A new theology?
A Catholic Experience
I grew up in an Catholic milieu in a South Australian country town. After Catholic schooling by nuns, brothers and priests, I spent five years in the Dominican Order learning to be a priest and monk. I managed solemn profession but never made it to the priesthood.
I was awestruck by the cosmic visions of Catholic theology but close study eventually convinced me that they are castles in the air. To one educated in twentieth century, credibility comes not from ancient authority but from the intelligent processing of experience we call scientific method.
I expressed my doubts and tried to discuss with my teachers the possibility of a modern scientific theology. I could make no progress and was asked to leave.
I was not prepared from the shock of losing my vocation. I went to university and found that all my hard won philosophy and theology was considered ludicrous by my teachers and certainly not worthy of credit toward a degree.
It did not take me very long to hear that religion is an archaic mode of thought, to be avoided if one is to be modern. I lost my faith as well as my vocation.
My theological and personal heritage was totally discredited, leaving me with nothing. From birth I had absorbed the belief that Catholic = top quality. Now it looked like rubbish. When my sister died of cancer, I drove for twenty four hours to be at her bedside for a final meeting, but fled the funeral. I could not bear to hear the empty words of Christian consolation.
The years that followed revealed to me the importance of belief, thought and literature in human life. I entered a long period of pain and retreat while I worked intensely and often quite blindly to realise a new model of existence.
Being a Roman Catholic had been hell for me. It was hell because all my instincts were, by groundless fiat, sins, and wages of sin were not just death, but an eternity of excruciating pain.
The magnitude of this pain was described to me (and my contemporaries) with meticulous care. Every year the Passionist Fathers came to terrify us into goodness by describing hell in vivid detail. Passionists - Wikipedia
Also described in loving detail were the agonies of Jesus' passion and death. God subjected itself to this much pain to save me from something equally bad. I knew perfectly what I was risking every time I touched myself or somebody else, or even thought about it.
The humanity of nuns, brothers and priests who taught us was twisted by the same iron lie, and they passed their pain on to us. We were alternately beaten, cuddled, driven and praised. The pain of sin was made to be a self fulfilling prophecy.
There was very little about heaven. Some of us might have been inclined to imagine it as a tropical paradise with lots of beautiful people and pleasant action, but this interpretation was forbidden. Paradise (beatitudo = blessedness) came across as a very abstract and mystical experience, well beyond the ken of small boys. It was to be striven for, nevertheless, because it was better than anything we could possibly feel in this life, and the only long term alternative to damnation. Aquinas, Summa, I, II, 3, 8: Is human blessedness the vision of the essence of God?
My 'vocation' was a direct result of the efficiency of my Dominican schoolteachers. By the end of school, I had become convinced that I was so bad that I would only get to heaven if I went right over the top in the service of God('supererogation'). This was probably not a good motive, but it was enough for me, and being the eldest son of a large Catholic family, the priesthood seemed a natural calling. Supererogation - Wikipedia
Reconstruction
After many years trying and failing to be married, to hold down a job and to be a good citizen, I washed up on the shores of hippiedom with a lot of other rejects and began to reconstruct myself. My feeling for the credibility of scientific method was reinforced. I became a greenie. I began to act on the scientific truth that the earth is our parent and a measure of our perfection.
