Science in Christian Perspective



Realism and Reverence*


Department of Chemistry
The University of Alberta
Edmonton, Canada T6G-2G2

From: PSCF 39 (June 1987): 75-87.
*Paper presented at the conference "Christian Faith and Science in Society," a joint Meeting of the Arnerican Scientific Affiliation, Canadian Scientific and Christian Affiliation and the Research Scientists' Christian Fellowship, held July 26-29,1985, at St. Catherine's College in Oxford, England.

It is argued that a realist understanding of our knowledge of creation is linked in its fundamental attitudes to the response of reverence toward God as Creator, and that this is a biblical view. The question is asked whether in the current development of natural science there are any indications that sound thinking leads legitimately to awareness of the dimension of religious meaning, as a consistent pursuit of truth, An important distinction introduced by Barfield between "alpha-thinking" (thinking about things) and "beta-thinking" (thinking about thinking) is discussed in its relation to modern scientific conceptual and logical developments, and several instances of scientific problems where the emergence of beta-thinking as a distinct activity from alpha-thinking has become a central issue are discussed briefly.

According to the Scriptures, the creation shows us the glory, majesty and eternal power of God-whether we look upward to the heavens or handle with fascination the things that have been made.1a I used to argue from these texts that if one presupposes the existence of God then creation speaks eloquently about Him; I wanted to make allowance for an apparent realism of the modern mind which is not reverent. But I realise now that this is not what the Scripture says. It has a different explanation for irreverence.1b The biblical claim is that a true understanding of creation leads to reverence as an intelligent response, and the point of these texts is this logical or rather ontological connection.2

The thesis of this essay is that realism and reverence are closely connected. In particular, the biblical claim that realism leads to reverence is relevant to philosopbical issues in our thinking about science and to further development of a genuinely scientific understanding of the world and its relation to God as the creator of all things. My concern is not just an abstract and academic one. Today there is a rising tide of pantheist religion which seeks on the one hand to transform the scientific tradition into an affirmation of human autonomy, the deification of man's will to power-and on the other to deny the real existence of a world beyond the mind and self of man, or any objective Other beyond himself to which he is responsible.

Against this background, I think it disastrous that some Christian apologists argue for views of scientific knowledge (and indeed all creaturely knowledge) which deny the possibility that it deals with truth. By doing this, they imply that creaturely knowledge is isolated, as a domain of thought and activity in which our understanding has no intrinsic relation to the Creator's actual handiwork and reverence is therefore merely an option, not an ontological necessity arising from the activity.

More positively, I believe that real progress in human understanding now requires a biblically inspired transformation of the attitudes to human knowledge which have marked the modern period. Christian thinkers can play a critical part in effecting such a transformation. When heard and understood, the Word of God always has a renewing influence on culture. For example, the roots of modern science are linked to biblical transformations in cultural and philosophical attitudes at the end of the Medieval period. We are again in a period of change; fundamental problems in logic and the conceptions of order, cause and meaning have emerged in nearly every area of scientific study. To resolve them we need a deeper understanding of the character of physical reality and our relation to it than we now possess-an understanding better able to appreciate the spiritual meaning of that relation. How far a corrupt, God-alienated culture can ever participate in such a transformation is quite uncertain, but I believe there is a biblical direction our thinking ought to take. It is worthwhile to ask what that might be, even if the culture fails to follow it. This may be a visionary hope, but Christian exercise of such hope has always had curiously practical consequences in the long run. In 1500, for example, who would have thought it much use for the actual future of humanity to bother about the nature of physical things?

In previous essays in this Journal3 I have addressed a general theme I may call "a biblical understanding of epistemology." I argued that such understanding is possible because (a) the Bible is concerned with the knowledge of God, (b) all our knowledge is held by us as creatures and God's self-revelation is consistently given in that context, (c) knowledge is integrated in the persons of knowers, and (d) this integration means that there is a unitary continuum of truth, not a plural collection of realities which have no intersection: their intersection is the human being. To support this I indicated how biblical themes such as the principle of faith, the functional role of theoretical and linguistic frameworks, the principle of manifestation,3c and the issues of inner attitude implicit in the epistemic similes of hearing, seeing, grasping, 3d emerge in a philosophy of personal knowledge as a sensible philosophy of science. On that basis I argued, as Michael Polanyi argued, for a realist epistemology and against either operationalist or rationalist views of knowledge; truth is the object and the potentially attainable goal of all creaturely knowledge, and it is in this hope and faith that all human knowing is sustained. This expectation toward the creation as God's handiwork was the mainspring of the scientific enterprise from the beginning, and the astonishing success of science is a very good argument that it is a justifiable expectation.

To make clear to Christians the fundamental reasons why a realist epistemology is so important to present thought, it is a helpful argument4 to show bow utterly unacceptable we should find an operationalist view Of theology to be. For example, consider the notion of 11 the God behind God" suggested by the existentialist theologican Tillich.5 To such an idea the biblical response must surely be that "what God is in selfrevelation and Incarnation, He is in Himself--a conviction rooted in the Scriptures and worked out in its theological implications in the credal formulations of the early Church. We consider that theology constructed in responsible commitment to the revelation of God in His Word is in some measure a true understanding of God Himself, even though it is a creaturely expression and understanding. Very helpful expositions of these theological points have been given by T. F. Torrance.' They show how the Incarnation is the basis for confidence that a creaturely knowledge of God granted to us by His revelation can nevertheless be a true knowledge.

However, I really raised the issue of theological realism because I wanted to persuade that operationalist or rationalist views of our knowledge of creation are also unacceptable. For the Christian, such views can only be defended by introducing a profound epistemological dualism between the knowledge of God and the knowledge of creation.3d This is a dualism which is not true to our actual living relation to God by faith,

Walter R. Thorson is Professor of Theoretical Chemistry at the University Of Alberta in Edmonton, Canada. His professional interests are in quantum mechanics, especially its application to problems in the theory of atomic collisions and molecular dynamics. He is a member of the American Physical Society, Canadian Association of Physicists, and the American Scientific Affiliation, and has published about 60 professional papers. He is actively interested as a layman in theology and Christian apologetics, especially in topics bearing on the epistemology of science and its relation to religious knowledge. He is a frequent lecturer at Regent College, Vancouver, B.C., where he is Adjunct Professor of the Philosophy of Science. Dr. and Mrs. Thorson and their family reside in Edmonton.

mediated to us by His continual giving of Himself to us in grace, and I believe it also fails to grasp the full implications of biblical teaching about God's selfrevelation.7

