Science in Christian Perspective

 

 

The Participatory Nature of Modern Science and Judaic-Christian Theism
W. JIM NEIDHARDT
Physics Department
New Jersey Institute of Technology
Newark, NJ 07102

From: JASA 36 (June 1984): 98-104.

Descartes and Galileo were instrumental in starting modern science by their commitmen to a method of investigation in which the detached observer first observes and then manipulates physical reality. This paradigm of detachment has been the model for scientific objectivity despite its inability to function well when applied to the social sciences and the fact that the creative researcher in the physical sciences often ignores its rules by allowing himself (or herself) to be guided by non-detached intellectual passions; that is personal and community (scientific) standards of rational beauty, unity, and simplicity. But recent developments in the philosophy of science, quantum physics, and cosmology have greatly weakened the validity of this paradigm, for the scientist is now believed to always be an active participator with the universe; indeed, human consciousness may even be a necessary condition for our universe's existence. This newly emerging paradigm of active participation has a number of striking implications for and resonances with Judaic-Christian theism. These implications and resonances are explored.


From Detachment to Participation in Scientific Method

Until recently modern philosophy has suffered from a fatal cleavage' due to the dualist split between the positivist tradition which views all truth as scientific truth obtained by an impersonal, objective, infallible process known as the scientific method and, on the other hand, the existential tradition which sees truth as a matter of subjective reference to one's self-knowledge and self-existence. These two traditions are very different and rather unrelated kinds of truth, and increasingly, in our science-dominated culture, scientific truth is taken as the only valid truth with its image of only the detached observer obtaining truly objective knowledge. From this positivistic perspective the scientist emerges as detached from the object of his investigation, his personal worldview as represented by his aesthetic, philosophical and religious commitments playing no role in his interrogation of the external object world (what figure 1 calls THE OTHER). Furthermore his world view, his many personal commitments are not enhanced and altered due to his interractions with external reality.

The origins of this fatal dualism can be traced back to the sixteenth century philosopher Descartes, who saw as the starting point for all philosophy the self-consciousness of the rational mind, the awareness by the thinking mind of its own activity constituting both the sufficient and necessary ground of existence. From this fact Descartes worked outward "to prove" the existence of God with the fatal flaw that the existence of God then depends upon the existence of the self. Then from God's existence Descartes argues that God has implanted mathematical patterns in physical reality. The mind, by formulating clear and distinct ideas based upon geometry, can discover truth about physical reality that possesses certitude. Indeed Descartes' model of scientific investigation is based upon geometric reasoning.2 First you subdivide the system being studied into small, easily manageable components, then you measure the properties of these individual components, and finally, since one can perceive directly and immediately what is clear and distinct in these simplest components one can combine the components in a logical fashion to reassemble the whole structure. Thus by this "atomistic" method of subdividing a thing into its smallest components, knowledge is gained in a mechanical fashion which possesses the certitude of geometric theorems, the chain of reasoning used in the investigation of the physical world (subdivide, measure, combine) being similar to those chains of reasoning which geometricians use in proving theorems. Note that the aim of such investigatory method is to produce knowledge that is certain, free of all risk; it is very different from the type of knowledge one would gain in personal relationships.

What are the implications of Descartes' starting point in the self-conscious ego? What presuppositions does it hide, for Descartes did not recognize his own tacitly-held presuppositions? Walter Thorson' very nicely summarizes these implications as follows:

a. I think therefore I exist is not grounded in a rational argument but is existentially grasped. Thus Descartes is a primary originator of existential philosophy.

b. Reality has only two categories-the egocentric knowing self and the object world which it knows. All reality other than self is objective. The object world is defined as that which is known by me. God, other persons, rocks are alike-the objects of my knowledge. Thus my knowing activity is emphasized as opposed to the nature of the other which is known or its activity.

c. The activity of self is defined only in terms of knowing and thinking. It is not enriched or altered by relationships with the other including, most importantly, personal relationships. It rejects as illegitimate for philosophy the identification of the self as I am he who trusts or believes.

d. Absolutely certain proof arising from the autonomous self poses impossible tasks for philosophy. How do we know that our knowledge is objective and not merely a product of our imagination? How do we certify the reality of the world?

How can we reach certainty? Any problem that does not yield certainty is rejected as meaningless.
e. The Cartesian self is God. All authority for knowledge stems
from the ego.

