My oldest brother Christopher recently wrote a book, The God Theorem: God seen through the eyes of a mathematician, in which he explains his worldview and spiritual faith, and discusses some tricky questions about life, philosophy and morality. Because he is a mathematician, his approach is through a system of logic. And a fundamental concept of logic and mathematics is that of axioms. An axiom is a statement that cannot be proved, but is considered true, to serve as a premise or starting point for further reasoning and proof. Many are seen as self-evident (e.g., “If a = b and b = c then a = c”) but do not have to be.
The following text is an edited version of chapter 3: “My Faith”.
I searched in my mind, perhaps even in my heart, for the fundamental axioms on which I base my worldview. Here they are:
Axiom 1: I exist.
“Cogito ergo sum – I think, therefore I am,” wrote René Descartes. The arms and legs that I see, and that I feel when they are touched, may not really exist. I could be completely “mind”. But it is clear that I exist.
Axiom 2: The external world exists.
Is it possible that the external world is just an illusion? People hear voices that do not exist, and they see visions. The phenomenon of phantom limbs after amputation is well known. In dreams, I see and hear things that do not exist. I once had a dream in which I woke up and thought, with some peace of mind, “Thank God it was just a dream.” Then, a little later, I really woke up – a dream within dream! What if what I now call “real life” is just a dream? Maybe when I die, I will really wake up permanently. However, life makes more sense if I accept that the external world actually exists.
Axiom 3: You exist.
No, this is not just a consequence of axiom 2. I can see and hear you, and maybe even touch you. According to axiom 2, I agree that your body exists. But you are not your body. Maybe I’m the only person who has consciousness. Maybe the rest of you are just robots.
There is a claim, often made by people who are supposed to have some knowledge of the brain, that any computer device with more than a little complexity is automatically conscious. But how can one decide the truth of such a claim? I can’t even prove that you are conscious! So I have to agree with it as an axiom.
Axiom 4: Memory is continuous.
We are what we remember. Imagine if, during the night, someone deleted my memories and replaced them with someone else’s. I would become that person. I would look at my face in the mirror and assume that someone had performed plastic surgery on me while I was sleeping. Who would I really be: the person whose memory sits in my brain, or the one in whose brain those memories now reside, and in whose body my brain sits?
Like most of you, I think my memories are pretty accurate. I can accept a few occasions when I have misunderstood certain things, but I am the one I remember being.
Axiom 5: Logic is valid.
I accept standard logic, according to which things are either TRUE or FALSE, logic with ‘AND’, ‘OR’, ‘IF’, ‘THEN’, and ‘NO’. At least I accept it, as long as I don’t try to use self-referential statements like “THIS SENTENCE IS FALSE.”
Some logicians have challenged this standard logic and come up with alternative versions. But I have noticed that when they write about their alternative logics, and in their ordinary life, they follow standard logic.
Most people accept standard logic subconsciously. They say, “You definitely didn’t leave the key on the table because it’s not there now,” but they don’t realise that they used the form of reasoning known as “proof by contradiction”.
Axiom 6: There is something beyond the material universe.
Here you may begin to disagree with me. Like all of the above axioms, I can’t prove it. That’s why I call it an axiom. Materialists deny this axiom. They argue that all thought is only a product of biochemical processes in the brain. “Love” is just the biological duty to reproduce that drives evolution. And so on.
I certainly accept a lot of what they say. The duty to reproduce is certainly an important factor in falling in love. Whether it still explains the self-dedication of married couples in their old age, I’m not so sure.
The problem with the doctrine of the materialist is the realisation that their credible arguments are only products of biochemical processes occurring in their brains. Maybe they are materialists just because of their genetics?
Axiom 7: We all have free will.
I meant to say, “I have free will,” but following axiom 3, I am willing to make it more general. I am the centre of the universe, but so are you.
I am the first to acknowledge that this free will has its limits. I am not completely free, and neither are you. External circumstances place limits on those we may choose to do.
So, with those qualifications, I believe this axiom. That puts a lot of responsibility on me. Will I make the right choices? I need to be able to anticipate the consequences of my choices. It would be so much easier if one were not responsible for one’s actions. If I were to commit a crime – well, I was programmed to do that. My moral would be very simple – just take care of myself, because my choice to do so must be pre-determined.
Axiom 8: God exists.
The “something” that created the universe is somehow a being, a person, capable of loving his beings and interacting with them. That is the biggest leap of faith of all. Like all the previous beliefs, I cannot prove it. But neither can it be denied. It is an axiom.
I can only say that belief in a personal God is the foundation of a worldview that makes sense to me. That is why we accept an axiom. It helps us make sense of things. Of course, we would not accept any belief that we can disprove, just because it helps us to make sense of the world. But if it is something indecisive – when we have to choose between two alternatives that we cannot prove – then the more convenient one is the one we choose. That’s what we do in mathematics, why not in life?
Ancient people always believed in some god or gods to explain things they did not understand, such as lightning. But now that science can explain such things, we can do without such gods as an explanation. But as the extent of the inexplicable has diminished, it is tempting to believe that one day it will disappear altogether and that science will explain everything.
That rational thinking can explain the outside world is not surprising. It is not surprising that rational thinking can explain much of our inner lives. That rational thinking can explain the deepest mysteries of rational thinking itself seems to be too much of a circular argument for me to accept. Anyone educated in the mathematical world knows that self-reference leads to problems.
So that’s my choice. You have the right to reject this axiom if it helps you to understand the world. Belief in God has nothing to do with intellectual ability. There were great thinkers who were atheists. But there were also many great thinkers who believed in God.
I am sorry to say that the quality of atheists has deteriorated in recent decades. Great thinkers, such as Friedrich Nietzsche and Bertrand Russell, could make great arguments in support of atheism. Yet many of today’s atheists have used the tactics of contemporary politicians: throwing mud and using slogans.
Axiom 9: Christianity provides a reliable framework by which to know God.
Why not Judaism or Islam? Why not Buddhism? I guess the main reason is that I grew up in a Christian environment. Christianity proved to be a very satisfying theism for me, so there seemed to be no reason to go anywhere else.
I reject the idea of doing a study of all the world’s major religions to find the best one. I did not follow that principle when I chose a wife. I love her so much and she is everything I would want in a wife. However, prudence suggests that somewhere I might find a wife a little more suitable for me. But life is short. The man who spends his whole life dating to find the right wife will be left alone for the rest of his life.
If I were to find myself growing out of Christianity, I would certainly go elsewhere. However, I grew up in Christianity and, as time went on, it became a more satisfying environment for all my spiritual needs. If I had been born into a Jewish or Muslim family, I might have stayed in one of those beliefs.
This does not mean that all religions are equal. As a Christian, I believe that through Christ I get a clearer picture of God than if I were Jewish or Muslim. But maybe if I were one of those people, I might as well think the same about those religions.
What about the one true religion? They are all more or less true. They really don’t contradict each other on any of the fundamentals. All three “religions of the Book” (Judaism, Christianity, and Islam) promote love of one’s neighbour, and most practitioners of all three religions seem to be seriously trying to lead a good life. I accept people from all three as fellow travellers. It’s just a personal choice for me to stay with Christianity.
To download this book, and others by Christopher Cooper, go to coopersbooks.net.