While these theological issues are really fundamental to the concerns of this essay, I do not propose to approach things that way. Firstly, I am not a theologian; secondly, I have a different object: to approach the topic from the creaturely perspective. This can make sense if in fact there is an epistemological unity in our relation as creatures to truth, the sort of unity suggested above."3b,3d Michael Polanyi' described how consistent development of responsible knowledge in human experience could lead to the appreciation of "larger contexts of meaning" in which human beings are placed, and has striven to describe how that might arise in the human community, through individual persons as agents of responsible commitment, or faith (to use the biblical term). Polanyi was very much aware that such an understanding of knowledge reopens the possibility of religious meaning. He understood that the myth of an impersonal scientific knowledge and method had become the enemy of the fundamental values which create such knowledge, and he recognized that those values ultimately originated in biblical thought. The formulation of a philosophy of personal knowledge, as Polanyi saw it, was aimed at a recovery of the basic unity of thought which previously marked Western culture, including the embedding matrix of religious meaning which made that culture possible in the first place. Polanyi's fundamental goals, and the relevance of his "project" in its broadest terms to contemporary thought and to Christian belief, have been very clearly explained in a recent book by Drusilla Scott entitled Everyman Revived: The Common Sense of Michael Polanyi;9 for those readers who wish to understand the issues in Polanyi's thought, presented in a different manner from my own scientifically oriented one, I strongly recommend this very readable work.

What would a consistent development of Polanyi's philosophy of personal knowledge imply for the question of religious truth itself ?10 I think the crucial point is that such an epistemological view necessarily leaves open the possiblity of divine revelation in the form of a creaturely Word, "God manifest in flesh," just the sort of revelation the Bible in fact proclaims. Polanyi of course did not argue positively for the existence of such a revelation, since he was primarily concerned with the nature of personal knowledge and the responsibility compatible with it.

The theme of this paper is a further commentary on what may be said from the creaturely perspective, more from Polanyi's starting point than from that of misunderstood as a claim to an autonomous creaturely knowledge of God; rather, we may say that there is a corroborating witness available in the knowledge of
creation. Although the Word of God is quite clear about the ultimate transcendence of God and the necessity of revelation as the fundamental basis for any knowledge we have of God, Scripture always proceeds on the
working principle that there is an actual continuity rather than a dichotomy in the experience of the creature seeking understanding. Reverence is indeed the intelligent consequence of realism. We might naively explain this continuity by saying that by the grace of God there never was and never will be a world in which there is no Holy Spirit present, and in which an Incarnation never in fact occurred. We might illustrate this biblical attitude with many texts, but as with so many other issues related to creation perhaps the clearest illustration is the way in which the opening chapters of Genesis lay out for us the peculiar setting of humanity as dust of the earth and image of God at one and the same time, and proceed on the basis of those two facts as an intersecting unity. So I consider that Polanyi's notion of ascending levels of awareness of objective reality, to which we as humans may be responsibly committed, is a proper understanding of creaturely response to truth. If that is so theologically, in that God has committed even Himself to a creaturely revelation, then consideration of the "pointers" to religious meaning from the "natural" side is not irrelevant.

Religious Meaning in Scientific Knowledge

The question of religious meaning recurs perennially in the heart of the scientific enterprise. Jastrow's "God
and the Astronomers"11 or the current discussions of the 11 anthropic principle"12 are good examples. The possibility that scientific truth may point beyond itself to more ultimate, metaphysical or religious meaning is
always latent. We have firstly to decide whether or not this expectation is ever legitimate, even in principle,
and then secondly whether we are warranted in connecting our expectation to any current scientific view
of the world.

Most of us have an instinctive reluctance to suppose that any direct relevance to metaphysical or religious
questions can be inferred from current understanding of scientific knowledge. We have all spent time refuting naive "God of the gaps" arguments and are very much aware that "God does not wear His heart on His
sleeve." Such caution seems well justified historically.

However, if it is maintained indefinitely as a matter of principle, this attitude has important philosophical
consequences. Are we really saying that scientific theology. Such a discussion should not, however, be knowledge can never point truthfully to religious meaning? The epistemological grounds for such a claim would appear to be based either on operationalism or on a view that religious meaning and scientific meaning can never be related. I believe there are good arguments against these views.3 A realist epistemology implies that if the questions raised by science are pursued far enough they lead to issues outside of science. 

We may then conclude that, in principle, it is legitimate to expect scientific truth eventually to point beyond itself, and that the real problem is to discern whether current knowledge truly suggests any

Fundamental problems in logic and the conceptions Of order, cause and meaning have emerged in nearly every area Of scientific study. To resolve them we need an understanding of the character of physical reality and our relation to it ... able to appreciate the spiritual meaning of human thought and agency in the creation.

such indication of larger meanings. If we believe that there has been cumulative progress in scientific knowledge, then we should expect such indications to become more evident as knowledge grows. I believe developments in many areas of science today indicate that we need to extend our categories of understanding and explanation in directions which give legitimate significance to religious questions, but in biblical, not pantheist terms. The intersection or point of convergence indicated is man himself and his thought.13

A Study in Idolatry

Owen Barfield's fascinating work Saving the Appearances: A Study in Idolatry" came to my attention some years ago when I had started to think about the biblical emphasis on reverence as proper response to knowledge. It has had a profound influence on my thinking, even though I do not agree fully with Barfield's metaphysical and epistemological views (as I understand them).

Barfield is concerned with the significance of science in the history and development of human thought. He uses metaphysical idealism or something close to it as a projective device, but his arguments really concern the relation of thought and perception. He adopts the Medieval "saving the appearances" argument: according to that view, the entities with which scientific theories are concerned can have no real existence but are merely devices for dealing with limited descriptions of "phenomena." However, the metaphysics or epistemology implicit in Barfield's use of the argument are not essential to the main issues. Barfield recognizes that the rise of science has profoundly affected human thought and experience, and that through this influence science has also become a kind of religious focal point in modern thought. He quite properly identifies this religious role as idolatrous, since he believes in the God of biblical religion.

Barfield has introduced a most important distinction between thinking about things, which he calls "alpha-thinking," and thinking about thinking itself, which he calls "beta-thinking." He argues that each mode of thought represents an important stage in the development of human consciousness and its relation to religious meaning in particular. This notion is important to us.

The emergence and eventual dominance of a-thinking as a way of experiencing and understanding the world is epitomized in the rise and development of modern science. Barfield argues that this mode of thinking and experiencing has replaced a much older and less intellectually controlled way of experiencing the world, which he calls "original participation."15 He suggests that this older mentality and perception was really qualitatively different from our own-a direct, unreflected sort of perception in which genuine religious elements were present and recognized as such. The triumph of alpha-thinking has progressively destroyed this type of perception and the unconscious integration of experience which accompanied it; it has "scoured away" from our consciousness any direct perception of transcendent meaning in experience, by imposing a rigid conceptual grid or filter of interpretation tied to theoretical, abstract representations of the world as thing. The "scientific world view" is a kind of intellectual, conscious statement of this largely unconscious process, which goes on in all our cultural experience. Thus, contrary to modern assumptions, it is modern, Dot primitive, man whose raw perception of the phenomenal world is most structured, filtered and restricted by what he already thinks and believes. Barfield shows how both our own language and past culture and the study of primitive cultures provide evidence for this.

