An argument against the Thomistic primary/secondary causation account of strong providence

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed. Some like me think one cannot have circularity in the order of explanation at all. I argued for this thesis in my previous post today. Now I want to draw an interesting application.

On one influential (and I think exegetically correct, pace Eleonore Stump) reading of Aquinas, God decides what our free choices will be. Our free choices cannot be determined by created causes, but they are determined by God. This is because God’s causation is primary causation which is of a different sort from the secondary causation which is creaturely causation. God can primarily cause you to freely secondarily cause something, and this is how providence and free will interact. Often the analogy between an author and a character is given: the author decides what the character will freely do and this does not infringe on the character’s freedom.

But now observe this (which was brought home to me by a paper of one of our grad students). On this picture, God will presumably sometimes providentially make earlier actions happen because of later ones. Thus, God may want you to perform some heroic self-sacrifice in ten years. So, right now God prepares you for this by having you freely engage in small self-sacrifices now. In the “because” corresponding to the explanatory order of providence and primary causation, we thus have:

1. You engage in small self-sacrifices because you will engage in a great self-sacrifice.

However, divine primary causation does not undercut secondary causation, and we have the standard Aristotelian story of habituation at the level of secondary causation in light of which we have:

2. You will engage in a great self-sacrifice because you are engaging in small self-sacrifices.

These explanations form a heterotypic explanatory loop (i.e., we have explanations of two different sorts in opposite directions). But if I am right that no explanatory loop is possible, the above story is not possible. However, there is nothing to rule out the above story if the above Thomistic account of primary and secondary causation’s role in providence is correct. Hence, I think we should reject that account.

If no homotypic circles of explanation, no heterotypic ones either

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed, i.e., there are no homotypic circles of explanation. Some like me think one cannot have circularity in the order of explanation at all. Why? One intuition might be that explanations of all types are still explanations, and so the circularity is still an explanatory circularity. :-) (Yes, that begs the question.) More seriously, heterotypic explanations (namely, explanations of different types) can be combined, sometimes chainwise (A explains B and B explains C, and thereby A explains C) and sometimes in parallel (A explains B and C explains D so A-and-C explains B-and-D). This means that the types of explanation are not quite as separate as they might seem.

Here is an argument building on the second intuition. We need two concepts. First, we can talk of two sets of explanatory relations as independent, namely without any interaction between the explanatory relations in the two sets. Second, given two type of explanation₁ and explanation₂, I will say that explanation_1|2 is a type of explanation where explanation₁ and explanation₂ are combined in parallel.

1. If circularity in explanation is possible, it is possible to have a two-item heterotypic explanatory loop.

2. If it is possible to have a two-item heterotypic explanatory loop, it is possible to have two independent two-item heterotypic explanatory loops where each loop involves the same pair of explanation types as the other loop.

3. Necessarily, if A explains₁ B and C explains₂ D, and the two explanatory relations here are independent, then A-and-C explains_1|2 B-and-D.

4. Necessarily, the relations explains_1|2 and explains_2|1 are the same.

5. It is not possible to have a circle of explanations of the same type.

6. Suppose circularity in explanation is possible. (Assume for reductio)

7. There is a possible world w, such that at w: there are A, B, C and D such that A explains₁ B, B explains₂ A, D explains₁ C and C explains₂ D, and the above explanatory relations between A and B are independent of the above explanatory relations between C and D. (6,1,2)

8. At w: A-and-C explains_1|2 B-and-D. (3,7)

9. At w: B-and-D explains_2|1 A-and-C. (3,7)

10. At w: B-and-D explains_1|2 A-and-C. (4,9)

11. At w: there is a circle of explanations of type 1|2. (8,10)

12. Contradiction! (5,11)

13. So, circularity in explanation is impossible.

I think the most problematic premise in this argument is (4). However, if (4) is not true, we have a vast multiplication in types of explanation.

A violation of the Principle of Sufficient Reason?

I have a number of times over my career claimed that in the ordinary course of life, we don’t take seriously the hypothesis that something we can’t find an explanation for has no explanation.

Well, I now had an opportunity for observing what happens psychologically to me when I can’t find an explanation.

