Causation and contingency

A correspondent yesterday reminded me of a classic objection to the “inductive” approach to the causal principle that all contingent things have causes in the context of cosmological arguments. As I understand the objection, it goes like this:

1. Granted, we have good reason to think that all the contingent things we observe do have causes. However, all these causes are contingent causes, and so we have equally good inductive support to think that all contingent things have contingent causes. Thus, to extend this reasoning to conclude that the cosmos—the sum total of all contingent things—has a cause is illegitimate, since the cosmos cannot have a contingent cause on pain of circularity.

An initial response is that (1) as it stands appears to rely on a false principle of inductive reasoning:

2. Suppose that all observed Fs are Gs, and that all observed Fs are also Hs. Then we have equally good inductive support for the hypothesis that all Fs are Hs as that all Fs are Gs.

But (2) is false. All observed emeralds are green and all observed emeralds are grue, where an emerald is grue if it is green and observed before 2100 or it is blue and not observed before 2100. It is reasonable to conclude that all emeralds are green but not that they are all grue. Or even more simply, from the facts that all observed electrons are charged and all observed electrons are observed, it is reasonable to conclude that all electrons are charged but not that all electrons are observed.

Nonetheless, this response to (1) does not seem entirely satisfying. The predicate “has a contingent cause” seems to be projectible, i.e., friendly to induction, in a way in which “is grue” or “is observed” are not.

Still, I think there is something more to be said for this response to (1). While “has a contingent cause” is not as obviously non-projectible as “is observed”, it has something in common with it. We are more suspicious of inductive inferences from all observed Fs being Gs to all Fs being Gs when being G includes features that are known prior to these observations to be concommitants of observation. For instance, consider the following variant of the germ theory of disease:

3. All infectious diseases are caused by germs that are at least 500 nm in size.

Until the advent of electron microscopy, all the infectious diseases whose causes were known were indeed caused by germs at least 500 nm in size, as that is the lower limit of what can be seen with visible light. But it would not be very reasonable to have concluded at the time that 500 nm is the lower limit on the size of a disease-causing germ. Now, something similar is happening in the contingent cause case. All observable things are physical. All physical things are contingent. So being contingent is a concommitant of being observed.

Finally, there is another epistemological problem with (1). The fact that some evidence gives as good support for q as for p does not mean that q is as likely to be true as p given the evidence. For the prior probability of q might be lower than that of p. And indeed that is the case in the reasoning in (1). The prior probability that everything contingent has a contingent cause is zero, precisely for the reason stated in (1): it is impossible that everything contingent have a contingent cause! But the prior probability that everything contingent has a cause is not zero.

An observation about the backwards-infinity branching view of possibility

In my dissertation, I defended a causal power account of modality on which something is possible just in case either it’s actual or something can bring about a causal chain leading to its being actual. I noted at the time that unless there is a necessary first cause, this leads to an odd infinite branching view on which any possible world matches our world exactly once you get far enough back, but nonetheless every individual event is contingent, because if you go back far enough, you get a causal power to generate something else in its place. Rejecting this branching view yields a cosmological argument for a necessary being. To my surprise when I went around giving talks on the account, I found that some atheists were willing to embrace the branching view. And since then Graham Oppy has defended it, and Schmid and Malpass have cleverly used it to attack certain cosmological arguments.

I want to note a curious, and somewhat unappealing, probabilistic feature of the backwards-infinite branching view. While it is essential to the view that it be through-and-through contingentist, assuming classical probabilities can be applied to the setup, then the further back you go on a view like that, the closer it gets to fatalism.

For let S_t be a proposition describing the total state of our world at time t. Let Q_t be the conjunction of S_u for all u ≤ t: this is the total present and past at t. Here is what I mean by saying that the further back you go, the closer you get to fatalism on the backwards-infinite branching view:

1. lim_{t→− ∞} P(Q_t) = 1.

I.e., the further back we go, the less randomness there is. In our time, there are many sources of randomness, and as a result the current state of the world is extremely unlikely—it is unlikely that I would be typing this in precisely this way at precisely this time, it is unlikely that the die throws in casinos right now come out as they do, and so on. But as we go back in time, the randomness fades away, and things are more and more likely.

This is not a completely absurd consequence (see Appendix). But it is also a surprising prediction about the past, one that we would not expect in a world with physics similar to ours.