This argument suggests that before the advent of a-thinking, the propriety of reverence as a response to the experience of the real world was much more obvious; the awareness of religious elements of meaning in the world was a matter of direct participatory experience. This pagan, primitive perceiving involved participation in the material world, whereas our sort of perceiving, structured by alpba-thinking, is fundamentally non-participating. We see objects, and distinguish them immediately from ourselves as beings; we have no feeling that their identity or spirit flows over into, or overlaps with, ours, nor do we sense anything numinous about them-but primitive man did.

A disturbing element in some contemporary thinking is the belief that this old synthesis of experience through an unreflected original participation should be recovered as a desirable goal, and that alpha-thinking and its formal expression in the culture of science should be rejected or suppressed. Theodore Roszak" has advocated this view explicitly, and (for example) a kind of return to it through the mentality of Far Eastern thought is implicit in the writing of Fritjof Capra.16 However, in contrast to these and other writers, Owen Barfield does not regard the emergence of alpha-thinking as a fundamental error. At a critical point in the book, he states

It may remove the risk of misunderstanding, if I mention at this early stage that it is not part of the object of this book to advocate a return to original participation.

Nevertheless, through the advent of a-thinking we have removed a perception or awareness that was previously present; we have scoured something away, even if, as a result, a world of objective realities comes into sharp focus, for by that very achievement the sense of the numinous has also been removed.

With this appreciation of earlier human culture it would be easy to interpret the biblical sense of continuity between realism and reverence as the expression of a context of original participation in which (supposedly) the Bible was written. However, this would be a fundamental mistake. Alpha-thinking had a beginning. Some of its roots may be traced to Greek philosophy and its interest in the nature of the physical world, but I think even deeper ones come from the Bible. The notion of an external, objective world independent of our minds has a primary origin in the biblical doctrines of creation and God's transcendence of the world system, and the critics of Western thought mentioned above easily recognize this fact."15,16

Owen Barfield pursues this theme. What was significant about the Hebrew culture, he argues, is that long before the emergence of a-thinking as the dominating presupposition of Western culture, the Hebrews had been taught to refrain from original participation as a religious obligation-not because there is no god, but on the contrary because there is one God. They were taught from the beginning that there is a mistake in original participation, the mistake of thinking that the divine presence is in the things themselves: Barfield puts it, "in the phenomena, and on the other side of them from man." Original participation is idolatry, the confusion of the Creator with the creature: "You shall not make any graven image."

This biblical root of a-thinking is very evident in the critique of idolatry given by the prophet Isaiah": the prophet argues idolatry is illogical. What has been taken from creation by man, seen by his eye, fashioned by his hand, made out of the same resources which he

A realist epistemology implies that if The questions raised by science are pursued far enough they lead to issues outside of science. I conclude then that in principle it is legitimate to expect scientific truth eventually to point beyond itself, and that the real problem is to discern whether current knowledge truly suggests any such indication of larger meanings.

uses to meet his practical needs, is given a status beyond its maker. The prophet appeals to thought to expose this error. It is thought which ought to lead the reflecting mind away from the idol to the conclusion, "Is there not a lie in my right band?" Here then is the religious motive of a-thinking; it is the beginning of a true understanding of the world and our relation to it. Alpha-thinking must inevitably destroy original participation and the pantheism (or rather "entheism") of Nature upon which it rests. The concept of animal husbandry is incompatible with the sacredness of cows as such; the discovery that the orbits of the planets are predictable with Newtonian mechanics divests them of inherent divinity. This "disgodding" of Nature is necessary religiously, and it is also a true, though limited, perception of reality.

But Barfield argues that in their turn the theoretical constructs of science, a-thinking rigorously formalized, have themselves become "idols of the study," replacing the old idols of the cave. To these new idols the critique made by the prophet is just as relevant as before. Again it must be thinking which penetrates the absurdity of a-thinking exalted beyond its proper role. It follows that a proper critique of a-thinking is not a repudiation of its value or its validity but a critique of its adequacy.3a

The key to the new critique is the recognition that beta-thinking, thinking about thinking, is not simply an indefinite extension of a-thinking into the domain of pure abstraction, but really requires a transcendence of it. I suggest that major conceptual problems in many areas of scientific thought today are closely related to the need to understand beta-thinking as a "clean different thing" from a-thinking. Logically, this difference appears in the peculiar character of self -reference and self-referencing structures in logical and symbolic argument. Ontologically, it appears as we attempt to understand our own identity and activity by pushing a-thinking to its limits.

Barfield's further argument diverges from that presented here, mainly for epistemological reasons. I believe that the representations of the physical world created through a-thinking are true, even though limited, accounts of the created reality, while I think Barfield might regard them as illusory. He adopts the fundamental Kantian distinction between the noumenal and phenomena/, while I believe that emphasis is contrary to the tenor of biblical thought and is eventually epistemologically destructive. Barfield's understanding of the notion and implications of betathinking is concentrated mainly in a discussion of language as symbol and metaphor. He argues that its end result is to discredit a realist metaphysics and to draw attention to human consciousness and its unfolding as a more basic reality than the representations of reality created by its thought. He argues that such a shift in thought would lead to a conscious perception of religious meaning in all experience, essential in a continued integration of meaning. He conceives of a new level of perception of material things, again participatory in character, but based on intelligent understanding. Given Barfield's generally Christian presuppositions, such "final participation" would be an integration of human experience in this world, in which a reverent awareness of God's presence could become a coherent and essential part of all intelligent activity. If I have interpreted Barfield's intention correctly, such a goal is not incompatible with the concerns of this essay.

