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. 

Creatio ex Deo and Pantheism

The following post draws mainly upon Robert Oakes, "Does Traditional Theism Entail Pantheism?" American Philosophical Quarterly, vol. 20, no. 1 (January 1983), pp. 105-112. Reprinted in Tom Morris, ed. The Concept of God (Oxford U. Press, 1987). 

The question arises:   Does my construal of creatio ex nihilo in terms of creatio ex Deo commit me to pantheism? If so, how does that comport with my avowed onto-theological personalism? I will try toshow that my construal does not commit me to pantheism, or at least not to the pantheism that Oakes seems to embrace.

The logically first question concerns just what pantheism is and is not. I’ll begin with what it is not.

A. Pantheism worth discussing is not the view that God (G) is identical to the physical universe (U). For that would amount to saying that God does not exist. Whether or not God exists, the divine nature excludes the possibility of God’s being a system of physical objects. The reduction of G to U thus amounts to the elimination of G. Therefore, the use of ‘God’ to refer to U is simply an egregious misuse of the term ‘God,’ a misuse on a par with Tillich’s misuse of ‘God’ to refer to one’s ultimate concern.

B. What of the opposite reduction of U to G? This is also a type of pantheism not worth discussing: it implies that God exists but the physical universe does not. For it is self-evident that the physical universe cannot exist unless it is in some sense distinct from G. After all, G is immutable whereas U is mutable; hence, by what McTaggart calls the Discernibility of the Diverse (the logical contrapositive of the Indiscernibility of Identicals), U cannot be identical to G if both exist.

C. If pantheism is to be worth discussing, it must somehow allow for a difference of some kind between God and the cosmos. It must steer a middle course between a strict identity of G and U and a type of difference that would render them ‘indifferent’ to each other, i.e., a type of radical difference that would allow the possibility of U existing without G existing. A viable pantheism must therefore avoid three positions: (1) God is world-identical; (2) The world is God-identical; (3) God and the world are externally related in the sense that either could exist without the other.

One way to satisfy these requirements is by saying, Spinozistically, that created entities are modes of God, or as Oakes says, "aspects or modifications" of God. (p. 106 et passim) For if x is a mode (aspect, modification) of y, then x is not identical to y, y is not identical to x, and x and y are not merely externally related.

It is important to realize that classical theism must also satisfy the requirements, (1)-(3). In particular, classical theism must deny that U can exist without G. For it is a central tenet of classical theism that God is not merely a cause of the inception of the universe, but a cause of its continuance as well. God is not merely a deistic 'starter-upper,' but a moment by moment conserver. How exactly creatio originans and creatio continuans fit together involves problems that cannot be discussed in this post.  (Cf. William F. Vallicella (2002), The Creation–Conservation Dilemma and Presentist Four-Dimensionalism, Religious Studies 38 (2):187-200.)  But there can be no doubt that for classical theism as it is found in Aquinas, Descartes, Leibniz, Berkeley and others, creation in the full sense involves both notions, both originating creation and continuing creation. 

Now given the fact just mentioned, how are we to distinguish classical theism (CT) from pantheism in the (C)-sense, the only sense in play here? Does (CT) perhaps entail pantheism? (To say that p entails q is to say that, necessarily, if p is true, then q is true. Equivalently, it is to say that it is impossible that p be true, and q false.)

You will notice that the doctrine of conservation ‘shortens’ the ‘ontological distance’ between creator and creatures. It implies that at each moment divine activity is required to keep the creature from lapsing into nonbeing. The point is not merely that God as a contingent matter of fact conserves creatures moment by moment, but that creatures are necessarily such that they are conserved moment by moment by divine activity. This suggests that the very being of creatures is their being-conserved moment by moment, which in turn gives rise to the following worry: How then can creatures retain any ontological independence?

Drawing on Oakes, the following Argument from Conservation can be mounted for the thesis that classical theism entails pantheism (but of course not pantheism in the absurd (A) or (B) senses). (The argument is in Oakes, but the reconstruction is mine.)

1. Every contingent being is necessarily such that it is existentially dependent on God at each moment of its existence.

2. If anything X is necessarily such that it is dependent on something Y at each moment of its existence, then X is a mode (aspect, modification) of Y.

