Maverick Philosopher

Explanation and Understanding: More on Bogardus

What follows are some further ruminations occasioned by the article by Tomas Bogardus first referenced and commented upon here. I will begin by explaining the distinction between personal and impersonal explanations.  The explanation I am about to give is itself a personal explanation, as should become clear after I define 'personal explanation.'

A lightning bolt hits a tree and it bursts into flame. A young child  coming on the scene sees a tree on fire and asks me why it is on fire. The child desires to understand why the tree is on fire. I seek to satisfy the child's desire by providing an explanation. I explain to the child that the tree is on fire because it was struck by a bolt of lightning.

Personal explanation

My explanation to the child  is an example of a personal as opposed to an impersonal explanation. One person explains something to another person,  or to a group of persons, or in the zero-case of personal explanation, to oneself.  Personal explanations of the first type -- the only type I will consider here -- have a triadic structure and involve a minimum of three terms: P1, P2, and E where E is a proposition. One person conveys a proposition to a second person. In the example, I convey the proposition A lightning strike caused the tree to explode into flame to the child. This communicative process or act of explaining is not itself a truth-bearer: it is neither true nor false.

Neither true nor false, it is either successful or unsuccessful.  The act of explaining is successful if  the recipient of the explanation 'gets it' and comes to understand something he did not understand before. It is unsuccessful if the recipient fails to 'get it.' Now I nuance the point with a further distinction.

Strongly successful versus weakly successful

Two conditions must be satisfied for a personal explanation to be what I will call strongly successful. First, the proposition conveyed must be true. Second, the proposition must be understandable and understood by the recipient of the explanation. If either condition goes unsatisfied, the personal explanation is not strongly successful. For a personal explanation to be what I will call weakly successful, it suffices that the recipient of the explanation be satisfied by the explanation, where satisfaction requires only that the recipient understand the proposition conveyed in the explanation, and find it believable, whether or not the proposition is true.

Although the act of explaining is not a truth-bearer and thus not a proposition, the act of explaining embeds a proposition. Call the latter the content of the act of explaining. Every act of personal explaining has a content which may or may not be true. But the explaining, although it includes a propositional content, is not itself a proposition.  As a performance of a concrete person it is itself concrete and thus not abstract as is a proposition. Note also that the performance as an individual event is categorially barred from being either true or false. 

Impersonal explanation

Impersonal explanations are two-termed, both terms being propositions that record events. For example Lightning struck the tree explains The tree burst into flame. Schematically, p explains q, where 'p' and 'q' are free variables the values of which can only be propositions. No person is a proposition, although of course there are plenty of (infinitely many) propositions about every person, some true, the others false. 

Now if two propositions are related by the impersonal explanation relation, then the result is itself a proposition. We could say that an impersonal explanation is a dyadic relational proposition.

I think it is obvious that the explains relation must not be confused with the causation relation, assuming that causation is in fact a relation. (To dilate further on whether causation is, strictly speaking, a relation would open up a can of worms that is best put on the back burner for the nonce, if you will forgive my highly unappetizing mixed metaphor).  What is the difference? Well, the impersonal explains relation relates propositions which are abstracta whereas the causal relation relates events which are concreta.  Roughly, explanation is at the level of thought; empirical causation is at the level of concrete reality.

Complete impersonal explanations

Now consider the second premise in Bogardus's main argument:

2) Any explanation can be successful only if it crucially involves no element that calls
out for explanation but lacks one.

In the simple example I gave, call the two events Strike and Ignition.  Strike is the salient cause of  Ignition. I won't pause to proffer a rigorous definition of 'salient cause,'  but you know what I mean. Salient cause as opposed to all the many causal factors that have to be in place for Ignition to occur.  If there is no oxygen in the atmosphere around the tree, for example, then there is no Ignition. Nobody will say that the cause of Ignition is the presence of oxygen even though its presence is a necessary condition of Ignition, a condition without which Ignition is nomologically impossible.  (The nomologically possible is that which is possible given the laws of nature.  These laws are themselves presumably broadly logically, i.e. metaphysically, contingent.)

