Lecture 1: Mathematical Theology

Introduction

1 The ideas I wish to display to you through these lectures have a long history. My involvement began with my conception and birth into this life of mine.

2 The world itself has a history which we can follow a few thousand years back to the invention of writing, a few million years back to the origin of our species, or back billions of years to the beginning of life and before than to the birth of our planet.

3 The planet itself is embedded in a star system of even greater age which is part of the universe whose beginning we see ten to twenty billion years ago. All this history is relevant to these lectures.

4 The history of the lectures themselves is shorter. Last year the Manning Peace Group approached 2BOB with the idea of paying for some radio programs with money provided by the International Year of Peace. These lectures are the outcome. I must thank the New South Wales Government for putting up some of the cost of these lectures. It was enough to get me going. ... I hope they are pleased with the result.

5 I owe more to the Department of Social Security which has done a lot to sustain me over the twenty years the lectures have been in preparation. Every Australian taxpayer has a share in this work. And many other people too, far too numerous to mention. They know who they are. I hope you will not regret supporting me.

6 Finally I must thank the Roman Catholic Church for much of the motivation and intellectual content of my work. The fact that my line of reasoning leads me to propose a radical revision of Catholic belief does not diminish the debt I owe the Church.

7 I was born and brought up a Catholic in a small country town. Eventually I went to the city and joined a Catholic religious order to become a priest.

8 The ideas that go into the training of a priest are very strong and very sublime. From the catechism I learnt to ask and answer cosmic questions like: who made the world? Who made me? Why did god make me? Where am I going? Questions like these are at the heart of every religion.

9 My monastic studies taught me the history of these ideas. When I understood their history, I began to understand their power. Ideas like these lie at the very heart of human life and survival. I discovered a very strong link between religion and peace.

The argument

10 I began to think about peace in a very practical way during the Viet Nam war. I was the right age to be called up. I was exempted because I was a clergyman, but despite the terrors that war held for me, I think I would have gone. It was my first whiff of the force of patriotism. To my amazement, it was strong enough to make even me face death.

11 In the Church, I became embroiled in a deeper war. Not a war between goodies and baddies, but the war between good and evil that lies at the heart of all human consciousness. Existence is a struggle. We need all the help we can get. Religion is part of that help.

12 I cannot go through all the lines of thought I have pursued during my religious career, but I can summarise the major events and that is sufficient to put this lecture in its correct personal context.

13 What do human beings seek? The traditional Christian answer is that we are driven by natural desire to seek the vision of god. The vision of god is heavenly bliss. Ultimate pleasure is our goal.

14 Yet we live in a world of manifest pain, death and disease. In this century of ever growing horrors, we have concocted a fate for ourselves so terrible that the health of the whole planet is at risk if we go to war.

15 It is the task of religion to reconcile the apparent contradiction between good and evil. It is that reconciliation, deeply and thoroughly believed, that gives us peace. The power of Christianity, the power of any religion, is measured by the serenity of its martyrs.

16 I became deeply immersed in this Christian peace within the walls of a Catholic monastery. All my beliefs and training pointed to the fact that I was on my way to heaven by the most heavenly possible route. But I was deluded. There came a time when the order could no longer tolerate the way I was thinking. I was ejected from paradise.

17 The emotional price I paid for that delusion has motivated my search for a better way.

18 The intellectual core of a religion, its statement of belief and arguments for this and that, are the subject matter of theology. Theology is the science of god. Practically, theology has two aims.

19 The first is to convince people beyond a shadow of doubt that life is worth living, and that despite the difficulties, we will reach bliss in the end if we do the right things.

20 The second is to devise means of actually reducing the pain of human life and increasing the pleasure. In both these tasks, theology is acting as peacemaker. Since I am theologically trained, and these lectures are to be about peace, they are theological.

21 I believe that the current state of tension and despair on the planet is a symptom that suggests that our religions are not performing their peacemaking tasks adequately. They have been left behind by history. They no longer have the power to convince an educated inhabitant of the world that life is worth living. They need to be brought up to date.