A couple of days ago, my wife found a significant pool of water in the morning on the top surface of our clothes dryer. When I looked at it, it was like 250ml or more. If it were on the floor or on the washer, I would expect it was from a washer-related leak. If our clothes dryer had a water connection for steaming clothes, a leak would make sense (ChatGPT 3.5 suggested this hypothesis). If the quantity were lower, it could easily be from wet clothes put carelessly on top of the dryer or condensation. If there was wetness in the cabinets above the dryer, it would likely be a leak in one of the many containers of cleaning, photo-developing and other chemicals stored there. If the ceiling showed a discoloration above the dryer, it would be a leak from upstairs. If the liquid smelled, it might be urine from the cat sneaking in.

But none of these apply, to the point where my best four explanations are all hard to believe:

1. a family member sleepwalking with a glass of water, wandering into the laundry room, spilling the water, and walking away,

2. God doing a miracle just to impress on me that there are more things in heaven and earth than are dreamed of in my natural philosophy,

3. a very precisely aimed horizontal leak from one of the faucets in the room, none of which are above the dryer (the next morning, there were slight leaks in two faucets in the room, but the leaks were a non-directional wetness rather than a jet aimed at a precise target).

4. a family member spilling water (from what?) on the dryer and forgetting all about it.

(A plumber called in for the faucet leaks could think of no explanation, except to note that there are many plumbing problems given our current Texas freeze.)

What is my psychology about this? I can’t get myself to believe any of (a)–(d), or even their disjunction. I find myself strongly pulled to just forget the event, to pretend to myself that the event was but a dream, and it now seems to me that that is one way in which we cope with unexplained events. But of course my wife remembers the event, and I can’t get myself to take seriously the idea that we both had the same dream (plus there was no waking up after it—after we cleaned up the spill, I launched into other activities rather than finding myself back in bed).

What about this option?

5. The event has an explanation: it violates the Principle of Sufficient Reason.

I also can’t take (e) seriously. But do I take (e) less seriously than the options in (a)–(d)? Speaking of subjective feelings, I don’t think I feel much more incredulous about (e) than about (a)–(d).

So what do I really think? I guess:

6. There is a mundane explanation and I am not smart enough to think of it.

A dilemma for best-systems accounts of laws

Here is a dilemma for best-systems accounts of laws.

Either:

1. law-based scientific explanations invoke the lawlike generalization itself as part of the explanation, or

2. they invoke the further fact that this generalization is a law.

Thus, if it is a law that all electrons are charged, and Bob is an electron, on (1) we explain Bob’s charge as follows:

3. All electrons are charged.

4. Bob is an electron.

5. So and that’s why Bob is charged.

But on (2), we replace (3) with:

6. It is a law that all electrons are charged.

Both options provide the Humean with problems.

If it is just the lawlike generalization that explains, then the explanation is fishy. The explanation of why Bob is charged in terms of all electrons being charged seems too close to explaining a proposition by a conjunction that includes it:

7. Bob is charged because Bob is charged and Alice is charged.

Indeed both (3)–(5) and (7) are objectionably cases of explaining the mysterious by the more mysterious: the conjunction is more mysterious than its conjunct and the universal generalization is more mysterious than its instances.

On the other hand, suppose that our explanation of why Bob is charged is that it’s a law that all electrons are charged. This sounds correct in general, but is not appealing on a best-systems view. For on a best-systems view, what the claim that it’s a law that all electrons are charged adds to the claim that all electrons are charged is that the generalization that all electrons are charged is sufficiently informative and brief to make it into the best system. But the fact that it is thus informative and brief does not help it explain anything.

Moreover, if the problem with (3)–(5) was that universal generalizations are too much like conjunctions, the problem will not be relieved by adding more conjuncts to the explanation, namely that the generalization is sufficiently informative and brief.

On two problems for non-Humean accounts of laws

There are three main views of laws:

• Humeanism: Laws are a summing up of the most important patterns in the arrangement of things in spacetime.

• Nomism: Laws are necessary relations between universals.

• Powerism: Laws are grounded in the essential powers of things.

The deficiencies of Humeanism are well known. There are also deficiencies in nomism and powerism, and I want to focus on two.

The first is that they counterintuitively imply that laws are metaphysically necessary. This is well-known.

