Author: Bill Vallicella

Composition: Formal or Informal Fallacy?

Although the fallacy of composition is standardly classified as an informal fallacy, I see  it is a formal fallacy, one rooted in logical form. Let W be any sort of whole (whether set, mereological sum, aggregate, etc.) Suppose each of the proper parts (if any) of W has some property P (or, for the nominalistically inclined, satisfies some predicate F). Does it follow that W has P or satisfies F? No it doesn't. To think otherwise is to commit the fallacy of composition: it is to argue in accordance with the  following invalid schema:
 
   1. Each member of W is F
   Therefore
   2. W is F.

To show that an argument form is invalid, it suffices to present an argment of that form having true premises and a false conclusion.  (This is because valid inference is truth-preserving: it cannot take one from true premises to a false conclusion. But it doesn't follow that invalid inference is falsehood-preserving: there are valid arguments with false premises and a true conclusion. Exercise for the reader: give examples.) Here is a counterexample that shows the invalidity of the above pattern: Each word in a given sentence is meaningful; ergo, the sentence is meaningful. (Let the sentence be 'Quadruplicity drinks procrastination.')  Since the premise is true and the conclusion false, the argument pattern is invalid. So every argument of that form is invalid, even in the case in which the premises and conclusion are both true.

Why then is Composition standardly grouped with the informal fallacies? Petitio principii is a clear  example of an informal fallacy. If I argue p, therefore p, I move in a circle of embarrassingly short diameter. But the inference is valid. (Bear in mind that 'valid' is a terminus technicus.) And if p is true, the argument is sound. Nevertheless, any argument of this form is probatively worthless: it it does not prove, but presupposes, its conclusion. Since this defect is not formal, we call it informal!

So there are clear examples of informal fallacies. But what about Equivocation? It is usually classed with the informal fallacies. Consider the syllogistic form Barbara (AAA-1):

   All M are P
   All S are M
   All S are P.

Suppose there is an equivocation on the middle term 'M.' Although this is an informal defect (in that it has not to do with logical syntax,  but with semantics) it translates into a formal defect, the dreaded quaternio terminorum or four-term fallacy, which is of course a formal fallacy: no syllogism with more than three terms is valid. (A syllogism by definition is a deductive argument having exactly two premises and exactly three terms.)

It can be shown that every equivocation on a key term in an argument induces a formal defect. So the standard classification of Equivocation as an informal fallacy cannot be taken too seriously. By  contrast, Petitio Principii is seriously informal in its probative defectiveness.

I say that Composition is like Equivocation: it is a formal fallacy in informal disguise. (And the same goes for Division, which is roughly Composition in reverse.) So I disagree with the author of a logic book who writes:

     . . . the fallacy of composition is indeed an informal fallacy. It
     cannot be discovered by a mere inspection of the form of an
     argument , that is, by the mere observation that an attribute is
     being transferred from parts onto the whole. . . . The critic must
     be certain that, given the situation, the transference of this
     particular attribute is not allowed. . . .

So the fallacy of composition is not always a fallacy, but only when it is a fallacy? That is the silliness that the author seems to be espousing. He is saying in effect the following: if you transfer an attribute from parts to whole, that is fallacious except in those cases in which it is not fallacious, i.e. those cases in which the transfer can legitimately be made.

But then what is the point of isolating a typical error in reasoning called Composition? What is the point of this label? Why not just say: there are many different part-whole relationships, and it is only be close acquaintance with the actual subject-matter that one can tell whether the attribute transfer is legitimate?

Logic is formal: it abstracts from subject-matter. So mistakes in logic are also formal. A mistake that is typical (recurrent) and sufficiently seductive to warrant a label is called a fallacy. To say or imply that the fallaciousness of a fallacy depends on the particular subject-matter of the argument is to abandon logic and  embrace confusion.

Example.  Every brick in this pile weighs more than five lbs; ergo, the pile weighs more than five lbs. This is an example of the fallacy of composition despite the fact that it is nomologically impossible that the pile not weigh more than five lbs.

Another example.  Every being in the universe is contingent; ergo, the universe is contingent.  This too is the fallacy of composition.  And this despite the fact that it is metaphysically impossible that a universe all of whose members are contingent be necessary.  