Therefore

3. Every contingent being is a mode (aspect, modification) of God, which amounts to pantheism.

The validity (formal correctness) of this argument is not in question, and premise (1) merely states the conservation doctrine, an essential subdoctrine of classical theism. So the soundness of the argument rides on premise (2).

Premise (2) fits some cases very well. A wrinkle in a carpet satisfies both the antecedent and the consequent of (2). Same holds for the dance and the dancer. Suppose Little Eva is doing the Locomotion ("C’mon baby, do the Lo-co-mo-shun . . ..) There is the dance-type and its various actual and possible tokens. Little Eva’s gyrations at time t constitute one of these tokens such that the token in question could not possibly exist except as an aspect or modification of Little Eva at t. Similarly for felt pleasures and felt pains. The esse of a pain just is its percipi: a pain cannot exist except as perceived. Pains and the like are therefore plausibly construed as aspects or modifications of perceivers. Finally, it is plausibly maintained that a particular thinking, believing, imagining, is an aspect or modification of a thinker or a believer or an imaginer.

But now consider an object imagined as opposed to the act of imagining it. I mean an object that does not exist apart from its being imagined, a purely intentional object. (A rich vein of gold at the base of Weaver’s Needle; a one-eyed, one-horned, flying purple people eater.) Said object does not exist on i
ts own, but only as the accusative of an act (or acts) of imagining. Now while it makes sense to say that the act (the occurrent episode) of imagining is an aspect or modification of an imaginer, it does not make much sense to say this of the intentional object (the accusative) of the act. Indeed, we cannot even say that the intentional object is an aspect or modification of the act trained upon it. Why not?

Note that if x is an aspect or modification of y, then x cannot exist without y, but y can exist without x. (A carpet wrinkle cannot exist without the carpet of which it is the wrinkle, but the carpet can surely exist without that, or any, wrinkle.) By contrast, if x is the intentional object of act y, then x cannot exist without y, AND y cannot exist without x. An imagining cannot exist except as the imagining of a definite object, and that object, qua intentional object, cannot exist without the act. I conclude from this difference that the intentional object cannot be an aspect or modification of the act. It is not a property of the act, but its object or intentum. A fortiori, it cannot be an aspect or modification of the subject of the act, the imaginer in the case of an act of imagining.

We therefore have a class of counterexamples to premise (2) above. The Argument from Conservation therefore fails, and classical theism does not collapse into pantheism – or at least not for the reason that Oakes provided in the article under discussion.

So far, then, I cannot see that I am committed to pantheism in any of the three senses lately distinguished by my construal of creatio ex nihilo  as creatio ex Deo.

Dolezal on Divine Simplicity: Does He Make a Mysterian Move?

Dr. James Dolezal kindly sent me a copy of his very recent book, God without Parts: Divine Simplicity and the Metaphysics of God's Absoluteness (Pickwick, 2011).  Herewith, some quick notes and commentary based on a partial reading. 

1.  God is an absolute, or rather the absolute.  That is a non-negotiable starting point for both of us.  To uphold the divine absoluteness, however, it is necessary to think of God as ontologically simple, as devoid of metaphysical complexity and composition.  For if God is absolute, then he cannot depend on anything else for his existence or nature.  It follows that God cannot be an instance of his attributes but must be them; nor can he be an existent among existents: he must be his existence and existence itself.  Indeed, God as absolute must be ipsum esse subsistens, self-subsisting Existence.  These are hard sayings and sharp heads, Plantinga being one of them, find them incoherent.  For details and a bit of a response to Plantinga, I refer you to my Stanford Encyclopedia article.  Note also that an absolute cannot be lacking anything or in need of developing itself: it is, eternally, all that it can be.  This implies that there is no act/potency distinction in God, no unrealized powers or potentialities.  In the classical phrase, God is actus purus, pure act, wholly actual.  Dolezal puts it very well when he writes, "The consideration of God as ipsum esse subsistens and actus purus is crucial for any confession of God's absolute existence." (214)