Proof of (1): Let t_n be any decreasing sequence of times going to  − ∞. Let Q be the infinite disjunction Q_t1 ∨ Q_t2 ∨ .... The backwards-infinite branching view tells us that Q is a necessary truth (because any possible world has Q_t is true for t sufficiently low). Thus, P(Q) = 1. But now observe that Q_t1 implies Q_t2 implies Q_t3 and so on. It follows from countable additivity that lim_n→∞ P(Q_tn) = P(Q) = 1.

Appendix: Above, I said that the probabilistic thesis is not absurd. Here is a specific model. Imagine a particle that on day  − n for n > 0 has probability 2⁻ⁿ of moving one meter to the left and probability 2ⁿ of moving one meter to the left, and otherwise it remains still. Suppose all these steps are independent. Then with probability one, there is a time before which the particle did not move (by the Borel-Cantelli lemma). We can coherently suppose that necessarily the particle was at position 0 if you go far enough back, and then the system models backwards-infinite branching. However, note an unappealing aspect of this model: the movement probabilities are time-dependent. The model does not seem to fit our laws of nature which are time-translation symmetric (which is why we have energy conservation by Noether’s theorem).

Partial and complete explanations

1. Any explanation for an event E that does not go all the way back to something self-explanatory is merely partial.

2. A partial explanation is one that is a part of a complete explanation.

3. So, if any event E has an explanation, it has an explanation going all the way back to something self-explanatory. (1,2)

4. Some event has an explanation.

5. An explanation going back to something self-explanatory involves the activity of a necessary being.

6. So, there is an active necessary being. (4,5)

I am not sure I buy (1). But it sounds kind of right to me now. Additionally, (3) kind of sounds correct on its own. If A causes B and B causes C but there is no explanation of A, then it seems that B and C are really unexplained. Aristotle notes that there was a presocratic philosopher who explained why the earth doesn’t fall down by saying that it floats on water, and he notes that the philosopher failed to ask the same question about the water. I think one lesson of Aristotle’s critique is that if it is unexplained why the water doesn’t fall down it is unexplained why the earth falls down.

Megavalue

In my previous post, I glibly talked of the infinite value of persons. I forgot that such talk was discredited by this argument. Instead, one should talk of relatively infinite value: being infinitely more times valuable than.

I think the argument of that post can be rescued. And while I am at it, I can modify the argument to avoid another objection, that higher animals like dogs and dolphins are not infinitely less valuable than persons. I do not know if the objection is sound, but it won't matter.

1. Definition: A thing has megavalue if and only if it is infinitely more times valuable than every portion of non-living reality in the universe.

2. The sum total of life in the universe has megavalue.

3. Nothing can cause something that has infinitely more value than itself.

4. If the sum total of life in the universe has a cause and that cause is wholly within the universe, then the cause is a portion of the non-living reality in the universe.

5. There is a cause of the sum total of life in the universe.

6. A cause of the sum total of life in the universe is not wholly within the universe.

A cosmological argument from the Hume-Edwards Principle

The Hume-Edwards Principle (HEP) says:

1. If you’ve explained every item in a collection, you’ve explained the whole collection of items.

This sounds very plausible, but powerful counterexamples have been given. For instance, suppose that exactly at noon, cannonball is shot out of a cannon. The collection C of cannonball states after noon has the property that each state in C is explained by an earlier state in C (e.g., a state at 12:01:00 is explained by a state at 12:00:30). By the Hume-Edwards Principle, this would imply that C is self-explanatory. But it plainly is not: it requires the cannon being fired at noon to be explained.

But I just realized something. All of the effective counterexamples to the Hume-Edwards Principle involve either circular causation or infinite causal regresses. We can now argue:

2. HEP is necessarily true.

3. If circular causation is possible, counterexamples to HEP are possible.

4. If infinite causal regresses are possible, counterexamples to HEP are possible.

5. So, neither circular causation nor infinite causal regresses are possible.

6. If there is no first cause, there is a causal circle or an infinite causal regress.

7. So, there is a first cause.

Similarly, it is very plausible that if infinite causal regresses are impossible, then causal finitism, the thesis that nothing can have an infinite causal history, is true. So, we get an argument from HEP to causal finitism.

