Change and matter

Aristotle’s positing matter is driven by trying to respond to the Parmenidean idea that things can’t come from nothing, and hence we must posit something that persists in change, and that is matter.

But there two senses of “x comes from nothing”:

1. x is uncaused

2. x is not made out of pre-existing materials.

If “x comes from nothing” in the argument means (1), the argument for matter fails. All we need is a pre-existing efficient cause, which need not be the matter of x.

Thus, for the argument to work, “x comes from nothing” must mean (2). But now here is a curious thing. From the middle ages to our time, many Aristotelians are theists, and yet still seem to be pulled by Aristotle’s argument for matter. But if “x comes from nothing” means (2), then theism implies that it is quite possible for something to come from nothing: God can create it ex nihilo.

There are at least two possible responses from a theistic Aristotelian who likes the argument for matter. The first response is that only God can make things come from nothing in sense (2), and hence things caused to exist by finite causes (even if with God’s cooperation) cannot come from nothing in sense (2). But there plainly are such things all around us. So there is matter.

Now, at least one theistic Aristotelian, Aquinas, does explicitly argue that only God can create ex nihilo. But the argument is pretty controversial and depends on heavy-duty metaphysics, about finite and infinite causes. It is not just the assertion of a seemingly obvious Parmenidean “nothing comes from nothing” principle. Thus at least on this response, the argument for matter becomes a lot more controversial. (And, to be honest, I am not convinced by it.)

The second and simpler response is to say that it’s just an empirical fact that there are things in the world that don’t come from nothing in sense (2): oak trees, for example. Thus there in fact is matter. This response is pretty plausible, but can be questioned: one might say that we have continuity of causal powers rather than any matter that survives the generation.

Finally, it’s worth noting that I suspect Aristotle misunderstands the Parmenidean argument, which is actually a very simple reductio ad absurdum:

3. x came into existence.
4. If x came into existence, then x did not exist.
5. So, x did not exist.
6. But non-existence is absurd.

The crucial step here is (6): the Parmenidean thinks the very concept of something not existing is absurd (presumably because of the Parmenidean’s acceptance of a strong truthmaker principle). The argument is very simple: becoming presupposes the truth of some past-tensed non-existence statements, while non-existence statements are always false. Aristotle’s positing matter does nothing to refute this Parmenidean argument. Even if we grant that x’s matter pre-existed, it’s still true that x did not exist, and that’s all Parmenides needs. Likewise, Aristotle’s famous actuality/potentiality distinction doesn’t solve the problem. Even if x was pre-existed by a potentiality for existence, it’s still true that x wasn’t pre-existed by x—that would be a contradiction.

To solve Parmenides’ problem, however, we do not need to posit matter or potentiality or anything like that. We just need to reject the idea that negative existential statements are nonsensical. And Aristotle expressly does reject this idea: he says that a statement is true provided it says of what is that it is or of what is not that it is not. Having done that, Aristotle should take himself as done with Parmenides’ problem of change.

A potential explanation why we don't observe violations of the PSR

A standard puzzle for the opponent of the Principle of Sufficient Reason (PSR) is to explain why we don’t observe objects coming into existence ex nihilo. Here is a thought that I think hasn’t been explored enough. Maybe when an object comes into existence ex nihilo, it is unlikely that the object would end up being spatiotemporally related to things already in existence. In other words, perhaps the typical object coming into existence ex nihilo forms a new universe, not spatiotemporally related with any other universe.

If this is right, then the opponent of the PSR should take multiverse hypotheses very seriously.

That said, such random multiverse hypotheses lead to very compellingly sceptical scenarios.

The paradox of the Jolly Givers

Consider the Grim Reaper (GR) paradox. Fred’s alive at midnight. Only a GR can kill him. Each GR has an alarm with a wakeup time. When the alarm goes off, the GR looks to see if Fred’s alive, and if he is, the GR kills him. Otherwise, the GR does nothing. Suppose the alarm times of the GR’s are 12:30 am, 12:15 am, 12:07.5 am, …. Then Fred’s got to be dead, but no GR could have killed him. If, say, the 12:15 GR killed him, that means Fred was alive at 12:07.5, which means the 12:07.5 GR would have killed him.

A Hawthorne answer to the GR paradox is that the GRs together killed Fred, though no one of them did.

Here’s a simple variant that shows this can’t be true. You hang up a stocking at midnight. There is an infinite sequence of Jolly Givers, each with a different name, and each of which has exactly one orange. There are no other oranges in the world, nor anything that would make an orange. When a JG’s alarm goes off, it checks if there is anything in the stocking. If there is, it does nothing. If there is nothing in the stocking, it puts its orange in the stocking. The alarm times are the same as in the previous story.

