Science in Christian Perspective

'PROBABILITY AND God's PROVIDENCE
CHARLES HATFIELD*

From: JASA 17 (March 1965): 16-22.

The models and images we (choose to) form of both the. world and God are our most characteristic possessions. The models of the world continually shift, and they should, lest acceptance of an inadequate model discourage search for a better. The probabilistic nature, of much of our knowledge of the world gives hope for a. fresher understanding of, the use God makes of it in his providential control over the universe, but the basic tension remains in trying to resolve the personal providence of God with the impersonal world which is the context of our life.

It is a commonplace observation that the enterprise known as science has much to its credit. When newspapers print whole pages on such technical subjects as modern mathematics and biochemistry, even if in semi-popular language, then it is safe to say that science is an integral part of the spirit of our age. More than one person of scientific bent, however, has had sobering thoughts about the role of science in human'life, for the science of a given age invariably has a strong effect upon personal creeds. Preoccupation' with science and its methodology means a focussing of attention upon knowledge and how we get it. Burtt thinks that "the central place of epistemology in, modern philosophy is no accident; it is a most natural corollary of something still more pervasive and significant, a conception of man himself, and especially of his relation to the world around him .. . . In the last analysis it is the ultimate picture which an age forms of the nature of its world that is its most fundamental possession." I believe that most Christians, while not wishing to detract from the importance of knowing the world about us, would feel constrained to amend this evaluation as follows: "it is the ultimate picture which an age forms of the nature of God that is its most fundamental possession." It is certain, of course, that the two pictures are not independent of one another.

I would like to illustrate the importance of science in determining the mental picture we have of the world

* Charles Hatfield is chairman of the department of mathematics of the University of Missouri at Rolla, Missouri. Presented -at conference on Christianity and Higher Education at University of Minnesota, spring, 1959.

by citing two personal testimonies. "Looking back I have seen clearly that at different periods of my life my mind became incarcerated within the narrow confines of some doctrine such as the scientific materialism of the last century, the idea advanced by Darwin that evolution occurred through the action of blind mechanical forces, or the equally pessimistic systems of psychology sponsored by Pavlov and Freud. And what is particularly apparent to me now that I have escaped from these mental prisons is that while confined in them I was completely satisfied with my surroundings. I firmly believed that the universe was a meaningless interplay of matter and forces, that life arose on this planet as an accident ... I was equally ready to accept the view that thought was only a reflex action and that religion was 'humanity's great obsessional neurosis'. While under the spell of these ideas I looked upon all forms of human experience other than those which had been utilized by the sciences as being unproductive of knowledge. For me, the artist's preoccupation with beauty, the philosopher's search for fundamental principles and the religious man's quest of the divine represented nothing but man's innate desire to escape from a forbidding reality into a realm of fantasies and dreams. It is only now that I realize how often in the past I mistook tentative theories for absolute truths, and temporary resting places for thought for permanent residences. It was not the inventors of these theories who were to blame for what had happened to me, but my own inability to understand the true function of science and the nature of the conclusions at which it arrives." (Kenneth Walker, Meaning and Purpose, p. 7 ff)

If our own memories do not contain some similar experiences, then it is probably only with a determined effort that we can capture some of the pathos of such conversion.

