IS SCIENCE FINITE?

At the turn of the century the physical sciences were not considered particularly good fields into which to enter. Many senior physical scientists were giving the following advice to bright, prospective students: “Consider carefully whether you want to go into physics or chemistry. There really is not much that is exciting to discover any more in these fields. After all, Newton’s laws of mechanics and Clark Maxwell’s formulation of the electromagnetic field laws have enabled us completely to understand the nature and behavior of physical reality. The only thing really that is left to do in the physical sciences is to work out the next decimal place in our quantitative understanding of the world.” If really pressed by the students, the senior scientists might admit that there were some small anomalies present with respect to our understanding of physics, in particular black-body radiation and the sharp lines observed in atomic spectra. But the senior scientist would say with a shrug: “It is only a matter of time before these small discrepancies in our current understanding of physics will be adequately explained.” Today we know that these two “small discrepancies” (and others) did not disappear but rather caused a huge “crack” to appear in the structure of classical physical theory. Indeed, completely new and revolutionary theories, relativity and quantum physics, were developed in order to make the “crack” shrink away. Planck, Einstein and Bohr, among others, developed this new theoretical structure which, while radically different from the old physics, nevertheless contains the laws of Newton and Maxwell as limiting cases (low velocity and large mass objects approximately obey Newton’s and Maxwell’s laws) of its more general formulation. Thus the whole structure of physical science was altered in revolutionary fashion; new laws of physical science were developed which led to prediction and successful observation of many strange new particles at the level of the very small and equally strange objects such as neutron stars and quasars at the level of the very large, i.e., all of outer space.
 

THE OPEN STRUCTURE OF SCIENTIFIC TRUTH

This little episode from the history of science serves as a warning to scientists never to assume their work as scientists is finished. And it opens up for discussion the general topic of whether man will ever have a fully complete and consistent theory of physical reality. Will the task of science ever be finished?

Kurt Gödel, one of the most brilliant mathematicians of this century, in 1931 devised a profound and significant mathematical theorem which sheds much light on this question. Gödel’s theorem has to do with the internal consistency of mathematical systems: “. . .it states among other things that if one builds a mathematical system based upon a set of consistent axioms, or postulates, then within the system statements will be discovered such that (1) no exception to these statements is ever found, yet (2) these statements cannot be proved, i.e., derived from the axioms of the system (true but not decidable from within the system, parentheses mine).”¹ As all theories of modern physics are based upon mathematical systems, Gödel’s theorem has great import for physics as well as mathematics. “…It tells us that if man ever builds what he regards as a complete theory of the physical world, one based upon a set of fundamental laws such as we have discussed, then new truths will be discovered, and these truths will require additional laws for their explanation. In other words, if at some time man wonders whether or not he has discovered all of the fundamental laws of nature, he can be sure that he has not and that there is at least one more fundamental law to look for. The search for new truths should never end.”² Thus as theoretical science ultimately depends upon mathematics in all its creative endeavors, Gödel’s theorem tells us that all such activities will be forever open-ended. To quote Stanley L. Jaki:

“In that creative existence of man (physics) the mathematical and scientific reflections played a prominent part. This is especially true of the mathematics that Einstein viewed as the creative principle of physical science. His was a conviction shared by most of his colleagues: since nature is the realization of the simplest conceivable mathematical ideas, we can therefore discover ‘by means of purely mathematical constructions the concepts and the laws connecting them with each others, which furnish the key to the understanding of natural phenomena.’ And in a veiled reference to the Pythagoreans, he stated his belief that in a certain sense ‘pure thought can grasp reality as the ancients dreamed.’ In a certain sense to be sure, for Einstein was not blinded by the successes of the antiphenomenological constructive method to its limitations. His belief that we can grasp the physical reality for the purposes of science only indirectly, that is, by speculative means or mathematical formalism, impelled him to state that for this very reason, the notions of science about physical reality could never be final. ‘We must always he ready,’ he warned, ‘to change these notions — that is to say, the axiomatic sub-structure of physics — in order to do justice to perceived facts in the most logically perfect way.’ It is on the ultimate success of such a quest that Gödel’s theorem casts the shadow of judicious doubt. It seems on the strength of Gödel’s theorem that the ultimate foundations of the bold symbolic constructions of mathematical physics will remain embedded forever in that deeper level of thinking characterized both by the wisdom and by the haziness of analogies and intuitions.”³

