Kurt Godel's unprovability theorem

Kurt Godel was a mathematician that lived in the early 1900's. Godel proved that any system that employed numbers could have statements expressed in that system that are true but not derivable from the basic axioms of that system. Thus, if the laws of nature are most fundamentally based on mathematics, then there may be things and/or events in the universe which do exist but are not derived from the more basic elements of the universe. It is difficult to adhere to a fully deterministic and logical universe if some things in it cannot be derived from the simpler elements. This would seem to deny cause and effect on which a deterministic point of view depends.

However, it should be noted that the operations that govern the relationship between numbers in and of itself has not been reduced to the propositional entities of "True", "False" and "Proof". So it is only inevitable that some things in such a system cannot be "proven". For "proof" is not even incorporated in that system. The number "2" does not prove anything. The operator "+" does not prove anything. And the truth of the fact that "1+1=2" is imposed by the understanding of mathematicians and is not derived by logic alone.

The arbitrary nature of the lack of proof that Godel found may have been introduced by the arbitrary nature of numbering things itself. For how the mathematician wishes to collect things for the convenience of his formulae may not reflect the true nature of the whole. For he may arrange his groups differently for different purposes. Also, the General Theory of Relativity suggests that there is no sharp distinction between particles of matter and the space around it. Particles of matter are singularities in the General Theory of Relativity which means that particles are like tiny black holes that curve space and time to an infinitesimal point which occupies no space at all. So if nothing can be distinguished from space and time, then it is arbitrary to group it into individual parts.

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