Dialectically, the above is very odd indeed. HEP was used by Hume and Edwards to oppose cosmological arguments. But the above turns the tables on Hume and Edwards!

Objection: Not every instance of causal regress yields a counterexample to HEP. So it could be that HEP is true, but some causal regresses are still possible.

Response: It’s hard to see how there is sufficient structural difference between the cannonball story and other regresses to allow one to deny the cannonball story, and its relatives, while allowing the kind of regresses that are involved in Hume’s response to cosmological arguments.

Final remark: What led me to the above line of thought was reflecting on scenarios like the following. Imagine a lamp with a terrible user interface: you need to press the button infinitely many times to turn the lamp on, and once you do, it stays on despite further presses. Suppose now that in an infinite past, Alice was pressing the button once a day. Then the lamp was always on. Now I find myself with two intuitions. On the one hand, it seems to me that there is no explanation in the story as to why the lamp was always on: “It’s always been like that” just isn’t an explanation. On the other hand, we have a perfectly good explanation why the lamp was on n days ago: because it was on n + 1 days ago, and another button press doesn’t turn it off. And I found the second intuition pushing back against the first one, because if every day’s light-on state has an explanation, then there should be an explanation of why the lamp was always on. And then I realized this intuition was based on somehow finding HEP plausible—despite having argued against HEP over much of my philosophical career. And then I realized that one could reconcile HEP with these arguments by embracing causal finitism.

A cosmological argument from a PSR for ordinary truths

Often in cosmological arguments the Principle of Sufficient Reason (PSR) is cleverly applied to vast propositions like the conjunction of all contingent truths or to highly philosophical claims like that there is something rather than nothing or that there is a positive contingent fact. But at the same time, the rhetoric that is used to argue for the PSR is often based on much more ordinary propositions, such as Rescher’s example of an airplane crash which I re-use at the start of my PSR book. And this can feel like a bait-and-switch.

To avoid this criticism, let’s suppose a PSR limited to “ordinary” propositions, i.e., the kind that occur in scientific practice or daily life.

1. Necessarily we have the Ordinary PSR that every contingent ordinary truth has an explanation. (Premise)

2. That there is an electron is an ordinary proposition. (Premise)

3. It is possible that there is exactly one contingent being, an electron. (Premise)

4. Necessarily, if no electron is a necessary being, then any explanation of why there is an electron involves the causal activity of a non-electron. (Premise)

5. Let w be a possible world where there is exactly one contingent being, an electron. (By 3)

6. At w, there is an explanation of why there is an electron. (By 1, 2 and 4)

7. At w, there is a non-electron that engages in causal activity. (By 4, 5 and 6)

8. At w, every non-electron is a necessary being. (By 5)

9. At w, there is a necessary being that engages in causal activity. (By 7 and 8)

10. So, there is a necessary being that possibly engages in causal activity. (By 9 and S5)

So, we have a cosmological argument from the necessity of the Ordinary PSR.

Objection: All that the ordinary cases of the PSR show is that actually the Ordinary PSR is true, not that it is necessarily true.

Response: If the Ordinary PSR is merely contingently true, then it looks like we are immensely lucky that there are no exceptions whatsoever to the Ordinary PSR. In other words, if the Ordinary PSR is merely contingently true, we really shouldn’t believe it to be true—we shouldn’t think ourselves this lucky. So if we are justified in believing the Ordinary PSR to be at least contingently true, we are justified in believing it to be necessarily true.

If materialism is true, God exists

Causal finitism is the doctrine that backwards infinite causal histories are impossible.

1. If the xs compose y, then y cannot have caused all of the xs.

2. If materialism is true and causal finitism is false, then it is possible to have a human being that (a) is composed of cells and (b) caused each of its cells via a backwards infinite regress.

3. So, if materialism is true, causal finitism is true. (1, 2)

4. If causal finitism is true, then God exists.

5. So, if materialism is true, God exists. (3, 4)

6. If God exists, the materialism is false.

7. So, materialism is false. (5, 6)

Premise (1) is a strengthening of a plausible principle banning self-causation.

Premise (2) follows from the fact that we are causes of all our present cells. If presentism is true, that completes the argument against materialism as in my previous post. But if eternalism or growing block are true, then we may also be composed of our past cells. And we didn’t cause our first cells. However if causal finitism is false, then it’s very plausible that backwards infinite causal regresses are possible, and so we could have existed from eternity, continually producing new cells, with the old ones dying.