“…This is why even the most bizarre sets of mathematical postulates and geometrical axioms can prove themselves isomorphic with some portion of the observational evidence and useful in systematizing it. This is why the physicist is apt to find himself time and again, as Wigner noted, ‘in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial.’ This is why the physicist might even be overcome by a mood of skepticism concerning the uniqueness of coordination between his mathematical tools and the actual features of the universe. Again, in view of the extreme richness of the features of the physical world, one should not marvel inordinately how space can be non-Euclidean or how complex numbers can he so successful in dealing with alternating currents and an almost endless array of physical processes. The novelty present in those processes is far from being exhausted. No one would dare assume today that there is nothing new for man to observe in the physical world. Consequently, the formulation of new mathematical theories useful for physics will very likely go on indefinitely. For it is not only himself that the mathematician cannot get away from; he cannot get away from the physical world either. It is there, in an immensely variegated nature and not in his finite intellect where ultimately lies the never-ending challenge for the mathematician.”⁴

Recent work by Ilya Prigogine⁵ on the thermodynamics of open systems has provided a credible theoretical description of how the process of emergence takes place; of how such highly ordered systems as living organisms could ever emerge from a world in which irreversible processes always tend to lead to an increase in entropy, in disorder.

“…In systems near to equilibrium, any fluctuations away from that state will be damped down and the system will tend to revert to its equilibrium state. What Prigogine and his colleagues have been able to show is that there exists a class of steady-state systems, ‘dissipative structures’, which by taking in matter and energy (hence being open systems, parentheses mine) can maintain themselves in an ordered, steady state far from equilibrium. In such states there can occur, under the right conditions, fluctuations which are no longer damped and which are amplified so that the system changes its whole structure to a new ordered state in which it can again become steady and imbibe energy and matter from the outside and maintain its new structured form. The instability of dissipative structures has been studied by these workers who have set out more precisely the thermodynamic conditions for a dissipative structure to move from one state to a new state which is more ordered than previously. It turns out that these conditions are not so restrictive that no systems can ever possibly obey them. Indeed a very large number of systems, such as the first living forms of matter which must have involved complex networks of chemical reactions, are very likely to do so, since they are non-linear in the relationship between the forces and fluxes involved (which is one of the necessary conditions for these fluctuations to be amplified).”⁶

Thus the thermodynamics of open systems provides plausible physical mechanisms for the basic thesis of cosmic, biological, and possibly cultural development; that thesis being the continual emergence of more and more complex structures that possess qualitatively new and different behaviors and properties. And if the evolution of more complex structures occurs, indeterminant behavior will increase in that new possibilities also increase as a result of the greater complexity. This greater indeterminancy of behavior leads to new behavior patterns; in a similar way new properties can emerge. The continual emergence of greater complexity in the universe has a direct correlation to the structure of scientific truth; if new behaviors and properties are continually coming into being, the scientific truth associated with these behaviors and properties is not static but is, on the contrary, ever expanding. Thus the very nature of the evolutionary process leads to an expanding structure of scientific truth; scientific truth is forever open.

Some last comments: I, personally, am willing to accept the possibility of God using evolutionary processes in His creative activity but I view these processes as suggesting that intelligence has been at work in creation (modern evolutionary theories make much use of the assumption that great order is inherent to all levels of the cosmos). Secondly I see chance entering evolutionary descriptions because humans don’t have God’s complete knowledge; l believe that it is possible to have a concept of chance that is fully compatible with God working in a purposeful, fully rational manner.

Figure 1 illustrates in schematic fashion this open-endedness of scientific truth. As time passes new and more encompassing theories are developed which resolve undecidable questions present in earlier theories, the older theory being a special case contained in the new. The new theory is more comprehensive as it encompasses the older theories and explains more phenomena but, eventually, problems are raised that are not decidable in the new theory so again a new, broader theory must be developed, a meta-theory and so on. Science, therefore, will never end; it will continue to expand until God “brings down the curtain on physical reality.”