The analogous Hawthorne answer would have to be that the JGs together put an orange in the stocking. But then one of the JGs would need to be missing his orange. But no one of the JGs is missing his orange, since no one of them took it out of his pocket. So, the orange would have had to come out of nowhere.

And, to paraphrase a very clever recent comment, if it came out of nowhere, why would it be an orange, rather than, say, a pear?

I think the JG paradox also suggests an interesting link between the principle that nothing comes from nothing and the rejection of supertasks.

Presentism and ex nihilo nihil fit

Consider these three theses:

1. There is at most one empty world, i.e., world where nothing exists.

2. Presentism is true.

3. Something can come from nothing.

By 3, the following should be possible: first there is nothing, and then there is something. But if something can come from nothing, a fortiori it is possible that nothing comes from nothing. Thus, by bivalence about the future, here are two metaphysical possibilities:

4. There is nothing now, but later there will be something.

5. There is nothing now, and there will never be anything.

By presentism, if there is nothing now, there is nothing. So, both 4 and 5 entail that the world is empty. But there is at most one empty world. So, 4 and 5 are true in the same world, which is absurd!

Thus, we should reject one of 1–3, or reject bivalence about the future.

Given the plausibility of bivalence as well as of 1, we have an argument that presentists should deny 3.

I myself deny 3, but since I’m not a presentist I deny it on other grounds.

Cats versus nothing

Suppose I insisted that the Big Bang happened due to a cat generating an extremely high energy hairball. You would think I’m crazy. But why is the cat theory any worse than a theory on which the Big Bang happened for no reason at all?

Granted, we haven’t ever seen such a high energy hairball coming from a cat. But we likewise haven’t seen something come from nothing.

Granted, we know something about the causal powers of cats, namely that they lack the power to originate high energy hairballs. But likewise we know about the causal power of nothing, namely that where there is nothing, there is no causal power.

However, this last response is too quick. For when we talk of the universe coming from nothing versus the universe coming from a cat, we are equivocating on “coming from”. When the atheist says the universe came from nothing, they don’t mean that nothing was something that originated the universe. Rather, they simply deny that there was something that originated the universe. Cats don’t have the power to generate universes, so universes don’t get generated by cats. Similarly, where there is nothing, there is no power to generate universes, so universes don’t get generated by nothing. But the atheist doesn’t say that the universe is generated by (a?) nothing—they simply deny that it was generated by something.

Thus, the problem with the universe coming from a cat is with the origination: cats just aren’t the sorts of things to originate universes.

I guess that’s right, but I still feel the pull of the thought that a cat comes closer to making it possible for a universe to come into being than nothingness does. After all, where there is a cat, there are some causal powers. And where there is nothing, there aren’t any.

Perhaps another way to make the argument go through is to say this: There is nothing less absurd about the universe appearing causelessly ex nihilo than there is about a cat causelessly ex nihilo gaining a universe-creating power.

A problem for some Humeans

Suppose that a lot of otherwise ordinary coins come into existence ex nihilo for no cause at all. Then whether a given coin lies heads or tails up is independent of how all the other coins lie in the sense that no information about the other coins will give you any data about how this one lies.

It is crucial here that the coins came into existence causelessly. If the coins came off an assembly line, and a large sample were all heads-up, we would have good reason to think that the causal process favored that arrangement and hence that the next coin to be examined will also be heads-up.

But now suppose that I know that Humeanism about laws is true, and there is a very, very large number of coins lying in a pile, all of which I know for sure to have come to be there causelessly ex nihilo, and there are no other coins in the universe. Suppose, further, that in fact all the coins happen to lie heads-up. Then when the number of coins is sufficiently large (say, of the order of magnitude of the number of particles in the universe), on Humean grounds it will be a law of nature that coins begin their existence in the heads-up orientation. But if the independence thesis I started the post with is true, then no matter how many coins I examined, I would not have any more reason to think that the next unexamined coin is heads than that it is tails. Thus, in particular, I would not be justified in believing in the heads-up law.