Premise (4) is backed by a version of the kalaam argument.

Premise (6) is definitional if we understand materialism strongly enough to apply not just to us but to all reality. If we understand materialism more weakly, then the argument “only” yields the conclusion (5) that if materialism is true, God exists.

Non-instrumental pursuits and uncaused causes

Here’s a curious fact: It is one thing to pursue something because it is a non-instrumental good and another to pursue it as a non-instrumental good, or to pursue it non-instrumentally. A rich eccentric might offer me $100 for pursuing some non-instrumental good. I might then do a Google Image search for “great art”, and spend a few seconds contemplating some painting. I would then be pursuing the good of contemplation because it is a non-instrumental good, but not as a non-instrumental good. (What if the eccentric offered to double the payment if I pursued the good non-instrumentally? My best bet would then be to just forget all about the offer and hope I end up pursuing some good non-instrumentally anyway.)

Thinking about the above suggests an important thesis: To pursue a good non-instrumentally is something positive, not merely the denial of instrumentality. Simply cutting out of the world the story about the rich eccentric and keeping my contemplation in place does not make the contemplation be pursued as a non-instrumental good. Rather, such world surgery makes the contemplation non-rational. To make the contemplation a non-instrumental pursuit of a good requires that I add something—a focus on that good in itself. We don’t get non-instrumental pursuit by simply scratching out the instrumentality, just as we don’t get an uncaused cause by just deleting its cause—rather, an uncaused cause is a cause of a different sort, and a non-instrumental pursuit is a pursuit of a different sort.

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.

Why the Five Ways don't prove the existence of five (or more!) deities

Here is a potential problem for Aquinas’ Five Ways. Each of them proves the existence of a very special being. But do they each prove the existence of the same being?

After giving the Five Ways in Summa Theologica I, Aquinas goes on to argue that the being he proved the existence of has the attributes that are needed for it to be the God of Western monotheism. But the problem now is this: What if the attributes are not all the attributes of the same being? What if, say, the being proved with the Fourth Way is good but not simple, while the being proved with the First Way is simple but not good?

I now think I see how Aquinas avoids the multiplicity problem. He does this by not relying on Ways 3–5 in his arguments for the attributes of God, even when doing so would make the argument much simpler. An excellent example is Question 6, Article 1, “Whether God is good?” Since the conclusion of the Fourth Way is that there is a maximally good being, it would have been trivial for Aquinas to just give a back-reference to the Fourth Way. But instead Thomas gives a compressed but complex argument that “the first effective cause of all things” must be desirable and hence good. In doing so, Aquinas is working not with the Fourth Way, but the Second Way, the argument from efficient causes.

Admittedly, at other times, as in his arguments for simplicity, St. Thomas relies on God not having any potentiality, something that comes directly from the First Way’s prime mover argument.

This reduces the specter of the attributes being scattered between five beings, corresponding to the Five Ways, to a worry about the attributes being scattered between two beings, corresponding to the First and Second Ways. But the First and Second Ways are probably too closely logically connected for the latter to be a serious worry. The First Way shows that there is a being that is first in the order of the actualizing of the potentiality for change, an unchanged changer, a prime mover. The Second Way shows that there is a being that is first in the order of efficient causation. But to actualize the potentiality for change is a form of efficient causation. Thus, the first being in the order of efficient causation will also be a prime mover. So there is a simple—so simple that I don’t recall Aquinas stating it in the Summa Theologica—argument from the conclusion of the Second Way to the same being satisfying the conclusion of the First Way.

Consequently, in the arguments for the attributes of God, Aquinas needs to only work with the conclusion of the Second Way, and all the attributes he establishes, he establishes as present in any being of the sort the Second Way talks about.

That still leaves a multiplicity problem within the scope of a single Way. What if there are multiple first efficient causes (one for earth, one for the moon, and so on, say)? Here Thomas has three solutions: any first being has to be utterly simple, and only one being can be that on metaphysical grounds; any being that is pure actuality has to be perfect, and only one being can be that; and the world has a unity and harmony that requires a unified first cause rather than a plurality of first causes.