Religion and Anthropomorphism with an Oblique Reference to Mormonism

A young man who was brought up Mormon, retains much if not all of the salutary character formation, but is now an atheist, writes (emphasis added):

I've been thinking about some of our conversations about theology and epistemology. Particularly the stuff on Mormonism. I'm sitting in on [Professor X's] medieval philosophy class reading St. Anselm among others, and I'm constantly struck by how far removed Anselm's view of God is from the one I grew up with. And, it seems to me, how far removed from the God of the Bible. I mean, Anselm and Aquinas both are absolutely relentless in denying God any anthropogenic [anthropomorphic?] qualities whatever. We are left with something that is faceless, devoid of human emotion, and about as difficult to relate to as anything I can even imagine. I can appreciate the intellect of men like Anselm and Aquinas, but this picture of God seems repugnant.

Being an atheist, I don't have a dog in this fight, but it does seem to me that there is more to be said for the Mormon view of God than most theists, you included, seem to realize. I recently read a book called The Theological Foundations of the Mormon Religion by Sterling McMurrin. I highly recommend you check it out and read it, especially the supplementary chapter in later versions on the question of whether God is a person. I think if you do, you will find yourself forced to take Mormonism a bit more seriously as a religion.

I have spoken more than once of the tension between Athens and Jerusalem, and Athens and Benares.  I am now tempted to speak of the tension between Athens and Salt Lake City, though this third tension is but an exacerbated form of the first.   My understanding of Mormonism is limited,  so I won't address it directly. But my understanding is that Mormons maintain that God is a physical being who inhabits a physical planet.  This conception of God, whether or not it is exactly what Mormons accept, is  as repugnant to me as the Anselmian-Thomistic one is to my correspondent.  This post raises the question of anthropomorphism in religion.

Imagine a spectrum of positions. 

1. At one end crude anthropomorphism:  God as a physical being, a superman, as is suggested by such phrases as 'the man upstairs'  and 'the big guy in the sky.'  This is the way many if not most atheists think of God and why they indulge in such mockeries as 'flying spaghetti monster,' and compare God with the Tooth Fairy (Dennett), Santa Claus, a celestial teapot (Russell), an angry unicorn on the dark side of the moon (Ed Abbey), etc.  Many if not most atheists, being most of them materialists, can only think in material terms:  the only way God could be real would be for him to be a physical being.  (The tacit assumption being that to be real = to be a denizen of spacetime.)  So they think that if God is real, then he must be a physical being; and since the 'highest' physical being is man, then God is a Big Man  literally out there somewhere.  (Does he perhaps drink Celestial Seasonings (TM) tea from Russell's teapot?)  On his 1961 suborbital flight, about a month before astronaut Alan Shepard's, Soviet cosmonaut Yuri Gagarin was reported to have said  that he didn't see any God.  When I heard the news report I was 11 years old.  I exclaimed: "That dumb commie doesn't know that God is a purely spiritual being!"  Atheists, who typically can think only in material terms, then naturally deny the existence of God since it is surely absurd to think of God as a Big Man, mit Haut und Haar (Schopenhauer), etc.  So I sincerely hope that Mormons do not hold that God is literally a physical being with skin, hair, a GI tract . . . .  If that were the only option for theists, then we should all be atheists.

2.  At the other end of the spectrum, a conception of God so attenuated and diluted as to turn God into a mere concept, or a mere feeling ('God is the feeling one has when one is with those one loves') or one's ultimate concern (Tillich), or an unconscious anthropomorphic projection (Ludwig Feuerbach) or perhaps a causally inert abstract object, a denizen of the Platonic menagerie. 

3.  The positions at both ends of the spectrum are demonstrably untenable.  Briefly, God cannot be a physical being because no physical being is a necessary being, and God is a necessary being.  By definition, God is the ultimate ground of the existence of everything contingent.  (He is more, of course, but at least that.)  As such, he cannot himself be contingent, and so cannot be physical.  That is just one argument.  I am not assuming that God exists; I am merely unpacking the concept of God.  It is equally easy to show that God cannot be a concept, or an anthropomorphic projection, or an abstract entity.  I needn't waste words on whether God is a feeling or one's ultimate concern.

