Martin: Improbability of God

I leave the previous post as if in mid-thought, saying that the post-Big Bang separation between maximum and total entropy accounts for the possibility of order, not its actuality. God must still have played a crucial role in determining the natural laws. Quentin Smith objects to this idea on the following grounds:

If God intends to create a universe that contains living beings at some stage in it history, then there is no reason for him to begin the universe with an inherently unpredictable singularity. Indeed, it is positively irrational.

It is a sign of incompetent planning to create as the first natural state something that requires immediate supernatural intervention to ensure that it leads to the desired result.

The rational thing to do is to create some state that by its own lawful nature leads to a life-producing universe. (47)

Note that Smith by design uses an outdated and now rejected cosmology that postulated a “singularity” at the beginning of the universe, i.e., a zero-dimensional point with infinite temperature, density, etc. But the argument I am interested in will be unaffected by this aspect of it. Let’s assume that prime energy has been created.

Smith’s mistake is two-fold. In the first place he assumes that it is possible to seed a singularity such that it “by its own lawful nature” leads to the right kind of mature universe. It is contended precisely that created nature is not as potent and creative in its own right as God is creative. Smith shows no sign of recognizing the possibility that the natures of the initial singularity (or whatever the beginning of the universe consisted in) and of all of its states subsequent to Big Bang are so far removed from the nature of God that their power, unlike God’s, is fundamentally and inescapably limited.

Smith’s argument depends on the following premise:

(2) It is possible for God to create

[a] an initial state S that deterministically or probably evolves toward an animate universe; and it is possible for God to create

[b] an initial state S’ that does not deterministically or probably evolves toward an animate universe. (69)

I reject this: (2a) is manifestly impossible or at least wildly improbable as contradicting all our human experience, sophisticated science, as well as the entire theistic (as opposed to deistic) tradition. No initial state’s nature can “evolve” very far on its own power.

(Smith’s only alternative is to argue that the world might have been created fully formed the way it is now or was 6,000 years ago, as per the literal Genesis. This, he would maintain, would be more “efficient” and “graceful” and “aesthetically valuable” than the Big Bang + later divine “interventions.” This is an interesting idea, even if I do say so myself; however, I am not prepared to evaluate it at this point.)

But what nature alone cannot do, nature assisted by grace might. Grace in it numerous manifestations is essentially creation of information, imparting a form, defining things, eliminating chaos and formlessness in favor of definiteness and even beauty. Since the singularity is assumed by Smith to be utterly chaotic, with maximum entropy allowed by it, it was, like prime matter for the schoolmen, “pure potentiality,” formless void susceptible to being informed or made into something, into anything. And doing that was God’s job. Just as a sculptor does not go around looking for a lump of clay that can by itself transform itself into a precisely chiseled statue (an impossible quest anyway, if I am right), neither does God go around looking for a universe that can make itself. Rather, He wants matter which, though it has its own mind, He can guide, by actualizing some possibilities and setting aside others even without expending any energy, towards His chosen goal; matter which can be intelligently designed into a form.

Imparting grace is not therefore a crude “intervention” in the sense of a miracle, but subtle “informing” or imparting of information. Smith seems aware of the difference but not fully. God does not move around particles of matter; He manipulates possibilities, allowing some event to happen and precluding every other event. He “chooses between.” It is not that the “inherently unpredictable singularity” wanted, according to some natural law, to do X, and God violently coerced it toward Y. On the contrary, the universe was in principle undetermined, capable of resulting in X but also in Y, Z, etc.; the outcome would be randomly generated. Even if Y was the one desired result among millions of undesirable ones, guiding the evolution of natural laws, stars and the solar system, animals and humans, does not irrational God make, any more than sculpting an initially cubical piece of marble into a bust of Smith makes the sculptor irrational, because through his actions he has prevented any other form from being attached to the matter of marble.

(The efficient cause of the universe, i.e., its natural laws, is below and so part or aspect of the formal cause of the universe.)

