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.

Skepticism and a causeless beginning to the universe

Suppose that the universe began with the Big Bang, and the Big Bang had no cause, so the universe came into existence ex nihilo. It then went through many (infinitely many if time is continuous) stages—the one-second-old universe, the ten-second-old universe, the five-minute-old universe, the one-year-old universe, the 7-million-year-old universe, before arriving at the present 13.7-billion-year-old universe, and then (presumably) going onward.

Question: Why did the universe start in the Big Bang state rather than in one of these many other states?

Assuming the universe has no cause, there does not seem to be any compelling reason to think the Big Bang state is somehow “more likely” as a starting state of the universe. (If anything, it seems a less likely state, because it has lower entropy than the later states.)

Now, granted, if the universe started in a sufficiently “late” (as compared to our state) stage, there would be no observers in that universe other than perhaps Boltzmann brains, due to the universe having expanded too much. So we have an interesting bit of fine-tuning: the universe started in a sufficiently early stage that there was still time for life.

Let’s ignore that otherwise intriguing observation, however, and push ahead. Let S_t be the t-units-of-time-past-Big-Bang stage of a universe like ours. And let’s ask:

• Conditioning on all our observations, and given that the universe has no cause, is it more likely that the universe starts with S₀ (i.e., starts with the Big Bang) than with, say, S_t1, where t₁ > 0?

If the answer is negative, then the supposition of a causeless universe leads to a skeptical hypothesis: we have no more reason to think the universe started with the Big Bang than that it started in the t₁ stage.

The answer may be positive in some cases. As we already saw, if t₁ is past the time of there being any observers—or just past the time of there being any observers making observations like ours—then we can be sure the universe didn’t start in S_t1.

If it turns out that evolutionary is logically necessary for consciousness, as some materialists think (because, basically, evolutionary history is necessary for defining proper function for making functionalism run), we might get a positive answer if t₁ is so close to the present that there was insufficient evolutionary history for our consciousness if the universe started at t₁.

But if t₁ is any time between 0 and about 3.7 billion years ago, our observations do not differentiate between the hypothesis that the universe started with S₀ or that it started with S_t1. Thus, the answer to the bulleted question above is negative. Moreover, it’s negative for each of the many t₁ in the relevant range (more than 0 but less than about 10 billion years). Thus, on a no-cause hypothesis we should not prefer the Big Bang hypothesis over a whole bunch of skeptical hypotheses holding that the universe started in a more developed form.

This argument will please theists who think the universe had a cause. Of course, the theist still has to find a way to give a positive answer to the bulleted question. I think there are two ways of doing so. First, likely a perfect being would have a preference for greater creaturely participation in creation, and creating the universe in, say, the 10 billion year stage, or indeed in any post-Big Bang stage, would pointlessly cut short creaturely participation in creation (e.g., in the 10 billion year stage, the Solar System would be created ex nihilo, rather than being generated from a star-forming nebula). Second, such a being would be likely to create a world that doesn’t make true what is intuitively to us a “skeptical hypothesis”.

The argument will also please the now-less-common atheist who thinks the universe is eternal.

Induction to the Causal Principle?

I’m curious whether one can infer the causal principle C that everything that comes into existence has a cause inductively on the basis of our observations of things with causes.

There are a couple of issues with such an inference. First, let’s think about the inductive evidence about causes globally. It seems to consist primarily in these two observations:

1. we have found causes for many things that come into existence, but

2. there are many things that come into existence for which we have yet to find causes.

It is worth noting that in terms of individuals, (b) vastly outnumbers (a). Consider insects. Of the myriad insects that we come into contact daily, we have found the causes of very few. Of course, we assume that the others have causes, causes that we suppose to be parent insects, but we haven’t found the parents.

For observations (a) and (b) to support C, these observations have to be more likely on C than on C’s negation. But now we have two problems. First, on the negation of C it doesn’t seem like we can make any sense of the probability that some item has or does not have a cause. Causeless events have no probabilities. Second, even if somehow assign such a probability, it is far from clear that the observations of (a) and (b) are more to be expected on C than on not C.

Second, I suspect that often when we claim to have found y to be the cause of x, our reason for belief that y is the cause of x depends on our assumption of C. Our best candidate for a cause of x is y, so we take y to be the cause. But I wonder how often this inference isn’t based on our dismissing the possibility that x just has no cause.

None of this is meant to impugn C. I certainly think C is true. But I think the reasons for believing C are metaphysical or philosophical rather than inductive observation.