However, I think Barfield's approach is not quite correct. It is vulnerable not only to an idealist metaphysics or an existentialist theology but to a radically false reinterpretation in terms of the egocentricity of mind which is endemic in Far Eastern thought." The fundamental problem is epistemological: the role of the human subject as the controlling center of knowledge is overemphasized. We may use the notion of "epistemic modes-3d as a way of understanding the problem of egocentricity in knowledge. Our language about knowing is based almost entirely on analogy with our perceptual skills: grasping, seeing, hearing. The analogy is appropriate if, as Polanyi argues, our conceptual skills are derived from the perceptual, inarticulate ones by the use of language. These different analogies describe different aspects of the process of integration of focal entities into subsidiary particulars of a larger whole which Polanyi describes. A key point is that knowing begins with an objective reality outside ourselves, and that our first awareness of a reality is mediated in a relation that is best described by the "hearing" analogy. This maximizes the emphasis on the other-than ourselves as the source of knowledge and is therefore inherently the least egocentric of the epistemic modes. This is why the Scriptures place such emphasis on speaking and hearing as the basic form of communication between God and man. I find however that Barfield's primary emphasis is given to the visual; this is true even of his interpretation of the role of language in biblical thought, since he conceives of language in almost exclusively figurative terms. What is lacking, I believe, is the emphasis on faith, hearing and the

Major conceptual problems in ... scientific thought today are closely related to the need to understand beta-thinking as a "clean different thing" from alpha-thinking ... this appears as we attempt to understand our own identity and agency by pushing alpha-thinking to its limits.

objective Other beyond our minds which is so fundamental to a biblical understanding, and which is the basis for realism and a realist epistemology. I am deeply indebted to Owen Barfield's brilliant insights in Saving the Appearances, but find-reluctantly-that some of the controlling assumptions differ from those implicit in biblical thought, and ultimately lead to a somewhat different conclusion. On the other hand, it may be that many points emphasized by Barfield will emerge even more clearly when we place them on a different epistemological foundation.

The Significance of Beta-thinking

Beta-thinking, thinking about thinking, provides the critique of the idolatry inherent in a-thinking as an ultimate and exclusive way of understanding. We can see it as idolatry if we consider examples such as the view of reality portrayed by Jacques Monod in Chance and Necessity,19 or even more grotesquely in some logical positivist philosophy.' The critique is fully anticipated by the prophet Isaiah":

No one considers, nor is there knowledge or discernment to say, "Half of it I burned in the fire, I also baked bread on its coals, I roasted flesh and have eaten; and shall I make the residue of it an abomination? Shall I fall down before a block of wood?" He feeds on ashes; a deluded mind has led him astray, and he cannot deliver himself or say, "Is there not a lie in my right hand?" (44:19-20)

As C. S. Lewis pointed out, "abomination" was originally "ab-homination," a thing utterly incompatible with what is properly human. Isaiah's critique makes sense when we apply it to the positivist deification of scientific knowledge as impersonal objective fact, and recognize the critique as that implicit in a philosophy of personal knowledge. Science is our creative response to a real physical world, and its objects and intentions are linked inextricably to the human eye and hand. What is in question is not the legitimacy of the entities or their objective reality, but the place they occupy. To be able to say "Is there not a lie in my right hand?" implies that one has understood one's own creative role in relation to the tool or framework employed to grasp reality; it is already the beginnings of beta-thinking. However, we also need to think about the prophet's other questions. They show a profound, divine compassion: the prophet understands the majesty of the divine image as the potentiality in the human personality, and recoils in horror from the folly of worshipping the creature. Without such divinely granted understanding there is no way to be delivered from the idols in the long run which explains why modern man has made an idol of a-thinking.

So I believe beta-thinking properly has a different outcome than Barfield anticipated. For him, it meant smashing the images of a-thinking, i.e., discrediting any claim to objective truth for the theoretical constructs and objects of science. But epistemological views which deny objectivity or truth to personal, creaturely knowledge are finally susceptible to radical egocentricity, precisely because they then make the autonomous self the ultimate critic.3d Operationalism interprets the autonomous will of man as its own end-as though the man in Isaiah's description were to think that a tree is there only as the expression of his own purposes. But the exaltation of the visual model,21 expressed in metaphysical idealism or more profoundly in the world-dissolving thought of the Far East, leads to the same end result, that man conceives himself and his own thoughts as an ultimate idol.

Instead, beta-thinking properly shows us that knowing involves ourselves, that what can be known must not only be what it is in itself but must be intelligible to our creaturely minds, and that if we intend to know what the human identity is these two problems are inseparably related. How shall we put ourselves in our theories in such a way that we do ourselves justice? The concern of a philosophy of personal knowledge is that we must

Epistemological views which deny objectivity or truth to personal, creaturely knowledge are finally susceptible to radical egocentricity precisely because they then make the autonomous self the ultimate critic.

certainly begin by acknowledging both objective reality and truth outside us and our participation through responsible commitment in all that we truly know. That is, we need an epistemology in which faith and hope placed legitimately outside ourselves are the recognized means by which knowledge is sustained; the reason for this, so simply and consistently communicated in the thought of the Bible, is that we can only then begin to understand ourselves and our true identity in the light of God's knowledge of and love for us.

Beyond epistemology lies the question of the "larger contexts of meaning," to which human beings may become responsible. These do not negate the reality Of the lesser meanings, but assimilate or integrate them as subsidiary particulars. Beta-tbinking can play a constructive part in that integration.

The Emergence of Beta-thinking in Science

Let me indicate some issues in science and thought today which seem to me to involve beta-thinking as the basis of either a meaningful question or a new sort of answer or demonstration. Many of these will already have been anticipated by readers and there are others not listed here. In this catalogue I am not pretending I really understand the problems at anything like the detailed level needed to solve them; I am just illustrating a common theme of some kind in them, something just on the edge of perception as a new sort of understanding. Their common feature is that they involve human beings and their consciousness as the latent intersection of thought and its object. We are holding some sort of mirror to ourselves.

The presentation below moves roughly from logical instances to those that might perhaps be termed ontological, but I believe all entail beta-thinking in some way.

(1) Gbdel's Theorem and Logical Self-Reference. The famous theorem of Godel22 is an assertion concerning certain types of logical or mathematical systems and the propositions constructible within them. It is conceived (and proved) by the use of a logical statement which refers to itself and a corresponding recognition of that statement as meaningful. The essential claim is that there are logical systems whose structure is stifficiently complex that we cannot decide on the basis of the stated axioms whether the axioms are complete or consistent: that is, propositions can be constructed within the system which cannot be decided as either true or false. Technically the basis for the proof is achieved by symbolic substitution or mapping of logical relations and operations onto the relations and operations of arithmetic. If a system is sufficiently complex to contain such a mapping of at least a part of it onto arithmetic, then undecidable propositions can be constructed within such a system. These form a special class of propositions which say concerning themselves, (upon a formally defined process of substitution) that they are not provable. As Gbdel himself observed they are logically very close to the liar paradox and other logical puzzles constructed with selfreference. In the proof of the G6del theorem, we conclude that it is true that these propositions (which refer to themselves) are undecidable. To understand the Godel theorem and its proof is to do a form of 0-thinking, since at some level one must transcend any completely formalized a-thinking statement and tacitly conceive the affirmation of the theorem as a statement about thoughts (or perhaps thinkers) themselves. It is not possible to formalize this act itself (except by a symbolic assignment).

