Thursday, August 09, 2007

The Edge of Reason

The BBC do occasionally show some decent programmes. Last night BBC4 showed a rather interesting programme called Dangerous Knowledge, documenting the lives of four great scientists: three mathematicians and a physicist, namely Cantor, Boltzmann, Goedel and Turing.

I've mentioned before the incompleteness theorems of Goedel, that for any logical system based on a finite number of axioms there will always be statements that cannot be proved true or false from within that system. Indeed there are true statements that are unprovable, unreachable by the methods of reason and logic.

Now one might think "okay, let's just avoid those statements," but then there's another little problem which Turing developed. While working on Computers, Computation and Computability, he managed to show that we cannot know which statements are ultimately provable or will turn out to be unprovable. This is known as the Halting Problem.

What does this mean? It means that, rationally speaking, there exists truth which cannot be proved true by human reasoning and that we will not know what that truth is through direct reasoning. Reason has reasoned its own edges.

This means that reasoning looks like a little island in a sea of unknowing - integral and consistent in the centre, but ragged and tatty at its edges with islands of truth separate from the main body effectively an infinite distance away.

Turing himself sought to reach these islands of truth by intuition. However modern Science rejects intuition as unempirical and therefore unscientific. In so doing, it maroons human thought to an island which they call scientific truth.

So, if God is unempirical, and I am intuitively aware of God (for want of a better phrase) am I necessarily wrong?

1 comment:

poetreader said...

From what basis other than intuition arises the conviction that intuition must be, or even can be excluded from rational discourse? I would contend that making that exclusion renders any argument either inadequate to the problem or altogether invalid.

On what basis other than intuition can we assert that observation is reliable or that logic really has any application?

In short, the rigorous application of so-called 'scientific thinking' to anything real is productive of complete nonsense if not based upon basically non-logical assumptions.

In short, as classic Anglicans have always asserted (via the 3-lregged stool), revelation (as Scripture and Tradition) is as essential as reason, and the lack of either results in useless nonsense.

ed