Finally, when all the attributes of God have been established, we can—though Aquinas apparently does not, perhaps because he thinks it’s too easy?—come back to Ways Three through Five and ask whether the being established by these ways is that same one God? The ultimate orderers of the world in the Fifth Way are surely to be identified with the first cause of the Second Way once that first cause is shown to be one, perfect, intelligent, and cause of all other than himself. Plausibly, the maximally good being of the Fourth Way has to be perfect, and Aquinas has given us an argument that there is only one perfect being. Finally, the being in the conclusion of the Third Way is also a first cause, and hence all that has been said about the conclusion of the Second Way applies there. So, Aquinas has the resources to solve the multiplicity problem.

All this leaves an interesting question. As I read the text, the Second Way is central, and Aquinas’ subsequent natural theology in the Summa Theologica tries to show that every being that can satisfy the conclusion of the Second Way has the standard attributes of God and there is only one such being. But could Aquinas have started with the Third Way, or the Fourth, or the Fifth, instead of the First and Second, in the arguments for the divine attributes? Would doing so be easier or harder?

The probability of the universe popping into existence

Consider the hypothesis that contingent reality popped into existence uncaused.

Now, either popping into existence uncaused is astronomically unlikely or not astronomically unlikely.

If it is astronomically unlikely, then we have a very strong Bayesian argument for theism. For then P(contingent reality | no God) is astronomically small while P(contingent reality | God) is at least moderately high.

If uncaused popping into existence is not astronomically unlikely, then there are two main options. The first option is that there is no meaningful probability of such an event. In that case, there is no meaningful probability of Maxwell’s Demon popping into existence for no cause at all in one’s lab. But if Maxwell’s Demon were to pop into existence in one’s lab, then one wouldn’t expect to get the predicted observations. Thus, if there is no meaningful probability of things popping into existence for no cause at all, then there is no meaningful probability of our scientific predictions, and science falls apart. That’s not acceptable.

The other option is that there is a probability, and it’s not astronomically small. But then at every moment of time, it is not astronomically unlikely that an object would causelessly pop into existence. Since there are astronomically many moments of time during a second (perhaps infinitely many, but at least equal to the number of Planck times in a second, i.e., of the order of 10⁴³), it seems we should expect to see lots of objects pop into existence causelessly. And we don’t observe that.

There is lots of technical detail to fix in this argument.

Two open-ended cosmological arguments

First argument:

1. There are no infinite causal regresses or causal loops.

2. Every ordinary entity has a cause.

3. So, there is an extraordinary entity.

Second argument:

4. There is a causal explanation why there are any ordinary entities.

5. Causal explanations are not circular.

6. So, there is an extraordinary entity.

Pruss and Rasmussen, Necessary Existence

Josh Rasmussen's and my Necessary Existence (OUP) book is out, both in Europe and in the US. I wish the price was much lower. The authors don't have a say over that, I think.

The great cover was designed by Rachel Rasmussen (Josh's talented artist wife).

Counting down from infinity

In one version of the Kalaam argument, Bill Craig argues against forming an infinite past by successive addition by asking something like this: Why would someone who had been counting down from infinity have been finished today rather than, say, yesterday? This argument puzzles me. After all, there is a perfectly good reason why she finished today: because today she reached zero and yesterday she was still on the number one. And yesterday she was on one because the day before she was on two. And so on.

Of course, one can object that such a regress generates no explanation. But then the Kalaam argument needs a Principle of Sufficient Reason that says that there must be explanations of such regressive facts and an account of explanation according to which the explanations cannot be found in the regresses themselves. And with these two assumptions in place, one doesn’t need the Kalaam argument to rule out an infinite past: one can just run a “Leibnizian style” cosmological argument directly.

A version of the cosmological argument from preservation

Suppose that all immediate causation is simultaneous. The only way to make this fit with the obvious fact that there is diachronic causation is to make diachronic causation be mediate. And there is one standard way of making mediate diachronic causation out of immediate synchronic causation: temporally extended causal relata. Suppose that A lasts from time 0 to time 3, B lasts from time 2 to time 5, and C lasts from time 4 to time 10 (these can be substances or events). Then A can synchronically cause B at time 2 or 3, B can synchronically cause C at time 4 or 5, and one can combine the two immediate synchronic causal relations into a mediate diachronic causal relation between A and C, even though there is no time at which we have both A and C.