(2) The Marks of Intelligence. The problem of logical self -reference is connected in some way with the capacity we have to 'leap outside' of a system of thought and argument and identify the system in a new context as a member of some other class or system. Any satisfactory description of intelligence-required to create a truly intelligent machine-must somehow find ways of describing this capacity. D. R. Hofstadter explores some aspects of this problem at a popular and readable level in the book Gbdel, Escher, Bach and in several monthly columns published in Scientific American .23 His articles serve as a useful source of citations on thinking relevant to self-reference and the problem of intelligence. However, I find the most interesting aspect of Hofstadter's discussions is the way in which his own attitude seems to move between occasional appreciation of the radical character of beta-thinking and a dominant, almost trivially reductionist a-thinking presuppositional basis. He understands that the capacity to leap out of a system is not formalized, but persists somehow in the belief that the problem involved is an aspect of some impersonal and mechanistic logic. The deepest flaw in his argumentation-and in many of the arguments he cites-is a tacit appeal to models of intelligent behaviour which are alleged to be mechanical, but on closer scrutiny are always found to require human intelligence to interpret them or give them meaning at a higher "metalinguistic" or "metalogical" level; that is, his models are games only people can play. To argue that these models provide the basis for understanding intelligence mechanically is a mistake: they show how specific acts of intelligence may be recognized or logically represented by one comparably or more intelligent being to another, but provide no account at all of the construction and recognition of intelligence from scratch. Merely because the Godel theorem can be stated, comprehended, and proved by us seems to imply to Hofstadter that its truth is then a kind of alpha-thinking truth. But the conclusion does not follow, since it begs the question by our including ourselves tacitly in the argument.

(3) Logical Indeterminacy. It is unnecessary for me to give a lengthy explanation of what is meant by "logical indeterminacy" since that has been done so well and in so many different contexts by Donald M. MacKay.24 MacKay supposes that we may set up a hypothetically determinist apparatus which makes predictions about the state of an (intelligent) person's brain. Such predictions may be verified by ourselves and by third parties, that is, they may deserve accreditation by persons other than the subject to whom they then have reference (or even a posteriori by the subject himself). However, their status as assertions concerning reality is completely different if they are offered to the subject in advance, as propositions for affirmation or denial; MacKay argues that strictly speaking the subject would be wrong to believe them, since believing them is itself an act which cannot be made compatible with the calculation. This logical indeterminacy of scientific information or prediction when we apply it to ourselves as part of the system is quite independent of any physical indeterminacy that may exist. In MacKay I s view this permits us to regard the freedom of human choice as an objective and logically justifiable truth. To understand MacKay's argument-and to accept it-is to do some beta-thinking.

One may go further, and ask about the possibility of such a machine. Might it not be the case that the existence of this logical indeterminacy makes it impossible for any such physically determinist predictingmachine to exist in the world? That is, if the outcomes of determinist processes are in definite predictive correspondence with beliefs ('states of mind')-a necessary condition for us to understand the machine's predictions-how could we ever construct a machine which can represent the recognition of logical indeterminacy itself as a possible "state" of an intelligent brain, and then proceed logically to compute a future state for it? Now this argument in itself may be seen as just another form of MacKay's argument for logical indeterminacy: no machine of the required sort could entertain or resolve the logical indeterminacy created by the feedback involved. However, it also seems to me that the creation of this sort of indeterminacy is already a possibility in the mind of an isolated subject, and the difficulty involved in constructing a predicting-machine of the required type already entails the problem of such indeterminacy, in the requirement that "beliefs" or "states of mind" be identifiably in correspondence with certain sets of physical brain states. If it existed, such a machine would have its own thoughts about the problem of indeterminacy! The phenomenon for which we must account is not the inarticulate behavior of cabbages or earthworms, though that is hard enough; nor is it that we have to account for their articulate formulation of calculations and predictions in relation to the world around them, though that is harder still. What we have to account for is that there are cabbages and earthworms which reflect on their own states of mind-who, as C. S. Lewis put it, give lectures on their origins and destiny.

(4) The Interpretation of Quantum Mechanics. To understand quantum mechanics, we have to resolve a conflict between beliefs we instinctively regard as logically self-evident and what is ontologically valid. The physical world's actual behavior disagrees with some of our most elementary beliefs about logical inference applied to space-time relations. As is well known this comes about because, in contrast to classical physics, quantum mechanics somehow includes the fact that we cannot possess knowledge of the world without interacting with it. The result is a calculus which makes probabilistic predictions about the results of measurements. There seems to be little doubt that this calculus agrees with the results of experiments, including recent critical tests.25

As to the interpretation of the formalism, however, the situation is confused. In the "orthodox interpretation, " the actual state of a closed system is described by an entity called the wave function, a unique, precisely defined object, given conditions specifying it at some time. The equation for the time-development of the wave function for a closed system is perfectly definite. The problem comes when we ask how the wave function is to be interpreted in terms of predictions about system properties. In the orthodox view, everything depends on whether a "measurement" is made at some particular point. If it is, then the mysterious "collapse of the wave function" occurs and subsequent time-development involves only that portion of the previous wave function corresponding to the measured outcome. If on the other hand no measurement is made , collapse" does not occur. The resulting predictions about subsequent behaviour are not the same in the two cases. This arbitrary procedure gives the correct results for the (probabilistic) outcomes of later measurements. The problem with it is the peculiar status it somehow gives to "measurement," since absolutely no account can be given within the theory of bow a wave function can "collapse" (after all, a quantum theoretical description of the system including a measurement device must be possible too, and how can its wave function "collapse"?).

Quantum mechanics is not incompatible with the existence Of a real world whose "state" . . . is independent of our knowledge of it . . . Its peculiar logic expresses what we who interact with a system can in fact know about that reality. Our problems with classical logic of probability would then seem to be a matter of thinking about thought rather than about things.

The history of the interpretation of this bizarre state of affairs is really an indication of the limits of ctthinking when applied not merely to logic but to real events."-' The positivist interpretation is that nothing meaningful may be said about reality itself and we must confine our statements exclusively to measurement values. There is a wide class of interpretations equivalent to various forms of metaphysical idealism, alleging that conscious observers somehow "decide" the state of the universe; an even more bizarre interpretation of the wave function is given by the "splitting universes" view.