22 I say this in all humility. I was once a believing catholic, and it was not my choice to find myself outside the church criticising it. There is a job to be done, however. I believe that thoughts along the lines I propose are necessary for global peace.

23 I take religion to be the foundation of peace. Theology is the backbone of religion. Since religion is failing to deliver the goods, it must be made over, starting with theology.

The strategy

24 I won't try to prove the proposition that world peace demands one world religion. I assume that and turn to the task of looking for the theological foundation of a world religion.

25 The first thing a religion must deliver is certain knowledge. What do we need for certainty? We know, for a start, that standards of certainty change. Once people believed that the story of creation in the book of Genesis was the literal truth. Now we know that it was exceedingly unlikely, given the evidence we have.

26 Each age has its highest standards of proof. Once it was the authority of the king or pope. Now, after science has evolved for more than four thousand years, we find ourselves with just one standard, consistency.

27 All science assumes that the universe, which includes all our scientific instruments and scientists themselves, is consistent. Never do we expect to find an irreducible contradiction. We often see the appearance of contradiction, but we believe that if we come to understand the situation well enough the contradiction will disappear.

28 The requirement of consistency was the guiding light of the last and greatest synthesis of Christian theology, written in the thirteenth century by Thomas Aquinas. The Dark Ages had ended, and Christian Europe was being flooded with the pagan knowledge of the ancient world which had for so long been driven into the Arab world on the fringes of Christendom.

29 Much of the established church feared that this new knowledge would corrupt the faith. Those with more vision saw that the faith could be transformed if they accepted the finest products of greek science and produced a christian synthesis of sacred and profane knowledge. The effect of this synthesis, they saw, was not to belittle their god, but to make the whole earth more sacred.

30 Thomas stuck to this program through thick and thin, and produced his Summa, one of the most wonderful intellectual documents I know.

31 I accept Thomas' starting point. I assume that the only guide that we can have in the search for global peace is consistency.

32 Now there is a science of consistency. It is mathematics. The task of mathematics, as I understand it, is to discover and explore all possible consistent structures. Since the task of science is to discover and explore all the structures in the universe, it is not surprising that science and mathematics work very closely together.

33 Your typical scientist is faced with a set of phenomena. His basic assumtpion is that these phenomena are rooted in some consistent structure. Since mathematics is the study of all possible consistent structures, the scientist expects that his phenomena will fit into some mathematical structure or another.

34 He or she might be able to find just the right structure in a mathematics book, or they might have to invent it for themselves. The fundamental assumption of science assures them, however, that there is a mathematical structure to be found if they look long enough.

35 The ordinary counting numbers lie at the heart of mathematics. They form a consistent system. We find them very useful for counting apples and oranges and anything else that comes in discrete units. They are so good for this that we barely realise that they have an independent existence. As with counting, so with the rest of mathematics. The more we look into the universe, the more we find that it and mathematics are consistent with one another.

36 I assume that religion is at the root of peace, and that the religion I am seeking is one that is consistent with all that we know.

37 Since mathematics is consistent with all that we know, we expect mathematics and religion to be consistent with one another. So I am led to a little department of knowledge of my own which I will call mathematical theology.

38 The political motivation for this is simple. If there is to be one world religion, it must be acceptable to everybody. Our current crop of religions manifestly does not fulfill this requirement. The reason for this is that their theologies contradict one another. Their theologies contradict one another because they have been built by people with different ways of looking at the world.

39 What we need to produce a unified theology is a unified view of the world. Mathematics is the one body of knowledge that transcends all national boundaries. No nation can hope to survive that wishes to contradict the fundamental truths of mathematics. The political payoff of binding theology to mathematics is the production of a theology that is acceptable to all people.

40 This is my strategy. To conclude this introductory lecture I wish to summarise my discoveries to date and link them back to peace.