I read "no element" in (2) as covering both salient causes and what I am calling causal factors. I also read (2) as telling us that one cannot provide a successful causal explanation of  any particular empirical fact unless (i) it is possible in principle to explain every temporally antecedent salient event and causal factor in the entire series of events  and factors culminating in the fact to be explained (Ignition in the example) subject to the proviso  that (ii) the explanation cannot 'bottom out' in brute  or unexplainable facts.

I am having trouble understanding (2): it strikes me as ambiguous as between

2a) Any personal explanation can be successful only if it crucially involves no element that calls out for explanation but lacks one

and

2b) Any impersonal explanation can be complete only if it crucially involves no element that calls out for explanation but lacks one.

It seems to me that (2a) is false, whereas (2b) is true.  (2a) is false because I can stop explaining right after citing the lightning strike.  I do not need to explain that lightning is an atmospheric  electrical discharge,  caused by  electrostatic activity occurring between two electrically charged regions, etc.  Same with the other example I gave. Kid asks, "Why did the crops fail, Grandpa?" Old man replies, "Because of the drought." The kid's desire to understand has been satisfied, and so the personal explanation is successful without being complete.  There is no need to regress further although one could, and in some context should.

To fully appreciate this, we must understand what Bogardus takes to be the link between explanation and understanding.  The following is from one of his endnotes:

Recall the link between explanation and understanding. A successful explanation can produce in us understanding of the phenomenon, an understanding of why or how it’s happening. But if there’s part of a proposed explanation that cannot be understood, because it’s brute – how can it produce in us understanding of why or how the phenomenon is happening? Yet if it cannot produce in us that understanding, then it isn’t a successful explanation. In each of these cases, there is a part of the proposed explanation that cannot be understood – in the first, the mare, in the second, the meal – and, so, in neither case do we have a successful explanation. To put it another way, to understand why (or how) is to understand an acceptable answer to the relevant ‘Why?’ (or ‘How?’) question. But if part of that answer is unintelligible, unable to be understood, totally mysterious, then one cannot understand the answer. And, in that case, one cannot understand why (or how) the phenomenon is happening. But, if so, then these answers cannot be successful explanations. In that case, they are not counterexamples to premise 2, despite appearances.

On the basis of this passage and other things Bogardus says in his article, I fear that he may be confusing personal with impersonal explanation.  He seems to be talking about personal explanation above. If so, how, given that our paltry minds are notoriously finite, could we grasp or understand any complete explanation? I am also wondering whether 'brutality,' brute-factuality is a red herring here.

Suppose I grant him arguendo that there are no brute facts.  I could then easily grant him that a complete impersonal explanation of an event such as Ignition must take the form of  proposition of the form X explains Y, where Y is the proposition Ignition occurs and X is a huge conjunction of propositions (and thus a conjunctive proposition) the conjuncts of which record all of the salient causes and causal factors involved at every step in the causal regress from Ignition back in time.

But as I said, our minds are finite. Being exceedingly finite, they cannot 'process,' i.e., understand an impersonal explanation given that an impersonal explanation is a proposition with a huge number of conjuncts, even if the number of conjuncts is itself finite.  An explanation we cannot understand may be, in itself, complete, but for us, must be unintelligible.  An unintelligible explanation, however, cannot count as either strongly or weakly successful as I defined these terms above.  To be either, it must be able to satisfy our desire for understanding.

Dilemma: Explanation is either personal or impersonal.  If the former, the explanation may be successful  in generating understanding,  but cannot be completely true.  If the latter, the explanation may be completely  true, but cannot be  successful in generating understanding in finite minds like ours.

I may take up the ex nihilo mare and meal examples in a separate post.

Naturalism, Ultimate Explanation, and Brute Facts and Laws

Malcolm Pollack solicited my comments on an article by Tomas Bogardus that appeared in Religious Studies under the title, If naturalism is true, then scientific explanation
is impossible.