God cannot be a concept because concepts depend for their existence on minds, and God, by definition, is a se,  and so cannot depend for his existence on anything, not even himself. ('Causa sui' is to be taken privatively, not positively: God does not cause himself, which would require that he be logically or temporally prior to himself; it is rather the case that God is not caused by another.)  There are of course concepts of God, but God cannot be a concept.

For similar reasons, God cannot be an anthropomorphic projection.  The concept of God is the concept of a being that exists whether or not humans exist.  Obviously, such a being cannot be an anthropomorphic projection.  So if one says that God is an anthropomorphic projection, that is just a roundabout way of saying that God does not exist.  Nor can God be an abstract entity.  Abstracta, by definition, are causally inert, and God, by definition, is the first cause.

4.  The interesting positions are somewhere in the middle of the spectrum.  God is not physical; God does not depend on any mind for his existence; God is not an abstract entity.  What is left but to say that God is a mind?  Now the only minds to which we have access in the first-person way, that way which alone reveals them in their true intrinsic nature, are our minds.  Since I know my own mind, and know it to be both causally efficacious and not physical, I conjecture that either God is a mind, or more like a mind than like anything else.  One's own mind provides a model whereby one can think about God. In fact, it is the only decent model we have.   So the most adequate, and only,  way to think about God is to think about God as an unembodied mind, or better as an unembodied person where a person is a "subsistent individual of a rational nature." (Aquinas, ST I, 29, 3.)  Thinking  of God as person might not be perfectly adequate, but the other ways I have mentioned are entirely  inadequate and utterly hopeless.  So God is a person but not  a man.  A person needn't be human.

5.  If we think of God as a bodiless person we avoid the Scylla of anthropomorphism.  God is not in the form of a man; it is the other way around; man is in the form of God.  God is not anthropomorphic; man is theomorphic.  This is how we ought to read Genesis 1, 26-27:

Faciamus hominem ad imaginem et similitudinem nostram . . . (Gen 1, 26) Let us make man in our image and likeness. . .

 Et creavit Deus hominem ad imaginem suam. . . (Gen 1, 27) And God created man in his image. . .

 An oft-repeated mistake is to take these spiritual sayings in a materialistic way as if to imply that God has the form of a man.  It's as if one were to argue:

Man is made in God’s image.
Man is a physical being with a digestive tract, etc.
Therefore
God is a physical being with a digestive tract, etc.

But that would be  like arguing:

This statue is made in Lincoln’s image.
This statue is composed of marble.
Therefore
Lincoln is composed of marble.

The point of Gen 1, 26-27  is not that God must be physical because man is, but that man is a spiritual being just like God, potentially if not actually. The idea is not that God is a big man, the proverbial ‘man upstairs,’ but that man is a little god, a proto-god, a temporally and temporarily debased god who has open to him the possibility of a higher life with God, a possibility whose actualization requires both creaturely effort and divine grace.

6.   The upshot is that God is a person, a pure spirit or unembodied mind, or at least more like a person than like anything else with which we are familiar.  The Scylla of anthropomorphism and 'spiritual materialism' is avoided by thinking of God as a bodiless person.  The Charybdis of abstractionism/conceptualism is avoided by thinking of God as a person, and thus as a concrete individual who knows, loves,  and freely acts.

If we stop right here we have a position in the middle of our spectrum, one that is represented by many contemporary theists, Plantinga being one of them.  But we can't stop here, as it seems to me.

For God  is also the absolute reality.  If God is absolute, then God is ontologically simple: he is Being itself in its prime instance, and wholly partless and incomposite, hence free of act/potency composition.  I can't repeat the arguments here.  The simple God of Augustine, Anselm, and Aquinas is a second position in the middle of the spectrum, one even farther from anthropomorphism than the first according towhich God is a bodiless person, but not simple. 

I can easily understand how my correspondent above would find the simple God to be, as he says, "repugnant."  We are left with something that is faceless, devoid of human emotion, and about as difficult to relate to as anything I can even imagine. In response I will say two things.

First, the simple God of Anselm, et al., despite  its difficulties — which intellectual honesty forbids me from 'papering over' –  is vastly superior to the crude anthropomorphism which Mormons apparently accept.  (If I have misrepresented the Mormon position, then I should like to hear exactly what their position is on the topic under discussion.)  