The second is perhaps less well-known. Nomism and powerism work great for fundamental laws, and for those non-fundamental laws that are logical deductions from the fundamental laws. But there is a category of non-fundamental laws, which I will call impure laws, which are not derivable solely from the fundamental laws, but from the fundamental laws conjoined with certain facts about the arrangement of things in spacetime.

The most notorious of the impure laws is the second law of thermodynamics, that entropy tends to increase. To derive this from the fundamental laws, we need to add some fact about the initial conditions, such as that they have a low entropy. The nomic relations between universals and the essential powers of things do not yield the second law of thermodynamics unless they are combined with facts about which universals are instantiated or which things with which essential powers exist.

A less obvious example of an impure law seems to be conservation of energy. The necessary relations between universals will tell us that in interactions between things with precisely such-and-such universals energy is conserved. And it might well be that the physical things in our world only have these kinds of energy-conserving universals. But things whose universals don’t conserve energy are surely metaphysically possible, and the fact that such things don’t exist is a contingent fact, not grounded in the necessary relations between universals. Similarly, substances with causal powers that do not conserve energy are metaphysically possible, and the non-existence of such things is at best a contingent fact. Thus, to derive the law of conservation of energy, we need not only the fundamental laws grounded in relations between universals or essential powers, but we also need the contingent fact that conservation-violators don’t exist.

Finally, the special sciences (geology, biology, etc.) are surely full of impure laws. Some of them perhaps even merely local ones.

One might bite the bullet and say that the impure laws are not laws at all. But that makes the nomist and powerist accounts inadequate to how “law” gets used in science.

The Humean stands in a different position. If they can account for fundamental laws, impure laws are easy, since the additional grounding is precisely a function of patterns of arrangement. The Humean’s difficulty is with the fundamental laws.

There is a solution, and this is for the nomist and powerist to say that “law of nature” is spoken in many ways, analogically. The primary sense is the fundamental laws that the theories nicely account for. But there are also non-fundamental laws. The pure ones are logical consequences of the fundamental laws, and the impure ones are particularly important consequences of the fundamental laws conjoined with important patterns of things in nature. In other words, impure laws are to be accounted for by a hybrid of the non-Humean theory and the Humean theory.

Now let’s come back to the other difficulty: the necessity worry. I submit that our intuitions about the contingency of laws of nature are much stronger in the case of impure laws than fundamental laws or pure non-fundamental laws. It is not much of a bullet to bite to say that matching charges metaphysically cannot attract—it is quite plausible that this is explained by thevery nature of charge. It is the impure laws where contingency is most obvious: it is metaphysically possible for entropy to decrease (funnily enough, many Humeans deny this, because they define the direction of time in terms of the increase of entropy), and it is metaphysically possible for energy conservation to be violated. But on our hybrid account, the contingency of impure laws is accounted for by the Humean element in them.

Of course, we have to check whether the objections to Humeanism apply to the hybrid theory. Perhaps the most powerful objection to a Humean account of laws is that it only sums up and does not explain. But the hybrid theory can explain, because it doesn’t just sum up—it also cites some fundamental laws. Moreover, it may be the case that the patterns that need to be added to get the impure laws could be initial conditions, such as that the initial entropy is law or that no conservation-violators come into existence. But fundamental law plus initial conditions is a perfectly respectable form of explanation.

Laws of nature are hyperintensional

Are the laws of nature hyperintensional? I.e., if p and q are logically equivalent, could it be that one of them is a law of nature and the other is not?

I am inclined to think so.

Argument 1: The laws of nature in our world do not make reference to particular substances. But if p is a law of nature, then let q be the proposition that p is true and either Biden is president or Biden is not presiden. Then p and q are logically equivalent, but q is not a law as it makes reference to a particular substance.

Argument 2: The laws of nature in our world are first-order. But any first-order proposition p is logically equivalent to the second-order proposition that p is true.