Malcolm summarizes:

I’ve just read a brief and remarkably persuasive philosophical paper by Tomas Bogardus, a professor of philosophy at Pepperdine University. In it, he argues that, if we are to have confidence in the explanatory power of science (and he believes we should), then the naturalistic worldview must be false.

Here is the abstract:

I begin by retracing an argument from Aristotle for final causes in science. Then, I advance this ancient thought, and defend an argument for a stronger conclusion: that no scientific explanation can succeed, if Naturalism is true. The argument goes like this: (1) Any scientific explanation can be successful only if it crucially involves a natural regularity. Next, I argue that (2) any explanation can be successful only if it crucially involves no element that calls out for explanation but lacks one. From (1) and (2) it follows that (3) a scientific explanation can be successful only if it crucially involves a natural regularity, and this regularity does not call out for explanation while lacking
one. I then argue that (4) if Naturalism is true, then every natural regularity calls out for explanation but lacks one. From (3) and (4) it follows that (5) if Naturalism is true, then no scientific explanation can be successful. If you believe that scientific explanation can be (indeed, often has been) successful, as I do, then this is a reason to reject Naturalism.

Keywords: philosophy of religion; philosophy of science; scientific explanation; naturalism; supernaturalism; theism; atheism

The gist of the argument is that science, which is in the business of explaining observable phenomena, must offer for every explanandum (i.e., that which is to be explained) some explanans (that which explains). But if the explanans itself requires explaining, the explanation is incomplete, and must rest upon some deeper explanans.

Bogardus’s paper explores the varieties of possible explanatory regression. Either a) we bottom out on a “brute fact”, or b) we encounter an infinite stack of explanations (“turtles all the way down”), or c) our explanations loop back on themselves (so that at some point every explanandum also becomes an explanans), or d) we come at last to some explanans that breaks the chain, by requiring no further explanation.

Bogardus argues that of all brute facts, infinite regressions, and circular explanations explain nothing; the only kind of thing that will serve is (d). But the “laws of nature” do not meet this requirement, because they do not (and cannot) explain themselves.

The heart of Bogardus’s argument, then, is that only some sort of necessary truth, some teleological principle that stands outside of the chain of scientific explanation, can serve as the anchor to which that chain must be fastened. And because Naturalism admits of no such entity, then if scientific explanations are to be considered valid, Naturalism must be false.

My Evaluation

It is given that nature is regular. She exhibits all sorts of regularities. Some of them are codified in scientific law statements. Coulomb's Law, for example, states that particles of like charge repel and particles of unlike charge attract. Another regularity we are all familiar with is that if a gas is heated it expands. This is why I do not store my can of WD-40 in the garage in the Arizona summer. The regularity is codified is Gay Lussac's law: the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.  Now why should that be the case? What explains the law? The kinetic theory of gases. If you heat a gas you give the molecules more energy so they move faster. This means more impacts on the walls of the container and an increase in the pressure. Conversely if you cool the molecules down they will slow down and the pressure will be decreased. The temperature of the gas varies with the kinetic energy of the gas molecules. 

But invoking the kinetic theory of gases is not an ultimate explanation.  What about those molecules and the laws that govern them?

So here is a question for Malcolm: Is Bogardus assuming that a genuine explanation must be or involve an ultimate explanation? And if he is making that assumption, is the assumption true?

Here is another example. Farmer John's crops have failed. Why? Because of the drought. The drought in turn is explained in terms of atmospheric conditions, which have their explanations, and so on. Question is: have I not explained the crop failure by just saying that that drought caused it?

Must I explain everything to explain anything? Is no proximate explanation a genuine explanation?