One might worry that I couldn’t know, much less know for sure, that the coins are there causelessly ex nihilo. A reasonable inference from the fact that lots of examined coins are all heads-up would seem to be that they were thus arranged by something or someone. And if I made that inference, then I could reasonably conclude that the coins are all heads-up. But my conclusion, while true and justified, would not be knowledge. I would be in a Gettier situation. My justification depends essentially on the false claim that the coins were arranged by something or someone. So even if one drops the assumption that I know that the coins are there causelessly ex nihilo, I still don’t know that the heads-up law holds. Moreover, my reason for not knowing this has nothing to do with dubious theses about the infallibility of knowledge. I don’t know that the heads-up law holds, whether fallibly or infallibly.

There is no problem for the Humean as yet. After all, there is nothing absurd about there being hypothetical situations where there is a law but we can’t know that it obtains. But for any Humean who additionally thinks that our universe came into existence causelessly, there is a real challenge to explain why the laws of our world are not like the heads-up law—laws that we cannot know from a mere sample of data.

This problem is fatal, I think, to the Humean who thinks that our universe started its existence with a large number of particles. For the properties of the particles would be like the heads-up and tails-up orientations of the coins, and we would not be in a position to know all particles fall into some small number of types (as the standard model in particle physics does). But a Humean scientist who doesn’t think the universe has a cause could also think that our universe started its existence with a fairly simple state, say a single super-particle, and this simple state caused all the multitude of particles we observe. In that case, the order-in-multiplicity that we observe would not be causeless, and the above argument would not apply.

Rambling thoughts on probability and multiverses

Imagine a countably infinite multiverse where there are no spatial relations between the different universes, but it makes sense to talk of a common time sequence measured by the duration of time elapsed from the beginning of a universe. Suppose all the universes start out the same way: they each consist of a closed box containing an unstable particle with a one-year half-life that decays into a stable particle. The only change there is is the decay of the particle.

Every year "half" of these particles decay. But now notice an oddity: from the second year on, there is a sense in which there are no global change at all. No matter how many particles have decayed, the global picture will forever be this: a multiverse consisting of universes infinitely many of which consist of a box with an unstable particle and infinitely many consist of a box with a stable particle. In other words, there is no qualitative change in the multiverse. Interesting and somewhat paradoxical: it looks like reality is unchanging and yet there is change. We capture the change when we keep track of non-qualitative features: this box had an unstable particle, and now this same box has a stable particle.

Now let's add one person to each universe. The person doesn't get to look inside the box, but knows the general setup. Each year, the person's probability that her box contains an unstable particle goes down by a half.

Lesson 1: self-locating probabilities cannot be read off of the qualitative features of the present state of the universe--either history or numerical identity matters. (This is the same lesson that Ian has been pushing me to learn from an earlier post.)

Now, in the above story, the universe started out with all the particles in the unstable state. But what if instead the universe started out with infinitely many of the particles in the stable state and infinitely many in the unstable state? What can we say about each person's probability that her box contains an unstable particle? Each year after the first, P(unstable now | unstable a year ago) = 1/2. But what about the unconditional probability? How likely is it after, say, one year that the particle in one's box is unstable? Well, it's half of the probability that it was unstable to begin with.

But what is the probability that it was unstable to begin with? Well, if we had a bit of a backstory, we could answer that. Let's say that God creates each multiverse, and he flips a fair coin as he gets to each, and puts in a stable particle on heads and an unstable one on tails. In that case, the probability that the particle in the box was unstable to begin with was 1/2. But if God instead rolled a die, and put in a stable particle on six and an unstable one otherwise, the probability of initial instability is 5/6. In other words, the probability of initial instability depends on backstory. But what if there is no backstory at all? What if this multiverse came into existence ex nihilo for no cause at all? It is tempting to assign probability 1/2 to instability. But why that? Why not, instead, 1/6 or 5/6 or something else? The choice seems arbitrary and the honest thing to say, I think, is just that there is no meaningful probability.

Lesson 2: Probability of initial conditions requires some sort of structure. A chancy causal structure will do. Perhaps a spatial structure could do--if the boxes were in a single spaced, arranged on a line, alternating between stable and unstable, it might be reasonable to say that the probability that one has instability is 1/2. Might be, but I'm not sure.

But of course probabilities in subsequent years will depend on initial probabilities. If we cannot say anything about initial probabilities without more structure, we can't say anything about probabilities in subsequent years, except conditionally.

Does anything in Lesson 2 hang on us working in a multiverse? I doubt it.

Ex nihilo nihil fit, and presentism

According to presentism, events come out of nothing (the future), have a flash of reality as they are briefly present, and then pass back into nothing (the past). But nothing comes out of nothing. So, it seems, presentism is false.

I wonder if the above argument equivocates on "comes out of nothing".