What I wanted was credible theology, which I came to realise meant scientific and ultimately mathematical theology. Over the years I slowly recognised that the metaphysical sort of mathematics represented by Cantor, Hilbert, Gödel and Turing provided the necessary tools to understand myself. Alan Turing - Wikipedia, Georg Cantor - Wikipedia, David Hilbert - Wikipedia, Kurt Gödel - Wikipedia
I was saved from despair by my scientific foundation. I am a Homo sapiens, descended through a line of life that stretches back three or four billion years. This life is itself based on the nature of a Universe forged over an additional ten billion years. Whatever Catholic doctrine says about 'original sin', my evolutionary origin guarantees that I am as perfect as the Universe can make me. Nor is there the slightest evidence to suggest that the Universe is imperfect or suffering from original sin. Evolutionary history of life - Wikipedia
Augustine said theology is faith seeking understanding. I had a new faith. All I needed was the intellectual underpinning to give this faith meaning and make it communicable. In the bush I simplified my life to minimise expense, spent all my spare cash on books, and settled down to some serious thinking. Fides quaerens intellectum - Wikipedia
After ten years I had enough to give a series of radio lectures on our newly established community radio, 2BOB. Now I feel ready to go seriously public. I feel two motivations for this. First, I need the income. I am getting too old to beg and dig for a living. Jeffrey Nicholls (1987): A theory of peace
Second, I realised that religion and theology are necessary components of peaceful human community. Religion is the technology (art) of peace, and theology the associated science. While the world is composed of distinct religious communities, the Malthusian nature of life guarantees that there will be conflict. If we are to have one human community living in harmony with the rest of the Universe, we need an theological picture of one world soul which binds us and the planet into one organism.
From this point of view, Catholicism has two major faults. First, it declares itself the true religion and labels all non-catholics deficient. Second, it sees this world as a defective place of trial which has no place in the final disposition of the Universe. One true church - Wikipedia, Pope John Paul II (7 December 1992): Catholic Catechism: §§ 399-400: God destroys Paradise
It is necessary, for the common good, to revise Catholicism and other religions with similar defects.
Thomas Aquinas
In the Dominicans it did not take me long to discover Thomas Aquinas and begin to read him from end to end, enthralled. I began to see the Catholic model of existence as a truly marvellous thing, and happily settled down to devote my life to understanding and preaching it. Monastic life suited me. Apart from a few prayers, food and a bit of exercise, one could read and write the whole day through. Thomas Aquinas - Wikipedia
My romance with Thomas began to falter in my third monastic year when I read Insight by Bernard Lonergan. Insight is a work of metaphysics, an attempt to understand the attributes that are common to all beings regardless of their particular nature. Bernard Lonergan: Insight: A Study of Human Understanding
Lonergan's purpose is to relocate Thomistic metaphysics in our current scientific and political culture. I think he succeeds to the extent that to go beyond him, one must go beyond Thomas and the classical Catholic world view.
Through Lonergan, I began to see that it is possible, in the spirit of Occam's Razor, to perform major corrective surgery on the Catholic model of God. Making God and the Universe distinct introduces both unnecessary complexity and consequent errors. It is consistent with both logic and experience to make God and the Universe one. Simply put, God is visible. Every experience of life is part of the vision of God. Every element of the Universe is divine.
This did not lead me to reject Thomas. I agreed with him that there could be no inconsistency between religious belief and scientific observation. Whatever God is, they are not a liar or trickster. I began to write little dialogues with Thomas to see what he might say about various issues if he know what we know today. These led to warnings that my career was at risk. Undeterred, I began planning a rewrite of the Summa. Thomas Aquinas (1225-1274): Summa theologiae
God
The first question for theology is does God exist? Thomas provides five arguments for the existence of God. All five identify some deficiency in the world and postulate God to fill the gap. The first proof begins with indisputable experience: things move or change in the world. Thomas Aquinas, Summa, I, 2, 3: Does God exist?
Thomas then introduces elements of a model derived from Aristotle. Assume that there are real entities corresponding to the symbols potentia and actus. Motion is defined using these symbols: Movere . . . nihil aliud est quam educere aliquid de potentia in actum (motion is nothing other than to lead something from potentiality to actuality). The experience of motion, the definition of motion in terms of potentia and actus, the rule that governs transition from potentia to actus (no potential can actualize itself), and the application of simple logical rules lead us to assert that God exists.
This argument looked pretty watertight to me, a faithful Catholic educated in a Thomist environment. My view changed when I saw Bernard Lonergan translate Thomas' model of God out of its native medieval Latin into English.
Aristotle's use of potency and act to model the world originated in his attempt to understand motion. The early Greek models of motion led to an impasse. Parmenides' logical analysis of motion led him to the view that it was impossible, a position bolstered by Zeno's paradoxes. For Parmenides, being was one, without origin or end, homogeneous and indivisible, immovable and unchangeable, full and spherical Lonergan, p 364.