Partial causation and causeless events

1. If ordinary events can happen without any cause at all, they can happen with a partial cause and no full cause.

2. A partial cause is a part of a full cause.

3. Nothing can happen with a partial cause and no full cause.

4. So, ordinary events cannot happen causelessly.

The argument for (2) is that (2) is the most obvious way to define a partial cause.

The argument for (1) is as follows. Suppose you and I lift a sofa in world w₁ in such a way that the exertion of each of us only partly explains the rising of the sofa, as neither exertion is enough to cause the rising. If ordinary events can happen without any cause at all, there is a world w₂ where the sofa rises causelessly, with neither you nor I doing anything. But if w₁ and w₂ are possible, likewise a world w₃ is possible where only I exert myself just as in w₁ and you sit back and the sofa rises in response to my exertion, and nothing else causally impacts the sofa’s rising. Since my exertion is not enough to cause the rising of the sofa in w₁, and in w₃ I exert myself to the same degree, my exertion is no more a full cause of the sofa’s rising in w₃ than it is in w₁. Hence, in w₃, I partially causes the sofa to rise, without there being a full cause, just as the consequent of (1) claims.

If I were inclined to deny (4), I would want to argue that (2) is not the right way to define a partial cause. But I don’t know a better way.

Existence, causation and individuation

Suppose a cause C produces horses, in the following way:

• When C produces a horse, a horse instantly comes into existence made out of some mass of non-equine matter M.

• The genetic makeup of the resulting horse is randomly distributed over all DNA compatible with being a horse.

(Imagine lightning striking a bog and randomly turning the bog mass into a horse.)

So now suppose that in world w₁, a female Arabian, Green Lightning, comes into existence as a result of C, while in w₂, a male Exmoor pony, Tigger, comes into existence as a result of C.

Presumably, Green Lightning and Tigger are numerically distinct horses. Why are they distinct? Presumably because they are qualitatively different—specifically, because their DNA is different. If in w₁ and w₂, C respectively produced horses that were exactly alike out of M, those horses would have to have been numerically identical. (Haecceitists will disagree.)

But now we have a puzzle for Aristotelians. Both Green Lightning and Tigger are of the same species. (If you think that breeds or sexes make for different metaphysical species, modify the example and make them be of the same sex and breed, but still very different from each other.) Let the Fs be the qualitative features that Green Lightning and Tigger initially differ in.

1. The Fs in are accidents in the Aristotelian sense: they are accidental to their horsehood, which is their form.

(They may not be accidents in the contemporary modal sense. It may be that it is impossible for a horse to be of another sex than it is.)

But:

2. The Fs make Green Lightning be distinct from Tigger.

3. If what makes Green Lightning be distinct from Tigger are the Fs, then the Fs help make Green Lightning be Green Lightning.

4. Nothing that helps make x be x can be explanatorily posterior to x.

5. So, the Fs are not explanatorily posterior to Green Lightning. (2-4)

6. The accidents of x are explanatorily posterior to x.

7. So, the Fs are explanatorily posterior to Green Lightning. (1,6)

8. Contradiction! (5,7)

The case where C makes a horse come into existence from non-equine matter makes the above argument a bit more vivid. In the ordinary case of equine reproduction, a sperm and egg contribute their DNA and give rise to the DNA of the offspring. There it could be argued that the relevant thing that helps make the resulting horse be the horse it is is the DNA in the sperm and the DNA in the egg.

One could conclude that a horse can’t come into existence from matter that doesn’t already contain implicit in it the DNA of the horse. But that is implausible, especially since God could create a horse even without any matter.

This puzzle worries me a lot. I initially thought it was a special puzzle for four-dimensionalist temporal-parts Aristotelianism, because it showed that the first temporal part of the horse was explanatorily prior to the whole, whereas Aristotelianism forbids parts to be prior to wholes. But then I realizes that the same point could be made about accidents without reference to four-dimensionalism.

Here is my best solution. There is something about Green Lightning that is prior to her being Green Lightning. It is her being caused by C to exist with the Fs (i.e., her being caused by C to exist as a female Arabian, etc.). Admittedly, that sounds just as much as an accident of Green Lightning as the Fs are. It’s not Green Lightning’s form, so what else could it be but an accident? There is no answer in Aristotle, but there is a potential answer in Aquinas: this could be Green Lightning’s act of being, her esse. And it is not crazy to take Green Lightning’s esse to be something that (a) is prior to Green Lightning, (b) Green Lightning could not exist without, and (c) an individuator of Green Lightning.