Argument 3: Plausibly, the values of fundamental constants like the fine-structure constant α are a part of the laws of nature. But now imagine that it turns out that the infinitely many significant digits of α express the infinite list of all arithmetical propositions and their truth values in some specific simple encoding scheme. There are two possibilities. Supposing that it is a law of nature that the digits of α have this curious property, then after verifying this property for a sufficiently large number of digits, we could know which of the remaining arithmetical propositions are true simply by measuring α to a high degree of precision. But if the law of nature is simply the brute fact that the digits are 0.007297352569…, and it just happens that these digits encode arithmetical truths in that encoding scheme, then we wouldn’t know truths by just measuring α. (Compare: Imagine a machine where you input an arithmetical proposition, and the machine flips a coin to yield an output of “True” and “False”. Even if we are so lucky that the machine always gives the right answer, that answer wouldn’t be knowledge. It would be just luck.) This means that there is a difference between having a law that says that the digits of α are determined by the arithmetical truths according to that encoding scheme and having an infinite law that simply states the digits, even though the two laws are logically equivalent (assuming the truths of arithmetic are logically necessary; if not, replace the truths of arithmetic by any sequence of hard to know logically necessary truths).

Argument 4: Laws of nature figure in explanations, but explanation is hyperintensional. The correct explanation of why the apple fell down is not that F = Gm₁m₂/r² and either Biden is president or Biden is not president, but simply that F = Gm₁m₂/r².

Argument 5: One of our best accounts of laws of nature is the Lewis-Ramsey best-systems model. But on that model it is very natural to identify the laws of nature with the axioms of the best system, and not just with propositions equivalent to the axioms of the best system.

Final note: I wonder, though, whether there is a unique proposition that expresses any given law of nature. Is there really a fact of the matter whether the law is F = Gm₁m₂/r² or F = m₁m₂(G/r²)?

Bidirectionality in means and ends

I never seem to tire of this action-theoretic case. You need to send a nerve signal to your arm muscles because there is a machine that detects these signals and dispenses food, and you’re hungry. So you raise your arm. What is your end? Food. What is your means to the food? Sending a nerve signal. But what is the means to the nerve signal?

The following seems correct to say: You raised your arm in order that a nerve signal go to your arm. What has puzzled me greatly about this case in the past is this. The nerve signal is a cause of the arm’s rising, and the effect can’t be the means to the cause. But I now think I was confused. For while the nerve signal is a cause of the arm’s rising, the nerve signal is not a cause of your raising your arm. For your raising your arm is a complex event C that includes an act of will W, a nerve signal S, and the rising of the arm R. The nerve signal S is a part, but not a cause, of the raising C, though it is a cause of the rising R.

So it seems that the right way to analyze the case is this. You make the complex event C happen in order that its middle part S should happen. Thus we can say that you make C happen in order that its part S should happen in order that you should get food. Then C is a means to S, and S is a means to food, but while S is a causal means to food, C is a non-causal means to S. But it’s not a particularly mysterious non-causal means. It sometimes happens that to get an item X you buy an item Y that includes X as a part (for instance, you might buy an old camera for the sake of the lens). There is nothing mysterious about this. Your obtaining Y is a means to your obtaining X, but there is no causation between the obtaining of Y and the obtaining of X.

Interestingly, sometimes a part serves as a means to a whole, but sometimes a whole serves as a means to the part. And this can be true of the very same whole and the very same part in different circumstances. Suppose that as a prop for a film, I need a white chess queen. I buy a whole set of pieces to get the white queen, and then throw out the remaining pieces in the newly purchased set to avoid clutter. Years later, an archaeologist digs up the 31 pieces I threw out, and buys my white queen from a collector to complete the set. Thus, I acquired the complete set to have the white queen, while the archaeologist acquired the white queen to have the complete set. This is no more mysterious than the fact that sometimes one starts a fire to get heat and sometimes one produces heat to light a fire.

Just as in one circumstances an event of type A can cause an event of type B and in other circumstances the causation can go the other way, so too sometimes an event of type A may partly constitute an event of type B, and sometimes the constitution can go the other way. Thus, my legal title to the white queen is constituted by my legal title to the set, but the archaeologist’s legal title to the set is partly constituted by legal title to the white queen.

There still seems to be an oddity. In the original arm case, you intend your arm’s rise not in order that your arm might rise—that you don’t care about—but in order that you might send a nerve signal. Thus, you intend something that you don’t care about. This seems different from buying the chess set for the sake of the queen. For there you do care about your title to the whole set, since it constitutes your title to the queen. But I think the oddity can probably be resolved. For you only intend your arm’s rising by intending the whole complex event C of your raising your arm. Intending something you don’t care about as part of intending a whole you do care about is not that unusual.

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.