If motion is impossible, the experience of motion must be illusory. Behind the evermoving world of experience, there must be the still reality of being. Thus was rationalised a dichotomy between material and spiritual worlds.
The origin of this dichotomy seems to lie in the origin of consciousness. Early people, when they became conscious, saw themselves as entirely different from the rest of the world. As Origen would later hold, we are spiritual beings trapped in material bodies. Origen - Wikipedia
Heraclitus, on the other hand, felt that everything moved. If this was so, there could be no true knowledge of the world, because as soon as any proposition was formulated the reality it referred to would be different, and the proposition no longer be true. We know now that everything moves, but some things change faster than others over a range of frequencies spanning about a hundred orders of magnitude. The human lifetime lies somewhere in the centre of this range. Heraclitus - Wikipedia
Aristotle needed a model of the world that would consistently accommodate both motion and stillness. He proposed a dual structure for the Universe: potency, which makes change possible, and act which makes things what they are between changes. His assumption that a potency can be only actualised by something already actual became, via Aristotle, a foundation stone of Catholic theology.
In the Metaphysics Aristotle uses this doctrine of potency and act to establish the existence of the primum movens immobile for which he is famous. In Thomas' hands, the unmoved mover metamorphosed into the Christian God. The unmoved mover already enjoyed a life similar to the Catholic God. Unmoved mover - Wikipedia, Aristotle: Metaphysics (1072b14 sqq)
The dichotomy of the world into matter and spirit was matched by a dichotomy of knowledge. While sensation was coupled to matter, we could only communicate with spirit through intellect, itself a part of the spiritual soul at the core of human being.
Lonergan uses the same model, deriving potency and act not from a study of physical change from A to B, but of psychological change, from ignorance to understanding. Like Plato, Aristotle and Thomas Lonergan begins with the assumption that being (true reality) is detected with the intellect. At most the senses provide input for intellectual processing. Being is the object of the pure desire to know. Lonergan, 348
Lonergan' s proof for the existence of God follows the same track as Thomas:
. . . the five ways in which Aquinas proves the existence of God are so many particular cases of the general statement that the proportionate Universe is incompletely intelligible and that complete intelligibility is demanded. . . . page 678.The proportionate Universe contains proportionate being. Proportionate being may be defined as whatever is known by human experience, intelligent grasp, reasonable affirmation. . . . page 391.
Lonergan claims that the proportionate Universe is incompletely intelligible because it contains empirical residue. The empirical residue . . . consists of positive empirical data, . . . is to be denied any immanent intelligibility of its own . . . . (25-26)
Lonergan approaches the empirical residue through
inverse insight: . . . while direct insight meets the spontaneous effort of intelligence to understand, inverse insight responds to a more subtle and critical attitude that distinguishes different degrees or levels or kinds of intelligibility. While direct insight grasps the point, or see the solution, or comes to know the reason, inverse insight apprehends that in some fashion the point is that there is no point . . . the conceptual formulation of an inverse insight affirms empirical elements only to deny an expected intelligibility. page 19
An example of an inverse insight is Newton' s conceptualisation and formulation of the first law of motion: . . . a body continues in its existing state of uniform motion in a straight line unless that state is changed by an external force. Newton's discovery is to be contrasted to the common view (developed from situations where friction is operative) that continued motion requires the continual application of force.
Almost as soon as I read Lonergan I became fixed on the idea that the proper framework to understand the world was established by the mathematical theories of computation and communication. A couple of readings later, I saw that Lonergan' s empirical residue was model dependent: it does not correspond to anything in reality. This has turned out to be the most important discovery of my life.
Lonergan' s misunderstanding is at least as old as Parmenides: he mistakes an abstraction for reality. In an abstract way it is true, as Lonergan says . . . that (1) particular places and particular times differ as a matter of fact, and (2) there is no immanent intelligibility to be grasped by direct insight into that fact.