The second testimony is that of a physicist who became Executive Director of the Oak Ridge Institute of Nuclear Studies in 1947 and who was ordained Priest in the Episcopal Church in 1954: Dr. Wm. G. Pollard. Again it is the problem of just how God could work his purposes in the world that science describes in such detail. Dr. Pollard writes: "In my own experience of coming into the Christian ministry from an already established career as a physicist, this question has been the most crucial of all. To me it seems a much more difficult and decisive question than that of the existence of God. I found extraordinary difficulty, when I thought about events in scientific terms, in imagining any kind of loophole through which God could influence them . . . I could not see any point in the world as it is known in physics at which the hand of God could be thrust in and providence, as it is known Biblically, actually exercised." And this, despite the fact that the Biblical concepts had become just as real and solidly based as the scientific terms to which he had become long accustomed. "There was no escaping", he writes, "the sense I had of the reality of God's grace and providence, of His judgment and redeeming power in life and his tory which lies at the core of the Biblical understanding. This reality could no more be denied than the reality of the world of electrons, atoms, and physical law which I knew in physics. Yet when I tried to put these two worlds together their apparent incompatibility baffled me . . . I had come to know two realities, each all ~ compassing and of universal scope, which were so firmly and broadly rooted in my own experience that it was unthinkable to give up or deny either of them." (Wm. G. Pollard, Chance and Providence, p.8) Our own experience of this issue may be lacking in such dramatic intensity, but for all that, the bafflement is to many not less real.

It is not only the scientist or the student of science who is confronted with the issue. The farmer who regards the rain as providentially sent to save his crops finds his simple belief challenged by the meteorological explanation of the falling of rain in terms of the physics of the movement of masses of air and water. The farmer's faith is thus in danger of being corroded by the science of his fellow man. The Good God has become for many "The Good Clouds" or "The Good Earth" which in turn becomes "The Good Natural Laws". It seems fair to suggest, in the light of the foregoing that part of the price we have paid for the science of the last 400 years has been the passing away of belief in the providence of God. In a survey of the history and destiny of man, Erich Frank says that "since the Renaissance the peoples of the Occident have taken an increasingly hostile stand against the religious interpretation of history, according to which mankind is guided by divine Providence. Modern man sees his destiny in this world; he has decided to take his fate into his own hands." (Philosophical Understanding and Religious Truth, p. 117)

I suppose that to those who know only its outer garment Christianity seems desperately intricate, if not downright inconsistent. In the main, however, it affirms that the solution of the world (sic) is extremely simple and astonishingly bold. Right in the center of the stage with all the lights of history and revelation focussed upon it and so glaring that we can hardly miss it, is the personal God: God the provider, guiding the vast galaxies as well as our own little planet with such a watchful care that nothing gets lost-not even a little chick-a-dee; and God the revealer who maintains constant and unremitting communication with every man, and that not in terms of his own pristine splendor, but rather on the level of and through the ways of human intelligence. Teilhard reminds us that in both St. Paul and in St. John we read that "to create, to fulfil, and to purify the world is, for God, to unify it by uniting it organically with himself. How does he unify it? By partially immersing himself in things . . . and then, from this point of vantage in the heart of matter, assuming the control and leadership." (The Phenomenon of Man, pp. 293f) But if we speak of God's "partial immersing of himself in things" it must be with care. In any case, we must avoid identifying the world with God as if they were the two sides of an equation. This were a confusion, than which none is greater, for it would make God the author and active agent for evil, relieving man of moral responsibility and thereby inducing false comfort. God is not the same as His world, but it is his world: his by creation and his because he constantly upholds it.

Christian faith is just as opposed, on the other hand, to deistic separation as it is to a pantheistic confusion of God and the world. If deism allows creation of the world by God, it also denies his continued access to it. It pictures God as walking away from what he had made, leaving it to fend for itself. The traditional image to describe succinctly this view is that of God as a clock-maker. It should not be supposed that deism and pantheism are completely discredited views and therefore of no concern. While Christian faith has little in common with either, they are both nevertheless positions which are constant temptations to men the world over. The image of the God of Scripture is more nearly provided by the modern science of cybernetics: that of the helmsman. Calvin suggests in a passage that still bears citation: "What is called providence describes God not as idly beholding from heaven the transactions which happen in the world, but as holding the helm of the universe, and regalating all events. Thus it belongs no less to his hands than to his eyes. When Abraham said to his son, 'God will provide' he intended not only to assert his prescience of a future event, but to leave the care of a thing unknown to the will of him who frequently puts an end to circumstances of perplexity and confusion. Whence it follows, that providence consists in action; for it is ignorant trifling to talk of mere prescience." (Institutes, Bk. 1, Ch. XVI, p. 222) Again Calvin wisely observes, "The providence of God governs all things in such a manner as to operate sometimes by the intervention of means, sometimes without means, and sometimes in opposition to all means." (Calvin, ICR, Bk. I, Ch. XVII, p. 232)