Choices on a spectrum

My usual story about how to reconcile libertarianism with the Principle of Sufficient Reason is that when we choose, we choose on the basis of incommensurable reasons, some of which favor the choice we made and others favor other choices. Moreover, this is a kind of constrastive explanation.

This story, though it has some difficulties, is designed for choices between options that promote significantly different goods—say, whether to read a book or go for a walk or write a paper.

But a different kind of situation comes up for choices of a point on a spectrum. For instance, suppose I am deciding how much homework to assign, how hard a question to ask on an exam, or how long a walk to go for. What is going on there?

Well, here is a model that applies to a number of cases. There are two incommensurable goods one better served as one goes in one direction in the spectrum and the other better served as one goes in the other direction in the spectrum. Let’s say that we can quantify the spectrum as one from less to more with respect to some quantity Q (amount of homework, difficulty of a question or length of a walk), and good A is promoted by less of Q and incommensurable good B is promoted by more of Q. For instance, with homework, A is the student’s having time for other classes and for non-academic pursuits and B is the student’s learning more about the subject at hand. With exam difficulty, A may be avoiding frustration and B is giving a worthy challenge. With a walk, A is reducing fatigue and B is increasing health benefits. (Note that the claim that A is promoted by less Q and B is promoted by more Q may only be correct within a certain range of Q. A walk that is too long leads to injury rather than health.)

So, now, suppose we choose Q = Q₁. Why did one choose that? It is odd to say that one chose Q on account of reasons A and B that are opposed to each other—that sounds inconsistent.

Here is one suggestion. Take the choice to make Q equal to Q₁ to be the conjunction of two (implicit?) choices:

1. Make Q at most Q₁

2. Make Q at least Q₁.

Now, we can explain choice (a) in terms of (a) serving good A better than the alternative, which would be to make Q be bigger than Q₁. And we can explain (b) in terms of (b) serving good B better than the alternative of making Q be smaller.

Here is a variant suggestion. Partition the set of options into two ranges R₁, consisting of options where Q < Q₁ and R₂, where Q > Q₁. Why did I choose Q = Q₁? Well, I chose Q over all the choices in R₁ because Q better promotes B than anything in R₁, and I chose Q over all the choices in R₂ because Q better promotes A than anything in R₁.

On both approaches, the apparent inconsistency of citing opposed goods disappears because they are cited to explain different contrasts.

Note that nothing in the above explanatory stories requires any commitment to there being some sort of third good, a good of balance or compromise between A and B. There is no commitment to Q₁ being the best way to position Q.

The structure of morality

In physics, we hope for the following unification: there is a small set of simple laws, and all the rest of physics derives logically from these laws and the contingencies of the arrangement of stuff.

In ethics, a similar ideal has often manifested itself. While I have a hope for the ideal being realized in physics, I have come to be more pessimistic about the ideal in ethics. Instead, I think we can have a looser unificatory structure. We can have a multilevel hierarchy of more general laws, and then more specific laws that specify or implement the more general laws.

I suspect the looser structure is what we have in Aquinas’s Natural Law. At the highest level we have the general law that the good is to be pursued and the bad to be avoided. This is then specified into three laws about promoting the goods of existence, species-specific life and reason. These three laws, I think, are then further specified.

There is thus a structure to the moral law, but it is not a deductive structure. The higher level laws make the lower level laws fitting, but do not necessitate them.

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.

Samuel Clarke on our ignorance of the essence of God

At times I am made uncomfortable by this objection to arguments for the existence of God: there feels like there is something fishy about inferring the existence of a being about which we know so very little. It may be that theism is the only reasonable explanation of the universe’s existence, but if we know so very little about that explanation, can the inference to the truth of that explanation be a genuine version of inference to best explanation?

Newton's disciple Samuel Clarke has a nice answer to this objection:

There is not so mean and contemptible a plant or animal, that does not confound the most enlarged understanding upon earth; nay, even the simplest and plainest of all inanimate beings have their essence or substance hidden from us in the deepest and most impenetrable obscurity.

In other words, all our ordinary day-to-day inferences are to things whose essence is hidden.

It may be thought that now that we know about DNA, we do know the essences of plants and animals. But even if that is true, which I am sceptical of, it doesn’t matter: for belief in plants and animals was quite reasonable even before our superior science. And even this day, our knowledge of the essences of the fundamental entities of physics (e.g., particles, fields, wavefunctions) is basically nil. All we know is some facts about the effects of these entities.