This reminds me of a line of thought in the Principle of Sufficient Reason book where I argued that the esse of a contingent being is its being caused. If my present solution is correct, that was only a partial description of the esse of a contingent being. And I think there may well be an argument for the principle that ex nihilo nihil fit in the vicinity, just as in the PSR book—for it is absurd to think that anything contingent could be prior to x if x has no cause, while this esse is something contingent.

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.

A Cosmological Argument based on the Empire State Building

Assume:

1. Necessarily, every exact duplicate of the Empire State Building has a cause.
2. Necessarily, if an exact duplicate of the Empire State Building never changes, then neither it nor any of its parts cause its existence.
3. Possibly, the only contingent beings ever are an unchanging duplicate of the Empire State Building and parts thereof.

Let w be a world where the only contingent beings ever are the unchanging duplicate of the Empire State Building and its parts. By (1), it has a cause. By (2), this cause cannot be the Empire State Building or a part thereof. Since those are all the contingent beings, the cause must be a necessary being, or include a necessary being as a part. So, possibly, there is a necessary being. By S5:

4. There is a necessary being.

Premise (1) is a version of the Causal Principle specialized to the sorts of entities that we are most confident of there being causes of. One might wonder about why one needs the "never changes" in (2). But there is reason for it. Some objects can perhaps be caused by their parts. Imagine a bunch of trees that grow together to form a tower. We could likewise imagine a bunch of moving stony and metallic beings that come together to form an exact duplicate of the Empire State Building. This is ruled out by the "never changes".

Scepticism, causal theories of reference and the Causal Principle

Suppose we agree that

1. Causal theories of reference have successfully answered the sceptic by ensuring that most of our empirical beliefs refer precisely to the situations that cause the beliefs (cf. Davidson).

Thus, the person whose body is a brain in a vat makes claims about the computer system that produces inputs for the brain, etc. Then, I suspect, we have to say that we know that the Causal Principle (CP) is true—that every contingent event has a cause. For suppose that contingent events could lack causes. Then causal theories of reference have not successfully answered the sceptic, because they are compatible with the Rob Koons' sceptical scenario of someone whose perceptions are all uncaused.

Let's think about what a causal theorist should say in Koons' scenario. For simplicity, assume physicalism. I think some of what I say generalizes to the non-physicalist case, but only some. I think we need some more detail about the scenario. Here are three versions:

2. The apparently perceptual beliefs occur without any cause.
3. Mental perceptual states (states relevantly like our state of being appeared to red-cubely) occur without any cause, and then cause beliefs.
4. Sensory nerve stimulations occur without any cause, and then causal mental perceptual states and beliefs.

I will consider version (2), though (3) and (4) are also interesting. As it stands, the causal theorist has to say that my description in (2) is incoherent. Granted, states that are neurally just like our own belief states occur in the victim. But these states, being systematically uncaused, are not about anything, and hence are not belief states. It seems, then, that on version (2) of the story, the causal theorist has escaped scepticism—it is still true that most of the victim's beliefs are true. But while (2) may be incoherent, there is still a sceptical scenario in the vicinity. For wouldn't it count as a sceptic's victory if the sceptic were to make us conclude that, perhaps, most of the empirical-belief-like mental states we have are not in fact beliefs? We can imagine what it is like. Suppose that an epistemic authority told us: "Yesterday, the borogoves were very mimsy." We would then acquire a neural state that would cause us to say: "I believe that yesterday, the borogoves were very mimsy." This neural state would not be a belief, perhaps, because the sentence is in fact nonsense—it does not express anything—but it would masquerade as a belief. And the scenario that most of the things that appear to us as empirical beliefs are like that would, surely, be a sceptical scenario. It seems plausible that any scenario on which it is not the case that most of those states that are not introspectively distinguishable from beliefs are not correct beliefs (i.e., are not correct or are not beliefs) is a sceptical scenario. If so, then a Koonsian scenario where most of our belief-like neural states are uncaused would be a sceptical scenario, and one that the causal theorist does not have an answer to.

I think the causal theorist's best answer compatible with (1) would be to deny that in the case where the empirical-belief-like states are uncaused that these states would be conscious, or to say that if our minds littered with too many empirical-belief-like states that are not empirical beliefs, then we would not be able to form the concept of an empirical belief. Perhaps that answer works. But I am not sure. One might, for instance, have a lot of empirical beliefs early on in one's life, which are in fact veridical, and these early ones could anchor one's concept of "empirical".

If this line of reasoning is right, then (1) requires an acceptance of the Causal Principle.