In many and varied areas the Bible details to us the extent of God's providence: it extends over

a. the universe at large: Ps. 103:19; Eph. 1:11 
b. the physical world: Ps. 104:14; Mt. 5:45
c. brute creation: Ps. 104:21, 28; Mt. 6:26
d. the affairs of nations: Job 12:23; Acts 17:6
e. man's birth and lot in life: Ps. 139:16; Gal. 1:15, 16 f. the seemingly accidental or insignificant things: Prov. 16:33; Mt. 10:30
g. the righteous: Ps. 4:8; 121:3; Rom. 8:28
h. his people in supplying their needs: Deut. 8:3; Phil. 4:19
i. those that pray, in providing answers: Ps. 65:2; Mt. 7:7
j. the wicked by punishment: Ps. 7:12, 13; 11:6

It is sometimes helpful to see in these varied actions of God three distinct elements: preservation, concurrence, and government. Let us look briefly at each of these.

1. Preservation-this encompasses both creation and God's continuous activity in sustaining and renewing the world. There is no evidence that God made anything to "work" by itself. More basic in theology than any datum of history, further back than sin, even beyond creation, is the absoluteness of God over his creation. He always gives himself top priority. This is not egotism, but honesty. He is but being true to himself as well as to us. The God of the prophets relays to us his word, "I am the first" (Isa. 41:4; 44:6; 48:12). The words foreknowledge, predestination, preparation, and pre-existence all bear upon the way in which God through and through, knew before it happened, actively prepared for and ante-dated all that he actually performed in the physical and psychical worlds. Nothing occurs without God willing it and willing it to happen beforehand. He called the prophet Jeremiah before he was born (Jer. 1:15) and the apostle Paul likewise was set apart before he was born (Gal. 1:15). Regarding the latter Warfield observes that "representations are sometimes made as if, when God wished to produce sacred books which would incorporate His will-a series of letters like those of Paul, for example-He was reduced to the necessity of going down to earth and painfully scrutinizing the men He found there, seeking anxiously for the one who, on the whole, promised best for His purpose; and then violently forcing the material He wished expressed through him, against his natural bent, and with as little loss from his recalcitrant characteristics as possible. Of course, nothing of the sort took place. If God wished to give His people a series of letters like Paul's, He prepared a Paul to write them, and the Paul He brought to the task was a Paul who spontaneously would write just such letters." (The Inspiration and Authority of the Bible, p. 155)

2. Concurrence-God concurs and cooperates in the use made of energies and capacities given to man, even though the use may be evil. He co-operates with men, but the moral responsibility for a deed is lodged with the doer. Even sinful acts are under his control. Sometimes he restrains men from evil deeds (e.g., via the dream of King Abimelech he warned against taking Sarah as a wife) but often he permits them to wallow for a season in their sin. His control is so complete that he can overrule the crime of selling a brother into slavery, making of the victim an instrument for their undeserved deliverance from famine. God does nothing by halves. A will to act is only half the act. God supplies continuously the power and energy to carry out what man projects.

3. Government-God orders the affairs and actions of his creatures not according to some external plan, but according to his own character and purposes, for the glory of his name and the welfare of man. He is not limited in means. He uses both ordinary and extraordinary. He allows wide, but not unlimited liberties to men. He permits one, hinders another, here directing, there determining. Here the essence of the word "providence" comes into focus. It is so named from providence, to see beforehand, All Scripture is but a brilliant mirror from which, in all directions, shines the watchful eye of God's loving care for his whole creation. If there is one aspect of providence which seems in need of further elucidation, it is the goal and purpose of God in it all. "Yahweh's intervention in the world," writes Edmund Jacob, "and his will to leave nothing outside his sovereignty give us the authority to speak of a biblical notion of providence which is exercised at the same time in creation and in history. The creation is maintained, not by virtue of autonomous laws, but by Yahweh's free will; its duration is eternal only in so far as Yahweh is pleased to preserve it. On the whole the biblical view is not directed towards the preservation of the world, but towards its transformation. The teaching of the prophets concerning creation is dominated by the hope of a new heaven and a new earth, so that they see in the present world, before all else, the signs of catastrophe, foreshadowing the great change." (Theology of The Old Testament, pp. 226ff)