Are free actions a counterexample to the PSR?

I’ve argued somewhat as follows in the past:

1. Necessarily, no one is responsible for a brute fact—an unexplained contingent fact.

2. Necessarily, someone is responsible for every free decision or free action.

3. So, it is impossible for a free decision or free action to be a brute fact.

But then:

4. Necessarily, a counterexample to the Principle of Sufficient Reason (PSR) is a brute fact.

5. So, no free decision or free action can be a counterexample to the PSR.

One may imagine someone, however, arguing that although a free decision or a free action cannot be a counterexample to the Principle of Sufficient Reason, a contrastive report, such as that x freely chose to do A rather than B, could be a counterexample to the Principle of Sufficient Reason. But notice that if x freely chose to do A rather than B, then x is responsible for choosing to do A rather than B. Similarly if x freely chose to do A for reason R rather than B for S, then x is responsible for doing so. Freedom implies responsibility. But no one is responsible for a brute fact, so such contrastive reports cannot be reports of a brute fact.

Objection 1: Incompatibilism is true, and on incompatibilism it is obvious that no possible explanation can be given for why x freely chose to do A for R rather than B for S. Hence the Principle of Sufficient Reason is false.

Response: Given that no one is responsible for what has no explanation, if the “no possible explanation” claim is correct, then free will is impossible. Thus, rather than showing that the PSR is false, the argument would show that if incompatibilism is true, free will is impossible. As a libertarian, I think free will is possible (and actual). But it is important to keep clear on what it is that is really endangered by the argument: it is free will and not the PSR.

Objection 2: Freedom is a necessary but not sufficient condition for responsibility.

Response: I am not sure about this. When I think about what other conditions we need to add to freedom to yield responsibility, the only one I can think of is something like knowledge of what is at stake. But it is arguable that without knowledge of what is at stake, a choice is not free. Moreover, even if one does not know what is at stake with A and B beyond what is contained in the respective reasons R and S, one will still be responsible for choosing A for R rather than B for S if one chooses freely for these reasons. One just won’t be responsible for the further aspects, beyond those captured by R and S, that one does not know.

But let’s grant for the sake of argument that other conditions need to be added to freedom to yield responsibility. If so, then the claim has to be that free but non-responsible decisions or actions or contrastive reports thereof are a counterexample to the PSR although free and responsible ones are not. In other words, one has to hold that the alleged additional conditions that need to be added to freedom to yield responsibility are what secures explicability. But given that the most plausible candidate for the other conditions is knowledge of what is at stake, this is implausible. For a free action based on mistaken or limited knowledge is no less explicable than an action based on full knowledge, once one takes into account the agent’s epistemic deficiency.

Could the PSR be contingent?

The Principle of Sufficient Reason (PSR) says that every contingent truth has an explanation. Most people who accept the PSR think it is a necessary principle. And there is good reason, because it seems more like a candidate for a fundamental necessary truth than a merely contingent fact. And epistemically, if the PSR is contingent, it is hard to see why we should think ourselves lucky enough for it to be true.

All that said, it is interesting to investigate the question a bit more. So, let’s suppose the PSR is contingently true. Then according to the PSR, the PSR has an explanation, like every other contingent truth. What could the explanation of the PSR be like?

Since we’ve assumed the PSR to be contingent, the explanation can’t simply involve derivation of the PSR from necessary metaphysical principle.

The explain a contingent PSR is to explain why no contingent unexplained thing has happened.

Here is one suggestion. Perhaps there is a necessary being which has the power to prevent the existence of contingent unexplained events. This necessary being freely, but with good reason that the necessary being necessarily has, chooses to exercise this power. Thus, the explanation of why no contingent unexplained thing has happened is that the necessary being freely chose to prevent all such things. And the necessary being’s free choice is explained by reasons.

I am not sure what I think of the plausibility of a hypothesis of a being as having the power to prevent things from popping into existence causelessly if such popping is otherwise metaphysically possible.