But we are philosophers in quest of the ultimate. That's just the kind of people we are. So we want ultimate explanations. And let us suppose, with Bogardus, that such explanations cannot be non-terminating, that is, they cannot be infinitely regressive or 'loopy,' i.e. coherentist.  Ultimate explanations must end somewhere.  Bogardus:

. . . I believe many Naturalists subscribe to scientific explanation in the pattern of Brute Foundationalism, either of the Simple or Extended variety, depending on the regularity. Here’s Carroll’s (2012, 193) impression of the state of the field: ‘Granted, it is always nice to be able to provide reasons why something is the case. Most scientists, however, suspect that the search for ultimate explanations eventually terminates in some final theory of the world, along with the phrase “and that’s just how it is”.’31

My question to Malcolm (and anyone): Why can't scientific explanations end with brute laws and brute facts? Has Bogardus given us an argument against brute laws? I don't see that he has. Or did I miss the argument for (2) below in Bogardus's main argument:

 

1) Any scientific explanation can be successful only if it crucially involves a natural
regularity.
2) Any explanation can be successful only if it crucially involves no element that calls
out for explanation but lacks one.
3) So, a scientific explanation can be successful only if it crucially involves a natural
regularity, and this regularity does not call out for explanation while lacking one.

4) If Naturalism is true, then every natural regularity calls out for explanation but
lacks one.
5) So, if Naturalism is true, then no scientific explanation can be successful.

Bogardus tries to argue for (2), but I don't see that he succeeds in giving us a non-question-begging reason to accept (2).

I myself reject naturalism and brute facts. My point is that Bogardus has failed to refute it and them. He has merely opposed it and them.  As I use 'refute,' it is a verb of success.  To oppose me is not to refute me. I will oppose you right back.

There is another question that I will address in a separate post:  Can it be demonstrated that there is a Necessary Explainer? Pace the presuppositionalists, the demonstration cannot be circular. A circular demonstration is no demonstration at all.  You cannot prove a proposition by presupposing it. You are of course free to presuppose anything you like. You can even presuppose naturalism and then 'argue': it is true because it is true, and then try to account for everything is naturalistic terms.

Can God Break a Law of Nature?

This is the fourth in a series of posts on Plantinga's new book.  They are  collected under the rubric Science and Religion.  In the third chapter of Where the Conflict Really Lies, Plantinga addresses questions about divine action and divine intervention in the workings of nature.  A miracle is such an intervention.  But aren't miracles logically impossible?  Plantinga doesn't cite Earman, but I will: 

John Earman, Hume's Abject Failure: The Argument Against Miracles (Oxford 2000), p. 8, writes:

 . . . if a miracle is a violation of a law of nature, then whether or not the violation is due to the intervention of the Deity, a miracle is logically impossible since, whatever else a law of nature is, it is an exceptionless regularity.

According to one way of thinking, miracles are violations of laws of nature. And so one may argue:

1. A miracle is an exception to a law of nature.
2. Every law of nature is an exceptionless regularity (though not conversely).
Therefore
3. A miracle is an exception to an exceptionless regularity.
Therefore
4. Miracles are logically impossible.

 Please note that (2) merely states that whatever a law of nature is, it is an exceptionless regularity. Thus (2) does not commit one to a regularity theory of laws according to which laws are identified with exceptionless regularities. The idea is that any theory of (deterministic) laws would include the idea that a law is an exceptionless regularity.

The above argument seems to show that if miracles are to be logically possible they cannot be understood as violations of laws of nature. To avoid the conclusion one must deny (1). How then are miracles to be understood?  Plantinga supplies an answer:

Miracles are often thought to be problematic, in that God, if he were to perform a miracle, would be involved in 'breaking,' going contrary to, abrogating, suspending, a natural law.  But given this conception of law, if God were to perform a miracle, it wouldn't at all involve contravening a natural law.  That is because, obviously, any occasion on which God performs a miracle is an occasion when the universe is not causally closed; and the laws say nothing about what happens when the universe is not causally closed.  Indeed, on this conception it isn't even possible that God break a law of nature. (pp. 82-83)

As I understand him, Plantinga is saying that a miracle is not a divine suspension of a law of nature, but a  divine suspension of causal closure.   Conservation and other natural laws apply to isolated or closed systems (78).  God cannot intervene without 'violating' closure; but that does not amount to a violation of a law since the laws hold only for closed systems.  "It is entirely possible for God to create a full-grown horse in the middle of Times Square without violating the principle of conservation of energy.  That is because the systems including the horse would not be closed or isolated." (79)

Plantinga is maintaining that it is logically impossible, impossible in the very strongest sense of the term, for anyone, including God, to contravene a law of nature.  But it is logically possible that God contravene causal closure.  This implies that causal closure is not a law of nature.