Second, religion is about transcendence and transcending, about reaching beyond the human-all-too-human, and beyond all the images  of  the picture-loving imagination.  Religion is not about the positing of a hinterworld that duplicates this world with the negative removed.  It is not about crude, materialistic, wish-fulfillment.  This is why we find the Islamic 72 virgins conception of paradise so paltry and ridiculous:  it is a blatant pandering to the basest elements in our nature, a pandering at once both superstitious and idolatrous.  Religion aims at a spiritualizationof the human being which cannot  be imagined and is just barely conceivable.  It is about theosis (deification) as is maintained in Orthodox Christianity.  And because the ultimate goal for humans is not imaginable and barely conceivable, it is repeatedly pictured in crude and absurd materialistic  ways — which only fuels the fires of atheism.  Actually, one ought to be an atheist in respect of the anthropomorphic God-conceptions.

This is a difficult topic to write about and of course no materialistically-minded worldling could possibly be persuaded by it.  No matter how much light one sheds on an object, a blind man won't see it — he lacks the requisite organ.   But perhaps an analogy may be of some use.  Imagine a fetus in the womb who finds his environment quite acceptable, and indeed the ultimate in what is real and worthwhile.  You try to persuade the fetus that staying  in the womb indefinitely is decidely suboptimal, a mistake in that he  is capable of a marvellous development after an event called  'birth.'  He of course doesn't know what you are talking about and is in no position to imagine what it is like to be born and develop.  And he will find it almost impossible to conceive. For him birth is death: the end of his cozy and secure womb-life.   His natural tendency is to say that you are 'bullshitting' him: 

"Look man, this is reality, this is what I know, this is what I have evidence for; you are pushing some fantasy projection, some opiate so that we we fetuses won't work to improve conditions here in the womb but will waste our time dreaming about some nonexistent goodies on the other side of what you call 'birth' but we know to be death and annihilation.  Sure,  it would be nice if there were something more, but there ain't.  Your talk of infants, and children, and adolescents, and adults, is just a lie to make people denigrate the only reality there is, the reality here and now, in what you call 'womb' but we anti-birthers  call 'reality.'"

Lavelle on Living in the Present

Louis Lavelle (1883-1951), The Dilemma of Narcissus, tr. W. T.  Gairdner (New York: Humanities Press, 1973), p. 153:

Life breaks the surface of reality and emerges at the present moment; we must not hold our gaze fixed on a future which, when it comes, will be merely another present. The unhappy man is he who is  forever thinking back into the past or forward into the future; the happy man does not try to escape from the present, but rather to penetrate within it and take possession of it. Almost always we ask of the future to bring us a happiness which, if it came, we would have to enjoy in another present; but this is to see the problem the wrong way round. For it is out of the present which we have already, and from the way we make use of it, without turning our eyes to right or to left, that will emerge the only happy future we will ever have.

Some Aptronyms

An aptronym is a name that "suits the nature or occupation of its   bearer," as the erudite Dr. Gilleland explains. Some examples from my  experience:

1. During part of my tenure at the University of Dayton, the secretary of the Philosophy Department was Mrs. Betty Hume.

2. While a graduate student in Boston in the 1970s, I heard tell of a knee specialist at Massachusetts General Hospital, one Dr. Patella.

3. A number of philosophers bear aptronymic names: John Wisdom, Gerald Vision, J.J.C. Smart, and others that escape me at the moment.

4. Wasn't Jimmy Carter's main spokesman a man by the name of Larry Speakes?

5. Joe Bastardi, Fox News meterologist, is not an aptronym because he is not a name, and his demeanor and delivery suggest that his name isn't either.

A Kierkegaardian Passage in Wittgenstein

Ludwig Wittgenstein, Culture and Value (Vermischte Bemerkungen), ed  von Wright, tr. Winch (University of Chicago Press, 1980), p. 53e:

     I believe that one of the things Christianity says is that sound
     doctrines are all useless. That you have to change your life. (Or
     the direction of your life.)

     It says that all wisdom is cold; and that you can no more use it
     for setting your life to rights that you can forge iron when it is
     cold.

     The point is that a sound doctrine need not take hold of you; you
     can follow it as you would a doctor's prescription. — But here you
     need something to move you and turn you in a new direction. —
     (I.e. this is how I understand it.) Once you have been turned
     around, you must stay turned around.