The problem has been usefully clarified, I believe, by a new interpretation of quantum mechanics called .1 consistent histories," devised by R. B. Griffiths. 28, 29 Consistent histories predicts exactly the same results as the orthodox version of quantum mechanics, so it is a new interpretation rather than a new theory. However, it differs substantially in the entities to which it ascribes meaning. In particular, it allows us to preserve something very much closer to a classically realist understanding of the behaviour and properties of a system even in the absence of measurement; conditional probabilities may be defined for physical properties of a system in a consistent relation to corresponding properties of measuring devices, so that "measurement" is a describable phenomenon not intrinsically different from less controlled or less humanly correlated interactions. No reference to "collapse of the wave function" ever appears, though the price for this is that the concept of a unique connection of a wave function with a "state" is sacrificed; instead attention is focused on the conditional probabilities of certain sequences of spatio-temporal events ("consistent histories"). One may then speak meaningfully of sequences of events or physical properties which exist independently of their actual measurement, and those forming consistent histories have probabilities which fit classical expectations of compatibility over contiguous sections of space and time. Of course the counterintuitive realities characteristic of quantum mechanics remain, but they appear in the rejection of certain histories as "inconsistent"-one may not, for example, give meaningf ul probabilities for sequences in which a property's value and its registration in the corresponding measurement device state are separated in time by an intervening, incompatible property or measurement value. However, I should not presume to give what must necessarily bean inaccurate understanding of Griffiths' formulation, and encourage you to read it for yourselves. What I find interesting about this interpretation is that it consistently allows us to believe that a system has a real sequence of consistent properties whether or not they are "measured." The bizarre characteristics of quantum mechanics are retained in the much weaker sense that they show up only when we try to assign conditional probabilities to states of affairs which cannot in fact be observed (e.g., simultaneous values for two properties whose dynamical operators do not commute). What such an interpretation seems to mean is that quantum mechanics is not incompatible with the existence of a real world whose "state," if isolated, is independent of our knowledge of it, but that its peculiar logic expresses what we who interact with a system can in fact know about that reality. Our problems with the classical logic of probability would then seem to be a matter of thinking about thought rather than about things (though I admit the connection to the previous instances of beta-thinking is fuzzy).

(5) Basis for the Recognition of Order. If one examines work in modern biology-let's take the coding and replication of genetic information in a cell as the best example-one finds a curious assumption tacitly involved in all such work, namely an assumed analogy to ordering principles characterizing intelligent design. This has been a tremendously fruitful assumption, and forms the basis for all our explanations of structure and function in these fantastically complex systems, but after all it is a pattern of meaning borrowed from experience well outside the literal domain of a-thinking. It is no accident that our understanding of the DNA coding of genetic information and its reproduction and constitution of functional chemical structures by the t-RNA/ribosome/m-RNA system

The essential issue at stake in philosophical realism ... is the declaration of our intention to go on being responsible to a reality beyond ourselves ... to keep on listening to it in the firm belief that what we hear will instruct and lead us to understanding, fuller vision and manifestation in expression.

has developed in parallel with the advent of the high speed digital computer. We interpret the behavior of the biological system by analogy with the logical ordering and controlled sequencing of function we have intelligently designed the computer to perform. We may well be able to work out a mechanism of control and function in a cell and its materials on this analogy, though of course we cannot be sure that it is adequate. However, it is then legitimate to ask what such an ordering, which after all is objectively real, can possibly mean. Isn't it at least an open possibility that just as the computer manifests and fulfills purposes transcending its hardware yet appropriately embodied in it, so the biological system is the result or embodiment of intelligent design, expressing some abstract existence or purpose which transcends the specific chemistry? This question cannot be answered unambiguously by the answer to any a-thinking problem. Many people will argue that it is not therefore a scientific question. I am not so sure, since-just as with the quantum mechanics-the meaningful question is one of intelligibility. There is a sort of mirror symmetry with the problem of describing intelligence which we discussed earlier. There the issue was whether our intelligence (acknowledged as real) could be accounted for on the basis of purely mechanical function; here the problem is to understand an actual functioning mechanism (as it appears) without appealing to direct symbolic transcription from the artifacts known to have been created by intelligence. Our notion of an objective order in nature is derived explicitly from appreciation of ourselves and our artificial creations. Either we suppose that the notion is our illusion or invention (a dangerous option)-or we recognize that the order is real and the meaning transcends the machine as concept.30

Beta-thinking and the Future of Science

The appearance of beta-thinking as a meaningful and even critical aspect of scientific understanding suggests a first step could be made toward intellectual awareness of the "larger contexts of meaning" anticipated by Polanyi. Such an awareness does not imply repudiation of the determinate, fixed descriptions of things and their relations which science has created. They have their legitimate (and even liberating!) role as limited models of reality. Increasingly, though, we may expect that the goals and settings for scientific problems, and the intelligibility of scientific theories, will involve some beta-thinking as a mode of understanding.

We may expect widespread debate between those who conceive of scientific questions as limited strictly to a-thinking, and those who will demand for meaning's sake that our understanding of "science" step beyond those lirnits.31 An important aspect of that debate will be the question of what may be called the 11 controlling paradigms of meaning." Up to the present time, it may be said that the dominant ideal of science has been the concept of the machine, with its linear, determinate and connective function; it has served as a model for the world, living things, and even human beings and society.32 Its limitations are evident now. Perhaps the next paradigm may be that of the biological organism, with its characteristics of global coherence, purposive structures and integrated flexibility of function. Such a motif is prominent in much that is written nowadays about the need for transformation in scientific and cultural thought (cf. for example, Ref. 16.). The idea contains important and useful elements; yet, as John MacMurray pointed out, " the human identity is more than that of the biological organism; it involves the personal. Here again, the old question of the imago Dei is involved. Can we truly understand the personal without ultimate reference to a personal Creator?

The issue involved in beta-thinking is much more than a matter of a controlling paradigm for science. We noted that the intersection of creaturely meanings is in the human identity. In the long run everything in human culture, not just science, will depend on our understanding of ourselves and our identity.

Some Reflections on Realism and Reverence

Recall that in the critique of idolatry given by the prophet Isaiah there are actually two appeals made to the intelligence. The second-the one we have considered here-recognizes that we ourselves are the makers of our idols ("Is there not a lie in my right band?"). We have seen how this is the effect of beta-thinking on alpha-thinking idolatrously reified. If we were so naive as to imagine that the models of the reality constructed by alpha-thinking were a kind of ultimate truth, we have had to learn (if we are logically consistent) that this apparent objectivity seems to be in danger of dissolving away into merely our self-expression or self -reflection. The attempt of positivism to establish an objective and impersonal truth through alpha-thinking has created insoluble problems when the apparatus is turned on man and his thought itself; continued insistence on the autonomy of the human mind, without commitments beyond ourselves, then leads either to operationalism or to a philosophy of illusion.

But the first question is just as important ("Shall I make an abomination of the residue? Shall I bow down to a block of wood?"). What it asks is that the thinker conceive of himself adequately and that in such a conception there be the appreciation of worth. This passage reveals the divine compassion, God yearning for us to share His own valuation and appreciation of us. Everything in human culture will depend on our understanding of ourselves and our identity. However, we should note the somber tone of the prophet's commentary: "A deluded mind has led him astray, so that he cannot deliver himself, or say. . . " The capacity for a correct understanding of ourselves and our own creativity cannot originate from within the human mind itself; that is epistemologically inconsistent. This is why 0-thinking in itself does not necessarily bring us to a true conclusion. It may be misinterpreted, and will be misinterpreted, by epistemological views founded upon egocentric inner attitudes. If we choose to believe that knowledge ultimately depends on ourselves or requires no commitment beyond ourselves, then the effect of 0-thinking will always be to discredit all claims to know truth and identify all knowing as merely the kaleidoscope of perception emanating from our own minds or the assertion of our self-fulfilment. Such a direction in culture would mean the death of the scientific tradition.