Figure 1 schematically portrays the Cartesian dualism. Man either is exploring what is beyond himself (THE OTHER) by methods patterned after pure thought, i.e., geometric, logical reasoning; or man is exploring the depths of his own self-consciousness. In either case the self rather than what is beyond one's self is the ultimate authority. And as Walter Thorson points out, the self has an "obsession for knowledge that is beyond doubt, beyond risks, rests on no presuppositions, is logical and objective, and has no commitments to aesthetics or the subjective commitments of persons-particularly as they relate to one another (author's comment). Man as a person is removed from his own world and replaced by an automaton acting under determinate laws. All real knowledge can be based upon an infallible procedure called the scientific method"4 which today is a more sophisticated variant of Descartes' subdivide, measure, and combine cycle. Detachment, from this perspective, is the main characteristic of scientific objectivity. But recent studies of scientific method and scientific creativity have revealed this method of detachment originating from Descartes is a caricature of how scientists really go about making actual scientific discoveries.

Figure 1.


This perspective of science as an activity of detached observers has been successfully challenged by Michael Polanyi in his masterful book Personal Knowledge5 and many other works. The scientist is a person deeply committed to the rationality and dependability of the behavior of that reality exterior to him (THE OTHER). He has tacitly learned, from the behavior of things and relationships shared with other persons, aesthetic and moral commitments which guide him in his exploration of and encounter with external reality. That reality, THE OTHER, is as much an authority to him as his own ego. Thinking is thus embedded in a presuppositional matrix tacitly held and acquired from one's encounters with the totality and richness of the flow of experience outside one's self. The necessity of commitment as an integral component of scientific activity is beautifully summarized by Thomas F. Torrance, a leading interpreter of Polanyi:

". . . Michael Polanyi has insisted that we must recognize belief or intuitive apprehension once more as the source of knowledge from which our acts of discovery take their rise, for it is in belief


W. Jim Neidhardt is Associate Professor of Physics at New Jersey Institute Of Technology. His professional interests are in quantum physics; systems theory; and the integration of scientific, philosophical, and religious perspectives, all being forms of personal knowledge as ably pointed out by the scientistphilosopher, Michael Polanyi. He is a member of the American Physical Society, American Association of Physics Teachers, Sigma Xi, and a Fellow of the American Scientific Affiliation, and has published twenty-six professional papers. He is also interested in the problems of educationally deprived collegebound students and has taught a college level integrated physics-calculus course for Newark high school seniors. Dr. and Mrs. Neidhardt and their family (all J's) reside in Randolph, N.J.



that our minds are in direct touch with reality, in belief that our thought is open to the invisible realm of intelligibility independent of ourselves, and through belief that we entrust our reason to the rational order and reliability of the contingent universe. Behind and permeating all our scientific activity, whether in critical analysis or discovery, there is an elemental, overwhelming faith in the rational constitution of things, but faith also in the possibility of grasping the real world with our concepts, and above all faith in the truth over which we have no control but in the service of which our rationality stands or falls. Faith and intrinsic rationality are interlocked with one another... Science does not operate from an axiomatic set of formally defined and verified propositions, as the positivists claim, but from ultimate informal assumptions which cannot be proved or refuted and which cannot be completely formalized, yet without implicit reliance on them would be no scientific knowledge at all. As examples of these ultimate assumptions we may refer to belief in truth or belief in the lawfulness of nature, neither of which we could prove for we would have to assume them in any attempted proof, but both of them are nevertheless all determining constituents in our fundamental frame of belief, affecting the entire shape and scope of our scientific activities and their results as well, Hence Polanyi insisted that the premises of science on which all its inquiry rests are the beliefs held by scientists on the intelligible nature of reality independent of themselves and its capacity to disclose itself in an indeterminate range of yet unknown and perhaps even unthinkable ways. Far from being subjective or irrational these beliefs have to do with the structural kinship between the knowing subject and the objective reality he seeks to know, and they arise in his mind as intuitive convictions which he cannot reasonably avoid for they are thrust upon him as elemental aspects of reality pressing for realization in his understanding."6