Indeed, providence, when carried completely through to its fulfillment, becomes indistinguishable from redemption. Kierkegaard observes that "A providence is no easier to understand (to grasp) than the redemption: both can only be believed. The idea of a providence is that God is concerned about the individual and for what is most individual in him . . . The Redemption is the continued providence that God will care for the individual and for what is most individual in him in spite of the fact that he has lost everything." (Journals, No. 602)

The essence of providence can be put this way: God made the world all by himself, he makes it work continuously and cooperatively, and he makes it work his own gracious purpose which includes us. He made the world, made it to work, and made it to work toward a goal. Paul's quotation from the poet Aratus is close to this summary: "In him we live and move and have our being." (Acts 17:28a)

Probability is a measure, or more accurately, a theory of measuring. It is a mathematical concept and likewise a concept that has to do with actual occurrences. As in the case of physical concepts we have for simplicity two modes of defining probability: one due to Laplace and called a priori or measure-theoretical probability; the other is due to Ellis, Cournot, and others, but is usually connected with the name of von Mises and called a posteriori, or more adequately the relative frequency definition. Margenau reminds us that "living science . . . owes its vitality to the fruitful interplay of two different modes of definition, one closely related to theory and law, the other to the rules of correspondence (between concept and data)." (The Nature of Physical Reality, p. 221) Time, for example, is defined operationally (Bridgman's term) by reference to clocks. This Margenau calls epistemic definition. Time is also defined as the independent variable in the equations of mechanics. The first of these, is a connection or correspondence with observables. The second is in the construct field, linking together other constructs. We note, in passing, that in pure mathematics constitutive definitions play a greater role than in the applied sciences, because mathematics is more concerned to generate systems, for which direct epistemic definitions are not usually available.

The necessity of two kinds of definitions is inherent in- science as it seeks to describe the world, for "without epistemic definitions", continues Margenau, "science degenerates to speculation; in the absence of constitutive definitions it becomes a sterile record of observational facts and its formulas take on the character of medical formulas. Physical laws must be regarded as mediators between the two types of definition for specific quantities." (Ibid., p. 243) "Instead of being pleased at Providence for equipping probability with both certificates it needs to enter science, the modern logician sometimes quarrels over which of the two is 'right'. Not seeing their connection through science, he mistakenly believes the two definitions to contradict each other." (Ibid., P. 253)

Laplace's definition takes the probability of an event to be the number of favorable cases divided by the total number of so-called "equipossible" cases. E.g., the probability of throwing a "4" with a pair of dice is 3/36 since there are three ways of forming a 'A" (3 + 1, 2 + 2, 1 + 3) and there are 6 x 6 = 36 possibilities for combining the numbers on the dice without repetition. The probability of throwing other than a 'A", is the complement of 3/36 with respect to 1, that is, 33/36. Laplace's formula is exact and involves no provision for assigning errors. This constitutive definition has difficulties. Right away, the case of an infinite number of possibilities puts us in trouble. The definition suggests no reasons for the "T' and the "5" to be equiprobable events in the case of throwing a single die. That the actual frequencies (in a real trial run) of "T' and "5" are very close to 1/6 for a large sample, is just as remarkable, but no more mysterious than that the formulas for falling bodies fit observed facts. The meaning of equipossibles is never clear and never prescribed by the Laplacian concept.