Again, God does not break nature (especially before it was even made!) but bends it by substituting intelligent design for random variation.

How the probabilities for X, Y, … were distributed and whether a good world would be much less probable than all the bad worlds put together is scarcely important. God does not play dice with the universe at all, and in fact would not, even if the probability of a good world were 99%. He would still be obliged to get involved and collapse randomness intelligently.

In other words, it is eminently rational to go and get oneself some matter, potential to any form, and then hew at it and chip at it in such a way as to create something definite and beautiful. And no one will deny that this world seems beautiful sometimes.

See also: William Dembski, The Design Revolution, Ch. 20, “Nature’s Receptivity to Information.”

The universe is too big, says Nickolas Everitt. And why has much time passed since the beginning of the universe until humans came onto the scene? It’s just so… “inapt,” unfitting, given what theists take God to be, unlike even the Genesis account. (Part 2, Ch. 1) Shouldn’t the universe be much closer to the “human scale”?

So far this is the funniest atheistic argument I’ve ever encountered. But I plead guilty to harboring such thoughts myself: before becoming Christian in a letter to a friend I asked: What about the dinosaurs? For what possible reason did these preposterous lizards exist?

There are some possibilities. For example, the universe must to a considerable extent be autonomous, self-sufficient, and “work.” Perhaps only a large universe like ours could satisfy these requirements, and a Genesis universe could not.

Case in point: in the very next paper in this book, Victor Stenger discusses a number of “anthropic coincidences,” writing in particular that “billions of years were needed for stars to assemble these heavier elements out of neutrons and protons… the formation of chemical complexity is only possible in a universe of great age — or at least in a universe with other parameters close to values they have in this one.” (129)

Perhaps there is alien life on numerous planets, and the purpose of vast cosmic distances is to separate and therefore to protect us from each other.

In a thousand years, perhaps we’ll have advanced to such an extent as to go to the stars and conquer the galaxy. The scale of the universe may match the ambitions of men, after all.

Perhaps the scale of the universe is to remind us of the truth of the prayer: “Glory be to the Father, and to the Son, and to the Holy Spirit; as it was in the beginning, is now, and ever shall be: world without end.” Though the universe is finite, and heaven, paradise, and human lives themselves are everlasting and infinite, nevertheless, the size of the universe shows forth the generosity and magnificence of God.

Everitt asks:

… if the history of life on earth is represented by a year, humans have appeared only in the final few seconds of the year.

Why the delay, given that theism must think that humans are the most valuable species created so far?

Who or what has gained, and how, from the colossal delay? (119)

First, no one lost in the “delay.” God is eternal, and for Him any delay is irrelevant. Since humans did not exist until recently, they did not suffer, such as from being forced to endure pain or unsatisfied desires for a long time. Even if there is pre-existence of the soul, time may well flow differently in heaven than it does on earth, and even the souls waiting to incarnate as humans may not have been inconvenienced.

Second, the enormous span of time during which life has “evolved” + been intelligently designed through subtle means was God’s doing “quality assurance” over His creatures. He was testing the lifeforms. We are the survivors of billions of years of struggle for existence by our ancestors, including non-human ones. We have fought nobly and earned our place in the scheme of things. It would have been folly for God to release weak, unfit, buggy, un-battle-hardened humans into this hostile world of ours.

God could have created rational creatures already fully formed, and did — they are called angels. Creation of humans required a more roundabout process. The main reason for this is the unique metaphysical evil of the human nature — a fundamental corruption hinted at indeed by Genesis not present in any other living thing.

Everitt goes on: regarding theists who lived before the development of modern cosmology, “why did it never cross their minds that given these initial assumptions, God might create a universe billions of times bigger and older than their contemporary cosmologists were contemplating?” (120) But there is an obvious answer: reason, unassisted by sophisticated math and instruments, told them nothing about how the universe “should” be, whether big or small; but they had the Bible which expressed an apparent opinion on the issue. The Bible (plus perhaps the Ptolemaic model) was their only source of cosmological data. For example, if the Bible had pushed the Big Bang instead, then that’s what the early theists would have believed. They accepted a mostly literal interpretation of it, because they had nothing better. As soon as something better did come along, the people including theists adjusted their understanding.

