Sunday, January 08, 2006

Küng – Der Anfang aller Dinge. Section A, pt 1.

A. A Unified theory for Everything? (Pt. 1)

The first section begins with a narrative detailing developments in science for the last few hundred years (and the largely poor reaction of the Church to these movements) – from Copernicus through to the proponents of Quantum theory and the Big-Bang ("Urknall").

This overview reaches its climax in his analysis of the optimism displayed by 20th century scientists that a World Formula ("Weltformel"), or Grand Unification Theory (GUT) could be discovered - a complete description of all Reality, with or without God. As Hawking famously suggested in the popular A Brief History of Time, such a theory would enable us to even 'know the mind of God'!

However, such confidence that a GUT or Weltformel could be discovered, has, Küng argues, turned out to be a great disappointment. In fact, he notes that none other than Hawking himself in a recent and surprising pronouncement states that he has 'given up' on the search for a GUT. But why has he given up?:

"Hawking beruft sich dabei überraschenderweise auf den ersten Unvollständigkeitssatz des österreichischen Mathematikers Kurt Gödel (1906-1978), vielleicht der bedeutendste Logiker des 20. Jh. Dieser Satz aus dem Jahr 1930 besagt, dass ein endliches System von Axiomen immer Formeln enthält, die in diesem System weder bewiesen noch widerlegt werden können. Die Sachlage ähnelt dem bekannten Beispiel aus der Antike, wo jemand die Aussage macht »Diese Aussage ist falsch«. Wenn man voraussetzt, dass alle Aussagen grundsätzlich entweder wahr oder falsch sind (dies wäre die Vollständigkeit des System), dann ist die genannte Aussage genau dann wahr, wenn sie falsch ist. Also ein Widerspruch." (33) [if anyone wants this translated, put a note in the comments]

This is a debate, of course, concerning the foundational presuppositions of mathematics. Referring to Gödel again, Küng notes that most "Axiomensysteme der Mathematik sind nicht in der Lage, ihre eigene Widerspruchsfreiheit zu beweisen", and thus "Man muß den Anspruch [of mathematics] auf einwandfreie Beweisführung aufgeben" ("The axiomatic systems of mathematics are not in the position to prove their own freedom from contradiction", and thus, "one ought to give-up the claim for faultless scientific/mathematic proof") (35-6). This is, in essence, what Küng wants to say, in one way or another, throughout the entire chapter.

He also notes that many mathematicians and physicists rarely busy themselves with admitting the reality of such debates. However, here I felt Küng was a little unfair on Hawking as his backtracking on the issue of Black-Holes and the escape of 'information' from them. The polemical nature of Küng's language is understandable in the light of what many theologians legitimately see as the pretentious and naïve confidence of mathematicians and physicists concerning the 'absolute truth' of their pronouncements. Nevertheless, such honest turnaround by Hawking is also something to be applauded - especially as the famous scientist lost a bet in the process as well!

to be continued …

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At 6/14/2007 5:35 PM, Anonymous reevesg002 said...

Please translate the untranslated Germain to English. I Must have everyword Kung has ever uttered.
Thank you,
a Hans Kung groupie


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