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Si Dieu n’existait pas, il faudrait l’inventer.
(If God did not exist, it would have been necessary to invent him.)

– Voltaire (1694-1778)

It was with some trepidation that I sat down to write this article. You see, I used to think that life was like a school textbook: full of difficult questions, but with the correct answers given at the end. And when I started my researches into PQR, I half hoped that they would allow me to prove the existence of God himself. Half hoped, and half feared, for what if God did not want his mysteries solved too soon? Would he strike me down with a Mack truck if he saw I was on the right track? But then I decided I could cross the road without fear, for God could not perform such an act (even if it appeared natural) without in effect admitting his own existence. And if on the other hand I were to prove that God did not exist, then again I should have nothing to fear (unless, of course, my proof was a load of dingo’s kidneys). So here goes....

In an earlier article I discussed Gödel’s incompleteness theorem, which states that any consistent system of logic will contain statements that are true but that cannot be proven from within the system. (We are assuming that the system is powerful enough to generate the Natural numbers.) There is an extension to this theorem (sometimes known as Gödel’s second incompleteness theorem), which states that you cannot prove the consistency of a system of logic from within itself. (Consistency means that no statement in the system can be proven both true and false.) In other words, you cannot use the system to prove its own consistency (unless, paradoxically, the system is inconsistent, in which case you could use it to prove anything).

What does this tell us about the Universe as a logical system? Well, first of all let’s assume that the Natural numbers are consistent, i.e. that there are no contradictions in arithmetic. (I’m not even going to consider the alternative possibility here–that’s another story altogether.) Then Gödel’s second theorem tells us that the Universe cannot contain a proof of its own consistency. Thus, although we may believe that Truth cannot contradict itself, this is something which we, as creatures of this Universe, can never prove: we must take it on faith. (So when Pontius Pilate asked “what is truth?” he was asking the unanswerable.)

Can miracles occur? If we define a miracle as an occurrence that cannot be explained by the laws of Nature, this theorem tells us that we can never prove miracles to be impossible. And of course PQR can never show that miracles do occur (or they would not be miraculous). So it is up to us to choose what to believe. Any apparent miracles can be attributed either to Divine Intervention, or to our own imperfect understanding of how the Universe operates, depending on our beliefs. (And our beliefs may change: at one time, eclipses were considered miraculous. We know better now.)

The same principle applies when we consider the miracle of creation, i.e. the idea of God as Creator of the Universe. God, as framer of the laws of Nature, cannot be explained by those laws, or we would be faced with a chicken-and-egg situation. Nor can the existence of a Creator be disproved by PQR Theory, which only talks about what happens within the physical Universe. Even if the theory could explain every phenomenon ever observed in the Universe, this still would not prove that there was no other Force at work behind the scenes. In short, PQR shows that we can neither prove nor disprove the existence of God. Ultimately, this must be a question of faith, of what we choose to believe.

And, as a species, we choose to believe what it suits us to believe. Any race of humans who believe they can fly off cliffs is likely to face rapid extinction. So we believe we cannot do this, even though most of us have never tried it for ourselves. Likewise, when it comes to belief in God, the godfearing nations have had an evolutionary advantage over the godless. Even though many people nowadays question or deny the existence of God, historically our society has been founded on a belief in a Creator who has given us laws by which to conduct our lives. We are encouraged to obey these laws by the promise (explicit or implied) of Divine Reward, with the accompanying threat of Divine Retribution if we disobey. Our civilizations have flourished enormously under the social order that flows from such beliefs. Thus it is not surprising that so many of us, as the products of these civilizations, do have a belief in God.

But why does any individual believe in God? A cynic would say that one’s belief in God is the product of evolution, and no doubt many people believe simply because they have been taught that this is the “right” thing to do. A pragmatist would say he chooses to believe in God because this is a less risky option than choosing not to: if we believe in a nonexistent god we have lost nothing, but if God exists and we ignore him, then we risk losing our eternal reward and perhaps also incurring eternal perdition. Likewise, many people do not consider themselves superstitious but choose to believe in God on the basis that it costs nothing and might improve their karma in life. An idealist may feel a duty to believe in God in order to participate in making the world a better place. And many of us would argue that we believe in God in order to fulfil our inborn spiritual needs.

All these viewpoints have some validity. My own personal belief is that the Universe is too wonderful a place to have come into existence by accident, but in the last analysis this is really only a gut feeling. So while I encourage everyone to think deeply about these questions, I can hardly expect anyone to change their beliefs based on my personal views. You will just have to decide for yourself. But whatever your beliefs, you should still take care when crossing the road.

Nick Mitchell, February 2009

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