     Wisdom is passionless. But faith by contrast is what Kierkegaard
     calls a passion.

Sound doctrines are useless? It would be truer to say that faith as a mere subjective passion is useless. The fideisms of Kierkegaard and Wittgenstein fall far below the balanced positions of Augustine and Aquinas. The latter thinkers understood that sound doctrine, though insufficient, was an indispensable guide. They neither denigrated reason nor overestimated its reach. Reason without faith may be existentially empty and passionless, but faith without reason is blind and runs the risk of fanaticism.

The Childless as Anthropological Danglers

Herbert Feigl wrote about nomological danglers.  Mental states as the epiphenomenalist conceives them have causes, but no effects. They are caused by physical states of the body and brain, but dangle nomologically in that there are no laws  that relate mental states  to physical states.

The childless are anthropological danglers.  They are life's epiphenomena. They have ancestors (causes) but no descendents (effects). Parents are essential: without  them we could not have come into fleshly existence.  But offspring are wholly inessential: one can exist quite well without them.

There is a downside and an upside to being an anthropological dangler.

The downside is that it unfits one for full participation in the life of the community, removing as it does weight and credibility from one’s opinions about pressing community concerns. As Nietzsche writes somewhere in his Nachlass, the man without Haus und Hof, Weib und Kind is like a ship with insufficient ballast: he rides too high on the seas of life and does not pass through life with the steadiness of the solid bourgeois weighted down with property and reputation, wife and children.  What does he know about life and its travails that his say should fully count?  His counsel may be wise and just, but it won't carry the weight of the one who is wise and just and interested as only those whose pro-creation has pro-longed them into the future and tied them to the flesh are interested.  (inter esse)

The upside to being an anthropological dangler is that it enables one’s participation in a higher life by freeing one from mundane burdens and distractions. In another Nachlass passage, Nietzsche compares the philosopher having Weib und Kind, Haus und Hof with an astronomer who interposes a piece of filthy glass between eye and telescope. The philosopher's vocation charges him with the answering of the ultimate questions; his pressing foreground concerns, however, make it difficult for him to take these questions with the seriousness they deserve, let alone answer them.

Someone who would be "a spectator of all time and existence" ought to think twice about binding himself too closely to the earth and its distractions.

Another advantage to being childless is that one is free from  being an object of those attitudes of propinquity — to give them a name — such as embarrassment and disappointment, disgust and dismissal that ungrateful children sometimes train upon their parents, not always unjustly.

The childless can look forward to a time when all of their blood-relatives have died off.  Then they will finally be free of the judgments of those to whom one is tied by consanguinity but not by spiritual affinity.

This opinion of mine will strike some as cold and harsh.  But some of us experience more of the stifling and suppressive in our blood relations than the opposite.   I do however freely admit that the very best human relations conceivable are those that bind people both by ties of blood and ties of spiritual affinity.  If you have even one blood-relation who is a soul-mate, then you ought to be grateful indeed. 

Are There Indexical Facts? Are They a Threat to Materialism?

1. Ernst Mach Spies a Shabby Pedagogue. In The Analysis of Sensations (Dover, 1959, p. 4, n. 1) Ernst Mach (1838-1916) offers the following anecdote:

     Not long ago, after a trying railway journey by night, when I was
     very tired, I got into an omnibus, just as another man appeared at
     the other end. 'What a shabby pedagogue that is, that has just
     entered,' thought I. It was myself; opposite me hung a large
     mirror. The physiognomy of my class, accordingly, was better know
     to me than my own.

When Mach got on the bus he saw himself, but not as himself. His first thought was one expressible by 'The man who just boarded is a shabby pedagogue.' 'The man who just boarded' referred to Mach. Only later did Mach realize that he was referring to himself, a thought that he might have expressed by saying, 'I am a shabby pedagogue.'

Clearly, the thought expressed by 'The man who just boarded is shabby' is distinct from the thought expressed by 'I am shabby.' After all, Mach had the first thought but not the second.  So they can't be the same thought.  And this despite the fact that the very same property is ascribed to the very same person by both sentences.  The difference emerges quite clearly if we alter the example slightly. Suppose Mach sees that the man who has just got on the bus has his fly open. He thinks to himself: The man who has just boarded has his fly open, a thought that leads to no action on Mach's part. But from the thought, I have my fly open, behavioral consequences ensue: Mach buttons his fly. Since the two thoughts have different behavioral consequences, they cannot be the same thought, despite the fact that they attribute the very same property to the very same person.