The physical models which we use to summarise the relationships of events in the Universe are formal constructs which were never meant to imply that there is no intelligibility in the relationships of real events such as the impact of a particular hammer on a particular nail at a particular time in the construction of a particular house. Einstein' s general theory of relativity does not require the existence of space and time independent of events.
I could see no reason to believe that the world is not completely intelligible. It just happens that neither Lonergan nor any other person understands it in its entirety. If the attempt to prove that God is other than the Universe falls down there is no reason to believe that the Universe is not divine. Nor is there any reason to believe that there is a real distinction between the entities symbolised by matter and spirit, sense and intellect or soul and body. These distinctions are simply elements of a model used to elucidate a seamless world. In reality, everything is concrete.
While I was thinking these things, aggiornamento was sweeping the Church: the Order was asking its members for suggestions for renewal. I couldn't wait to announce my new approach to theology. If I was right, the Church could take a new grasp on reality and rise above the ancient texts that seemed so strange and violent to modern ears. Aggiornamento - Wikipedia
My ultimate effort was short paper which attempted to show that there is no limit to the size of the Universe. It may, in fact, be as big as God. The model in this paper was far too small (being only countably infinite), and justly criticised for its naivete. What I had not anticipated was that my student publication was fatal to my career as a priest. I had stepped outside the pale of orthodoxy. Jeffrey Nicholls (1967): How universal is the universe?
The specific problem was that I appeared to contradict some of the twenty four theses propounded in 1914 by Pius X in his Motu Proprio Doctoris Angelici, 29 July 1914. Henricus Denzinger (1963): Enchiridion Symbolorum, Definitionum et Declarationum de Rebus Fidei et Morum, §§3601-3624, 24 Thomisitic theses: Pope Pius X in Motu Proprio Doctoris Angelici, 29 July 1914.
These theses attempt to reproduce in concise form the Thomistic model of being. The first three theses are sufficient for now:
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1. Potency and act divide being so that whatever exists is either pure act, or of necessity unites potency and act as first and inward elements
Potentia et actus ita dividunt ens, ut quidquid est, vel sit actus purus, vel ex potentia et actu tamquam primis atque intrinsecis principiis necessario coelescat.
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2. Act, since it is perfection, is limited only by potency, which is the capacity for perfection. Hence, in the region where act is pure, it exists unlimited and unique; where act is finite and of many different kinds, it is found in true composition with potency.
Actus, utpote perfectio, non limitatur nisi per potentiam, quae est capacitas perfectionis. Proinde in quo ordine actus est purus, in eodem nonnisi illimitatus et unicus existit; ubi vero est finitus ac multiplex, in veram incidit cum potentia compositionem.
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3. Because only God, one and completely simple, exists in the realm of pure being, all other things which participate in being have a nature which limits their being and are synthesised from the really distinct principles, essence and existence.
Quapropter in absoluta ipsius esse ratione unus subsistit Deus, unus est [sic] simplicicissimus, cetera cuncta quae ipsum esse participant, naturam habent qua esse coarctatur, ac tamquam distinctis realiter principiis, essentia et esse constant.
An alternative
The starting point for true theology is the same as that for any other science: our shared experience of the world and our common acceptance of mathematics. This community has unified the 'hard' sciences (eg mathematics, physics and biology), which no longer see national, cultural or religious boundaries. We now need a similar unification in theology to generate the foundations of religion based on evidence, not simply on ancient text and tradition.
Science translates the language of nature into human language. The purpose of scientific method is to guarantee the truth of this translation. Translations are tested by translating them back the other way to complete a cycle. We can then test the original and the retranslation against one another. If they agree, good. If not, either the translation or the retranslation or both are at fault and further work is necessary to get a reliable result.
True expression of nature is necessary to design technology that will work. We daily experience the benefits of modern physics, chemistry and biology. With a scientific theology, we can expect similar wealth from religion. We begin by assuming that there is no real distinction between God and our Universe of experience.
This new assumption, if it can be shown to be true, demands a reinterpretation of the whole of Roman Catholic theology and all the Christian theology that is contained in Catholic theology or derived from it.