The problem with this approach is explaining the persistence of A, B and C over time. If we believe in irreducibly diachronic causation, then we can say that B’s existence at time 2 causes B’s existence at time 3, and so on. But this move is not available to the defender of purely simultaneous causation, except maybe at the cost of an infinite regress: maybe B’s existence from time 2.00 to time 2.75 causes B’s existence from time 2.50 to time 3.00; but now we ask about the causal relationship between B’s existence at time 2.00 and time 2.75.

So if we are to give a causal explanation of B’s persistence from time 2 to time 5, it will have to be in terms of the simultaneous causal efficacy of some other persisting entity. But this leads to a regress that is intuitively vicious.

Thus, we must come at the end to at least one persisting entity E such that E’s persistence from some time t₁ to some time t₂ has no causal explanation. And if we started our question with asking about the persistence of something that persists over some times today, then these times t₁ and t₂ are today.

Even if we allow for some facts to be unexplained contingent “brute” facts, the persistence of ordinary objects over time shouldn’t be like that. Moreover, it doesn’t seem right to suppose that the ultimate explanations of the persistence of objects involve objects whose own persistence is brute. For that makes it ultimately be a brute fact that reality as a whole persists, a brute and surprising fact.

So, plausibly, we have to say that although E’s persistence from t₁ to t₂ has no causal explanation, it has some other kind of explanation. The most plausible candidate for this kind of explanation is that E is imperishable: that it is logically impossible for E to perish.

Hence, if all immediate causation is simultaneous, very likely there is something imperishable. And the imperishable entity or entities then cause things to exist at the time at which they exist, thereby explaining their persistence.

On the theory that God is the imperishable entity, the above explains why for Aquinas preservation and creation are the same.

(It’s a pity that I don’t think all immediate causation is simultaneous.)

Problem: Suppose E immediately makes B persist from time 2 to time 4, by immediately causing it to exist at all the times from 2 to 4. Surely, though, E exists at time 4 because it existed at time 2. And this “because” is hard to explain.

Response: We can say that B exists at time 4 because of its esse (or act of being) at time 2, provided that (a) B’s esse at time 2 is its being caused by E to exist at time 2, and (b) E causes B to exist at time 4 because (non-causally because) E caused B to exist at time 2. But once we say that B exists at time 4 because of its very own esse at time 2, it seems we’ve saved the “because” claim in the problem.

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.

A defense of the five minute hypothesis (given a certain false assumption)

Plausibly:

1. If the universe came into existence either for no cause at all or randomly, it is a priori more likely that it came into existence in a higher-entropy state rather than a lower-entropy one.
2. If the universe came into existence fully-formed five minutes ago ("five minute hypothesis"), it came into existence in a higher-entropy state than if it came into existence 13.8 billion years ago ("scientific orthodoxy").
3. So, if the universe came into existence either for no cause at all or randomly, the five minute hypothesis would be a priori more likely than scientific orthodoxy.
4. But there is no a posteriori evidence for scientific orthodoxy over the five minute hypothesis.
5. So, if we think the universe came into existence either for no cause at all or randomly, it is not rationally consistent for us to believe scientific orthodoxy over the five minute hypothesis.

I personally think premise (1) is dubious: I doubt there are meaningful probabilities for the universe to come into existence for no cause at all or randomly. But if there are no meaningful probabilities, then it is not a priori more likely that it come into existence as scientific orthodoxy claims, and the rest of the argument should continue to go through.

Of course, I think we should believe scientific orthodoxy over the five minute hypothesis, so we should reject the no-cause and randomness hypotheses in (1).

An amusing rhetorical way to present the argument is that if the universe came into existence for no cause at all or randomly, we shouldn't prefer scientific orthodoxy to certain young earth views.

An Aristotelian argument for a causal principle

Start with these assumptions:

1. Laws of nature are grounded in the powers of things. (I.e., Aristotelian picture of laws.)
2. Space can be infinite.
3. Newtonian physics is metaphysically possible.

There is a somewhat handwaving argument that if (1)-(3) are true, then an object cannot come into existence ex nihilo for no cause at all, and hence we have a causal princople.

Here's why. Say that a gridpoint in a Newtonian three dimensional space is a point with coordinates (x,y,z) where x,y and z are integers (in some fixed unit system).