But if they attribute the same property to the same person, what exactly is the difference between the two thoughts?

Linguistically, the difference is that between a definite description ('the man who just boarded') and the first person singular pronoun 'I.'   Since the referent (Frege's Bedeutung) is the same in both cases, namely Mach, one will be tempted to say that the difference is a difference in sense (Frege's Sinn) or mode of presentation (Frege's Darstellungsweise). Mach refers to himself in two different ways, a 3rd-person objective way via a definite description, and a 1st-person subjective way via the first-person singular pronoun.

If this is right, then although there are two different thoughts or propositions, one indexical and the other non-indexical, it might seem  that there need only be one fact in the world to serve as truth-maker for both, the fact of Mach's being shabby.  This is a non-indexical fact.  It might seem that reality is exhausted by non-indexical facts, and that there are no such indexical or perspectival facts as those expressed by 'I am shabby' or 'I am BV' or 'I am the man who just got on the bus.' Accordingly, indexicality is merely a subjective addition, a projection: it belongs to the world as it appears to us, not to the world as it is in reality.  On this approach, when BV says or thinks 'I,' he refers to BV  in the first-person way with the result that BV appears to BV under the guise of 'I'; but in reality there is no fact corresponding to 'I am BV.'

2. But is this right? There are billions of people in the world and one of them is me. Which one?  BV. But if the view sketched above is correct, then it is not an objective fact that one of these people is me. That BV exists is an objective fact, but not that BV is me.  BV has two ways of referring to himself but there is only one underlyingobjective fact.  Geoffrey Maddell strenuously disagrees:

     If I am to see the world in a certain way, then the fact that the
     world seen in this way is apprehended as such by me cannot be part
     of the content of that apprehension. If I impose a subjective grid
     on the world, then it is objectively the case that I do so. To put
     it bluntly, it is an objective fact about the world that one of the
     billions of people in it is me. Mind and Materialism, 1988, p.
     119.)

Maddell's point is that the first-person point of view is irreducibly real: it itself cannot be a subjective addition supplied from the first-person point of view. It makes sense to say that secondary qualities are projections, but it makes no sense to say that the first-person point of view is a projection. That which first makes possible subjective additions cannot itself be a subjective addition.

Consider the phenomenal redness of a stop sign. It makes sense to say that this secondary quality does not belong to the sign itself in reality, but is instead a property the sign has only in relation to a   perceiver. In this sense, secondary qualities are subjective. But to say that subjectivity itself, first-person perspectivity itself, is a subjective projection is unintelligible. It cannot belong to mere   appearance, but must exist in reality. As Madell puts it, "Indexical  thought cannot be analysed as a certain 'mode of presentation', for the fact that reality is presented to me in some particular way cannot be part of the way in which it is presented." (p. 120)

3. Trouble for materialism. According to materialism, reality is exhausted by non-indexical physical facts. But we have just seen that  indexical thoughts are underpinned by indexical facts such as the fact of BV's being me. These facts are irreducibly real, but not physically real. Therefore, materialism is false: reality is not exhausted by  non-indexical physical facts.

The Marriage Killer

My angelic wife doesn't nag, so I don't have this problem.  But you might.  She doesn't nag, but she becomes inordinately happy when I do any work around the house.  Curiously irrational but delightful nonetheless.  Women are unduly attuned to the values of domestic order and cleanliness.  Not that these aren't values; but in a sound axiological hierarchy they must be assigned a position well below the values of, say, playing chess and writing philosophy, hiking and biking, acquiring and reading more books, building bookshelves to house them . . . .

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.)

A Temple to Atheism in the Heart of London?

Alain de Botton's proposal  to enshrine atheistic and this-worldly values has raised the hackles of Richard Dawkins on the ground that "the money was being misspent and that a temple of atheism was a contradiction in terms."  If I were an an atheist, I would support, or at least not oppose, de Botton's idea.  It is the negativism of the Dawkins Gang that turns many away from the New Atheism, a virulent example being A. C. Grayling's rant against religion as child abuse.