Two philosophers who have clearly grasped the nature of science’s open-endedness are Michael Polanyi and Thomas F. Torrance. Polanyi precisely recognized that the true objectivity of a scientific theory is due to its open-ended structure:

“One may say, indeed, quite generally, that a theory which we acclaim as rational in itself is thereby accredited with prophetic powers. We accept it in the hope of making contact with reality; so that being really true, our theory may yet show forth its truth through future centuries in ways undreamed of by its authors. Some of the greatest scientific discoveries of our age have been rightly described as amazing confirmations of accepted scientific theories. In this wholly indeterminate scope of its true implications lies the deepest sense in which objectivity is attributed to a scientific theory (emphasis mine).”⁷

“…We make sense of experience by relying on clues of which we are often aware only as pointers to their hidden meaning; this meaning is an aspect of a reality which as such can yet reveal itself in an indeterminate range of future discoveries. This is in fact, my definition of external reality: reality is something that attracts our attention by clues which harass and beguile our minds into getting ever closer to it, and which, since it owes this attractive power to its independent existence, can always manifest itself in still unexpected ways. If we have grasped a true and deep-seated aspect of reality, then its future manifestations will be unexpected confirmations of our present knowledge of it. It is because of our anticipation of such hidden truths that scientific knowledge is accepted, and it is their presence in the body of accepted science that keeps it alive and at work in our minds. This is how accepted science serves as the premise of all further pursuit of scientific inquiry. The efforts of perception are induced by a craving to make out what it is that we are seeing before us. They respond to the conviction that we can make sense of experience, because it hangs together in itself. Scientific inquiry is motivated likewise by the craving to understand things. Such an endeavor can go on only if sustained by hope, the hope of making contact with the hidden pattern of things. By speaking of science as a reasonable and successful enterprise, I confirm and share this hope. This is about as much as I can say here in justification of a pursuit of knowledge based largely on hidden clues and arrived at and ultimately accredited on grounds of personal judgment. I believe that this commitment makes sense in view of man’s position in the universe.”⁸

“….As the universe becomes progressively disclosed to our scientific inquiries it is found to be characterized by an intrinsic intelligibility of an ever deepening dimension which far out-ranges our power of comprehension, invoking from us awe and wonder. Moreover, we become aware of being confronted in and behind it all with a transcendent reality over which we have no control but which, while utterly independent of our minds has an indefinite capacity for revealing itself to them in quite unanticipated ways. It is indeed in response to this transcendent reality that our minds develop their own powers of comprehension and in recognition of it that they derive their primary thrust in passionate search for understanding and truth. However, the more intensively we probe into the inherent profundity of the universe, the deeper the dimension in which its objectivity and intelligibility become disclosed to us, the more we find our epistemic relation to it being reversed: we are up against a reality that towers above our intelligence, which we cannot know or reflect about by trying to occupy some epistemic stance ‘above’ it. This is the kind of reality which we may know by inquiring into it from 'below', as it were, by submitting our minds to the authority of what it actually is and seeking to apprehend it by allowing our understanding to fall under the power of its intrinsic but transcendent intelligibility, but this is to embark upon a course of humble discipline in which our minds will be stretched beyond our capacities which they may claim to have in themselves. As Polanyi has argued, this is the kind of experience we have even in the study of some great historical personality where ‘we need reverence to perceive greatness, even as we need a telescope to observe spiral nebulae’.”⁹

