don't generally ruin a movie for me, unless the movie exists primarily because of the plot, or unless the holes are so numerous and gaping that they take me out of the story. Superhero movies don't generally rest on the integrity of their plots. They're more about character and action. So I'm usually able to forgive a large number of gaping holes. I think you have to, if you're a fan of the genre. In this case, the action and characters weren't strong enough to keep me happy, so the plot holes were a major nuisance. The action in this movie was okay. Nothing special, nothing original, but not particularly boring. The biggest problem was the characters. I just didn't believe them. They had some moments, but rarely engaged me enough.

One of Russell Blackford's major complaints is what the movie does with the character of The Mandarin. You might come away from the movie thinking that the entire character is fictional (a fiction within the fiction of the movie itself). Kingsley's character was supposed to be The Mandarin, but he turns out to be the farthest thing from a supervillain. I think the idea is that Killian was The Mandarin all along--a point which Killian inexplicably and ridiculously announces to Stark at the end of the movie. Killian has at least some of the powers traditionally attributed to the Mandarin. He is an excellent fighter, able to destroy an Iron Man suit with his bare hands, and he has fire-breathing and heat-inducing abilities. So he resembles the traditional Mandarin a little. They just had to give him a few more abilities and worked the rings in somehow. They totally could've done that. I attribute the failure to laziness. But I like the idea of a bait-and-switch. And it was fun watching Kingsley take full advantage of the role of the pathetic actor.

Saturday, May 11, 2013

Musical Interlude: Plod-ting

I haven't recorded much of my piano playing lately.  I've been playing a lot of Chopin and Prokofiev, with a little Beethoven and Mozart, too.  I might record some of that soon.  For now, here's an improvisation from last year.  This is one of my favorite recordings of my own playing.  Not sure why I didn't share it here before.  It's been on YouTube for a while.

The title is meant to suggest an ambivalence between plodding (as in, "to move or walk heaviliy or laboriously") and plotting (as in, scheming).

Sunday, April 14, 2013

Is moral anti-realism immoral?

Over at Philosophy, et ceteraRichard Chappell questions the common assumption that "one's metaethical views are more or less independent of one's first-order moral views."  Chappell says that moral anti-realists act as if people really mattered, because people do matter to them.  However, he says, that is not the same as believing that people matter in and of themselves.  Can anti-realists believe that people matter simpliciter?  Sure, they can act as if they do, but that is not the same as really believing it.  If they don't really believe it, he says, then moral anti-realism may be morally suspect.

There is a brief but interesting discussion in the comments section of Chappell's blog.  One good point which was raised is this:  An anti-realist need not recognize a difference between acting as if people deserve respect and really believing that they do.  In other words, anti-realists can be dispositionalists about belief.  While that response to Chappell might satisfy some anti-realists, it  might not satisfy non-cognitivists or expressivists, and anyway, it doesn't satisfy Chappell.

I think Chappell is probably wrong to reject this point too quickly.  I also think he may be too quick to dismiss expressivism.  In any case, I raised a couple of different issues in a comment.  Here's what I wrote:

I wonder if your argument amounts to a rejection of consequentialism.  If you agree that the moral anti-realist can act in all the same ways as the moral realist, but merely lacks some propositional attitude, then you can't be judging the moral worth of that attitude in terms of its consequences.  You might say that the moral realist does act in some ways which are different: specifically, the moral realist avows moral realism.  But does the mere avowal of moral realism produce a greater good (or reduce more suffering) than the avowal of moral anti-realism?  If we are to be consequentialists, I think you need to find a bigger behavioral difference between moral realists and moral anti-realists to convince me that one is of more moral worth.  If you were prepared to reject consequentialism, however, then your argument might be more persuasive.  The moral anti-realist would do the same things as the moral realist, but would presumably be regarding people as means, and not just as ends.  This would be a problem for a deontologist like Kant.   
I think some moral anti-realists might be open to a limited reading of Kant, though.  A moral anti-realist could believe that people are ends in themselves, and that there are facts in the universe which make it so.  They might even say this is so in all possible universes.  The argument could be that dignity is a necessary aspect of rational agency, which itself is a prerequisite for social contracts.  Moral anti-realists can say it is impossible to conceive of rational agents without dignity.  Thus, there is a fact of the matter which makes people ends in themselves.   
I can see two ways the moral anti-realist can go about this.  One is to claim that personhood is not a natural kind, and that there is no fact of the matter about whether or not an organism is (or should be treated as) a person.  The other option is to claim that there is no fact of the matter about whether or not we should recognize the dignity of any particular person.  So, the moral anti-realist can say that all persons have dignity, but the universe does not determine what is or is not a person.  Or the moral anti-realist can say that there are objective persons, but there is no objective reason to respect the dignity of any particular person.  In both cases, the moral anti-realist does genuinely believe in the dignity of persons.  However, their moral attitudes do still admit of contingencies.  But this does not seem so morally suspicious.  It seems fair to suppose that personhood is not a natural kind.  It also seems fair to suppose that there are circumstances in which a person loses their moral right to have their dignity respected.  Neither of these views suggests that the moral anti-realist is too superficial in their attitudes or insincere in their behavior.