Nor did these early theists try to prove the existence of God from their (incorrect) cosmology. St. Thomas’ Five Ways, for example, do not depend on his geocentrism at all.

Therefore, the “ex post” justifications of scale such as above are hardly “arbitrary” or ad hoc. It is surely unfair for Everitt to pose a challenge to the theist to justify the ways of God to him and then complain when the theist does just that!

Upon deeper reflection, Everitt’s insistence that the Genesis universe is a priori more plausible than the Big Bang universe given existence of God (i.e., that P(Big Bang | Theism) < 0.5 < P(Genesis | Theism)) seems singularly nonobvious. Hence the Bayesian inference that P(Theism | Big Bang) < P(Theism) does not go through.

In short, showing that this is the best possible world is an exceedingly non-trivial task. The argument from scale then is at the most a puzzle. It would be evidence against theism if Everitt could prove that the puzzle is both perverse and unsolvable. But his paper does not do so, and future developments may shed light on things; hence the argument fails.

“Anthropic coincidences,” expounded upon by Victor Stenger, cannot be a near-deductive argument for theism, because it can always be objected that man is nothing special. Humans, an atheist will argue, are no more interesting, or uninteresting, than sand or bugs. “We” lucked out in the universe-selecting lottery, but so what?

In other words, the near-deductive argument requires a suppressed premise, such as “We were meant to be.” Again, the atheist will request proof of that. If it is replied that we are meant to be because “God loves us,” then this assertion obviously entails “God exists” which presupposes precisely what we are trying to prove.

The fine-tuning argument can be rescued by rephrasing it in Bayesian, and therefore much more inductive, terms.

Let T = theism, FT = the proposition “the universe is fine-tuned for intelligent life.” Then

P(T | FT) = P(T) * [P(FT | T) / P(FT)].

Now P(FT | T) = 1. Remember that theism in its most developed Christian form does insist that humans (together with angels) are the crown jewels of creation. They were always meant to be. Unlike angels, humans have material bodies and physical needs. Hence the universe God created to be a home for man must needs be fine-tuned.

An anthropic argument for the existence of God will then claim that P(FT) is extremely low, and therefore FT confirms T. This is the stage where Stenger comes in with an attempted refutation of this opinion. He proposes 3 objections to it.

1. Stenger attacks “the wholly unwarranted assumption that only one type of life is possible — the particular form of carbon-based life we have here on earth.” (134)

In fact, he speculates, “life might be likely with many different configurations of laws and constants of physics.” (135)

Even stronger, “perhaps life of some sort would have happened whatever form the universe took.” (141)

Well, perhaps. But “perhaps X” implies that X is possible not that it is probable. The fine-tuning argument’s main assumption is precisely the extremely narrow ranges of permitted values which Stenger himself dutifully lists in the first part of the paper.

To put some meat on this objection, Stenger writes that he “analyzed 100 universes in which the values of the four parameters were generated randomly,” etc. “Over half the universes have stars that live at least a billion years. Long life is not the only requirement for life, but it certainly is not an unusual property of universes.” (144) This is an admirable effort but still rather inconclusive, all things considered.

Nevertheless, I agree that we don’t actually know the relevant probabilities of FT in any detail, and this purely logical attack must be judged somewhat successful.

2. There exist in fact numerous but a finite number of actual universes. “André Linde proposed that a background spacetime ‘foam’ empty of matter and radiation will experience local quantum fluctuations in curvature, forming many bubbles of false vacuum that individually inflate into mini-universes with random characteristics. In this view, our universe is one of those expanding bubbles…” (145)

Stenger suggests that the number of universes thereby spawned may be infinite, but that’s a mistake. Since we’re dealing with an actual physical process, this number must be finite, as infinities — mathematical abstractions — are not permitted in physics as far as the ontology of its models is concerned. There can be no actual infinite of real objects.