The frequency definition of probability has penetrated deeply into science. It begins with the simple Observation that the frequency of an event sometimes shows a marked tendency to become more or less constant for large values of the number of trials. Thus the frequency of heads in 10,000 tosses of a coin would be very near %. The "constant" in the definition is taken to be the limit of the sequence of numbers made up of the frequencies recorded after each throw or trial of the given event. This practical or epistemic definition is used in the determination of a variety of "probabilities", and now it will be seen that the word is ambiguous unless we can somehow reconcile them. Recent discussions of the meaning of probability by philosophers show little evidence of agreement. The divergence in views persists. It is an old old story of voluminous rhetoric and partisan tenacity. As with Job's comforters, there is a "darkening of counsel with words". Let it be clearly understood, however, that there is no difficulty in getting good agreement between the two values, even striking agreement. The frequency definition is used to find the probability that a molecule has a given velocity by measuring the density of molecules on a rotating disk; the probability for various energies of an atom at a certain temperature is obtained by measuring the distribution of spectral intensities which it emits. Life expectancy is found by a careful counting process.

It is clear that the frequency concept has its limitations: it is rationally barren. It is "hooked, up" to data, it is true, but not to formulas that enable us to predict compound probabilities. It is simply too clumsy to refer all probabilities to inductive generalization, which is what the frequency concept amounts to. "The vital link", suggests Josephine Mehlberg, "between the mathematical theory of probability and the unusually valuable applications of this theory to observational data is unaccounted for both in the measure-theoretical and the limiting-frequency approach . . . probability as explored by the mathematician is a theoretical construct functioning in the empirical sciences as other theoretical constructs do." (Current Issues in The Philosophy of Science, AAAS, 1959, p. 295)

The typical investigator who employs probability studies a large number of repeated instances of behavior under similar circumstances and then expresses his findings in terms of certain norms; the probability of deviation from the norm in a future instance is then made on the basis of already developed theory. Such methods are used to determine the fish population of a lake, vocational fitness, population trends, crime incidence expectation; they are used to study industrial management, in psychological testing, and to study accident frequency, to name but a few applications. The last-named is made familiar to us through the grim holiday predictions of the National Safety Council. There is no stronger argument, its users feel, for the validity of the assumptions made in such statistical probabilities than the obvious and striking success of the techniques to which it leads. Here is a good example of the fact that people believe in science because "it works".

In the summer of 1960 a Minneapolis advertising agency sought the help of mathematicians in estimating the possible liability of a certain car manufacturer who was to provide the cars to be used as prizes In a cereal-sponsored contest involving a sweepstakes drawing. They sought to determine, at the '195 percent conJidence level," how many cars they would give away, assuming a certain number of persons entered the contest by sending in cereal box tops. Without knowing any probability theory themselves the agency was willing to take our figures for the probable number of cars to be given away.

A thoroughgoing causality or determinism seems to be inescapably characteristic of science. In physics, chemistry, astronomy, biology, physiology, and in a host of related disciplines it has seemed essential to regard observed events as dependent upon what are called natural laws. These natural laws, in a sense, -required the particular outcome that was in fact observed. By determinism we mean here the common-sense notion that all events are caused. There are, broadly speaking, two recognizably distinct strains of determinism. Following the psychologist Paul Meehl, we distinguish between methodological determinism which is simply a working rule or practical orientation, and metaphysical determinism which is the radical thesis that is by nature an absolute ontological presupposition. Methodological determinism is the attitude which seeks (and even hopes for) laws in a given domain. If we discover laws that hold strictly, good enough; if they are at best probabilistic, we'll settle for even that, for they may prove useful. This kind of determinism is not merely a pet prejudice of atheistic scientists, but rather the expression of their hope or even faith that lawfulness u7ill be found. It is an implicit working assumption to which we all hold pretty much as a matter of course. It is difficult to see how any rational person could find fault with such a policy of investigation. It is close to Hans Reichenbach's view of induction "he who wants to catch fish, while he has no assurance of success, must at least cast his net."