The issue truly at stake in philosophical realism, then, is the declaration of our intention to go on being responsible to a reality beyond ourselves, and to keep on listening to it in the firm belief that what we hear will instruct us and lead us to understanding, fuller vision and manifestation in expression. This attitude, with its emphasis on the contingent reality of creation and yet the expectation of a divinely created order and meaning to be found in it, originates in the Word of God, and it is sustained by a continuing expectation that yet more is to be heard.' But the final object of such an attitude can only be God Himself.

Reverence is a realistic response for those who see truly, but for human beings it must be based on reconciliation.' Hence we do not suppose it is an expected response from those who do not know themselves to stand on that basis, no matter how realistic or reasonable it is. Yet we may appeal to those who do have faith, that they should rightly understand the situation. I really do not believe that an operationalist, phenomenalist or idealist philosophy of the created order is proper for us; we should not so understand our activities or our identity. I should like to end this essay with two passages from the Bible, which make the link between realism and reverence plain.

First consider the other great creation Psalm, which we have not so far mentioned, and with which I certainly am less familiar (perhaps understandably, as an inveterate a-thinker!). Psalm 139 concerns our understanding of our own selves in the awareness of God's having created us and of His continuing presence with and knowledge of us. It bears something of the same spiritual relation to #-thinking that Psalm 19 bears to a-thinking. I may mention just two points in it. The first is the Psalmist's profound awareness of God's presence in all creation and in his own innermost thoughts; and the second, coupled with it, is his appreciation that a proper response to his own complexity and depth is not self-adulation but fear and awe toward God-"such knowledge, too wonderful for me." It is no use for us to suppose that we can relate to creation in any way as if God were not there, least of all as we try to understand what we do there. Long ago, this was put so simply and yet so well by Isaac Watts:

There's not a plant or flower below, but makes Thy glory known, and clouds arise, and tempests blow, by order from Thy throne; while all that borrows life from Thee is ever in Thy care, and everywhere that man can be, Thou, God art present there.

Watts wrote that in the eighteenth century, and it is not my impression that be supposed its truth to be incompatible with the unfolding truth of science.

The second passage is the account of creation given in Genesis 2:4-25. As is well known this has a different emphasis from Genesis 1:1-2:4, which seems more comprehensive of both space and time and emphasizes humanity's relation to God's purpose in creation. Here the emphasis is placed rather on man's relation a, creature to the rest of creation, and his relation to God is seen in that perspective. The account comes to a first, pause with the creation of woman and recognition of the unique relation of man and woman as "heir-, together of the grace of life." However, en route to this, a great deal is said about the relation of humankind to the rest of creation. In particular, the unique authority, gifts and vocation of human beings in relation to & garden is indicated by the story of the naming of the animals (v. 19). This passage forms a paradigm for the enterprise of science. The issues relevant to science. viz., the contingency of the world, the role of the human mind in recognizing and bringing to light the order in nature, the capability and authority given us to do so, and above all the value placed on the activity b,. God, are all evident. God was interested "to see what the man would call them." Such interest and concern of God continues throughout the story as it unfolds in the rest of the Scriptures. God is not absent, but present.

The creation is not a domain of thought and activity in which we have no relation to or an independence of the Creator. Surely we should learn the relevance of this lesson for our care of the earth." But equally it seems to me that operationalism as a philosophy of science really presumes that we are responsible only to our own minds and our own purposes for what we think about the world-so that God, so to speak, has no interest or concern with those activities and we have none with Him, except as an option. Such a dualist separation of the purposes and objects of redemption from those of creation seems completely wrong to me. since then reverence has no necessary relation to the understanding of creation.

For human culture, everything depends on our understanding of ourselves and our identity. That understanding cannot come from our own minds, but from hearing the Word of God. Our ability to hear, and therefore our capacity to see things as they really are, is closely linked to our reverent willingness to listen. Conversely, a realist belief, that the listening so basic to the scientific enterprise leads not to illusion or convenience, but to truth, is the belief most compatible with reverence for God in what we do and think here. Realism and reverence really are inseparable.


1. (a) Psalm 19:1-14; (b) Romans 1: 18-23.

2. T. F. Torrance has used the term ontological to describe those contingent relations created by God, and accessible to creaturely knowing as aspects of an objective reality. Such relations are not merely logical, but are relations of actual being, even though they are consistent with our creaturely logic as the tool which apprehends them. (a) T. F. Torrance, Divine and Contingent Order, Oxford Univ. Press, Oxford (1981); (b) ibid., Reality and Scientific Theology, Scottish Academic Press, Edinburgh (1985); (c) ibid., The Christian Frame of Mind. Handsel Press, Edinburgh (1985).

3. (a) W. R. Thorson, "Reflections on the Practice of Outworn Creeds," Journal of the American Scientific Affiliation (JASA) 33, 3-11 (1981); (b) ibid., "Science as the Natural Philosophy of a Christian," JASA 33, 65-73 (1981); ibid., "The Biblical Insights of Michael Polanyi," JASA 33, 129-138 (1981); (d)ibid., "Scientific Objectivity and the Word of God," JASA 36, 88-97 (1984).

4. This paper is a revision of the second of two papers presented at the joint Conference on Science and Faith of the American Scientific Affiliation, Canadian Scientific and Christian Affiliation, and Research Scientists' Christian Fellowship (UK), Oxford, July 1985. The discussion of theological "operationalism" referred to was presented in the first paper, "Toward a Biblical Understanding of Human Knowledge." Since most of the ideas in that paper may be found in Refs. 3a-d, I have preferred not to publish it.

5. Paul Tillich, The Courage to Be. Yale Univ. Press, New Haven, Conn. (1952); ibid., Dynamics of Faith. Harper & Row, New York (1956).

6. (a) T. F. Torrance, "Karl Barth and Patristic Theology" [to be published], (b) ibid., "Theological Realism," in The Philosophical Frontiers of Christian Theology: Essays Presented to D. M. MacKinnon, Eds. B. Hebblethwaite and S. Sutherland; Cambridge Univ. Press, Cambridge (1982).

7. Cf. T. F. Torrance, Reality and Evangelical Theology; Westminster Press, Philadelphia (1982).

8. Michael Polanyi, Personal Knowledge: Toward a Post-Critical Philosophy. Routledge and Kegan Paul, London (1958). Repr. in Paperback Ed., Harper Torchbooks, Harper & Row, NY. (1966).