Moreover, it seems to me that within the universe as it was during its earliest Planck epoch — a black hole of Planck length filling all the tiny space of the universe — only one fluctuation could occur, and it would be both necessary and sufficient to cause the separation of gravity from the superforce, then the separation of positive energy from the negative gravitational energy, and finally expansion and inflation.

Stenger mentions another speculative theory in which “each universe is the residue of an exploding black hole that was previously formed in another universe.” (145) There is “natural selection” as collapsing black holes turn into random universes, such that “by chance some small fraction of universes will have parameters optimized for greater black hole production. These will quickly predominate…” (146) This differs from Darwinism pointedly in that the universes do not interact with one another, and unfit universes do not get eaten or starved by the fit ones. The problem with this idea, of course, is that this process selects for black hole production efficiency and not for intelligent life.

Lastly, if the number of possible worlds is infinite (and there are infinities of ideal objects), then these hypotheses solve nothing: the probability of any finite number n of worlds being randomly spawned is exactly n / ∞ = 0, which means simply that it is impossible fairly to consider for random selection of one member all members of an infinite set. No mechanical random world generator could function under such conditions.

3. There is an infinite number of actual universes: “Tegmark has recently proposed what he calls ‘the ultimate ensemble theory’ in which all universes that mathematically exist also physically exist.” (146)

Again, there can be no such thing; I have suggested that this fact serves as a “sanity test“: those who reject it are not playing with a full deck.

However, if, per impossibile, there could be an infinitude of reals, then I agree that the fine-tuning argument would in that case be undone.

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Finally, we have the Stenger’s hypothesis of how natural law was given. He splits this process into two parts:

(1) the breaking of the Planck-epoch primordial perfect symmetries which is itself law-bound; and

(2) random “spontaneous” crystallization or freezing of law as the universe “cooled.”

As regards (2), it uses a bad analogy: “cooling” can freeze matter, not the natural law according to which matter freezes. Further, the random law generator again could work only if the number of possibilities for natural laws were finite, but I think it is infinite.

The bigger problem, however, is with (1), since it postulates a meta-law governing the cosmic becoming. I don’t see how this helps Stenger. Who laid down the alleged meta-law that the symmetries shall be broken?

See also: Cosmological Fine-Tuning: The Good, The Bad, and The Ugly.

The essential problem with Michael Ikeda and Bill Jeffreys’ analysis (3.3) is that the authors don’t know what they are talking about. Let me therefore address only one aspect of their paper, namely, the charge that anthropic arguers are mired in a contradiction. Some but not all of the following will use their terminology. Let

L = “The universe exists and contains Life.”
F = “The conditions in the universe are ‘life-Friendly’.”
S = “We are explicitly and directly via a continuous miraculous intervention being kept on life Support.”
T = Theism.

The truth of S would mean that we would be having a direct experience of God keeping us alive supernaturally in a hostile and unfriendly to life universe, rather like Shadrach, Meshach, and Abednego in the fire (Dan 3).

The contradiction being alleged is that, according to the fine-tuning argument, both

P(T | F & L) > P(T) and
P(T | ~F & L) > P(T).

Thus, both F and ~F support T which seems strange. To solve this, consider:

L → F ⊕ S.
Thus, given L, both F → ~S and ~F → S.
(⊕ is “exclusive or,” i.e., either one or the other but not both.)

We can then define:

F & L = “There is naturally, through fine-tuning, supported life.”
S & L = “There is supernaturally supported life.”

Now that we see that, given L, ~F is simply S, the contradiction vanishes:

p(L | T) = 1 = P(F ⊕ S | T);

P(F) is low by the main assumption of fine-tuning; and

P(S) is low, because “a generic Judeo-Christian-Islamic deity” (160) would never be so irrational as to create a universe whose nature is self-contradictory and whose every impulse He would be required to counteract personally by miracles that violate the natural course of events in order to make this universe work.