But to say that absolutely all events, including human psychological events, merely instantialize universal laws, and to hold this as an absolute which no empirical evidence can be permitted to gainsay is to assert a personal creed, and as such goes far beyond a working rule. It is a vast speculative generalization, which, while it represents an extrapolation from a large and impressive body of scientific knowledge, is nevertheless an idealization, and however suggestive it may be, the facts simply do not suffice to coerce all rational men to accept it. Scientific naturalism, which is another name for this view, is regarded by Meehl as a powerful foe to the faith. "Scientific naturalism", he writes, "(philosophically underpinned by logical empiricism) often in an unquestioned and even unstated form is today the strongest intellectual enemy of the church and among educated people gives the most powerful no to the church's proclamation." (Paul Meehl, et al, What Then Is Man?, p. 173)

THE STATISTICAL NATURE OF SCIENTIFIC KNOWLEDGE

We turn now to chemistry to illustrate the fact that much of our scientific knowledge is statistical in nature. I am indebted to Pollard for the data on radioactive iodine, a type widely used today in the treatment of certain thyroid disorders. Neither touch, taste, nor smell would tip you off as to the difference between this and ordinary medicinal tincture of iodine. But the nucleus of its atom has four more neutrons than an atom of ordinary iodine. The atoms of radio-iodine can exist in alternative physical states in which one of the neutrons has changed into a proton by the process of radioactivity, and when this occurs, its nucleus changes into that of the gas xenon. Now every such atom has these two alternative states at any given time, but no known forces, either external or internal can eliminate the element of randomness from this picture. All we can state is the probability that a given atom of it will explode and change to xenon during a given period of time. This probability finds convenient expression in terms of half-life. The half-life of a radioactive substance is the time required for half of it to decay Into some other. The half-life of radioiodine is eight days. Thus, if we should start with 16,000,000 atoms of it today, in eight days we should have only 8 million and in 16 days 4 million, etc., so that by six months we should have no more atoms than the fingers on each hand. We never know when a given atom is going to change, but we know empirically that a certain number will change in a given interval of time. Half-lives of radioactive substances vary from a very small fraction of a second up to 5 billion years.

We seem to be faced with a basic characteristic of atomic and molecular phenomena for which the theory of probability is indispensable. "The basic characteristic," relates Pollard, "which forced the transformation of classical mechanics into quantum mechanics was formulated by the German physicist Werner Heisenberg in his now famous principle of indeterminacy . . . For very small objects such as electrons of an atom, this indeterminacy becomes decisive and makes it impossible to specify both their position and their velocity simultaneously with precision. If either one is precisely known, then the other will be wholly indeterminate." Roughly put, the numerical product of the range of error in measuring the velocity of a particle with the range of error in measuring the position of the same particle is approximately (Planck's) constant. Here we must not be led astray. It is a theory, of course, and some very respectable physicists remain unconvinced (DeBroglie, Bohm, Einstein, and Planck), despite the championing efforts of Niels Bohr, Max Born, and Heisenberg himself. It has been one of the hottest debates in physics. More than once in the history of science a new theory started out as statistical, only to be replaced by a precise theory. The dispute is over whether the same will happen to quantum theory. If we assume that a precise law must exist, then the question becomes: "is the precise law statable in a human language?" Those who oppose the quantum theory allow that it has made a significant contribution to our knowledge of the world. They believe, nevertheless, that the theory will be supereeded by a precise overall theory of microphysics. This is an issue not settled by majority vote or by prestigious proponents. It awaits the further development of science.

ON THE NOTION OF CAUSALITY

It is worth observing, suggests N. R. Hanson, that the concept of cause is not often used in actual practice in physics. The terms "cause" and "causal chain" have rarely occurred in the texts, treatises, and tracts of physics for the past 300 years. Be that as it may, one continues to suspect that the search for cause-effect relationships has been going on under other names.