Here is another much less metaphysically loaded attempt. It seems to me that whether one accepts the PSR or not, one should accept instances of the following kind of explanatory schema for contingent events E:

1. Event E did not happen because there is no explanation of E.

If the PSR is necessarily true, then the fact that there is no explanation of E entails that E did not happen. However, I think we should accept instances of (1) even if the PSR is contingently true and even if it is not true at all. In those cases, that there is no explanation of E may not entail that E did not happen, but we shouldn’t think that explanations must entail the events they explain. (If we thought that, we would have to reject most scientific explanations.)

Now imagine we have an infinite list of all possible contingent events that could happen but did not happen, E₁, E₂, ..., and an infinite list of all contingent events that did happen, F₁, F₂, .... We can then say:

2. The PSR is true because E₁ did not happen, E₂ did not happen, E₃ did not happen, while on the other hand F₁, F₂, ... did happen.

And why did E_i not happen?

3. E_i did not happen because there is no explanation of E_i.

And of course each of the F_i does have an explanation, because the PSR is, we have assumed, true.

This seems like an explanation of the contingent truth of the PSR.

Both options seem a bit fishy, though. I can’t say exactly what’s wrong with them, though.

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.

"Despite" explanations

The phenomenon of contrastive explanations has been explored by a number of authors. There is another phenomenon in the vicinity, that of explanations of despite-claims, that has not received as much attention, even though it’s also interesting. Suppose Bob hates bananas and eats a banana.

1. Why did Bob eat a banana? – Because he was hungry.

2. Why did Bob eat a banana despite hating bananas? – Because he was very hungry.

A contrastive request for explanation, say

3. Why did Bob eat a banana rather than an apple?

doesn’t so much ask for an explanation of a special contrastive proposition, but rather constrains what kind of answer is acceptable—an answer that provides a contrastive answer. Thus, saying that Bob was hungry is not an acceptable answer since it fails to be contrastive between the banana and apple options, while saying that Bob was hungry and a banana was closer at hand is an acceptable answer. However, whenever one constrains what kind of an explanation is acceptable, one runs the risk that—even without any violation of the Principle of Sufficient Reason—there is no answer. For instance, the question

4. Who killed the mayor and why?

is a request for explanation that has no answer if the mayor died from a tornado, because (4) constrains us to agentive explanation, and in this case there is no agentive explanation.

Are requests for explanations-despite like requests for contrastive or agentive explanations, requests that constrain the type of explanation that is acceptable, rather than simply modifying the proposition to be explained?

I am inclined to think that the answer is negative. Here is a preliminary analysis for what is going on when we ask:

5. Why p despite r?

First, the question carries a presupposition that the fact that r is antiexplanatory of p or that it has a tendency against p. If that presupposition is false, the question has no answer, being akin to one of the standard trick questions with false presuppositions (like “Have you stopped beating your spouse?”).

Second, what we are asking is something like this:

6. How was the antiexplanatory force of the fact that r against its being the case that p countered such that p is true?

And this seems to be a straightforward request for an explanation of an admittedly complex proposition, without any constraints being placed on what explanations are acceptable.

If I am right about this, then while a failure to have a good answer to contrastive explanation question does no damage to the Principle of Sufficient Reason (PSR), a failure to have a good answer to an explanation-despite question, when the presuppositions of the question are correct, would be a violation of the Principle. This suggests that some of the attention focused on contrastive explanation in connection with critique of the PSR should be redirected towards explanation-despite. I think the PSR can survive such attention, but the investigation is worthwhile.

Antiexplanation

If an explanation is a truth or hypothesis that removes or would remove mystery from the proposition to be explained, then an antiexplanation is a truth or hypothesis that adds or would add mystery to the proposition to be explained. Like in the case of explanations, we need to be sensitive to context with antiexplanations. That Alice dislikes bananas is, in typical contexts, antiexplanatory of why Alice ate the banana. But if we add to the background that it’s Lent and Alice wishes to do penance, then Alice’s dislike of bananas becomes explanatory.

It is widely held, though still moderately controversial, that:

1. The fact that a hypothesis p is explanatory of some known truth is evidence for p.

A parallel claim about antiexplanations would:

2. The fact that a hypothesis p is antiexplanatory of some known truth is evidence against p.

This sounds even more plausible than (1). In a typical context, the antiexplanatoriness of a dislike of bananas to actual consumption of a banana provides evidence that Alice who ate a banana does not dislike bananas. Similarly, the fact that Bob is in perfect health is antiexplanatory of Bob’s death, and hence if Bob has died, we have evidence that Bob’s health was imperfect.