THE RELIGIOUS DIMENSION AND TRUTH

This open-endedness of scientific truth is a special case of a much more general open-endedness which is characteristic of all truth, not only scientific truth. Let us recognize that truth could not exist if it were not for God who is the source and standard of all truth, for He himself is the truth. Truth exists because there is no deception in God; He keeps truth forever; His steadfastness, consistency, and His reliability in being and action guarantees the very existence of truth. As God is the source of truth His nature will determine the characteristics of truth. In particular the Bible portrays God as the Infinite One, who does not exist in any necessary relations, because He is self sufficient, but at the same time can freely enter into various relations with His creation as a whole. God, as infinite Being, is free from all limitations; to quote Orr: “Perhaps we can say that infinity in God is ultimately: (a) internally and qualitatively absence of all limitation and defect; (b) boundless potentiality.”¹⁰ A classic Biblical Statement of this is found in Psalm 145:3 - “Great is the Lord and greatly to be praised and His greatness is unsearchable (emphasis mine).” Absence of all limitations implies that the Infinite God in all His creating and sustaining activities toward His creation acts freely, not necessarily; as Psalm 115:3 puts it - “Our God is in the Heavens, He does whatever He pleases (emphasis mine).” God’s freedom in His creative activities is one aspect of His transcendence with respect to what He has created, for God is independent and different from all His creatures. As Isaiah 55:8-9 puts it — “For my thoughts are not your thoughts, neither are your ways my ways, says the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.”

Thus we see that the open-endedness of all truth contained in created reality is a reflection of the very nature of God, the source of all truth. God, who is transcendent with respect to His created order, is the Infinite One, being without limitations and inexhaustible in His creativity possessing boundless potentiality. All of God’s creating and sustaining activity toward His created order is furthermore done in a perfectly free manner, there is no necessity in all God’s actions. God, the source of all truth, is free and inexhaustible in His creativity: is it not therefore reasonable to expect that all truth found in created reality would be open-ended in nature always pointing beyond itself, ultimately pointing back to God, the author of all truth?

One last point. Curiosity is a trait deemed essential to all human creativity, especially scientific creativity.¹¹ Indeed, curiosity may well be one aspect of man being made in the image of God. For God in His own way was and always is curious; as one example, God asked the first man to name the animals for “He brought them to the man to see what He would name them (Gen. 2:19).” It is particularly appropriate therefore that God has created reality in such a way that it can only but enhance man’s curiosity and hence his creativity. The open structure of truth continually motivates man to exercise his curiosity in all of his explorations of the created order. God’s created reality continually startles man with new and unexpected objects and relationships; it is both very simple and yet at the same time very complex; only the very curious can penetrate into its inner depths. Thus it can be readily seen that there is one attitude that will really stop all human creativity; that attitude is a closed mind, a mind not receptive to the open-endedness of truth, a mind that believes all is known and nothing more remains to be explored and understood. Christians have traditionally believed that God has revealed Himself to man through two “books” - the Bible, God’s written word, and the “bible of nature.’ I think that one can historically argue that the Christian and scientific communities have been the most unproductive and ineffective in their respective missions when they assumed that either the Bible or the “bible of nature” could be represented by some closed, final system.

Footnotes

¹ F. Woodbridge Constant, Fundamental Laws of Physics, Addison-Wesley Publishing Co., Inc. Mass., 1963, p. 380.

² Constant, Ibid., p. 381.

³ Stanley L. Jaki, The Relevance of Physics, The University of Chicago Press, Chicago, 1966, pp. 128-129.

⁴ Jaki, Ibid., p. 131.

⁵ G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems, John Wiley and Sons, New York, 1977.

⁶ A. R. Peacocke, Creation and the World of Science, Clarendon Press, Oxford, 1979, pp. 98-99.

⁷ Michael Polyani, Personal Knowledge, University of Chicago Press, Chicago, 1958, p. 5.

⁸ M. Polanyi, Knowing and Being, University of Chicago Press, Chicago, 1969, pp. 119-120.

⁹ Thomas F. Torrance, Space, Time and Resurrection, William B. Eerdmans Publishing Co., Michigan, 1976, pp. 191-192.

¹⁰ L. Berkhof, Systematic Theology, Wm. B. Eerdmans Publishing Company, Michigan, 1941, p. 60.

¹¹ For an interesting discussion of the importance of curiosity in the creative personality see James H. Austin, Chase, Chance and Creativity, Columbia University Press, New York, 1978, pp. 104-112.
 
 

Last updated: January 19, 2002