Thursday, April 4, 2013

The Right To Interpret The United States Constitution

Republican lawmakers in North Carolina want a state religion and are trying to fight for it by calling the interpretation of the Constitution into question.  Their argument looks valid, but I don't think it is sound.


The first premise is the 10th Amendment of the United States Constitution:

(1) The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.

The second premise is this:

(2) The power to determine what is or is not constitutional is not delegated to the United States by the Constitution, nor prohibited by it to the States.

If both of these premises are accepted, then the following conclusion seems inevitable:

(3) The power to determine what is or is not constitutional is reserved to the States respectively, or to the people.

As stated in their recently filed bill, Republicans in North Carolina draw this final conclusion:

(4) "Each state in the union is sovereign and may independently determine how that state may make laws respecting an establishment of religion."

The most obvious line of criticism, I think, is to reject the second premise.  Article III of the Constitution vests the United States with a judicial system.  The courts must interpret the Constitution in order to carry out their duty, and by so interpreting it, they determine what is or is not constitutional.  (2) is therefore false and the rest of the argument collapses.

One might also question the move from (3) to (4), but that looks like murkier territory to me.  The argument is plainly unsound.

Tuesday, March 26, 2013

A Universe From Nothing?

There are various issues that I'd like to address regarding the 2013 Isaac Asimov Memorial Debate, but one in particular is bugging me.  Lawrence Krauss says that science can give us a plausible explanation of how a universe like ours could spontaneously "pop into existence" out of timeless, spaceless, lawless void.  Jim Holt says that Krauss is talking nonsense:  The idea of a universe "popping into existence" implies that there is a point in time in which that event occurs.  Yet, by Krauss' definition, there is no time (or space) for the universe to pop into.  I think Holt's point is valid, but it does not get resolved.

Here's the whole exchange (starting @ 0:50:00):

Krauss: Quantum mechanics says things fluctuate, and if gravity is a theory of space and time, if you make space and time quantum mechanical variables, then it is perfectly possible for universes to pop into existence--space and time to pop into existence where there was no space and time before.

Krauss wants to continue, but Holt interrupts.

Holt: Space and time pop into existence?  You make that sound like a temporal process, a process in time.

Krauss: Well, because I said it so you can understand it.

Holt: Huh?

Krauss: No, I mean I used words, and the problem with words are [sic], as T. S. Eliot says, they're sort of slippery.

Holt: But becoming implies time.  You can't have time coming into existence as itself a temporal process. That makes no sense. That's why it's good to have philosophers around, which I'm not one, to help you use language precisely.

Krauss: Okay, so let me just pretend there--let me just say there's a global time and at some time a space pops into existence. Okay, will that make you happier?

This does not satisfy Holt, however, and I can understand why.  Krauss started by claiming to have an explanation of how time itself can come into existence out of a timeless void.  Now, however, he's saying that there is a global time out of which the universe sprung.  So he's changed his story.  Something fishy seems to be going on.  But before Krauss and Holt can make headway, Neil deGrasse Tyson steps in to moderate.

Tyson: Lawrence, you are saying that because we have quantum phy--because we are illuminated by the actions of quantum physics, mentally, we can think about whatever is our best understanding of nothing, and quantum physics then pops into existence in that nothing an entire universe, and if that's the case, I would then pick up Jim's point and ask you--

Krauss: I was gonna try and ex--Where do the quantum physics come from?

Tyson: No, no, no.  No, no, no.  That's not what I'm gonna ask you.  I'm gonna ask you--that had to happen at some point.  Why isn't it happening all the time and everywhere at all times?

Krauss went on to answer that question.  Unfortunately, that is not the question that Holt was raising, and Holt never tried to raise the point again.  Holt's question was, what sense is there in talking about space and time coming into existence?

Krauss' claim is that the universe may have originated out of a timeless, spaceless void.  His theory (from what I gather) is that such a void would be inherently unstable, and so would tend to produce stuff.  The question then is, what sense is there in referring to a timeless, spaceless, lawless "nothing" as being unstable?  Stability and instability are properties which persist in objects over time.  If there is no space or time, then there is no instability.  Furthermore, what sense is there in claiming that the creation of the universe occured in a spaceless, timeless nothing?  If there is no space or time, then there is no such thing as occurence.   It defies logic to speak the way Krauss is speaking.

