Science and Religion II: Towards Mathematical Spirituality

One thing people do not appreciate about Science is that it relies on statements of faith. However, scientists don't actually call these "statements of faith" but refer to them as assumptions or axioms, and these form the bedrock of any theory, and likewise any religion.

The terms "statement of faith" and "assumption" are effectively equivalent since both refer to a statement that cannot be supported by proof from within the system in which one is working. Religious people call this process (and I have defined it below in part one) Revelation.

At the centre of scientific communication is mathematics, a subject which I love deeply for its beauty, subtlety and, above all for the Presence of God Who moves unseen behind each theorem.

Mathematics has its limitations. Here are a couple of rather important theorems:

Goedel's First Incompleteness Theorem. Any adequate axiomatizable theory is incomplete. In particular the sentence "This sentence is not provable" is true but not provable in the theory.

Goedel's Second Incompleteness Theorem. In any consistent axiomatizable theory (axiomatizable means the axioms can be computably generated) which can encode sequences of numbers (and thus the syntactic notions of "formula", "sentence", "proof") the consistency of the system in not provable in the system.

(Statements from Dale Myers' site on Kurt Goedel http://www.math.hawaii.edu/~dale/godel/godel.html)

What these essentially say is that no finite collection of axioms can actually make a theory complete within itself, there are always statements which are true but cannot be proved from within the theory one is working.

Now Science has difficulty with these because the very language that it uses to communicate its ideas and generate its conclusions cannot adequately describe the Universe as it really is. Science is limited, rather like a 2D plane in a 3D universe, infinite in extent but unable to make deductions perpendicular to the plane of its existence.

That's not to say that Religion fares any better. Why? Because the difference between Science and Religion is practically non-existent. Both rely on sets of axioms, both require reasonable deductions. However, the major advantage that Religion has over Science is the fact that it can cope with its own limitations, indeed it is aware that it has limitations, and freely speculates on a truth that cannot register on any instrumentation.

For me, the best expression of Religion is Christianity, that the Ultimate Truth lies in the peculiar person of Jesus Christ who possesses two natures, one human and the other Divine. I find His Presence with me not only real, but also entirely reasonable. God does not hate Reason, indeed He uses it to devestating effect through His Incarnation and through St Paul.

Of course, St Paul also says something about the limitations of Reason - "Knowledge puffs up, but Love builds up." Love is not Reasonable unless one steps outside the box and sees things from God's point of view. In the tiny, tiny bits of Revelation that I have been given (and these tiny fragments are far too wonderful for me) the Love of God is Reasonable, but using the Reason of God.