As a result,

P(T | F & L) > P(T);
P(T | ~F & L) = P(T | S & L) > P(T), or simply

P(T | L) > P(T). QED.

Michael Martin reasons as follows:

(1) In terms of our experience, all created entities of the kinds we have so far examined are created by one or more beings with bodies. [Empirical evidence]

(2) The universe is a created entity. [Supposition]

(2a) If the universe is a created entity, then it is of the same kind as the created entities we have so far examined. [Empirical evidence]

[Probably]
(3) The universe was created by one or more beings with bodies. [From (1), (2), and (2a) by predictive inference]

(4) If the theistic God exists, then the universe was not created by a being with a body. [Analytic truth]

[Therefore]
(5) The theistic God does not exist. [From (3) and (4) by modus tollens] (203)

In an analogous manner Martin “proves” that there must likely have been multiple creators, fallible, finite, and working with preexisting matter. In other words, if there is a God, then He is very much like a committee of human beings aided perhaps with superior technology.

Now this is a good argument. St. Thomas’ first question on the nature of God is: “Whether God is a body?” He starts his inquiry as if a complete novice in philosophy, even a primitive superstitious savage. But he does not, unlike Martin, end there.

Thus, Martin writes:

Premise (1) does not assume that all created entities are created by one or more beings with bodies.

It simply says that, as far as we can tell from our experience, all created entities of the kind we have so far examined are created by one or more beings with bodies. (203-4)

But the universe is not a “created entity” among many others; rather, it is everything that has been made. By “examining” it most generally, we can prove that God is disembodied or, more precisely, with a body that is materially simple and efficiently free.

Premise (2a) is therefore false upon further investigation.

In a depressingly uncomprehending “critique” of intelligent design in biology, Bruce and Francis Martin (BF) appeal to two elements of animal bodies: (1) vestigial features and (2) anatomical inefficiency to cast doubt on design.

It is not generally within my competence to evaluate the truth of their particular claims. However, our authors mention perhaps the most famous allegedly vestigial organ, saying that “in humans the appendix serves no apparent purpose,” and of course, modern research has revealed the considerable utility of the appendix to humans:

The appendix, therefore, may act as a “safe house” for beneficial bacteria.

This reservoir of bacteria could then serve to repopulate the gut flora in the digestive system following a bout of dysentery or cholera or to boost it following a milder gastrointestinal illness.

In any case, let me grant BF’s examples of vestigial features and anatomical inefficiencies. All they have possibly shown is the truth of evolution, not the falsity of intelligent design. For no biologist working in the design paradigm denies that Darwinian evolution and intelligent design work side by side and complement each other sweetly.

Evolution then is “nature,” and ID is “grace” that completes what nature cannot bring to a finish. It is even possible that evolution subsequent to a design event can harm the designer’s handiwork. Inefficiencies then may be due not to the design itself but to random and partially destructive mutations that survive after the design has been implemented. That is, instead of improving design, the blind watchmaker can degrade it.

They further propound irrelevant theological objection to ID. To them I reply thus:

1) Suboptimal or inefficient design is still design. A 1960s computer is exceedingly primitive by today’s standards, yet it is designed.

2) Non-functioning design that causes a creature to die and leave no offspring in the natural selection is still design. A broken engine makes the car useless, but it is still designed.

For example, BF appeal to “selection pressures during evolution.” But such pressures exist and are fully enabled for intelligent design, as well. It’s just that ID theorists argue that in addition to random variation, there is good reason to postulate intelligent variation, as well, insofar as randomness + selection is not a powerful enough force on its own to generate information-rich complex biological structures.

3) A man-made artifact that is used for evil ends is still designed. Thus, a nuclear bomb and computer virus are both designed.

In particular, it does not follow from the fact than some biomolecular machines exhibit signs of being intelligently designed that the designer is benevolent, omniscient, or omnipotent. Hence the objection from the problem of evil, i.e., that the designer finds “sport from visiting on humans and other mammals all sorts of afflictions including parasitic bacteria, viral diseases, cancer, and genetic diseases” (218) misses the mark.