9. Drusilla Scott, Everyman Revived: The Common Sense of Michael Polanyi. The Book Guild Ltd., 25 High Street, Lewes, Sussex, England (1985).

10. There is some ambiguity and perhaps even inconsistency in what "meaning" Polanyi himself supposed religious truth to have. There has been scholarly debate as to whether Polanyi did or did not intend the existentialist interpretation of religious meaning set forth in his last book, written as a co-author with H. Prosch [M. Polanyi and H. Prosch, Meaning, Phoenix Books, U. of Chicago Press, Chicago (1977)]. However interesting to scholars such debate about Polanyi's own views might be, it is not directly relevant to the question which really concerns us: what view is consistent with the general epistemological approach? Lady Scott (loc. cit., Ref. 9) has made the same point and reaches the same conclusion as I do: a view of religious truth as referring to objective reality is fully consistent with the epistemology of personal knowledge. Given his view of his work as a beginning exploration toward the truth, Polanyi himself would have been the first to encourage discussion of the issue on its merits.

11. R. A. Jastrow, God and the Astronomers. Norton & Co., New York (1978).

12. A good bibliography on the "anthropic principle" maybe found in W. J. Neidhardt, "The Anthropic Principle: A Religious Response," Journal of the American Scientific Affiliation 36, 201 (1984). Cf. sources also cited by Neidhardt: P. Davies, The Accidental Universe, Cambridge Univ. Press, Cambridge, (1982); E. R. Harrison, Cosmology-The Science of the Universe, Cambridge Univ, Press, New York (1981); B. J. Carr and M, J. Rees, "The Anthropic Principle and the Structure of the Physical World," Nature 278, 605 (1979).

13. For the ardent feminists among my readers let me say that I have struggled humanfully with the problem of 'man' in the sense of "human" as distinct from merely "male;" where possible a neutral term conveying both genders as one unity has been used. There remain a few isolated cases where I felt that such unwomanly violence would be done to simplicity, clarity or rhetorical strength that I opted for the traditional word. I apologize to those for whom this creates a block, but I believe there are more important issues in our time than this one.

14. Owen Barfield, Saving the Appearances: A Study in Idolatry. PB Edition (USA), Harcourt, Brace & World, Inc., New York (1965),

15. Theodore Roszak, Where the Wasteland Ends. PB Ed., Anchor Books, Doubleday & Co., Inc., Garden City, NY (1973); ibid, The Making of a Counter-Culture; PB Ed., Anchor Books, Doubleday & Co., Inc. (1969).

16. Fritjof Capra, The Turning Point. P13 Ed., Bantam Books, Inc., New York (1983).

17. Isaiah 44:9-20.

18. At one point in Saving the Appearances, Barfield acknowledges the danger of a pantheist interpretation of his work: loc. cit., Ref. 14, pp. 144-150.

19, Jacques Monod, Chance and Necessity. A. Knopf & Sons, Inc. New York (1971).

20. A. J. Ayer, Ed. Logical Positivism. Free Press, Glencoe, 111. (1959); A. J. Ayer, Language, Truth and Logic. V. Gollancz, Ltd., London (1949); ibid., Philosophical Essays. MacMillan & Co., New York (1954); Bertrand Russell, Our Knowledge of the External World. 2nd Ed., Allen & Unwin, New York (1922); ibid., Human Knowledge: Its Scope and Limits. Allen & Unwin, New York (1971).

21. Toward the end of "Saving the Appearances," [loc. cit., pp. 158-9] Barfield portrays the role of beta-thinking as a recovery of the ancient conception of vision as the ray emanating from the eye of man and returning to him-as if that were true! Surely piety requires instead our admission that what is true physically is also true metaphysically and epistemologically, namely that we see because there is light filling the world and by that light we see reflected all the things in the world.

22. See for example J. van Heignenoort, From Frege to Gbdel. Harvard Univ. Press, Cambridge, Mass. (1967),

23. D. R. Hofstadter, Gbdel, Escher, Bach: An Eternal Golden Braid . Basic Books, Inc., New York (1979). Cf. also the column "Metamagical Themas" in Scientific American; see issues for January 1982; September 1982; January 1983. See also the notion of mind advanced by P. Davies, God and the New Physics. Simon and Schuster, New York (1983).

24  Donald M. MacKay, The Clockwork Image. InterVarsity Press, Downers Grove, Ill. (1974); ibid., Brains, Machines and Persons. Wm. B. Eerdmans Publ, Co., Grand Rapids, Mich. (1980); ibid., Science, Chance, and Providence. Oxford Univ. Press, Oxford (1978).

25. A. Aspect, J. Dalibard and G. Roger, Physical Review Letters 49, 1804 (1982).

26. J. C. Polkinghorne, The Quantum World. Longman Group, Ltd. London & New York (1984).

27. See for example J. A. Wheeler and W. H. Zurek, Eds., Quantum Theory and Measurement, Princeton Univ. Press, Princeton, NJ (1983); also M. Jammer, The Philosophy of Quantum Mechanics. John Wiley & Sons, New York (1974).

28, R. B. Griffiths, "Consistent Histories and the Interpretation of Quantum Mechanics," Journal of Statistical Physics 36, 219 (1984). Ref. 29 is a brief, non-technical account.

29. R. B. Griffiths, "Philosophical Implications of Quantum Theory" [Paper presented at Conference on Science and Faith, Oxford, July 1985].

30. A similar point has been made by C. B. Thaxton, W. L. Bradley and R L. Olsen in The Mystery of Life's Origin: Reassessing Current Theories, see Epilogue. Philosophical Library, New York (1984).

31. In spite of arguments given in this paper it is not obvious to me which side of the debate is right. I favor the more conservative view that while meaning and setting for scientific questions, and intelligibility of scientific theories, may legitimately entail some beta-thinking, the focal objects of scientific investigation must properly remain within alpha-thinking limits. Confusion often evident in the "social sciences" is the result of Dot keeping these limits sharply defined, and illustrates my concern.

32. Machine and biological organism as contrasting models for scientific understanding have a long history. Cf. Ian Barbour, Issues in Science and Religion, Chapter 11, Prentice-Hall, Inc., New York (1966); PB Ed., Harper Torchbook TB 1566, Harper & Row, New York & London (1971). A good assessment of the limitations of the organismic model, in relation to the personal, is found in John MacMurray, The Selfas Agent. Faber & Faber, Ltd., London(1957).

33. Cf. Isaiah 6:1-7; Hebrews 12:18-29.

34. Loren Wilkinson, Ed., Earthkeeping: Christian Stewardship of Natural Resources. Wm . B. Eerdmans Publ. Co., Grand Rapids, Mich. (1980).