Hence, contrary to Descartes, thinking is always embedded, often tacitly, in a framework of trust and belief. In science one trusts in an integrated conceptual framework of interacting basic presuppositions, theories, and models concerning external reality. And as one, in trust, interacts with what is beyond oneself, one's thinking processes enhance and alter this partially tacitly held conceptual framework. Thus, as portrayed in Figure 2, reality external to one's Self, THE OTHER, becomes in the last analysis the ultimate authority rather than one's self-conscious ego. Note that a person's beliefs concerning external reality arise in one because they are forced upon one by the very nature of the reality one is in experiential contact with; and its inherent intelligibility constrains one rationally and morally not to resist it Polanyi, by recognizing the deeply personal role of commitment in all knowledge acquisition has done much to heal the dualism introduced by Descartes between the self-conscious ego and the external object world. Now the knower is no longer a detached observer but an active participator through his commitments to the portion of reality being explored. Lastly, absolutely certain, risk-free knowledge is not possible for finite human knowers according to Polanyi but risk is minimized as the knower responsibly commits himself to reality that is outside himself (THE OTHER). Objectivity is now based upon the common agreements of communities of knowers deeply and responsibly committed to their respective disciplines. For detailed documentation (with many examples) of the role commitment plays in all aspects of scientific knowledge see Personal Knowledge.

The participatory nature of modern scientific method is clearly brought out by the method outlined by one of our greatest modern scientists, Albert Einstein; his scientific method contrasting sharply with that of Descartes.7 Einstein envisions the scientist as beginning with the world of experience and experiments. On the basis of nothing more than physical intuition and intellectual convictions, the scientist makes an intuitive leap, a jump of imaginative insight, from the realm of experience to abstracting a system of axioms. This is a conceptual jump far beyond where any experiment could check it and before any supporting evidence was available. Furthermore, G. Holton, a leading interpreter of Einstein's scientific methodology, envisions this imaginative jump as taking place through a framework of the scientist's deepest intellectual commitments which Holton calls themata.8 These tbemata serve as a filter with respect to possible alternative, imaginative jumps. Finally, once a system of axioms is established, the axioms are used to deduce specific theoretical results capable of being experimentally checked. Thus one is brought back to the realm of experience. If experiments do not agree with the theoretical results, the system of axioms on which they are based is considered faulty and must be modified or a completely new set of axioms created. This vulnerability of the system of axioms to falsification is in keeping with positivist views of science; but the intuitive or imaginative jump from experience to the set of axioms is contrary to all positive dogma. The scientist cannot rationally deduce the system of axioms from experience, since it transcends experience. Only an act of inspired imagination can create the system of axioms; to quote Einstein: "For the creation of a theory, the mere collection of recorded phenomena never suffices-there must always be added a free invention of the human mind that attacks the heart of the matter."9 Figure 3 illustrates Einstein's method for scientific discovery. From the discussion contained in Polanyi's major work, Personal Knowledge, one can argue that of the three parts of Einstein's discovery cycle-the imaginative jump, the deducing of predictive propositions, and experimental testing of these predictive propositions-only the deductive steps are free from personal judgements and commitments and so in principle could be programmed to be done by a machine.

The Participatory Universe

Figure 2.


always be done in a completely detached way. Such detachment is no longer possible when one attempts to observe a microscopic quantum object like an electron as the physicist John Wheeler forcefully points out:

"It was long natural to regard the observer as in ef feet looking at and being protected from contact with existence by a 10 cm. slab of plate glass. In contrast, quantum mechanics teaches the direct opposite. It is impossible to observe even so miniscule an object as an electron without in effect smashing that slab and reaching in with the appropriate measuring equipment. Moreover, the installation of apparatus to measure the position coordinate, x, of the electron automatically prevents the insertion in the same region at the same time of the equipment that would be required to measure its velocity or its momentum, P; and conversely. The act of measurement typically produces an unpredictable change in the state of the electron. This change is different according as one measures the position or the momentum. The choice one makes about what he observes makes an irretrievable difference in what he finds. The observer is elevated from 'observer' to 'participator.' What philosophy suggested in times past, the central feature of quantum mechanics tells us today with impressive force. In some strange sense this is a participatory universe."10

Thus the quantum theory requires that what an observer decides to measure influences the measurement; what is actually going on in the quantum realm depends on how one decides to observe it. Or, as many physicists currently interpret the mathematical formalism of quantum mechanics, reality is in part created by the observer through his participation! Quantum reality is still rational but no longer visualizable in the sense in which the behavior of a baseball is visualizable to a human being. This quantum rationality requires that participation rather than detachment be an essential part of the perception of physical reality at the quantum level (atomic and subatomic systems). According to Neils Bohr's interpretation of quantum physics (The Copenhagen Interpretation) if we look closely at the world-at the level of quantum objects-then its actual state of existence depends in part on how we observe it and what we choose to see. The quantum realm does not exist in a definite state until one actually sets up an apparatus and observes it. From this standpoint Bohr's perspective is super-realistic-no imaginery scenarios or rationalizations about physical reality are allowed.