My fundamental assumption

41 Catholic theology holds that the universe we experience is not capable of explaining its own existence. Instead it is the creation of a god who is the fullness of being, existing eternally outside this universe of space, time and pain. All the rest of the Catholic story, from the creation in Genesis through the fall of Adam and Eve in the Garden of Eden to the redemption by Jesus Christ is fitted into this framework.

42 Thomas found this view consistent to the best of his knowledge. From his understanding of the philosophy of Aristotle, he was forced to the view that the visible universe cannot explain itself.

43 I believe that modern mathematics has removed the constraint that Thomas read into the work of Aristotle. We can now base our theology on the simpler assumption that the universe is self sufficient, quite capable of explaining its own existence. It is therefore fittingly called god.

44 Since the universe is here for all of us to see, it is the one god that will unify our planet. All we have to do is reach scientific agreement on the nature of the god of which we are part.

45 In traditional theology, the only constraint on the nature of god is that it be consistent. However peculiar and outrageous acts of god may seem to us, we accept that god knows what he is doing and is acting consistently by his own standards.

46 Since we assume that the universe is god, we assume that the only constraint on the existence of the universe is that it be consistent. Since we have already noticed that this is the only constraint on mathematics, we are led to the basic physical assumption of these lectures, that the visible universe is in fact mathematics incarnate.

47 Where does this lead us? To see, we must explore mathematics.

Mathematics

48 I have already defined mathematics as the study of all possible consistent structures. This is my working definition, and I don't mind is you disagree. Just follow me for a few lectures, and if you don't think a consistent story is coming together, please tell me.

49 The last hundred years have seen some momentous results in mathematics. They are all linked, but for the sake of clarity, I will centre these lectures of Gödel's theorems. They are named for Kurt Gödel, and were published in the nineteen thirties.

50 Gödel discovered that, subject to a few provisos, a consistent system can never be complete. What this means is that a consistent system will always lead you to places where there is no possibility of deciding whether where you are is consistent with where you've been or not. I interpret this to mean that consistency leads to uncertainty.

51 We have assumed that the universe is mathematics incarnate. Gödel's theorem leads us immediately to see that the universe, if it is to be consistent, must be incomplete. For us, this means that there are questions that have no answer. But this result does not apply to us alone. It applies to the whole universe. This leads us to a very pleasing coincidence.

52 The most indigestible intellectual product of this century has been, without a doubt, Heisenberg's uncertainty Principle. In the early days of quantum mechanics, Werner Heisenberg found that if this strange new theory was to be internally consistent, there must be uncertainty in the motions of subatomic particles.

53 Some have claimed that this uncertainty results from our current ignorance, but I don't think so. If I have interpreted Gödel's theorem correctly, a consistent universe must have uncertainty.

54 I have not time now to go further. In subsequent lectures we will see that space and time too are consistent with the nature of god. We will find that a consistent system must create itself into a more and more complex structure. It must change and evolve, as we see the universe doing. In the process we come to a plausible mathematical definition of peace and violence. Armed with this definition, we discover how to move along the line that joins peace and violence.

55 The answer, it turns out, is simple and obvious enough. To get closer to peace, increase communication. To get closer to violence, decrease communication. It sounds easy, but there are a lot of side issues. When we have explored them all, we will have made quite an interesting tour of mathematics, and have, I hope, the mathematical foundations for some very meaningful dialogue about world peace.

Conclusion

56 Peace is not just the absence of war. It is the whole remarkable structure of what exists. If we are to understand peace well enough to bring it within our grasp, we must understand the creative process that brings the world to be.

57 The source of creation we call god. In this theory of peace I assume that god is not outside the universe, as many have believed, but that that the whole universe itself is god. Since it is god, there for all of us to see, we must eventually find out how it works, and so agree on how the universe structures itself. If we can agree on this, we can agree on how to structure ourselves into a peaceful society.

58 In the next nine lectures we will follow these ideas through in many different directions.

59 I hope I have got your interest, I realise that this is not easy stuff to listen to on a winter's night.

Originally broadcast on 2BOB Radio, Taree, NSW on 18 June 1987

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