This reinterpretation will change none of the facts. It will simply put them in a different light. It is what Thomas Kuhn calls paradigm change. A famous episode in the history of science illustrates what I mean. There was once intense debate about whether the Earth stands still and the Sun rotates around it, or the Sun stands still and the Earth revolves. Either way, the movement of the Sun across the sky seems the same to a person standing on the Earth. The Sun rises in the east, crosses the sky, and sets in the west. Thomas Kuhn (1996): The Structure of Scientific Revolutions
It eventually became clear that it was much simpler to put the Sun at rest and let the Earth and the other planets revolve around it. Not only did the whole picture become clearer with the Sun at rest, but the new point of view led to new and deeper insights into the structure of the heavens.
The new paradigm not only fits a wider ranger of observations better, but it explains how people arrived at the old paradigm and shows clearly where they oversimplified reality. Newton, for instance, ignored the finite velocity of propagation of force through space. When we take this into account, we get Einstein' s relativity.
The dethronement of Earth and its inhabitants from the centre of the Universe also caused a profound change in people's view of the planet and their place in the Universe. This change has continued. These days, we, or at least our children, are quite prepared to accept that we are one of millions of intelligent species on planets scattered throughout the Universe. Some of these aliens may be hostile, but others, like ET, are cute.
Copernicus' results came from mathematical work in astronomy. They followed logically from a few simple assumptions and observations and have stood the test of time. Their strength is not in the authority of Copernicus, whose only power was his ability to look and think, but in their fidelity to the evidence. Nicolaus Copernicus - Wikipedia
The laws of nature are here for all to see. Who actually discovers them seems to depend partly on chance and partly on who is looking for them. They are not subject to human whim.
King Canute demonstrated this fact very elegantly. His sycophants (the story goes) told him that he was so wise that even the tides would obey him. He had his throne put at the waters edge at low tide and commanded the waters to stay where they were. They didn't. No king or pope or dictator can tell the world how to behave.
I am not an authority. I am not even an expert. My words must stand or fall on their own internal logic and their demonstrable relationship to the world of experience. Their strength has got nothing to do with me. Anyone could say these things.
From a practical point of view, the most significant effect of my model is to change our understanding of original sin. Original sin is not a defect in humanity, but rather in the institutions that have evolved to bind people into groups.
A new model
To prove or disprove the statement that the Universe is God, we need some ground for judgment. This ground is the further assumption that what exists is consistent. If the assumption that the Universe is God leads to inconsistency, we consider it disproved, and must throw it out. This could lead us to assert that the Universe is not God.
So we need to prove the existence of God. To begin, we need a model of God. My starting point was Thomas's model of the Trinity. The problem with the Trinity is how to assert consistently that there are three distinct persons in God while yet maintaining God's unity, eternity and simplicity. Nicene Creed - Wikipedia
There is a similar problem in asserting that all the myriad entities which make up the visible Universe are 'personalities' of one God. We cannot see the Christian God, but we can imagine that the three Persons see themselves as distinct and communicate with one another, just as we see ourselves as distinct and communicate with one another.
Thomas' model of the Trinity is developed from his model of knowledge and will in human beings. My programme for a long time has been to build on Lonergan' s update of Thomas to expand the doctrine of the Trinity to deal with an infinite set of 'persons', so that we may understand that the multiple world of experience is in fact one and divine. The history of this programme is long and tortuous. I will state the conclusion now. My story, further developed in the years since this essay was first written, is laid out in the rest of this website and its companions. This work is part of the testing phase of the model. Aquinas, Summa, I, 27, 1: Is there procession in God?, Bernard Lonergan (1997): Verbum: Word and Idea in Aquinas, Lonergan (2007): The Triune God: Systematics
Metaphysics is the study of being as such. It models observations that are common to all beings. It is a generalisation of physics, which models the interactions of all the different particular beings we observe.
Physics has developed since Aristotle's time, and we can expect parallel changes in metaphysics. Lonergan documents many of these changes, particularly the introduction of 'genetic method'.