To summarize, quantum physics differs from classical physics in two fundamental ways. First, quantum reality is not deterministic in its behavior; our perception of quantum reality is fundamentally indeterminant in structure. Secondly, the world of quantum objects is not objective like the

 

                                                                                                                                                    Figure 3. A modified representation of Einstein's method for Scientific Discovery (Adapted from diagram of Holton's).
NOMENCLATURE:

Double-line arrows--Process embedded in personal judgements and commitments. Single-line arrows-Process completely logical, automatic. 
E-- Plane" of sense experience. A-A system of axioms. P-Propositions, predictions. 
J-Jump of imaginative insight: a bold leap, a "wildly" speculative attempt to understand, a "groping" constructive attempt to understand. 
1, 2, 3. . .-Thematic presumptions that guide and constrain the imaginative jump; these themata (Holton's term) serve as a filter with respect to possible imaginative jumps. Some of Einstein's themata: "primacy of formal (rather than materialistic) explanation; unity (or unification); and cosmologlical scale (generalizability, and egalitarian applicability of laws throughout t e total realm of experience); logical parsimony and necessity; symmetry; simplicity; completeness, continuum; and of course causality, constancy and invariance."18 
D-Deducing propositions, predictions from the system of axioms. 
ET-Experimental testing against experience.

classical world. It is not out there, existing independently of our observing it; what is "there" in the quantum realm depends in part on what we choose to see-reality is partially created by the observer. Thus the observer can no longer detach himself from what he is observing; participation with the object being observed must, in principle, be part of the observation process."

Does this new perspective necessarily destroy realism? Not necessarily, for as J. C. Polkinghorne points out:

"Physicists have so vivid an impression of discovery and of the cosmos standing over against its investigators that they are almost all realists in their view of the world. How does realism survive for the elusive protean objects of quantum theory which are not the carriers of pictorable quantities like position and momentum but only (in a famous phrase of Heisenberg) the potentiality for such quantities? In the end I feel the touchstone of reality is not sensibility or picturability but intelligibility. The quantum world for all its peculiarity and elusiveness is real because we are able to gain understanding of it. If this emphasis upon intelligibility as the key to reality is correct then it gives physics an important common ground with theology, as the latter attempts the more difficult task of understanding the ways of God with man." (J. C. Polkingborne, "The Quantum World," The Irish Astronomical journal, Volume 15, Number 3, March, 1982, p. 237.)

Thus the new perspective emphasizes that the intelligibility of physical objects exists and acts independently of scientists and their activity.

A recent development in cosmology further emphasizes what quantum mechanics has stressed: the significance of observers in the creation of physical reality:

". .. the idea that the mere presence of intelligent life can have some explanatory power has recently been introduced into cosmology, where the task is to understand the history not of a single planet but of the entire universe. It is easy to imagine a universe quite different from the observed one. For example, changing the physical constants might give rise to a universe where the chemical elements heavier than helium are never formed or where all stars are large, hot and short-lived. In most such imaginary reconstructions of the universe it is unlikely that an intelligent form of life would appear. The fact that the real universe does harbor intelligent observers therefore places certain constraints on the diversity of ways the universe could have begun and on the physical laws that could have governed its development. In other words, the universe has the properties we observe today because if its earlier properties had been much different, we would not be here as observers now. The principle underlying this method of cosmological analysis has been called the anthropic principle, from the Greek anthropos, man."12

Simply stated the anthropic principle says that our universe is the kind of universe it is because it is necessary for the existence of intelligent observers; somehow human observers and the existing universe are profoundly bracketed together. It should be pointed out that there is a wide spectrum of data to back up the arguments that led to the formulation of the anthropic principle. Slight changes in physical constants at either the quantum level or the macroscopic level (ex. The Gravitational Constant) would result in universes so different from our existing one that intelligent life could not come into being; stars would not be formed or would be so hot that proper planetary systems could not form, to cite a few examples. Sir Bernard Lovell cites a striking example:

"When the universe was one second from the beginning of the expansion, if the rate of expansion had been reduced by only one part in a thousand billion, then the Universe would have collapsed after a few million years. Can it really be that out of all possible universes the only one which can exist, in the sense that it can be known, is simply the one which satisfies the narrow conditions necessary for human life? The essence of our presence in the Universe today is that we require the Universe to have certain properties. Long before we reach the problems of biological evolution on earth 3 to 4 billion years ago we face this more fundamental question. At least one essential condition is that the Universe must expand at almost precisely the rate at which we measure it to be expanding. If the rate had been less by an almost insignificant amount in the first second, then the Universe would have collapsed long before any biological evolution could have taken place."13

The physicist John Wheeler relates the anthropic principle to the connection quantum physics maintains between the observer and the quantum phenomena he observes. Bohr's interpretation of quantum physics states that the observer contributes to reality by the very act of observation. Wheeler builds upon this perspective postulating that "for a universe to be real it must evolve in such a way that observers come into existence.... Wheeler rejects the common view that life and observership are only accidents in a universe independent of observers and argues instead that 'quantum mechanics has led us to take seriously and explore the direct opposite view that the observer is as essential to the creation of the universe as the universe is to the existence of the observers." 14

Resonances with Biblical Theism13

First we have seen that scientific methodology is actually not of detached investigation but, rather, depends upon personal commitments by the knower actively guiding and being modified by his scientific investigations. These commitments are acquired by the knower through his active participation with the scientific community and with the particular area of reality he is exploring. Here we have a striking parallel with biblical teachings on how a person is to gain knowledge of God, for these teachings stress that one must be actively committed to the notion that God exists and that He reveals Himself in the concrete events of biblical history. Furthermore one must be committed to and willing to be instructed by the Christian community (the Church) just as the scientist must be committed to and willing further to be taught by his fellow colleagues in science. In short, in order to gain knowledge of God or of His created reality one cannot adopt the stance of a detached investigator but one must enthusiastically commit oneself to the reality being investigated and learn of and share commitments with fellow explorers, whether they be scientific colleagues or fellow Christians.

Secondly, we have seen that at the level of physical reality itself modern quantum physics views the investigator as a participator, not a detached observer, in any observation of reality that he makes. Participation is a key component of both scientific knowing and, it seems, of the partial creation of physical reality itself-if the current interpretation of quantum physics is correct. Participation means that relationships are established between different persons, persons and things, and things and things (the measuring apparatus and the quantum object). Cannot this perspective that relationships be established at all levels of reality be a dim reflection of the Creator-God's nature? Biblically God is understood to be Father, Son, and Holy Spirit in continual relationships of love and communication with one another.

Let Christians however, be very tentative in linking Christian concepts to the currently most accepted interpretation of quantum phenomena, the Copenhagen interpretation with its observer-created reality. It is always possible that future modifications of the quantum theory will restore the more usual notions of an objective reality governed in deterministic fashion. One of the developers of quantum theory P.A.M. Dirac has tentatively hinted at this possibility:

"It seems clear that the present quantum mechanics is not in its final form. Some further changes will be needed just as drastic as the changes which one made in passing from Bohr's orbit to a quantum mechanics. Some day a new relativistic quantum mechanics will be discovered in which we do not have these infinites occurring at all. It might very well be that the new quantum mechanics will have determinism in the way that Einstein wanted. This determinism will be introduced only at the expense of abandoning some other preconceptions which physicists now hold, and which it is not sensible to try to get at now.