There are lots of explanatory arguments in philosophy based on (1). But it would be worth exploring whether one can’t also give antiexplanatory arguments based on (2).

In fact, I think some fairly intuitive arguments can be rephrased as antiexplanatory arguments. For instance:

3. Materialism is antiexplanatory of consciousness.

4. Consciousness is a known fact.

5. So, we have evidence against materialism.

The thought behind (3) is simply that there is intuitively something particularly mysterious about a purely material thing having a conscious point of view.

C. S. Lewis’s version of the moral argument for theism can be taken to be in part an antiexplanatory argument.

6. Atheism is antiexplanatory of moral law.

7. Moral law is a known fact.

8. So, we have evidence against atheism.

Further evaluation of such arguments would call for a deeper philosophical analysis of antiexplanation and an examination of (2). This is a task worth doing. Someone should do it.

Free will and the PSR

Even though I think one of the biggest challenges to the Principle of Sufficient Reason (PSR) is the feeling that something is unexplained in the case of free actions. I think this can be answered: see Section 4 here. But in this post I want to make a very small and simple point that just occurred to me.

The puzzle of free actions is not the lack of reasons. It is a surfeit of reasons. Suppose I eat a donut rather than an apple. It is easy to give a reason: the donut is more delicious. If that’s all we had, there would be no felt difficulty about the explanation. But the felt difficulty comes from the fact that while the donut is more delicious, the apple is more nutritious, and hence while I have a reason for eating the donut rather than the apple, I also have a reason for eating the apple rather than the donut.

But while a shortage of reasons would be a problem for a principle like the PSR that affirms the existence of reasons, a surfeit of reasons is not a problem for it!

So whatever one might say about the puzzle of free will, it is not problem for the PSR.

A necessary truth that explains a contingent one

Van Inwagen’s famous argument against the Principle of Sufficient Reason rests on the principle:

1. A necessary truth cannot explain a contingent one.

For a discussion of the argument, see here.

I just found a nice little counterexample to (1).

Consider the contingent proposition, p, that it is not the case that my next ten tosses of a fair coin will be all heads, and suppose that p is true (if it is false, replace “heads” with “tails”). The explanation of this contingent truth can be given entirely in terms of necessary truths:

2. Either it is or is not the case that I will ever engage in ten tosses of a fair coin.

3. If it is not the case that I will, then p is true.

4. If I will, then by the laws of probability, the probability of my next ten tosses of a fair coin being all heads is 1/2¹⁰ = 1/1024, which is pretty small.

My explanation here used only necessary truths, namely the law of excluded middle, and the laws of probability as applied to a fair coin, and so if we conjoin the explanatory claims, we get a counterexample to 1.

It is, of course, a contingent question whether I will ever engage in ten tosses of a fair coin. I have never, after all, done so in the past (no real-life coin is literally fair). But my explanation does not require that contingent question to be decided.

This counterexample reminds me of Hawthorne’s work on a priori probabilistic knowledge of contingent truths.

Explanation and understanding

In the 1960s, it dawned on philosophers of science that:

1. Other things being equal, low-probability explanation confers equally good understanding as high-probability explanation.

If I have a quantum coin that has a probability 0.4 of heads and 0.6 of tails, and it yields heads, I understand why it yielded heads no less well than I would have had it yielded tails—the number is simply different.

On the other hand, the following thesis (which for years I’ve conceded to opponents to low-probability explanations):

2. Other things being equal, low-probability explanations are less good than high-probability ones.

Finally, add this plausible comparative thesis:

3. What makes an explanation good is how much understanding it confers (or at least would confer were it true)

which plausibly fits with the maxim that I’ve often been happy to concede that the job of an explanation is to provide understanding.

But (1)–(3) cannot all be true. Something must go. If (2) goes, then Inference to Best Explanation goes as well (I learned this from Yunus Prasetya’s very recent work on IBE and scientific explanation). I don’t want that (unlike Prasetya). And (1) seems right to me, and it also seems important to defending the Principle of Sufficient Reason in stochastic contexts.

Reluctantly, I conclude that (3) needs to go. And this means that I’ve overestimated the connection between explanation and understanding.