But isn't it a proposition of physics that the physical universe is causally closed, that every cause of a physical event is a physical event and that every effect of a physical event is a physical event?  No, says Plantinga.  Causal closure is a "metaphysical add-on," (79) not part of physics.  That's right, as far as I can see.  I would add that it is the mistake of scientism to think otherwise.

Whether or or not God ever intervenes in the physical world, I do it all the time.  It's called mental causation.  That it occurs is a plain fact; that mental causes are not identical to physical causes is not a plain fact, but very persuasively arguable, pace Jaegwon Kim.   So if a frail reed such as the Maverick Philosopher can bring about the suspension of causal closure, then God should be able to pull it off as well.  (This comparison with mental causation is mine, not Plantinga's.)

Of Summertime in the Desert and Miracles

When cold water comes out of the 'hot' tap, and hot water out of the 'cold,' is it a miracle? No, it is summertime in the desert. (The pipe from the water heater runs through the air-conditioned house; the cold water line comes from outside where the temperature is in the triple Fahrenheit digits. So if I want nice cold water for a short time, I turn on the 'hot' tap.)

What appears to be an exception to an exceptionless regularity is not one at all, for the apparent exception is itself regular. The statement, "Hot from 'hot,' cold from 'cold'," has a counterexample. But it does not follow that the underlying regularity has an exception. For if the underlying regularity were to be captured in a complete statement, that statement would be seen to have no counterexamples since all the exceptions would have been built into it.

This is just a little 'warm-up' for a further series of posts on miracles.  And I just noticed that Frege (whom to have on one's side in a logic fight is like having Doc Holliday on one's side in a gunfight) seems to be on my side:

The word 'law' is used in two senses. When we speak of laws of morals or the state we mean regulations which must be obeyed but with which actual happenings are not always in conformity. Laws of nature are the generalization of natural occurrences with which the occurrences are always in accordance. (First paragraph of "The Thought: A Logical Inquiry")

A law may be more than an exceptionless regularity, but it is at least one.

Laws of Nature, Civil Laws, and the Idea of 'Breaking' a Law

In Kant on Miracles,  I wrote:

The advantage of the epistemic approach [to miracles] is that it rescues us from the rank absurdity, pointed out by Hume, of having to say that there are laws of nature that admit of exceptions. Since our understanding is imperfect, our formulations of the laws of nature will some of them admit of exceptions. But it is hard to credit the idea that the laws themselves could admit of exceptions.

This assertion that (deterministic) laws cannot have exceptions drew heavy fire. 'Ockham' commenting at my old blog, wrote:

If a law couldn't be broken, why do we ever use the word 'broken' in the same vicinity as 'law'? Indeed, at this point I could use a 'contrast argument' which I know Bill hates. It only makes sense to talk about laws not being broken, if laws can be broken. Ergo, laws can be broken.

We do speak of breaking laws and of laws being broken. But this is almost always in the context of civil (legal) laws and moral laws. The latter are prescriptive and proscriptive: You shall do X and you shall refrain from doing Y. Laws of these forms are often broken.  But when they are broken, this has no tendency to show that they are not valid or binding. Legally and morally, one must feed one's children; but it would be absurd to argue that since some parents do not feed their children that these laws do not hold.

But in the case of laws of nature, violations do show that they are not valid. A law of nature that could be violated would not be a law of naure. A legal or moral law that could not be violated, by contrast, would not be a legal or moral law. The latter are 'laws of freedom,' laws that legislate with respect to free beings. A necessary feature of them is that they allow the possibility of their own violation. By contrast, a necessary feature of laws of nature is that they be exceptionless.