Given (1)-(3) and assuming that objects can pop into existence ex nihilo, it should possible to start with a universe of finite total mass and then for a Newtonian particle of equal non-zero mass to simultaneously pop into existence at all and only those gridpoints (x,y,z) where z is positive, with nothing popping into existence elsewhere. Here's why. At each gridpoint, the object should be able to pop into existence. But objects that pop into existence causelessly at one location in space would be doing so in complete oblivion of what happens at other gridpoints. There should be total logical independence between all the poppings into existence. If so, then any combination of poppings or non-poppings should be able to happen at the gridpoints, and in particular, it should possible to have particles of equal mass pop into existence at the gridpoints with positive z-coordinates but nowhere else. But if this happened, then each particle would experience an infinite force in the direction of the z-axis (this follows from Newton's shell theorem and some approximation work), which would result in an infinite acceleration, which is absurd.

A relativistic version of this argument would require that spacetime can be infinite, so we could arrange the particles popping into existence along a single backwards light-cone.

There is a more general point here. The above example will remind regular readers of an argument I recently gave for causal finitism. I think many paradox-based arguments for causal finitism can be turned into arguments for causal principles in something like the above way. If this is right, this is very cool, because we can get both premises of a Kalaam Cosmological Argument out of the paradoxes then.

Infinite dependence regresses and set theory

Given the Axiom of Dependent Choice, the Axiom of Regularity in set theory is equivalent to the statement that there are no backwards infinite membership regresses, i.e., no cases where we have a backwards infinite sequence of sets ...,A₋₃,A₋₂,A₋₁,A_-0, where each set is a member of the next. Why think this is true? Well, intuitively, a set depends on its members. That suggests that the reason to believe the Axiom of Regularity is that there cannot be an infinite dependency regress. And that in turn has all sorts of other consequences (including that there is a first cause).

Against per se ordered infinite sequences of causes

Say that a sequence of events is per se causally ordered provided that each event not only causes the next but also causes everything in the next that is involved in causing the one after that (if there is one after that).

1. Any possible chunk of contingent reality is such that it is possible for something internally just like it to have a cause.
2. It is not possible to have a cause for an infinite per se causal regress of contingent causes.
3. Anything internally just like an infinite per se causal regress of contingent causes is an infinite per se causal regress of contingent causes.
4. So an infinite per se causal regress of contingent causes is impossible.

In the argument, (1) is a weak causal principle. The reason for the "something internally just like" phrase is that without the phrase the premise would immediately imply that every possible chunk of contingent reality has a cause given essentiality of origins. Premise (3) requires a non-Humean account of causation. I am going to ignore metaphysical questions about chunks of reality: perhaps we can reformulate in terms of pluralities, perhaps in terms of sets.

A crucial controversial premise is (2). Here's an intuitive line of thought that inclines me to (2). Suppose we have a backwards-infinite per se causal sequence of chickens and eggs, each chicken fully deterministically causing an egg with all of its relevant causal power, and each egg deterministically causing a chicken with all of its relevant causal power. And imagine this regress has a cause, say, G. How can G cause that whole sequence? Well, it couldn't do it by causing one particular chicken or one particular egg, for that wouldn't account for the chickens and eggs that came before that. The only picture I get of how something could cause the whole sequence would be if it caused each one of the eggs and chickens, or each one prior to some point in time, or more generally some backwards-infinite subsequence. The argument will be the same in each of the three cases, so I will just focus on the simplest.

So the cause G caused each of the eggs and chickens, and thereby caused the sequence. But of course each egg is caused by a chicken, too. So a given egg has two causes: it is caused by a chicken and by G. But the chicken caused the egg fully, with everything the egg needed to do its job of causing the next thing. So what did G contribute? Nothing really crucial to the sequence, since everything crucial to it was contributed by the chicken. Rather, it looks like it's going to be a case of overdetermination. The egg is caused by G and it's caused by the chicken. But G's causing of the regress as a whole isn't overdetermined (or so we may surely assume, modulo some technicalities), since in the absence of G the whole sequence wouldn't be caused. And if you take away a non-overdetermining cause, the effect disappears. So if you took away G, the whole regress should disappear. But why should taking away G matter, given that all of the causal influences by which G allegedly causes the regress are individually overdetermined?

If this is all right, then the critical attention will shift to (1).