2. But to uphold the divine absoluteness, it is also necessary that God be libertarianly free in his production of creatures.  For suppose there is something in the divine nature that necessitates God's creation.  Then God would depend on the world to be himself and to be fully actual.  He would need what is other than himself to actualize himself.  This entanglement with the relative would compromise the divine absoluteness.  God would need the world as much as the world needs God.  Each would require the other to be what it is.  (210)

3.  So God must be both simple and free to be absolute.  But it is very difficult to understand how a simple being could be free in the unconditional 'could have done otherwise' sense.    If God is simple, then he is pure act in which case he is devoid of unrealized powers, potentialities or possibilities.  To act freely, however is to act in such a way that one (unconditionally) could have done otherwise, which implies unrealized possibilities.  Now Dolezal's view if I have understood him — and he can correct me in the ComBox if I am wrong — is that it is not only difficult to reconcile simplicity and freedom, but impossible for us, at least in our present state.  "Though we discover strong reasons for confessing both simplicity and freedom in God, we cannot form an isomorphically adequate notion of how this is the case." (210)  In footnote 55 on the same page, Dolezal brings up wave-particle duality: light behaves both like a particle and like a wave.  We have good reason to believe that it is both despite the difficulty or impossibility of understanding  how it could be both.  On the basis of the quotation and the footnote I hope that Dolezal will forgive me for pinning the label 'mysterian' on him, at least with respect to the simplicity-freedom problem which is only one subproblem within the the divine simplicity constellation.

 4. I grant that if we have good reason to believe that p is true, and good reason to believe that q  is true, then we have good reason to believe that p and q are logically  consistent (with each other) despite an absence of understanding as to how they could be mutually consistent. What is actual is possible whether or not one can render intelligible how it is possible.  To give an example of my own, motion is actual, hence possible, despite my inability in the teeth of Zenonian considerations to understand how it is possible. Many similar examples could be given.

And so a mysterian move suggests itself:  We are justified in maintaining both that God is simple and that God is free despite the fact that after protracted effort we cannot make logical sense of this conjunction.  The fact that the conjunction  — God is simple & God is free — appears to us, and perhaps even necessarily appears to us, given irremediable cognitive limitations on our part, to be or rather entail  an explicit  logical contradiction is not a good reason to reject the conjunction.  The mysterian is not a dialetheist: he does not claim that there are true contradictions. Like the rest of us, the mysterian eschews them like the plague.  His point is rather that a proposition's non-episodic and chronic seeming to be a contradiction does not suffice for its rejection.  For it may well be that certain truths are inaccesible to us due to our mental limitations and defects, and that among these truths are some that appear to us only in the guise of contradictions, and must so appear.

Of course, Dolezal's  mysterian move cannot be reasonably made unless the extant attempts (by Barry Miller, Eleonore Stump, Brian Davies, et al.)  to reconcile simplicity and freedom are failures.  Since I agree with Dolezal that they are, I grant him this.

5.  So what are some possible questions/reservations?

First, if  a (conjunctive) proposition's seeming, after careful and repeated scrutiny, to be or entail an explicit logical contradiction is not sufficient evidence of its being a contradiction, what would be?  To put it another way, my inability to explain how it could be true both that p and that q does seem to be pretty good evidence that p and q are not both true.  Now  I said above that the actual is possible whether or not I can explain how it's possible.  Granted, but if I cannot explain the how, doubt is cast on the actuality.

How adjudicate between these opposing lines of argument:  A:  Because X is actual, X  is possible, whether or not anyone can explain how it is possible! B:  Because no one can explain how it is possible, it is not possible, and therefore not actual!

Second,  if all extant attempts to reconcile simplicity and freedom fail, it does not follow that there isn't a solution right over the horizon.  How can a mysterian rule out the possibiity of a future solution?  The mysterian seems committed to saying that it is impossible (at least in this life) that there be a solution.  How can he be sure of this?

Third,  if a proposition appears under careful scrutiny to be or entail a contradiction, then is there even a proposition before the mind?  If you require for my salvation that I believe that God is one and God is three, what exactly are you demanding that I believe?  Before I can affirm a proposition as true I must understand it, but how can I affirm as true a proposition that appears necessarily false?  Such a 'proposition' is arguably not a proposition at all.  (This requires development, of course . . . Richard Cartwright's Trinity paper will help you see what I am getting at.))