Theory revision is an integral part of the scientific method. It takes place because of the recognition of the error which has become apparent within the previous generation of the theory; in other words, as the system of propositions is found to have become self-contradictory. Evidence may, of course, be weighed for or against the theory but, it is important to note that this commonly held, and scientifically respectable tenet is really no more than that. A.J.Ayer says, in his book Language, Truth & Logic, that whereas a mathematical, or geometrical, proof must be conclusive, proof for empirical propositions simply cannot exist: ‘to say that a geometrical proposition, or a system of geometrical propositions, is false is to say that it is self-contradictory. But an empirical proposition, or a system of empirical propositions, may be free from contradiction and still be false79’.

We will close this brief section on the nature of proof by considering the limitations of the system of mathematics. All systems, including mathematics, are built upon certain axioms; for example in Euclidean geometry - the sort with which we will be familiar - one axiom states that parallel lines can never meet; another states that the shortest distance between two points is a straight line. But it is possible to invent other non-Euclidean geometries, in which parallel lines are permitted to meet; and the shortest distance between two points is a curve. In order for these statements to be true in the real world, we would need to be living within a universe in which space-time itself is distorted.

Just as it is possible to construct non-Euclidean geometries, so it is also possible to construct non-linear mathematical systems, which are internally consistent, and yet defy mathematical logic. This disturbing development was the imaginative result of the work of the German mathematician Godel80. The important conclusion he reached, which we must here consider, is that mathematical proofs are themselves only valid if the axioms of the system are correct; and we have no way of proving them.

So, following on from Godel's work, we must recognise that internal consistency is all we can expect from mathematics; relative proof rather than absolute proof. There is an interesting parallel in language, which is similarly, a circular-referenced system: not only do we define our mathematical terms with reference to other mathematical terms which are similarly defined; but in language, we define words with other words which are themselves defined by words. And just as our mathematical reasoning depends upon axioms which cannot be proved, so is language based upon a similar system of eqivalence, known as tautologies.

However, as C.S. Lewis pointed out in his book Miracles, 'unless human reasoning is valid no science can be true'81. It is from the firm, and most practical base of human reason that mankind has completed his greatest achievements. From the building of the ancient pyramids to the completion of the Apollo space missions which put men on the moon, human reason has proved itself to be an extremely effective and exceedingly valuable commodity. Lewis further commented that theories such as Godel's simply amounted to 'an argument which proves that no argument was sound - a proof that there are no such things as proofs' which, he says, 'is nonsense'82.