We believe that evolution occurs because fitness is reproduced and unfitness allowed to die out. This is true both for models and for organisms. This statement is effectively tautological, because we define fit by saying that it is what survives. Since all living organisms seem to have finite lives, survival requires reproduction. Charles Darwin (1859): The Origin of Species: By Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life
People say that tautologies have no content, they are simply formal logic. Nevertheless they can come alive when we look at how they are implemented. At the molecular level, evolution is extremely interesting because it has faced and overcome some exceedingly difficult problems. It is only since we have begun building automata ourselves that we have become aware of these problems and learnt to marvel at the elegance of their natural solutions.
We are now beginning to look at our planet and the Universe as a whole, and see how its various parts fit together. The literature describing the interactions of all the identified parts of the earth (atoms, molecules, cells, continents, etc etc etc) runs to billions of pages.
We imitate the behaviour and interactions of all these components with mathematical models. Modern physics is becoming applied software engineering. Software engineering is the physical implementation of the formal discoveries of mathematics in the computing machines imagined by Alan Turing. Andrew Hodges (1983): Alan Turing: The Enigma
Mathematics began to talk about itself at the time of Cantor, and reached its first great results in the period from Hilbert to Gödel and Turing. In this period, we might say, mathematics has become conscious of itself. An important consequence of these developments is that it is no longer sufficient to see mathematics as the study of number. Mathematics is now the symbolic exploration of the properties of all symbols, numbers included.
This development of self awareness has happened before with natural languages. Philosophy is based on the study of language. This became possible when people became conscious of their speech and began to analyse it. It may be that this development coincided with the invention of efficient systems of writing, that is of recording the spoken word in some medium (stone or quantum storage device makes no difference).
All our practical experience at software engineering in on finite machines, even though they may be very big, with terabytes of memory and gigaflops of processing power. Even when all the computers on earth are linked into one big network, the processing power will still be finite. A simple calculation reveals that there of more processing power in a grain of sand than all the computers in the world. Jeffrey Nicholls (2017): Computing power of a grain of sand: the calculation
The theory of this machinery, however, deals with infinite machines as well as finite ones, and tells us what they can and can't do. This infinite realm is big enough to model both individual human existences, the interactions of all humans with eachother, and the whole Universe.
We cannot implement it with a finite machine, because it is infinite, but we can approximate it. It seems to me that the infinite theory is implemented only in the Universe itself, which we may consider to be at least as rich as an infinite universal machine.
We cannot implement it, but we can represent it symbolically. Let us therefore specify a structure called a transfinite network. The source of this formal structure is Cantor' s theorem which establishes the endless hierarchy of transfinite cardinal and ordinal numbers. The transfinite ordinals can be used to represent the individual entities of the Universe. As Cantor notes, a transfinite ordinal number can represent anything thinkable (including a Turing machine). We can make this network and use Cantor's theory to create transfinite versions of it because there is a one to one correspondence between the set of Turing machines and the set of natural natural numbers: both are countably infinite.
Each entity can be considered as a black box with certain inputs and outputs. The mapping of inputs to outputs is achieved by a computer within the black box. To apply the model, we map named black boxes onto named elements of the observed Universe.
The theory of communication and the theory of computation (and all the other theorems of mathematics) enable us to delineate structures in this model. Science uses these mathematical structures to implement finite models of the things it studies. As computers become bigger and bigger, these models can be made to approximate more closely to the infinite reality.
Does God exist?
I want to finish this paper with an outline of a proof for the existence of an image of God in the transfinite network.
Let us begin with the assumption that God is the mysterious controller of the Universe. Does God so defined exist? In the formal world, exist means to follow necessarily without contradiction from the assumptions of the model.