The necessity that attaches to moral and legal laws is moral necessity or obligatoriness. Now the following is a consistent set: {It is obligatory that All Fs are Gs; Some Fs are not Gs). By contrast, the necessity that attaches to laws of nature is nomic necessity. The following is an inconsistent set: {It is nomically necessary that All Fs are Gs; Some Fs are not Gs.)

If we bear clearly in mind the distinction between laws of nature on the one hand, and legal/moral laws on the other, then we will not speak of the breaking of laws of nature.

With respect to Ockham's contrast argument, I concede that it is bound up with the very sense of 'legal/moral law' that it be possible for such laws to be broken. But a law of nature is not a law in this sense. Events in nature can neither abide by laws of nature nor break them. That one and the same word 'law' is used both for legal/moral imperatives and also for nature-descriptive declaratives is an interesting fact, but it looks to be a case of pure equivocation.

Ceteris Paribus Laws and Miracles

Here is a passage from a paper by Nancy Cartwright, In Favor of Laws that are not Ceteris Paribus After All, for you to break your eager heads against:

Turn now to what Earman, Roberts, and Smith call “special force laws”, like the law of universal gravitation (A system of mass M exerts a force of size GMm/r^2 on another system of mass m a distance r away) or Coulomb’s law (A system with charge q1 exerts a force of size ε0q1q2/r^2 on another system of charge q2 a distance r away). These are not strict regularities. Any system that is both massive and charged presents a counterexample. Special forces behave in this respect just like powers. This is reflected in the language we use to present these laws: one mass attracts another; two negative charges repel each other. Attraction and repulsion are not among what Ryle called ‘success’ verbs. Their truth conditions do not demand success: X can truly attract Y despite the fact that Y is not moved towards X. But perhaps, as with the delights of our universe or the Ratman’s desire for the death of his father, the requisite effects are really there after all. Earman, Roberts, and Smith feel that the arguments against this position are not compelling. I think they are: the force of size GMm/r^2 does not appear to be there; it is not what standard measurements generally reveal; and the effects we are entitled to expect –- principally an acceleration in a system of mass m a distance r away of size GM/r^2 – are not there either.

Kant on Miracles

Earlier posts uncovered epistemic as opposed to ontic conceptions of miracles in Augustine and in Spinoza; but Immanuel Kant too seems to favor an epistemic approach. "If one asks: What is to be understood by the word miracle? it may be explained . . . by saying that they are events in the world the operating laws of whose causes are, and must remain, absolutely unknown to us." (Religion Within the Limits of Reason Alone, Harper Torchbooks, p. 81) There is no talk here, as in Hume, of a miracle as involving a "transgression" of a law of nature. The idea is that in the case of miraculous events there are laws of nature operating but these laws are unknown to us. This seems to imply that the miraculousness of a miracle is an appearance relative to our ignorance. If we knew the laws, there would be no miracles.

Spinoza's Epistemic Theory of Miracles

Chapter Six of Spinoza's Theologico-Political Treatise is entitled, "Of Miracles." We do well to see what we can learn from it. Spinoza makes four main points in this chapter, but I will examine only two of them in this entry.

We learned from yesterday's discussion of Augustine that there is a certain tension between the will of God and the existence of miracles ontically construed. Miracles so construed violate, contravene, suspend, or otherwise upset the laws of nature. But the laws of nature are ordained by God, and that would seem to be the case however laws are understood, whether as regularities or as relations of universals or whatever. So it seems as if the theist is under a certain amount of conceptual pressure to adopt an epistemic theory of miracles. We heard Augustine say, Portentum ergo fit non contra naturam, sed contra quam est nota natura: A portent, therefore, happens not contrary to nature, but contrary to what we know as nature. We find a similar view in Spinoza, despite the very considerable differences between the two thinkers:

Swinburne on Miracles: Quotes and Notes

Herewith, a bit of commentary on R. G. Swinburne's "Miracles" (Phil. Quart. vol. 18, no. 73, October 1968. Reprinted in Rowe and Wainwright, pp. 446-453) To be fair, I should consider what Swinburne says in his later publications on this topic; perhaps in subsequent posts.