A mere glance at the literature on causality shows that it is often associated wtih some notion of inherent necessity. Invariable succession is all some are able to make out of their observations. Max Planck, for example, understands it as a regular connection between cause and effect. He is quick to ask the inevitable question: "What constitutes this specific type of connection?" "Is there any infallible sign to indicate that a happening in nature is causally determined by another?" His approach to an answer to these questions is along the avenue of prediction. (Illustration: the farmer who wanted to demonstrate dramatically the virtues of fertilizer to the skeptical peasants spread his product so that the clover under its influence would spell out the letters, "THIS STRIP WAS FERTILIZED WITH CALCIUM SULFATE".) Planck defines an occurrence to be causally determined if it can be predicted with certainty. By the side of this definition or principle is another, which he calls a "firmly established fact": "it is never possible to predict a physical occurrence with unlimited precision." But even the invariable succession meaning of causality is useless, since we don't know of any particular succession that will always be invariable. Moreover, we need to treat the successions which have not been invariable. It is abundantly evident from the works of both philosophers and scientists that there is astonishingly small agreement on the meanings of some of the most commonly used terms.

For Margenau causality is simply the invariability of physical laws with time. "Causality holds if the laws of nature (differential equations) governing closed systems do not contain the time variable in explicit form." (Nature of Physical Reality, p. 405.) Whether we conceive of causality in terms of equations, or in terms of psychological certainty, or in some other terms, the Christian has long felt it is a helpful distinction to make between God as the primary cause of all in the providential sense and the secondary causes which in the physical sciences, at any rate, are completely impersonal. Mascall relates the secondary cause to probability, while reserving the absolute character of the primary cause. "To the secondary cause it belongs merely to determine that there is a certain probability of the event occurring, and even this, does only as a result of its conservation by the primary cause which is God. To the primary cause alone it belongs to determine whether the event shall occur, and when and where; the secondary causes have no part or lot in this. Thus the relative autonomy which God has given to his creatures does not in the least diminish his sovereignty; whether a particular event happens or not depends in the last resort upon his choice and upon it alone." (Christian Theology and Natural Science, p. 201)

Wittgenstein's treatment of cause has a radicality, if not an honesty, that blows in some needed fresh air. "Laws", he reminds us, "like the law of causation, etc., treat of the network and not of what the network describes." It's all quite legitimate to make a model of the world in our attempt to understand it. But then we must be sure to draw conclusions about the model rather than about the world. Here is where the confusion is sometimes the most subtle. The same care is needed in theology, for here too we are wont to exalt one attribute of God out of proportion and the model becomes an idol.

And let us be thoroughly honest about this matter of causality and necessity. Is it not true, as Wittgenstein asserts, that "a necessity for one thing to happen because another has happened does not exist. There is only logical necessity. At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena." (See Gen. 8:22) Natural laws are themselves creatures of God, for he gave us the regularities of sun and moon, day and night, the seasons, the tides, to name but a few. They are, as the German language has it, Gesetze, i.e., "settings". God set them to be. "They are limitations," Brunner observes, "for our freedom, not for His. His freedom is above all settings or laws, they are not fetters upon His action, and some day they shall be no more. For 'the frame of this world perishes'. The contingent is also the transient, the perishable, the non-eternal . . . natural laws are not absolutes, nor ultimates, they don't determine His purposes. Rather they are instruments, organs, servants of His will." (Christianity and Civilization, 1, p. 23f)

Time was when an idea could be squelched by showing that it was contrary to religion. Result; theology became the greatest single source of fallacies. Today an idea can be discredited by being branded as unscientific. Likewise, science has become in its turn the greatest single source of error. Our use of the law of causality in our scientific endeavor must not obscure its nature as an approximation. It is neither true nor false. Rather, it is a hueristic principle, a most valuable and productive idea in understanding some particular aspects of the physical world.