Now, maybe Krauss has a point about the limitations of ordinary language.  There's a long tradition, from Galileo to Heisenberg, of regarding math and math alone as suitable for grasping the truth of physics and, by extension, reality.  Once you start using non-mathematical terms, you lose the sense, beauty and truth of the model.  But if that is so, and mathematics is the only coherent way to talk about reality, then what does that say about reality?  Is all non-mathematical language incoherent?  Should we be Platonists, and accept that the only truth is purely mathematical?  Is everything else just illusion?  This is philosophy, not physics, but it's what Krauss might be suggesting.

Even if we avoid Platonism, isn't Krauss suggesting that physics is beyond comprehension?  Does that mean physicists should just shut up and calculate?  If so, then Krauss really shouldn't be trying to talk about these things at all, should he?  He says he's trying to describe the physics in a way so that we can understand it, but apparently that is impossible.  And that raises the question: How well do Krauss and other physicists understand it?

I don't think physicists should just shut up and calculate.  However, I do think they sometimes need to be more careful in the way they present their ideas.  And they should also be more open to philosophical scrutiny in that area, since philosophers have experience and conceptual tools for exploring the logical space of our discourse.  (Krauss denies that philosophers have any expertise to bring to the table at all, which is unfortunate.)

Krauss' argument seems to be this:  Our universe may ultimately have sprung out of a timeless, spaceless, lawless void.  This could be so because, in such a void, every possible law obtains (which, for Krauss, is the same as saying that no laws obtain.)  The laws of quantum mechanics are possible, and so those laws also obtain in The Nothing.  And according to those laws, universes can pop into existence.  One problem with this view is that there must be something to exist in which those laws can obtain.  If there is really is nothing at all, then there is nothing on which the laws can act.  So the explanation doesn't work.

Let's say Krauss finds some way around that problem.  There is still another problem:  Couldn't there be some laws which are not consistent with quantum mechanics, and which, in fact, say that universes cannot pop into existence?  If all laws obtain in The Nothing, then we could have one law which says universes can pop into existence and another law which says they cannot.  In that case, a universe popping into existence would be physically impossible--it would break one of the laws of nature.  Krauss needs to explain why such a law--a law against universes popping into existence--is impossible.  If it's not impossible, then his account does not work.

Krauss also suggests a slightly different argument which starts with an assumption: Everything which is possible is actual.  In that case, every possible arrangement of quantum variables is real.  That means that every possible universe exists and also that the "ground state of a gapped quantum system" (as Eve Silverstein calls it) is also real.  So The Nothing is as real as our universe.  And so there is a temptation to say that our universe--all universes--came out of The Nothing.  However, this doesn't overcome Holt's objection.  We still can't say that all of the other states of the quantum system came from the ground state, because the ground state does not exist in any particular place or time.  It's not clear in what sense the ground state can exist at all.  Maybe we can still say that the ground state, like all the other states, is real, since reality does not necessarily imply existence (for example, it is not hard to admit that numbers are real, but it's very hard to say in what sense they might exist), but we're still left with the question:  How did the quantum system come into existence in the first place?

If you want to talk about what caused the universe, then you're asking for a first cause.  Krauss seems to want it both ways here.  He says science doesn't need a first cause.  That's true.  Philosophy doesn't, either.  But then Krauss hasn't explained how the universe (or multiverse) might have come into existence.  If he wants to explain that, then he really does seem to be looking for a first cause.

What many physicists seem to prefer--and I think J. Richard Gott is one of them--is to say that the universe (or multiverse) just is.  Nothing caused it to occur.   Krauss might even agree, in which case all his arguments about universes popping into existence seem like a waste of time.  Whatever Krauss thinks, it is philosophically respectable to say that the very question, What caused the universe to exist?, is meaningless, because "the universe" is not the sort of thing that can be caused to exist.  The universe, the multiverse--the quantum system--just is.  It didn't come from nothing.  It didn't come, period.

I'll end with a note on the meaning of the term "universe" as physicists today understand it.  According to Gott and Krauss, the word "universe" has a different meaning nowadays.  Krauss says "universe" is defined as "everything you could have once interacted with, or you can ever interact with.  So everything you can have physical contact with, either in the past or in the future, is a universe."  Different universes can share a causal history, but they don't have to.  They might be completely and utterly independent of each other.  Now, if we're talking about multiple universes which share a common history--a common trunk, as Gott puts it--then aren't there going to be moments in my universe which can have physical contact with moments that aren't in my universe?  In other words, the differentiation of universes is relative and not absolute.  While "my" universe has some unique physical properties, not everybody in "my" universe will draw the boundaries of their universe the same way I draw the boundaries of mine.  This isn't necessarily a problem, but I find it curious.

P.S. If you want to know what philosophers have to say about nothing, the SEP entry on Nothingness is a good place to start.