1. What is a miracle? Swinburne writes,

I understand by a miracle a violation of a law of Nature by a god, that is, a very powerful rational being who is not a material object (viz., is invisible and intangible). My definition of a miracle is thus approximately the same as Hume's: "a transgression of a law of nature by a particular volition of the Deity or by the interposition of some invisible agent." (446)

Three Senses of 'Law' Distinguished

1. There is a distinction between a law of nature and a law of science. If there are laws of nature, they have nothing to do with us or our theorizing. They are 'out there in the world.' For example, if we adopt a regularity theory of laws, and I am not saying we should, the regularities, and thus the laws, exist independently of our theorizing. Surely, if there are physical laws at all, and whatever their exact nature, their existence antedates ours. Laws of science, on the other hand, are our attempts at formulating and expressing the laws of nature. They are human creations. Since physics is a human activity, there were no laws of physics before human beings came on the scene; but there were physical laws before we came on the scene. Physics is not the same as nature; physics is the study of nature, our study of nature. It is obvious that physics cannot exist without nature, for it would then have no object, but nature can get on quite well without physics.

Are Miracles Logically Possible? Part II

The problem raised in the first post in this series is whether we can make logical room for miracles, specifically, divine interventions in, or interferences with, the natural course of events. Now nature is orderly and regular: it displays local and global ('cosmic') uniformities. If that were not the case, it would not be possible to have science of it. (But we do have science, knowledge, of nature, ergo, etc.) For example, it is a global uniformity of nature that any two electrons anywhere in the universe will repel each other, that no signal, anywhere, can travel faster than the speed of light, etc. Here is the form of a global uniformity, an exceptionless regularity:

1. Wherever and whenever F-ness is instantiated, G-ness is instantiated.

Now for various reasons which we may consider later, a law of nature cannot be identified with an exceptionless regularity. (For one thing, law statements support counterfactuals while statements of global uniformity do not support counterfactuals.) But laws manifest themselves in global uniformities. (This talk of 'manifestation,' which I find felicitous, I borrow from D. M. Armstrong.)

Are Miracles Logically Possible?

John Earman, Hume's Abject Failure: The Argument Against Miracles (Oxford 2000), p. 8:

. . . if a miracle is a violation of a law of nature, then whether or not the violation is due to the intervention of the Deity, a miracle is logically impossible since, whatever else a law of nature is, it is an exceptionless regularity.

According to a standard way of thinking, miracles are violations of laws of nature. This approach has an impressive pedigree. Thus Thomas Aquinas writes, in the Summa Theologica (Q. 110, art. 4, respondeo), "A miracle properly so called takes place when something is done outside the order of nature." Thomas makes it clear that by 'nature' he means the whole of created nature, and not just physical nature. He concludes that God alone can work miracles.

Thomas also alludes (in Reply Obj. 2) to a distinction between miracles ontically and epistemically construed. This is not his terminology. He speaks of miracles "absolutely" considered and miracles "in reference to ourselves." Something that occurs by a power unknown to us may appear miraculous to us and yet not be miraculous absolutely.  We could call that an epistemic miracle: an event  which does not contravene a law of nature, but appears to do so due to our ignorance.  Genuine miracles, events that in fact do contravene laws of nature, we could call ontic miracles.  But don't be misled by the terminology: the suggestion is not that there are two kinds of miracles, epistemic and ontic, but two senses of 'miracle.'  'Epistemic' in 'epistemic miracle' is an alienans adjective.

Now consider:

1. A miracle is an exception to a law of nature.
2. Every law of nature is an exceptionless regularity (though not conversely).
Therefore
3. A miracle is an exception to an exceptionless regularity.
Therefore
4. Miracles are logically impossible.

This argument seems to show that if miracles are to be logically possible they cannot be understood as violations of laws of nature. How then are they to be understood?  Please note that (2) merely states that whatever a law of nature is, it is an exceptionless regularity.  Thus (2) does not commit one to a regularity theory of laws according to which laws are identified with exceptionless regularities.  The idea is that any theory of  (deterministic) laws would include the idea that a law is an exceptionless regularity.