In the shaping of history there are no laboratory controls. The most improbable event, from the point of view of our probability model of the universe may be precisely the one that occurred. We should see history as a succession of time-points, each of which in the hands of God can become a turning point of special significance. The appearance of chance and accident in history are to be welcomed because it is so far as we have been enabled to see, a permanent feature (until God sees fit to change it) of the world. Pollard even goes so far as to make the appearance of chance and accident in history the "key to the Biblical idea of Providence". (Pollard, Chance and Providence p. 66)

Even stronger is Pollard's assertion that it is "only in a world in which the laws of nature govern events in accordance with the casting of dice can the Biblical view of a world whose history is responsive to God's will prevail" (Ibid., p. 97). This seems to say that the Biblical concept of providence requires the laws of nature to have a form governed by the casting of dice. If so, it is going too far. As long as we know only that God works providentially and not precisely how, he works-that is, we do not know all the mechanisms by which he carries out his will-and as long as the foundations of probability are not thoroughly understood, we must confine ourselves to more modest assertions. Indeed, Pollard elsewhere expressed himself more modestly: "It lies at the heart of the Biblical idea of providence that there be no method of verifying by means of controlled tests or experiments whether or not a particular event in the past occurred because God willed that that particular alternative should be selected on that particular occasion." (Ibid., p. 96) And a little later we read that Itevents in themselves share in both realities of order and providence" so that "the enigma of history resides in the fact that every event is at one and the same time the result of the operation of universal natural laws and the exercise of the divine will." (Ibid., p. 114)

There is a persistent demand on the part of many for some objective demonstration of the reality of God and the fact of His providential ordering apart from his self-revelation through personal agents: the prophets, angels, the apostles, but preeminently through Jesus Christ. But to the author this seems but a gossamer: wishful thinking at best. It is a quest which can only come full circle back to the original question. God is ever resistant to our efforts to convert a faith problem into a knowledge problem. But in the very nature of things faith problems have only faith answers. The message God gave to Isaiah for Ahaz was so pointed: "If you will not believe, surely you shall not be established." (Isa. 7:9)

We do well to heed the experience of others who have been similarly engaged in the harmonizing of a new discovery with Christian faith (should there be a need for it). C. S. Lewis reminds us, from quite a different context, of the periodicity of such issues when he writes that "Each new discovery, even every new theory, is held at first to have the most wide-reaching theological and philosophical consequences. It is seized by unbelievers as the basis for a new attack on Christianity; it is often, and more embarrassingly, seized by injudicious believers as the basis for a new defense. But usually, when the popular hubbub has subsided and the novelty has been chewed over by real theologians, real scientists, and real philosophers, both sides find themselves pretty much where they were before. So it was with Copernican astronomy, with Darwinism, with Biblical Criticism, with the new psychology. So, I cannot help expecting, it will be with the discovery of 'life' on other planets-if that discovery is ever made." (The World's Last Night)

It seems to me that it is more accurate to say that the key to understanding Biblical providence is with the nature of God, as discerned in both his performed deeds in the world, along with his own interpretation of them. In any event, we cannot tie God's hands or deny him access to his own world by any particular model we make of the world. Whether we use the principle of determinism or of indeterminacy in our view of the world, God is necessarily above all. Whatever rapprochment we shall find between Providence and the concept of probability, there will likely be a residuum of mystery about God. In fact, I would venture to say that the probability of the mystery is V We need not believe that we moderns are the first to travel this road whose illumination is beyond our view. The Apostle himself, after a long and somewhat inconclusive discourse on the philosophy of history in general, and the destiny of his own fellow Israelites, in particular, is reduced to adoration: "0 the depth of the riches and wisdom and knowledge of God! How unsearchable are his judgments and how inscrutable his ways! 'For who has known the mind of the Lord, or who has been his counselor? Or who has given a gift to him that he might be repaid?' For from him and through him and to him are all things. To him be glory forever." (Rom. 11:33-36) We should not claim to have explanations for everything. The acceptance of an inadequate explanation can discourage search for a better. Our scientific endeavor is not a contemplative repose in the sumptuous setting of knowledge already acquired, but it is an indefatigable quest that takes us up slopes never scaled before.