So under these conditions I think it is very likely, or at any rate quite possible, that in the long run Einstein will turn out to be correct, even though for the time being physicists have to accept the Bohr probability interpretation-especially if they have examinations in front of them. "15

A special word about the anthropic principle is in order. The idea that the universe has the properties it has in order to allow intelligent observers to come into being is not the only way to interpret the many varied pieces of evidence that show the universe to be uniquely congenial to man's existence. Indeed, the anthropic interpretation if carried too far can be used to unduly exalt man and as such is, from the standpoint of Christian theology, the ultimate blasphemy. However, one can just as well give the interpretation "that a Creator has designed our finely tuned Universe specifically for the containment of life. This is the theistic principle as elaborated by mythology and theology."16 The theistic principle sees the existing universe providing a fit habitat for man as a direct consequence of the rational, creative activity of a loving Creator-God who provided a universe fit for man in order that man, the pinnacle of God's creation, may explore and manage that universe as a steward responsible to God. And as man continues his exploration he becomes more and more aware of another theistic feature of the universe, that it exists in a state of contingent freedom so that the results of his explorations are forever open-ended in structure. To quote Thomas F. Torrance:

"The contingent freedom of the universe, then, is not something bound up with randomness or chance, for it is no more arbitrary than the freedom of the God of infinite love and truth upon which it rests and by which it is maintained. It is a freedom that derives from the unlimited freedom of God, but it is a contingent freedom and is therefore a limited freedom. An unlimited contingent freedom would be an inherent contradiction-that would spell arbitrariness. Limited though contingent freedom is, it is limited by the very freedom of God on which it is grounded. It is nonetheless a genuine freedom, the kind of freedom proper to a finite and contingent universe. On the other hand, because it is contingent upon the unlimited freedom of God, it is a freedom that embraces inexhaustible possibilities. That is why as we explore the universe in our scientific activities, it keeps on surprising us, disclosing to us patterns and structures of an indefinite range of intelligibility, which we could never anticipate on our own.... The universe constantly takes us by surprise in this way because it is correlated to the infinite, inexhaustible freedom and rationality of God, its Creator. It is understandable, therefore, that Christian theology should think of the creation as grounded upon the grace of God, for grace is the free love of God, which always takes us by surprise.... It is certainly in respect of its contingent freedom as well as its contingent intelligibility that the universe disclosed to us by modern scientific inquiry stands out more and more as an open universe that we may grasp only through open structures of thought."17


REFERENCES

1Walter Thorson, "The Problem of Truth the Word of God," Regent College summer lecture series. Available on cassette, order from Alpha Tape Ltd. 2130 Wesbrook Mall, Vancouver, Canada, V6TlW6. This lecture contains much helpful material on the dualist cleavage in modern philosophy.

2Morris Berman, The Reenchantment of the World, Cornell University Press, Ithaca, N.Y., 1981, pp. 27-46.

3Thorson, Op. cit.

4Thorson
Ibid.

5Michael Polanyi, Personal Knowledge, the University of Chicago Press, Chicago, 1958.

6Thomas F. Torrance, Christian Theology of Scientific Culture, Oxford University Press, New York, 1981, pp. 63-66.

7Gerald Holton, "Constructing a Theory: Einstein's Model," The American Scholar, Summer, 1979, pp. 309-340.

8Holton, Ibid., pp. 333-340.

9Heinz R. Pagels, The Cosmic Code; Quantum Physics as the Language of Nature, Simon and Schuster, New York, 1982, p. 58.

10John A. Wheeler, "Genesis and Observership." In: University of Western Ontario Series in the Philosophy of Science, R. Butts, J. Hintikka (eds.), Reidell, Boston, Mass, 1977. Quote contained in: John C. Eccles, The Human Mystery, Springer International, New York, 1979, p. 30,

11Pagels, Op. Cit., The Cosmic Code, has an excellent discussion of the various interpretations of modern quantum theory.

12George Gale, "The Anthropic Principle," Scientific American, Vol. 245, No. 6, Dec. 1981, p. 154.

13Sir Bernard Lovell, from a lecture entitled; "A Contemporary View of Man's Relation to the Universe," given October 13, 1977 at St. Johns, Newfoundland. The quote is contained in: Eccles, Op. cit., p. 32.

14Gale, Op. cit., p. 171.

15P.A.M. Dirac, from paper: "Unification, Aims and Principles," given at Jerusalem Einstein Centennial Symposium, March 20, 1979. Quote contained in: Robert Resnick, "Misconceptions About Einstein," Journal of Chemical Education, Vol. 57, No. 12, Dec. 1980, p. 8W.

16Edward R. Harrison, Cosmology, Cambridge University Press, New York, 1981, p. 113.

17Thomas F. Torrance, The Ground and Grammar of Theology, University Press of Virginia, Charlottesville, 1980, pp. 59-60.

189Holton, Op. Cit., p. 334.