If we find that the model faithfully represents reality, and that computations in the model are valid, we have faith in its predictions. The general theory of relativity, for instance, predicts the existence of black holes. The theory fits the Universe as we observe it, and Penrose, Hawking and Ellis has shown that black holes (singularities) are not simply a mathematical artefact. Astronomers are therefore spending big money searching for black holes and think they might have found a few (1996). Now (2000s) we have detected gravity waves, another prediction of relativity. The Large Scale Structure of Space-Time, Gravitational-wave observatory - Wikipedia
Cantor soon became aware that his theory of transfinite sets could lead to paradox. This and similar paradoxes led to a careful reexamination of the foundations of mathematics. The upshot of this work has been that there are some aggregates too big to talk sense about. Such aggregates must remain mysterious. Michael Hallett (1984): Cantorian Set Theory and Limitation of Size
An important attack on the foundation problem was led by David Hilbert. Hilbert treated mathematics as a purely formal game played with marks on paper (or any other sort of symbols). The only rule is to avoid inconsistency. The assumption behind this approach is that the paradoxes of set theory arose from something concealed in the semi-natural language used by the mathematicians of the day. By eliminating natural language altogether, Hilbert hoped to eliminate paradoxes. Formalism (philosophy of mathematics) - Wikipedia
In 1928 Hilbert was able to encapsulate his thoughts on the nature of mathematics in three questions: Is mathematics consistent? Is mathematics complete? Is mathematics computable?
He believed that the answer to all three questions would be yes, proving that there were no limits to mathematics. He was to claim in 1930 that there is no such thing as an unsolvable problem.
Gödel and Turing destroyed this belief. Consistency in mathematics can only be bought at the expense of incompleteness and undecidability, just as consistency in quantum mechanics requires us to accept uncertainty. I feel that these results are related and that the exploration of this relationship may lead to a new understanding of motion and stillness and open the way for a new understanding of God.
Gödel and Turing showed that some of the apparently pathological behaviour which Hilbert attributed to natural language was essential to consistent formal systems. Mathematics is complete if every mathematical statement that obeys the formal rules can be either proved or disproved. Mathematics is computable if there exists a definite mechanical process, like the execution of a computer program, which can decide whether a given proof is valid or not. The proof of completeness is thus logically dependent on the proof of computability.
Turing proved that mathematics contained incomputable statements by devising a universal machine that could perform all possible logical operations and showing that there were proofs that this Turing Machine could not complete. Using the structure of the Turing machine as a mapping tool, Turing transformed the problem of computability into a question about the relationship between ℵ0, the cardinal number of the set of rational numbers and ℵ1, the cardinal number of the set of reals, using the diagonal argument pioneered by Cantor.
We might extend this argument to get a transfinite hierarchy of computability. This generalization of Turing's argument is based on the notion that for n greater than m a system whose complexity is measured by ℵn cannot be computed by a system whose complexity is measured by ℵm.
Now assume that one system A may know another system B only insofar as B is computable using the resources of A. Assume further that insofar as the complexity of B is beyond the computing resources of A, we are justified in calling B mysterious relative to A (musterion = Greek secret). Since we know from Cantor's theorem that given any system X there must be a system of greater complexity Y we are therefore guaranteed the existence of mystery for any system. This, in outline, is a proof for the existence of God.
A similar argument shows that God controls the Universe. Cybernetics is founded on the principle of requisite variety: one system can only control another system if the controller is of equal or greater complexity than that controlled. Since the mysterious is mysterious because it is more complex than the knower, this principle tells us that the visible cannot control the mysterious. Since there is control (the system is stable) it must come from the mysterious. This mysterious controller we call God. W. Ross Ashby (1964): An Introduction to Cybernetics, pp 202 sqq
Conclusion
This article is a brief taste of an enormous body of data and theory which I have been exploring alone.
I have often tried to find collaborators without success, my latest effort being an honours degree in the Philosophy department at the University of Adelaide, 2018-19. On the one hand all the theology I have been able to discover in the established religions is based on ancient scriptures. On the other hand, very few people with a scientific and mathematical education want to have anything to do with traditional theology and religion. My fondest hope is that if this article is ever published, I may be able to find a community of people who share my faith that theology and religion have a scientific and technological future. A prolegomenon to scientific theology
(January 1996, revised January 2022)
